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9 Years’, , JEE MAIN, Solved Papers, 2013 to 2021, , 64 Online &, Offline Papers
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CONTENTS, JEE Main Online Solved Papers 2021, February Attempt, —, , 24 Feb, 2021 (Shift I), , 3-12, , —, , 24 Feb, 2021 (Shift II), , 13-22, , —, , 25 Feb, 2021 (Shift I), , 23-32, , —, , 25 Feb, 2021 (Shift II), , 33-42, , —, , 26 Feb, 2021 (Shift I), , 43-52, , —, , 26 Feb, 2021 (Shift II), , 53-62, , March Attempt, —, , 16 March, 2021 (Shift I), , 3-14, , —, , 16 March, 2021 (Shift II), , 15-24, , —, , 17 March, 2021 (Shift I), , 25-34, , —, , 17 March, 2021 (Shift II), , 35-44, , —, , 18 March, 2021 (Shift I), , 45-55, , —, , 18 March, 2021 (Shift II), , 56-66, , July Attempt, —, , 20 July, 2021 (Shift I), , 3-11, , —, , 20 July, 2021 (Shift II), , 12-20, , —, , 22 July, 2021 (Shift II), , 21-30, , —, , 25 July, 2021 (Shift I), , 31-40, , —, , 25 July, 2021 (Shift II), , 41-49, , —, , 27 July, 2021 (Shift I), , 50-59, , —, , 27 July, 2021 (Shift II), , 60-70
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August Attempt, —, , 26 Aug, 2021 (Shift I), , 3-12, , —, , 26 Aug, 2021 (Shift II), , 13-23, , —, , 27 Aug, 2021 (Shift I), , 24-33, , —, , 27 Aug, 2021 (Shift II), , 34-43, , —, , 31 Aug, 2021 (Shift I), , 44-54, , —, , 31 Aug, 2021 (Shift II), , 55-64, , —, , 1 Sep, 2021 (Shift II), , 65-74, , JEE Main Online Solved Papers 2020, September Attempt, —, , 2 Sep, 2020 (Shift I), , 3-11, , —, , 2 Sep, 2020 (Shift II), , 12-21, , —, , 3 Sep, 2020 (Shift I), , 22-30, , —, , 3 Sep, 2020 (Shift II), , 31-39, , —, , 4 Sep, 2020 (Shift I), , 40-49, , —, , 4 Sep, 2020 (Shift II), , 50-58, , —, , 5 Sep, 2020 (Shift I), , 59-67, , —, , 5 Sep, 2020 (Shift II), , 68-76, , —, , 6 Sep, 2020 (Shift I), , 77-86, , —, , 6 Sep, 2020 (Shift II), , 87-95, , January Attempt, —, , 7 Jan, 2020 (Shift I), , 3-10, , —, , 7 Jan, 2020 (Shift II), , 11-19
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—, , 8 Jan, 2020 (Shift I), , 20-28, , —, , 8 Jan, 2020 (Shift II), , 29-37, , —, , 9 Jan, 2020 (Shift I), , 38-46, , —, , 9 Jan, 2020 (Shift II), , 47-55, , JEE Main Online Solved Papers 2019, April Attempt, 8 April, 2019 (Shift I), , 3-13, , 8 April, 2019 (Shift II), , 14-24, , 9 April, 2019 (Shift I), , 25-34, , 9 April, 2019 (Shift II), , 35-44, , 10 April, 2019 (Shift I), , 45-55, , 10 April, 2019 (Shift II), , 56-66, , 12 April, 2019 (Shift I), , 67-78, , 12 April, 2019 (Shift II), , 79-88, , January Attempt, 9 Jan, 2019 (Shift 1), , 3-13, , 9 Jan, 2019 (Shift 2), , 14-23, , 10 Jan, 2019 (Shift 1), , 24-33, , 10 Jan, 2019 (Shift 2), , 34-44, , 11 Jan, 2019 (Shift 1), , 45-54, , 11 Jan, 2019 (Shift 2), , 55-64, , 12 Jan, 2019 (Shift 1), , 65-74, , 12 Jan, 2019 (Shift 2), , 75-86
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JEE Main Offline Solved Papers 2018-13, JEE Main 2018, , 1-10, , JEE Main 2017, , 11-20, , JEE Main 2016, , 21-30, , JEE Main 2015, , 31-41, , JEE Main 2014, , 42-52, , JEE Main 2013, , 53-62
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3, , FEBRUARY ATTEMPT~ 24 Feb 2021, Shift I, , JEE Main 2021, 24 FEBRUARY SHIFT I, , PHYSICS, Section A : Objective Type Questions, 1. The work done by a gas molecule in an 2, isolated system is given by, W = αβ 2e, , −, , x, αKT, , ,, , where x is the displacement, k is the, Boltzmann constant and T is the, temperature, α and β are constants., Then, the dimensions of β will be, a. [M 2 L T 2 ], , b. [M 0 L T 0 ], , c. [M L T − 2 ], , d. [M L 2 T − 2 ], , 2. Two stars of masses m and 2m at a distance, d rotate about their common centre of mass, in free space. The period of revolution is, a., , 1, 2π, , c. 2 π, , 3Gm, d, , 3, , 3Gm, d, , 3, , b. 2 π, d., , 1, 2π, , d3, 3Gm, d3, 3Gm, , 3. Four identical particles of equal masses 1 kg, made to move along the circumference of a, circle of radius 1 m under the action of their, own mutual gravitational attraction. The, speed of each particle will be, a., , (1 + 2 2 )G, 2, , c. G(1 + 2 2 ), , G, (1 + 2 2 ), 2, G, d., (2 2 − 1), 2, , b., , 4. Moment of inertia (MI) of four bodies, having, same mass and radius, are reported as, I1 = MI of thin circular ring about its diameter,, I2 = MI of circular disk about an axis, perpendicular to the disk and going through, the centre,, , a. I1 + I 2 = I 3 +, , 5, I4, 2, , c. I1 = I 2 = I 3 < I 4, , b. I1 + I 3 < I 2 + I 4, d. I1 = I 2 = I 3 > I 4, , 5. Consider two satellites S1 and S 2 with periods, of revolution 1 h and 8 h respectively,, revolving around a planet in circular orbits., The ratio of angular velocity of satellite S1 to, the angular velocity of satellite S 2 is, a. 8 : 1, , b. 1 : 8, , c. 2 : 1, , cubic shape is a at room temperature T , the, coefficient of linear expansion of the metal, sheet is α. The metal sheet is heated, uniformly, by a small temperature ∆T , so that, its new temperature is T + ∆T . Calculate the, increase in the volume of the metal box., a. 4 πa 3α∆T, 4, c. πa 3α∆T, 3, , b. 4a 3α∆T, d. 3a 3α∆T, , 7. If Y, K and η are the values of Young’s, modulus, bulk modulus and modulus of, rigidity of any material, respectively. Choose, the correct relation for these parameters., 9Kη, N/m 2, 2η + 3K, Yη, N/m 2, c. K =, 9η − 3Y, a. Y =, , 9Kη, N/m 2, 3K − η, 3YK, N/m 2, d. η =, 9K + Y, b. Y =, , 8. If the velocity-time graph has the shape AMB,, what would be the shape of the, corresponding acceleration-time graph ?, Velocity (v), B, , A, , I3 = MI of solid cylinder about its axis, and I4 = MI of solid sphere about its, diameter. Then,, , d. 1 : 4, , 6. Each side of a box made of metal sheet in, , Time (t), M
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4, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 11. In the given figure, a mass M is attached to a, , a, , a, a., , t, , c., , t, , a, , a, b., , t, , d., , t, , horizontal spring which is fixed on one side, to a rigid support. The spring constant of the, spring is k. The mass oscillates on a, frictionless surface with time period T and, amplitude A. When the mass is in equilibrium, position as shown in the figure, another, mass m is gently fixed upon it. The new, amplitude of oscillation will be, , 9. n mole of a perfect gas undergoes a cyclic, , m, , process ABCA (see figure) consisting of the, following processes., , k, , A → B : Isothermal expansion at temperature, T , so that the volume is doubled from V1 to, V2 = 2V1 and pressure changes from p1 to p2., , M, , B → C : Isobaric compression at pressure p2, to initial volume V1., C → A : Isochoric change leading to change of, pressure from p2 to p1., Total work done in the complete cycle ABCA is, p, , a. A, , M+ m, M, , b. A, , M, M+ m, , c. A, , M− m, M, , d. A, , M, M−m, , 12. A cell E 1 of emf 6 V and internal resistance 2 Ω, is connected with another cell E 2 of emf 4 V, and internal resistance 8Ω (as shown in the, figure). The potential difference across, points X and Y is, , A, , p1, , p2, , C, , B, , P, , E1, 6 V, 2 Ω, , V1, , a. 0, , V2=2V1, , Y, , 4 V, 8 Ω, , V, , b. nRT ln 2, 1, d. nRT ln 2 − , , 2, , 1, c. nRT ln 2 + , , 2, , E2, , X, , 10. Match List-I with List-II., , a. 2.0 V, c. 5.6 V, , b. 3.6 V, d. 10.0 V, , 13. A current through a wire depends on time as, , i = α 0t + βt 2, where α 0 = 20 A/s and, β = 8 As − 2. Find the charge crossed through a, , List-I, , List-II, , A., , Isothermal 1., , Pressure constant, , section of the wire in 15 s., , B., , Isochoric, , 2., , Temperature constant, , a. 260 C, c. 11250 C, , C., , Adiabatic, , 3., , Volume constant, , D., , Isobaric, , 4., , Heat content is constant, , Choose the correct answer from the options, given below., A, B, C, D, A, B, C, D, (a) 1, 3, 2, 4, (b) 3, 2, 1, 4, (c) 2, 4, 3, 1, (d) 2, 3, 4, 1, , b. 2100 C, d. 2250 C, , 14. Two equal capacitors are first connected in, series and then in parallel. The ratio of the, equivalent capacities in the two cases will be, a. 1 : 2, b. 2 : 1, c. 4 : 1, d. 1 : 4
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5, , FEBRUARY ATTEMPT~ 24 Feb 2021, Shift I, 18. Given below are two statements :, , 15. A cube of side a has point charges, + Q located at each of its vertices except at, the origin, where the charge is − Q. The, electric field at the centre of cube is, x, +Q, , +Q, , +Q, , –Q, , z, , +Q, , a, , y, , a., b., c., d., , −Q, 3 3 πε0a, Q, , 3 3 πε0a, −2Q, , r, c. f = −, 2, , $ + y$ + z$ ), (x, , 3 3 πε0a 2, 2Q, 3 3 πε0a, , curvature r of the spherical convex mirror by, a. f = r, , $ + y$ + z$ ), (x, , 2, , 2, , $ + y$ + z$ ), (x, , collector current changes by 3.5 mA. The, value of β will be, b. 0.875, , c. 0.5, , d. 3.5, , 17. In the given figure, the energy levels of, hydrogen atom have been shown alongwith, some transitions marked A, B, C, D and E. The, transitions A, B and C respectively represent, +eV, , Continuum, , 0 eV, –0.54 eV, – 0.85 eV, –1.51 eV, , n=5, n=4, n=3, , B, , C, , D, , –3.4 eV, , n=2, A, n=1, , b. f = − r, r, d. f = +, 2, , 20. In a Young’s double slit experiment, the, , 16. If an emitter current is changed by 4 mA, the, a. 7, , a. Both Statement I and Statement II are true., b. Both Statement I and Statement II are false., c. Statement I is true but Statement II is false., d. Statement I is false but Statement II is true., , 19. The focal length f is related to the radius of, , $ + y$ + z$ ), (x, , 2, , Statement II If the wavelength of photon is, decreased, then the momentum and energy, of a photon will also decrease., In the light of the above statements, choose, the correct answer from the options given, below., , +Q, +Q, , +Q, , Statement I Two photons having equal, linear momenta have equal wavelengths., , E, –13.6 eV, , a. The first member of the Lyman series, third, member of Balmer series and second, member of Paschen series., b. The ionisation potential of hydrogen, second, member of Balmer series and third member, of Paschen series., c. The series limit of Lyman series, second, member of Balmer series and second, member of Paschen series., d. The series limit of Lyman series, third, member of Balmer series and second, member of Paschen series., , width of the one of the slit is three times the, other slit. The amplitude of the light coming, from a slit is proportional to the slit-width., Find the ratio of the maximum to the, minimum intensity in the interference, pattern., a. 4 : 1, c. 1 : 4, , b. 2 : 1, d. 3 : 1, , Section B : Numerical Type Questions, 21. The coefficient of static friction between a, wooden block of mass 0.5 kg and a vertical, rough wall is 0.2. The magnitude of, horizontal force that should be applied on, the block to keep it adhere to the wall will, be ........ N., [Take, g = 10 ms − 2], , 22. An unpolarised light beam is incident on the, polariser of a polarisation experiment and, the intensity of light beam emerging from, the analyser is measured as 100 lumens., Now, if the analyser is rotated around the, horizontal axis (direction of light) by 30° in, clockwise direction, the intensity of emerging, light will be ....... lumens., , 23. A ball with a speed of 9 m/s collides with, another identical ball at rest. After the, collision, the direction of each ball makes an, angle of 30° with the original direction. The, ratio of velocities of the balls after collision is, x : y , where x is ........... .
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6, , ONLINE, , 24. A hydraulic press can lift 100 kg when a mass, m is placed on the smaller piston. It can lift, ...... kg when the diameter of the larger piston, is increased by 4 times and that of the smaller, piston is decreased by 4 times keeping the, same mass m on the smaller piston., , 28. In connection with the circuit drawn below,, the value of current flowing through 2kΩ, resistor is ....... × 10− 4 A., 1kΩ, 2 kΩ, , 25. An inclined plane is bent in such a way that, the vertical cross-section is given by y =, , JEE Main 2021 ~ Solved Papers, , 5V, , 2, , x, 4, , where, y is in vertical and x in horizontal, direction. If the upper surface of this curved, plane is rough with coefficient of friction, µ = 0.5, the maximum height in cm at which a, stationary block will not slip downward is, .......... cm., , 26. A resonance circuit having inductance and, , resistance 2 × 10− 4 H and 6.28 Ω respectively, oscillates at 10 MHz frequency. The value of, quality factor of this resonator is .......... ., [Take, π = 3.14], , 27. An audio signal v m = 20 sin 2π(1500 t), amplitude modulates a carrier, , 10 V, , 29. An electromagnetic wave of frequency, 5 GHz, is travelling in a medium whose, relative electric permittivity and relative, magnetic permeability both are 2. Its, velocity in this medium is ...... × 107 m/s., , 30. A common transistor radio set requires, 12 V (DC) for its operation. The DC source is, constructed by using a transformer and a, rectifier circuit, which are operated at 220 V, (AC) on standard domestic AC supply. The, number of turns of secondary coil are 24,, then the number of turns of primary, are ............ ., , v c = 80 sin 2π(100000 t), The value of per cent modulation is ......... ., , CHEMISTRY, Section A : Objective Type Questions, 1. Which of the following are isostructural pairs ?, A. SO24 − and CrO24 −, , B. SiCl4and TiCl4, , C. NH 3 and NO−3, , D. BCl3 and BrCl3, , a. A and B only, , b. A and C only, , c. B and C only, , d. C and D only, , 2. In Freundlich adsorption isotherm, slope of AB, line is, B, , x, log m, , A, , a. n with (n = 0.1 to 0.5) b. log n with (n > 1), 1, 1, 1, d. with = 0 to 1, c. log with (n < 1), n, , n, n, , 3. Consider the elements Mg, Al, S, P and Si,, the correct increasing order of their first, ionisation enthalpy is, a. Al < Mg < Si < S < P, b. Mg < Al < Si < P < S, c. Mg < Al < Si < S < P, d. Al < Mg < S < Si < P, , 4. Which of the following ore is concentrated, using group 1 cyanide salt ?, a. Calamine, c. Siderite, , b. Malachite, d. Sphalerite, , 5. (A) HOCl + H2O2 → H3O+ + Cl− + O2, (B) I2 + H 2O2 + 2OH − → 2I − + 2H 2O + O2, log P
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7, , FEBRUARY ATTEMPT~ 24 Feb 2021, Shift I, HO, , Choose the correct option., a. H2O 2 acts as oxidising agent in equations (A), and (B)., b. H2O 2 acts as reducing agent in equations (A), and (B)., c. H2O 2 act as oxidising and reducing agent, respectively in equations (A) and (B)., , CH3, , d., CH3, , HO, , 11. What is the major product formed by HI on, reaction with, , CH3, , CH3, a., , CH3, , C, , a. X = Na[Al(OH) 4 ], Y = SO 2 , Z = Al2O 3, b. X = Al(OH) 3 , Y = SO 2 , Z = Al2O 3 ⋅xH2O, c. X = Al(OH) 3 , Y = CO, Z = Al2O 3, d. X = Na[Al(OH) 4 ], Y = CO 2 , Z = Al2O 3 ⋅xH2O, , 7. The electrode potential of M 2 + / M of, a. Fe, , b. Co, , c. Zn, , a. Cu, Sn and Zn, c. Cu, Ni and Fe, , b., , CH3, , C, , a. acid rain, b. global warming and cancer, c. corrosion of metals, d. ozone hole, , CH, , CH3, , CH3, I, CH3, , c., CH3, , b. Cu, Zn and Ni, d. Al, Cu, Mg and Mn, , degradation of vegetation may lead to, , CH2I, , CH3, , d. Cu, , 9. The gas released during anaerobic, , CH, , CH3 H, , 3d-series elements shows positive value for, , 8. The major components in Gun metal are, , CH2 ?, , C, , CH3, , 6. Al2O3 was leached with alkali to get X. The, solution of X on passing of gas Y, forms Z. X,, Y and Z respectively are, , CH, , CH3, , d. H2O 2 acts as reducing and oxidising agent, respectively in equations (A) and (B)., , C, , CH, , CH3, , CH3 I, d., , CH3, , CH, , CH, , CH3, , I, , CH2, , CH3, , 12. Which of the following reagent is used for, the following reaction ?, , 10. Which of the following compound gives pink, colour on reaction with phthalic anhydride in, conc. H 2SO4 followed by treatment with, NaOH?, CH3, a., , CH 3CH 2CH 3 , ?→ CH 3CH 2CHO, a. Copper at high temperature and pressure, b. Molybdenum oxide, c. Manganese acetate, d. Potassium permanganate, , 13. The product formed in the first step of the, reaction of, Br, , HO, CH3, , CH3, , CH2, , CH, , CH2, , CH, , CH3 with excess, , Br, , b., OH, , Mg/Et2O (Et = C2H5) is, a. CH3 CH2 CH CH2, , H 3C, , CH3, , CH3, , CH, , CH2, , c., HO, , OH, , CH3, b. CH3, , CH, CH, , CH3, , CH, , CH3, , CH, , CH2, , CH3
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9, , FEBRUARY ATTEMPT~ 24 Feb 2021, Shift I, , 23. A proton and a Li3+ nucleus are accelerated, , 18. Match List-I with List-II., List-I, (Monomer Unit), A., , Caprolactum, , List-II, (Polymer), 1., , Natural, rubber, , by the same potential. If λ Li and λ P denote, , the de-Broglie wavelengths of Li3 + and, λLi, is, proton respectively, then the value of, λP, , x × 10−1. The value of x is ......... ., , B., , 2-chloro buta-1,3-diene 2., , Buna-N, , (Rounded off to the nearest integer), , C., , Isoprene, , 3., , Nylon-6, , (Mass of Li3 + = 8.3 mass of proton), , D., , Acrylonitrile, , 4., , Neoprene, , Choose the correct answer from the options, given below, a., b., c., d., , A, 1, 4, 2, 3, , B, 2, 3, 1, 4, , C, 3, 2, 4, 1, , D, 4, 1, 3, 2, , 19. Out of the following, which type of, interaction is responsible for the stabilisation, of α-helix structure of proteins ?, a. van der Waals’ forces, b. Covalent bonding, c. Ionic bonding, d. Hydrogen bonding, , 20. Given below are two statements., Statement I Colourless cupric metaborate is, reduced to cuprous metaborate in a, luminous flame., Statement II Cuprous metaborate is, obtained by heating boric anhydride and, copper sulphate in a non-luminous flame., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Both statement I and statement II are true., b. Both statement I and statement II are false., c. Statement I is true but statement II is false., d. Statement I is false but statement II is true., , Section B : Numerical Type Questions, 21. 4.5 g of compound A (MW = 90) was used to, make 250 mL of its aqueous solution. The, molarity of the solution in M is x × 10− 1. The, value of x is ......... . (Rounded off to the, nearest integer)., , 22. The coordination number of an atom in a, body centered cubic structure is ......... ., [Assume that the lattice is made up of, atoms.], , 24. For the reaction, A ( g) → B ( g), the value of, the equilibrium constant at 300 K and 1 atm, is equal to 100.0. The value of ∆ rG for the, reaction at 300 K and 1 atm in J mol − 1 is − xR,, where x is ......... . (Rounded off to the nearest, integer), (R = 8.31 J mol − 1 K − 1 and ln10 = 2.3), , 25. When 9.45 g of ClCH2COOH is added to, 500 mL of water, its freezing point drops by, 0.5°C. The dissociation constant of, ClCH 2COOH is x × 10− 3. The value of x is ........ ., (Rounded off to the nearest integer), [K f (H2 O) = 1.86 K kg mol − 1], , 26. At 1990 K and 1 atm pressure, there are, equal number of Cl2 molecules and Cl atoms, in the reaction mixture. The value of k p for, the reaction Cl2( g), , -, , 2Cl( g ) under the, , above conditions is x × 10−1. The value of x is, ......... ., (Rounded off to the nearest integer), , 27. The reaction of sulphur in alkaline medium is, given below, S 8 ( s) + aOH − (aq) → bS 2− (aq) + cS 2O23− (aq), + dH 2O( l), The value of ‘a’ is ....... . (Integer answer), , 28. Gaseous cyclobutene isomerises to, butadiene in a first order process which has, a ‘k’ value of 3.3 × 10− 4 s − 1 at 153°C. The time, in minutes it takes for the isomerisation to, proceed 40 % to completion at this, temperature is ....... ., (Rounded off to the nearest integer), , 29. Number of amphoteric compounds among, the following is ......... ., a. BeO, c. Be(OH) 2, , b. BaO, d. Sr(OH) 2
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10, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 30. The stepwise formation of [Cu(NH3) 4 ]2 + is, given below, Cu2 + + NH 3, , K1, , [Cu(NH 3)]2 + + NH 3, , K2, , [Cu(NH 3) 2 ]2 +, , K3, , [Cu(NH 3) 2 ]2 + + NH 3, , K4, , [Cu(NH 3) 4 ]2 +, , -, , The value of stability constants K1, K 2 , K 3 and K 4, are 104 , 1.58 × 103 , 5 × 102 and 102 respectively., The overall equilibrium constants for, dissociation of [Cu(NH3 )]2 + ] is x × 10− 12 . The, value of x is ........ . (Rounded off to the nearest, integer), , [Cu(NH 3)]2 +, , -, , [Cu(NH 3) 3 ]2 + + NH 3, , [Cu(NH 3)]2 +, , MATHEMATICS, Section A : Objective Type Questions, 1. Let f : R → R be defined as f ( x) = 2x − 1and, 1, 2, ., g : R − { 1} → R be defined as g( x) =, x −1, , a., , 1, 2, x, , b. x 2 − 2x + 16 = 0, , c. x − 2x + 8 = 0, , d. x 2 − 2x + 2 = 0, , 2x − 4 y − 2z = 6, is inconsistent, if, 4, 5, 4, c. k = 3, m ≠, 5, , b. k = 3, m =, , 5. If e (cos, , 2, , 1, 15, , d. 0, , 6, , − 2 sin x + (2x − 1) cos x, , 1, 1, b. decreases in , ∞ , a. increases in , ∞ , 2 , 2 , 1, 1, c. increases in − ∞ , d. decreases in − ∞ , , , , 2 , 2 , , b. 1625, , c. 560, , d. 575, , 2x − 1, f ( x) = [ x − 1]cos , π, where [⋅] denotes the, 2 , , 4, 5, , d. k ≠ 3, m ∈ R, , greatest integer function, then f is, , 4. The value of − 15C 1 + 2 ⋅ 15C 2 − 3⋅ 15C 3 + K, , − 13, , c., , 9. If f : R → R is a function defined by, , a. k ≠ 3, m ≠, , c. 2, , 4 x 3 − 3x 2, , a. 1050, , x + 2y − z = 5 m, , 13, , 3, 2, , Indians and 8 foreigners, which includes at, least 2 Indians and double the number of, foreigners as Indians. Then, the number of, ways, the committee can be formed, is, , 3x − 2 y − kz = 10, , a. 216 − 1, , b., , 8. A scientific committee is to be formed from 6, , 3. The system of linear equations, , C1 +, , is equal to, , x3, , 2, 3, , f ( x) =, , a. x 2 − 2x + 136 = 0, , 14, , d. 2 3, , 7. The function, , that p + q = 2 and p4 + q 4= 272. Then, p and, q are roots of the equation, , − 15 ⋅ 15C 15 +, is, , 3, 2, , t )dt, , 0, , x→ 0, , a., , 2. Let p and q be two positive numbers, such, , 2, , 6. lim, , c., , 2, , ∫ (sin, , x−, , Then, the composition function f ( g (x )) is, a. one-one but not onto, b. onto but not one-one, c. Neither one-one nor onto, d. Both one-one and onto, , b. 3, , C3 +, , 14, , C5 + K +, , 14, , 14, , C 11, , b. 213 − 14, d. 214, , x + cos4 x + cos6 x + K ∞ ) log e 2, , satisfies, the equation t 2 − 9t + 8 = 0, then the value, of, 2 sin x, π, , 0 < x < is, 2, sin x + 3 cos x , , a. discontinuous only at x = 1, b. discontinuous at all integral values of x except, at x = 1, c. continuous only at x = 1, d. continuous for every real x, , 10. If ∫, , sin x + cos x , dx = a sin− 1, + c,, , , b, 8 − sin 2x, , cos x − sin x, , where c is a constant of integration, then the, ordered pair (a, b) is equal to, a. (3, 1), c. (− 1, 3), , b. (1, 3), d. (1, − 3)
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11, , FEBRUARY ATTEMPT~ 24 Feb 2021, Shift I, 11. The area (in sq. units) of the part of the circle, x 2 + y 2 = 36, which is outside the parabola, y 2 = 9x , is, , a. 24 π + 3 3, c. 12 π + 3 3, , b. 24 π − 3 3, d. 12 π − 3 3, , 12. The population P = P(t) at time t of a certain, species follows the differential equation, dP, = 0.5P − 450. If P(0) = 850, then the time at, dt, which population becomes zero is, a. log e 9, c. log e 18, , 1, b. log e 18, 2, d. 2 log e 18, , arithmetic mean of the reciprocals of the, intercepts of this line on the coordinate axes, 1, is . Three stones A, B and C are placed at, 4, the points (1,1), (2, 2) and (4, 4), respectively., Then, which of these stones is / are on the, path of the man ?, b. B only, c. C only, , segment joining the focus of the parabola, y 2 = 4ax to a moving point of the parabola, is, another parabola whose directrix is, b. x = −, , c. x = 0, , d. x =, , a, 2, , a, 2, , 15. If the tangent to the curve y = x 3 at the point, P(t , t 3) meets the curve again at Q, then the, ordinate of the point which divides PQ, internally in the ratio 1 : 2 is, b. 2t 3, d. − 2t 3, , a. 0, c. − t 3, , 16. The equation of the plane passing through, the point (1, 2, −3) and perpendicular to the, planes 3x + y − 2z = 5 and 2x − 5 y − z = 7, is, a. 6x − 5 y + 2z + 10 = 0, b. 11x + y + 17z + 38 = 0, c. 6x − 5 y − 2z − 2 = 0, d. 3x − 10 y + 2z + 11 = 0, , 17. The distance of the point (1, 1, 9) from the, point of intersection of the line, =, , z −5, 2, , 18. An ordinary dice is rolled for a certain, number of times. If the probability of getting, an odd number 2 times is equal to the, probability of getting an even number 3, times, then the probability of getting an odd, number for odd number of times is, , 1, 32, 5, c., 16, , a., , 3, 16, 1, d., 2, b., , height of one is three times that of the other., If from the middle point of the line joining, their feet, an observer finds the angles of, elevation of their tops to be complementary,, then the height of the shorter pole (in, metres) is, a. 25, c. 20 3, , b. 30, d. 25 3, , 20. The statement among the following that is a, tautology is, , 14. The locus of the mid-point of the line, , a. x = a, , b. 19 2, d. 38, , 19. Two vertical poles are 150 m apart and the, , 13. A man is walking on a straight line. The, , a. A only, d. All the three, , a. 2 19, c. 38, , x −3, 1, , =, , and the plane x + y + z = 17 is, , y−4, 2, , a. A ∧ (A ∨ B ), b. A ∨ (A ∧ B ), c. [ A ∧ (A → B )] → B, d. B → [ A ∧ (A → B )], , Section B : Numerical Type Questions, 21. If the least and the largest real values of α,, , for which the equation z + α | z − 1| + 2i = 0, (z ∈ C and i = − 1) has a solution, are p and q, respectively, then 4( p2 + q 2) is equal to .....…, .... ., , 22. Let B i (i = 1, 2, 3) be three independent events, in a sample space. The probability that only, B1 occur is α, only B 2 occurs is β and only B 3, occurs is γ. Let P be the probability that none, of the events B i occurs and these 4, probabilities satisfy the equations, (α − 2β)P = αβ and (β − 3γ)P = 2βγ (All the, probabilities are assumed to lie in the, P(B1), is equal to ……… ., interval (0,1)). Then,, P(B 3), 3 − 1 − 2, 23. Let P = 2 0 α , where α ∈R. Suppose, , , 3 − 5 0 , Q = [q ij ] is a matrix satisfying PQ = kI3 for
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12, , ONLINE, a, , some non-zero k ∈ R . If q 23 = − k / 8 and, k2, | Q | = , then α 2 + k 2 is equal to ......... ., 2, , 27. If ∫ (| x | + | x − 2|)dx = 22, (a > 2) and [ x ], −a, , denotes the greatest integer ≤ x, then, , 24. Let M be any 3 × 3 matrix with entries from, , −a, , ∫ (x + [ x ]) dx is equal to ........ ., , the set {0, 1, 2}. The maximum number of, such matrices, for which the sum of diagonal, elements of MT M is seven, is ......... ., , a, , 28. If one of the diameters of the circle, , x 2 + y 2 − 2x − 6 y + 6 = 0 is a chord of another, circle ‘C’, whose centre is at (2, 1), then its, radius is ............ ., , 25. Let A = {n ∈ N : n is a 3-digit number}, B = { 9k + 2 : k ∈ N }, and C = { 9k + l : k ∈ N } for some l(0 < l < 9), , 29. Let three vectors a, b and c be such that c is, , coplanar with a and b, a⋅c = 7 and b is, perpendicular to c, where a = − i$ + $j + k$ and, b = 2i$ + k$ , then the value of 2| a+ b+ c |2 is, ........ ., n, , , 1, 30. lim tan ∑ tan− 1, is equal to, 2 , n→ ∞, 1 + r + r , r = 1, ……… ., , If the sum of all the elements of the set, A ∩ (B ∪ C ) is 274 × 400, then l is equal, to ........... ., , 26. The minimum value of α for which the, 4, sin x, solution in 0,, , equation, , +, , JEE Main 2021 ~ Solved Papers, , 1, = α has at least one, 1 − sin x, , π, is ........ ., 2, , Answers, For solutions scan, the QR code, , Physics, 1. (c), 11. (b), 21. 25, , 2. (b), 12. (c), 22. 75, , 3. (*), 13. (c), 23. 1, , 4. (d), 14. (d), 24. 25600, , 5. (a), 15. (c), 25. 25, , 6. (d), 16. (a), 26. 2000, , 3. (a), 13. (d), 23. 2, , 4. (d), 14. (d), 24. 1380, , 5. (b), 15. (d), 25. 34.4, , 6. (d), 16. (c), 26. 5, , 7. (c), 17. (d), 27. 25, , 8. (a), 18. (c), 28. 25, , 9. (d), 19. (d), 29. 15, , 10. (d), 20. (a), 30. 440, , Chemistry, 1. (a), 11. (b), 21. 2, , 2. (d), 12. (b), 22. 8, , 7. (d), 17. (d), 27. 12, , 8. (a), 18. (d), 28. 26, , 9. (b), 19. (d), 29. 2, , 10. (b), 20. (b), 30. 1.26, , 7. (a), 17. (c), 27. 3, , 8. (b), 18. (d), 28. 3, , 9. (d), 19. (d), 29. 75, , 10. (b), 20. (c), 30. 1, , Mathematics, 1. (a), 11. (b), 21. 10, , 2. (b), 12. (d), 22. 6, , 3. (c), 13. (b), 23. 17, , 4. (b), 14. (c), 24. 540, , Note (*) None of the option is correct., , 5. (a), 15. (d), 25. 5, , 6. (a), 16. (b), 26. 9
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13, , FEBRUARY ATTEMPT ~ 24 Feb 2021, Shift II, , JEE Main 2021, 24 FEBRUARY SHIFT II, , PHYSICS, Section A : Objective Type Questions, , 5., , A, B, , 1. When a particle executes SHM, the nature of, , C, , graphical representation of velocity as a, function of displacement is, , The logic circuit shown above is equivalent to, , a. circular, c. parabolic, , a., , A, B, , C, , b., , A, B, , C, , c., , A, B, , C, , d., , A, B, , b. elliptical, d. straight line, , 2. Two electrons each are fixed at a distance, 2d. A third charge proton placed at the, mid-point is displaced slightly by a distance, x( x < < d) perpendicular to the line joining, the two fixed charges. Proton will execute, simple harmonic motion having angular, frequency?, (m = mass of charged particle), 1, , 1, , πε md 3 2, b. 0 2 , 2q, , , 2q 2 2, a. , 3, πε0 md , 1, , , 2, q, c. , 3, 2πε0 md , 2, , 2 πε0 md , d. , , q2, , , 3, , 1, , C, , 2, , 3. On the basis of kinetic theory of gases, the, gas exerts pressure because its molecules, a. continuously lose their energy till it reaches, wall, b. are attracted by the walls of container, c. continuously stick to the walls of container, d. suffer change in momentum when impinge on, the walls of container, , 4. A soft ferromagnetic material is placed in an, external magnetic field. The magnetic, domains, a. increase in size but no change in orientation, b. have no relation with external magnetic field, c. decrease in size and changes orientation, d. may increase or decrease in size and change, its orientation, , 6. The period of oscillation of a simple, pendulum is T = 2π, , L, . Measured value of L, g, , is 1.0 m from metre scale having a minimum, division of 1 mm and time of one complete, oscillation is 1.95 s measured from, stopwatch of 0.01 s resolution. The, percentage error in the determination of g, will be, a. 1.13%, c. 1.33%, , b. 1.03%, d. 1.30%, , 7. Given below are two statements:, Statement I p-n junction diodes can be used, to function as transistor, simply by, connecting two diodes, back to back, which, acts as the base terminal.
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14, , JEE Main 2021 ~ Solved Papers, , ONLINE, Statement II In the study of transistor, the, amplification factor β indicates ratio of the, collector current to the base current., In the light of the above statements, choose, the correct answer from the options given, below., a. Statement I is false but Statement II is true., b. Both Statement I and Statement II are true., c. Both Statement I and Statement II are false., d. Statement I is true but Statement II is false., , 11. If one mole of an ideal gas at ( p1, V1) is allowed, to expand reversibly and isothermally, (A to B ), its pressure is reduced to one-half of, the original pressure (see figure). This is, followed by a constant volume cooling till its, pressure is reduced to one-fourth of the, initial value (B → C ). Then, it is restored to its, initial state by a reversible adiabatic, compression (C to A). The net work done by, the gas is equal to, , 8. In the given figure, a body of mass M is held, , P, , between two massless springs, on a smooth, inclined plane. The free ends of the springs, are attached to firm supports. If each spring, has spring constant k, then the frequency of, oscillation of given body is, , p1, , k, k, , p1, 2, , B, , p1, 4, , C, , M, , V1, , α, , 1, k, a., 2 π 2M, 1 2k, c., 2π M, , A, , 1, b., 2π, 1, d., 2π, , 2k, Mg sin α, k, Mg sin α, , 2V1, , , 1 , a. RT ln 2 −, , 2(γ − 1) , , , b. −, , c. 0, , d. RT ln2, , V, , RT, 2(γ − 1), , 12. An X-ray tube is operated at, , 9. Figure shows a circuit that contains four, , identical resistors with resistance R = 20, . Ω,, two identical inductors with inductance, L = 2.0 mH and an ideal battery with, electromotive force E = 9 V. The current i just, after the switch S is closed will be, , 1.24 million volt. The shortest wavelength of, the produced photon will be, a. 10− 3 nm, c. 10− 2 nm, , b. 10− 1 nm, d. 10− 4 nm, , 13. Which of the following equations represents, a travelling wave?, a. y = A sin(15x − 2t ), c. y = Ae x cos(ωt − θ), , b. y = Ae − x (vt + θ), d. y = A sin x cosωt, 2, , S, L, , A, E=9 V, , +, – i, , R, , R, R, , L, , 14. According to Bohr atom model, in which of, the following transitions will the frequency, be maximum ?, a. n = 4 to n = 3, c. n = 5 to n = 4, , b. n = 2 to n = 1, d. n = 3 to n = 2, , R, , a. 2.25 A, c. 3.37 A, , b. 3.0 A, d. 9 A, , 10. The de-Broglie wavelength of a proton and, α-particle are equal. The ratio of their, velocities is, a. 4 : 3, c. 4 : 2, , b. 4 : 1, d. 1: 4, , 15. If the source of light used in a Young's, double slit experiment is changed from red, to violet, then, a. the consecutive fringe lines will come closer, b. the central bright fringe will become a dark, fringe, c. the fringes will become brighter, d. the intensity of minima will increase
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15, , FEBRUARY ATTEMPT ~ 24 Feb 2021, Shift II, a, 16. A circular hole of radius is cut out of a, , 2, circular disc of radius a as shown in figure., The centroid of the remaining circular, portion with respect to point O will be, Y-axis, , 19. A particle is projected with velocity v 0 along, X-axis. A damping force is acting on the, particle which is proportional to the square, of the distance from the origin, i.e., ma = − αx 2 . The distance at which the, particle stops is, 1, , 3 mv 02 2, a. , , 2α , 1, , a/2, , O, , a, , X–axis, , 2 mv 02 2, c. , , 3α , , 1, , 2 mv 0 3, b. , , 3α , 1, , 3 mv 02 3, d. , , 2α , , 20. A body weights 49 N on a spring balance at, , 1, a. a, 6, 5, c. a, 6, , the North pole. What will be its weight, recorded on the same weighing machine, if it, is shifted to the equator ?, GM, (Use, g = 2 = 9.8 ms − 2 and radius of earth,, R, R = 6400 km), , 10, a, 11, 2, d. a, 3, b., , 17. Zener breakdown occurs in a p-n junction, having p and n both, a. lightly doped and have wide depletion layer, b. heavily doped and have narrow depletion, layer, c. lightly doped and have narrow depletion layer, d. heavily doped and have wide depletion layer, , 18. Match List-I with List-II., List-I, , List-II, , A. Source of microwave 1. Radioactive decay of, frequency, nucleus, B. Source of infrared, frequency, , 2. Magnetron, , C. Source of gamma, rays, , 3. Inner shell electrons, , D. Source of X-rays, , 4. Vibration of atoms, and molecules, , 6. R - C circuit, , Choose the correct answer from the options, given below., A, 6, 6, 2, 2, , B, 4, 5, 4, 4, , C, 1, 1, 6, 1, , D, 5, 4, 3, 3, , b. 48.83 N, d. 49.17 N, , Section B : Numerical Type Questions, 21. A uniform metallic wire is elongated by, 0.04 m when subjected to a linear force F ., The elongation, if its length and diameter is, doubled and subjected to the same force will, be ……… cm., , 22. A cylindrical wire of radius 0.5 mm and, , conductivity 5 × 107 S/m is subjected to an, electric field of 10 mV/m. The expected value, of current in the wire will be x 3 π mA. The, value of x is ……… ., , 23. A uniform thin bar of mass 6 kg and length, , 5. LASER, , a., b., c., d., , a. 49 N, c. 49.83 N, , 2.4 m is bent to make an equilateral, hexagon. The moment of inertia about an, axis passing through the centre of mass and, perpendicular to the plane of hexagon is, ……… × 10− 1 kg - m2 ., , 24. Two solids A and B of mass 1 kg and 2 kg, respectively are moving with equal linear, momentum. The ratio of their kinetic, A, energies (KE) A : (KE) B will be , so the value of, 1, A will be ……… ., , 25. The root mean square speed of molecules of, a given mass of a gas at 27°C and 1, atmosphere pressure is 200 ms − 1. The root
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16, , ONLINE, mean square speed of molecules of the gas, at 127°C and 2 atmosphere pressure is, x, ms − 1. The value of x will be ……… ., 3, , 26. A point charge of + 12 µC is at a distance, 6 cm vertically above the centre of a square, of side 12 cm as shown in figure. The, magnitude of the electric flux through the, square will be ……… × 103 N - m2 / C ., , JEE Main 2021 ~ Solved Papers, , cable length is 20 km. The power received at, receiver is 10− x W. The value of x is ……… ., P , [Gain in dB = 10 log10 0 ], Pi , , 28. A series L-C -R circuit is designed to resonate, , at an angular frequency ω 0 = 105 rad/s. The, circuit draws 16 W power from 120 V source, at resonance. The value of resistance R in the, circuit is ……… Ω., , +q, , 29. Two cars are approaching each other at an, equal speed of 7.2 km/h. When they see, each other, both blow horns having, frequency of 676 Hz. The beat frequency, heard by each driver will be ……… Hz., [Velocity of sound in air is 340 m/s.], , 6 cm, , 30. An electromagnetic wave of frequency 3 GHz, , cm, , cm, , 12, , 12, , 27. A signal of 0.1 kW is transmitted in a cable., , The attenuation of cable is − 5 dB per km and, , enters a dielectric medium of relative electric, permittivity 2.25 from vacuum. The, wavelength of this wave in that medium will, be ……… × 10− 2 cm., , CHEMISTRY, Section A : Objective Type Questions, 1. What is the correct sequence of reagents, used for converting nitrobenzene into, m-dibromobenzene?, NO2, , 3. The correct order of the following, compounds showing increasing tendency, towards nucleophilic substitution reaction is, Cl, , Cl, , (i), , NO2, (ii), , Br, , Br, +, , H, a. NaNO, 2 → / HCl, → / KBr, → / , →, Br2 /Fe, NaNO 2 /HCl, b. , → / Sn/HCl, → / , → / CuBr/HBr, , →, H+, c. Sn/HCl, → / KBr, → / Br, 2 → / , →, Br, d. Sn/HCl, → / 2 → / NaNO, 2 → / NaBr, , →, , Cl, , Cl, NO2, , NO2, , O2N, , 2. Most suitable salt which can be used for, efficient clotting of blood will be, a. NaHCO 3, b. FeSO 4, c. Mg(HCO 3 ) 2, d. FeCl3, , NO2, (iii), a. (iv) < (iii) < (ii) < (i), c. (iv) < (i) < (iii) < (ii), , NO2, (iv), b. (iv) < (i) < (ii) < (iii), d. (i) < (ii) < (iii) < (iv)
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17, , FEBRUARY ATTEMPT ~ 24 Feb 2021, Shift II, 7. Match List-I with List-II., , 4. According to Bohr’s atomic theory,, Z2, n2, II. the product of velocity (v) of electron and, principal quantum number (n), ‘vn’ ∝ Z 2 ., III. frequency of revolution of electron in an orbit is, Z3, ∝ 3, n, IV. coulombic force of attraction on the electron is, Z3, ∝ 4, n, I. kinetic energy of electron is ∝, , a. Only III, b. Only I, c. I, III and IV, d. I and IV, , O, , R C Cl → R CHO, , A., , R CH2 COOH, , B., , A, 2, 3, 2, 3, , B, 1, 4, 4, 1, , 455.5 nm, , B., , NaCl, , 2., , 670.8 nm, , C., , RbCl, , 3., , 780.0 nm, , D., , CsCl, , 4., , 589.2 nm, , C, 4, 1, 1, 4, , D, 3, 2, 3, 2, , a., , B, 2, 1, 4, 4, , C, 3, 4, 2, 3, , D, 1, 3, 3, 1, , value) for species [FeCl4 ]2 − , [Co(C 2O4 ) 3 ]3 − and, MnO24 − respectively are, , CH3, , C, , H, , O, b., , C, , CH3, O, , c. CH3, , CH2, , C, , H, , O, d. CH3, , C, , CH2CH3, , 9. In polymer buna-S: ‘S’ stands for, a. sulphonation, b. strength, c. sulphur, d. styrene, , 6. The calculated magnetic moments (spin only, a. 5.82, 0 and 0 BM, b. 4.90, 0 and 1.73 BM, c. 5.92, 4.90 and 0 BM, d. 4.90, 0 and 2.83 BM, , A, 4, 2, 1, 2, , O, , 2. H2 / Pd - BaSO 4, , Choose the correct answer from the options given, below., a., b., c., d., , 1., , compounds cannot be prepared by, addition of water on an alkyne in the, presence of HgSO4 and H 2SO4 ?, , 1. Br2 / NaOH, , O, 4. Cl2 / Red P, H2O, , R C CH3 → R CH2 CH3, , D., , LiCl, , 8. Which one of the following carbonyl, List-II, , → R C H COOH, , Cl, O, 3. Zn(Hg) / Conc.HCl, , R C NH2 → R NH2, , C., , (Flame colour, wavelength), , A., , a., b., c., d., , List-I, , List-II, , (Salt), , Choose the correct answer from the, options given below., , Choose the most appropriate answer from the, options given below., , 5. Match List-I with List-II., , List-I, , 10., ?, O
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18, , ONLINE, Which of the following reagent is suitable for, the preparation of the product in the above, reaction?, È, , ⊕, , b. NH2 NH2 / C 2H5 ONa, d. Red P + Cl2, , a. NaBH4, c. Ni / H2, , 11. Match List-I and List-II., List-II, , A., , Valium, , 1., , Antifertility drug, , B., , Morphine, , 2., , Pernicious, anaemia, , C., , Norethindrone, , 3., , Analgesic, , D., , Vitamin B12, , 4., , Tranquiliser, , Choose the correct answer from the option, given below., A, 4, 4, 2, 1, , B, 3, 3, 4, 3, , C, 2, 1, 3, 4, , D, 1, 2, 1, 2, , List I, , List II, (Ores), , A., , Aluminium, , 1., , Siderite, , B., , Iron, , 2., , Calamine, , C., , Copper, , 3., , Kaolinite, , D., , Zinc, , 4., , Malachite, , Choose the correct answer from the options, given below., a., b., c., d., , C, 2, 1, 3, 4, , D, 1, 3, 4, 2, , 13. Which one of the following compounds is, non-aromatic ?, a., , b., O, +, , c., , d., +, , a. Cr < Zn < Co < Cu < Fe, b. Zn < Cu < Co < Fe < Cr, c. Zn < Cr < Fe < Co < Cu, d. Cr < Fe < Co < Cu < Zn, , Statement I The value of the parameter, “Biochemical Oxygen Demand (BOD)” is, important for survival of aquatic life., Statement II The optimum value of BOD is, 6.5 ppm., In the light of the above statements, choose, the most appropriate answer from the options, given below., a. Statement I is false but statement II is true., b. Both statements are true., c. Statement I is true but statement II is false., d. Both statements are false., , is, , (Metal), , B, 3, 4, 2, 1, , elements with respect to their density ?, , 16. The incorrect statement among the following, , 12. Match List-I with List-II., , A, 4, 2, 1, 3, , 14. What is the correct order of the following, , 15. Given below are two statements., , List-I, , a., b., c., d., , JEE Main 2021 ~ Solved Papers, , a. VOSO 4 is a reducing agent., b. Cr2O 3 is an amphoteric oxide., c. RuO 4 is an oxidising agent., d. Red colour of ruby is due to the presence of, Co 3+ ., , 17. The correct shape and I I I bond angles, respectively in I−3 , ion are, , a. distorted trigonal planar, 135º and 90º, b. T-shaped, 180º and 90º, c. Trigonal planar, 120°, d. Linear, 180°, , 18. Given below are two statements., One is labelled as Assertion A and the other is, labelled as Reason R., Assertion A Hydrogen is the most abundant, element in the universe, but it is not the most, abundant gas in the troposphere., Reason R Hydrogen is the lightest element. In, the light of the above statements, choose the, correct answer from the options given below., a. A is true but R is false., b. Both A and R are true and R is the correct, explanation of A., c. A is false but R is true., d. Both A and R are true but R is not the correct, explanation of A.
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19, , FEBRUARY ATTEMPT ~ 24 Feb 2021, Shift II, 19. The diazonium salt of which of the following, compounds will form a coloured dye on, reaction with β-naphthol in NaOH ?, CH3, N, , CH2NH2, , CH3, , b., , a., , NH2, , NH2, , CH3, , d., , c., , both pairs are in correct order of melting point, is, a. LiF > LiCl, MgO > NaCl, b. LiCl > LiF, NaCl > MgO, c. LiF > LiCl, NaCl > MgO, d. LiCl > LiF, MgO > NaCl, , Section B : Numerical Type Questions, 21. The total number of amines among the, following which can be synthesised by, Gabriel synthesis is ……… ., CH3, CH, CH3, b., , CH2, , gas at 50°C and 740 mm Hg pressure is ……L, (Rounded off to the nearest integer)., [Given, R = 0.0826 L atm K − 1 mol− 1], , 25. C 6H6 freezes at 5.5°C. The temperature at, which a solution 10 g of C 4H10 in 200 g of, C 6H 6 freeze is ………°C. (The molal freezing, point depression constant of C 6H 6 is, 5.12ºC/m.), , 26. The magnitude of the change in oxidising, , 20. The correct set from the following in which, , a., , 24. The volume occupied by 4.75 g of acetylene, , NH2, , power of the MnO−4 / Mn2 + couple is x × 10− 4, V, if the H + concentration is decreased from, 1 M to 10− 4 M at 25ºC. (Assume, concentration of MnO−4 and Mn2 + to be same, on change in H + concentration). The value of, x is ……… (Rounded off to the nearest, 2.303 RT, , , integer). Given,, = 0.059, , , F, , 27. The solubility product of PbI2 is 80, . × 10− 9 ., The solubility of lead iodide in 0.1 molar, solution of lead nitrate is x × 10− 6 mol/L. The, value of x is ……. (Rounded off to the nearest, integer)., [Given, : 2 = 141, . ], , 28. Sucrose hydrolyses in acid solution into, glucose and fructose following first order, rate law with a half-life of 3.33 h at 25°C., After 9 h, the fraction of sucrose remaining is, 1, f . The value of log 10 is ……… × 10− 2, f, , CH3CH2NH2, CH2, , NH2, , c., , (Rounded off to the nearest integer)., [Assume, ln 10 = 2.303, ln 2 = 0.693], , NH2, d., , 29. 1.86 g of aniline completely reacts to form, 22. Among the following allotropic forms of, sulphur, the number of allotropic forms,, which will show paramagnetism is ……… ., a. α-sulphur, c. S2 -form, , b. β-sulphur, , 23. The formula of a gaseous hydrocarbon,, which requires 6 times of its own volume of, O2 for complete oxidation and produces, 4 times its own volume of CO2 is C xH y . The, value of y is ……… ., , acetanilide. 10% of the product is lost during, purification. Amount of acetanilide obtained, after purification (in g) is ……… × 10− 2 ., , 30. Assuming ideal behaviour, the magnitude of, log K for the following reaction at 25ºC is, x × 10− 1. The value of x is ……… (Integer, answer), 3HC ≡≡ CH( g ), C 6H6 (l ), [Given, ∆ fGº (HC ≡≡ CH) = − 2.04 × 105 J mol− 1,, ∆ fGº (C 6H6 ) = − 1.24 × 105 J mol− 1,, R = 8.314 J K − 1 mol− 1], , -
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20, , ONLINE, , JEE Main 2021 ~ Solved Papers, , MATHEMATICS, Section A : Objective Type Questions, 1. For the statements p and q, consider the, following compound statements, A. [~ q ∧ (p → q )] → ~ p, B. [(p ∨ q ) ∧ ~ p ] → q, , a. (A) and (B) both are not tautologies., b. (A) and (B) both are tautologies., c. (A) is a tautology but not (B)., d. (B) is a tautology but not (A)., , P(a, 6, 9) with respect to the line, x− 3 y −2 z −1, is (20, b, − a − 9), then, =, =, 7, 5, −9, | a + b | is equal to, c. 84, , d. 90, , 3. The vector equation of the plane passing, through the intersection of the planes, r ⋅ ( i$ + $j + k$ ) = 1 and r ⋅ ( i$ − 2$j ) = − 2 and the, point (1, 0, 2) is, 7, a. r ⋅ ($i + 7$j + 3k$ ) =, 3, c. r ⋅ ($i + 7$j + 3k$ ) = 7, , b. r ⋅ (3i$ + 7$j + 3k$ ) = 7, , 4. If P is a point on the parabola y = x + 4, which is closest to the straight line y = 4 x − 1,, then the coordinates of P are, b. (1, 5), , c. (− 2, 8), , point A on the ground is 60°. After a flight of, 20 s at the speed of 432 km/h, the angle of, elevation changes to 30°. If the jet plane is, flying at a constant height, then its height is, b. 3600 3 m, d. 1200 3 m, , 6. If n ≥ 2 is a positive integer, then the sum of, the series, n +1, C 2 + 2 ( 2 C 2 + 3C 2 + 4C 2 + … + nC 2 ) is, n (n − 1) (2n + 1), 6, n (2n + 1) (3n + 1), c., 6, , a., , a. (− ∞ , − 5) ∪ (4 , ∞ ), c. (− ∞ , − 5) ∪ (− 4 , ∞ ), , b. (− 5, ∞ ), d. (− 5, − 4 ) ∪ (4 , ∞ ), , defined on R, such that f (0) = 1, f ′ (0) = 2 and, f ( x) f ′ ( x), = 0, for, f ′′ ( x) ≠ 0 for all x ∈ R . If, f ′ ( x) f ′′( x), all x ∈ R , then the value of f (1) lies in the, interval, a. (9, 12), , b. (6, 9), , c. (0, 3), , d. (3, 6), , 9. For which of the following curves, the line, x + 3 y = 2 3 is the tangent at the point, 3 3 1, , ?, , 2 2, a. x 2 + y 2 = 7, c. 2x 2 − 18 y 2 = 9, , 1, x, 6 3, 2, 2, d. x + 9 y = 9, b. y 2 =, , n (n + 1) (2n + 1), 6, n (n + 1) 2 (n + 2), d., 12, b., , 10. The value of the integral ∫ [ x 2 − 2x − 2] dx ,, 1, , where [x] denotes the greatest integer less, than or equal to x, is, a. − 2 − 3 + 1, c. − 5, , d. (2, 8), , 5. The angle of elevation of a jet plane from a, , a. 1800 3 m, c. 2400 3 m, , x≥ 4, , 3, , 7, d. r ⋅ ($i − 7$j + 3k$ ) =, 3, 2, , a. (3, 13), , x< −5, − 5≤ x < 4, , 8. Let f be a twice differentiable function, , 2. Let a , b ∈ R. If the mirror image of the point, , b. 86, , − 55 x ,, if, , , f (x ) = 2x 3 − 3x 2 − 120x ,, if, 2x 3 − 3x 2 − 36x − 336, if, , , Let A = {x ∈ R: f is increasing}. Then, A is equal to, , Then, which of the following statement(s), is/are correct?, , a. 88, , 7. Let f :R → R be defined as, , b. − 2 − 3 − 1, d. − 4, , 1, , 11. A possible value of tan sin− 1, 4, , a., , 1, 7, , b. 2 2 − 1, , c. 7 − 1, , 63 , is, 8 , d., , 1, 2 2, , 12. The negative of the statement ~ p ∧ ( p ∨ q) is, a. ~ p ∨ q, c. ~ p ∧ q, , b. p ∨ ~ q, d. p ∧ ~ q, , 13. If the curve y = ax 2 + bx + c, x ∈ R, passes, through the point (1,2) and the tangent line, to this curve at origin is y = x , then the, possible values of a , b, c are, 1, 1, a. a = , b = , c = 1, 2, 2, c. a = 1, b = 1, c = 0, , b. a = 1, b = 0, c = 1, d. a = − 1, b = 1, c = 1
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21, , FEBRUARY ATTEMPT ~ 24 Feb 2021, Shift II, , (E) The system has infinite number of solutions,, if k ≠ − 2., , 14. The area of the region, R = {(x , y ): 5x ≤ y ≤ 2x + 9} is, 2, , 2, , a. 11 3 square units, c. 9 3 square units, , b. 12 3 square units, d. 6 3 square units, , 15. If a curve y = f ( x) passes through the point, dy, + y = bx 4 , then for, dx, 62, ?, f ( x) dx =, 5, , (1, 2) and satisfies x, 2, , what value of b, ∫, , 1, , a. 5, , b. 10, , c., , 62, 5, , d., , 31, 5, , 16. Let f ( x) be a differentiable function defined, on [0, 2], such that f ′ ( x) = f ′ (2 − x), for all, x ∈ (0, 2), f (0) = 1and f (2) = e 2 . Then, the value, 2, , of ∫ f ( x) dx is, 0, , a. 1 − e 2, c. 2(1 − e 2 ), , b. 1 + e 2, d. 2(1 + e 2 ), , 17. Let A and B be 3 × 3 real matrices, such that A, is symmetric matrix and B is skew-symmetric, matrix. Then, the system of linear equations, ( A 2B 2 − B 2 A 2 ) X = O, where X is a 3 × 1 column, matrix of unknown variables and O is a 3 × 1, null matrix, has, a. no solution, b. exactly two solutions, c. infinitely many solutions, d. a unique solution, , 18. Let a , b, c be in an arithmetic progression., Let the centroid of the triangle with vertices, 10 7, (a , c), (2, b) and (a , b) be , . If α , β are the, 3 3, roots of the equation ax 2 + bx + 1 = 0, then, the value of α 2 + β 2 − αβ is, a., , 71, 256, , b., , 69, 256, , c. −, , 69, 256, , d. −, , 71, 256, , 19. For the system of linear equations, x − 2 y = 1, x − y + kz = − 2, ky + 4 z = 6, k ∈ R,, consider the following statements, (A) The system has unique solution, if k ≠ 2,, k ≠ −2., (B) The system has unique solution, if k = − 2., (C) The system has unique solution, if k = 2., (D) The system has no solution, if k = 2., , Which of the following statements are correct ?, a. (C) and (D), c. (A) and (E), , b. (B) and (E), d. (A) and (D), , 20. The probability that two randomly selected, subsets of the set {1, 2, 3, 4, 5} have exactly, two elements in their intersection, is, a., , 65, 27, , b., , 65, 28, , c., , 135, 29, , d., , 35, 27, , Section B : Numerical Type Questions, 21. For integers n and r, let, n, n C r , if n ≥ r ≥ 0, r = , 0,, otherwise, The maximum value of k for which the sum,, k, 10 15 k + 1 12 13 , ∑ i k − i + ∑ i k + 1 − i exists, is, i=0, i=0, equal to ……… ., , 22. Let λ be an integer. If the shortest distance, between the lines x − λ = 2 y − 1 = − 2z and, , x = y + 2λ = z − λ is, , 7, ,then the value of| λ |, 2 2, , is ……… ., , 23. If a + α = 1, b + β = 2 and, β, 1, af ( x) + αf = bx + , x ≠ 0, then the value, x, x, 1, f ( x) + f , x, of expression, is ……… ., 1, x+, x, , 24. Let a point P be such that its distance from, the point (5, 0) is thrice the distance of P, from the point (− 5, 0). If the locus of the, point P is a circle of radius r, then 4 r 2 is equal, to ……… ., , 25. If the area of the triangle formed by the, positive x-axis, the normal and the tangent, to the circle ( x − 2) 2 + ( y − 3) 2 = 25 at the, point (5, 7) is A, then 24A is equal to ……… ., , 26. If the variance of 10 natural numbers 1, 1,, 1,...., 1, k is less than 10, then the maximum, possible value of k is ……… .
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22, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 27. The sum of first four terms of a geometric, , 65, and the sum of their, 12, 65, respective reciprocals is . If the product of, 18, first three terms of the G.P. is 1 and the third, term is α, then 2α is ……… ., , progression (G.P.) is, , 29. Let i = − 1. If, , ( − 1 + i 3) 21, (1 − i) 24, , +, , (1 + i 3) 21, (1 + i) 24, , =k, , and n = [| k |] be the greatest integral part, of| k |., Then,, , n +5, , n +5, , j=0, , j=0, , 2, ∑ ( j + 5) −, , ∑ ( j + 5) is equal to, , ………… ., , 28. The students S1, S 2 , … , S10 are to be divided, into 3 groups A , B and C such that each group, has at least one student and the group C has, at most 3 students. Then, the total number of, possibilities of forming such groups is ……… ., , 30. The number of the real roots of the, equation, (x + 1) 2 + | x − 5| =, , 27, is ………… ., 4, , Answers, For solutions scan, the QR code, , Physics, 1. (b), 11. (a), 21. 2, , 2. (c), 12. (a), 22. 5, , 3. (d), 13. (a), 23. 8, , 4. (d), 14. (b), 24. 2, , 5. (d), 15. (a), 25. 400, , 3. (d), 13. (a), 23. 8, , 4. (d), 14. (c), 24. 5, , 5. (c), 15. (c), 25. 1, , 6. (a), 16. (c), 26. 226, , 7. (a), 17. (b), 27. 8, , 8. (c), 18. (d), 28. 900, , 9. (a), 19. (d), 29. 8, , 10. (b), 20. (b), 30. 667, , 7. (d), 17. (d), 27. 141, , 8. (c), 18. (b), 28. 81, , 9. (d), 19. (c), 29. 243, , 10. (b), 20. (a), 30. 855, , Chemistry, 1. (b), 11. (b), 21. 3, , 2. (d), 12. (d), 22. 1, , 6. (b), 16. (d), 26. 3776, , Mathematics, 1. (b), 11. (a), 21. (*), , 2. (a), 12. (b), 22. 1, , 3. (c), 13. (c), 23. 2, , 4. (d), 14. (b), 24. 56.25, , Note (*) None of the option is correct., , 5. (d), 15. (b), 25. 1225, , 6. (b), 16. (b), 26. 11, , 7. (d), 17. (c), 27. 3, , 8. (b), 18. (d), 28. 31650, , 9. (d), 19. (d), 29. 310, , 10. (b), 20. (c), 30. 2
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23, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift I, , JEE Main 2021, 25 FEBRUARY SHIFT I, , PHYSICS, Section A : Objective Type Questions, 1. Given below are two statements: one is, labelled as Assertion A and the other is, labelled as Reason R., Assertion (A) When a rod lying freely is, heated, no thermal stress is developed in it., Reason (R) On heating, the length of the rod, increases., , (Given, radius of Earth = 6400 km, mass of, Earth = 6 × 1024 kg), a. 1.33 × 103 s, c. 4.24 × 103 s, , 4. The angular frequency of alternating current, in an L-C-R circuit is 100 rad/s. The, components connected are shown in the, figure. Find the value of inductance of the, coil and capacity of condenser., , In the light of the above statements, choose, the correct answer from the options given, below, a. Both A and R are true but R is not the correct, explanation of A., b. A is false but R is true., c. A is true but R is false., d. Both A and R are true and R is the correct, explanation of A., , 2. A student is performing the experiment of, resonance column. The diameter of the, column tube is 6 cm. The frequency of the, tuning fork is 504 Hz. Speed of the sound at, the given temperature is 336 m/s. The zero, of the meter scale coincides with the top end, of the resonance column tube. The reading, of the water level in the column when the, first resonance occurs is, a. 13 cm, , b. 16.6 cm c. 18.4 cm d. 14.8 cm, , 3. Two satellites A and B of masses 200 kg and, 400 kg are revolving around the Earth at, height of 600 km and 1600 km, respectively., If TA and TB are the time periods of A and B, respectively, then the value of TB − TA is, , A, E, , B, , b. 3.33 × 102 s, d. 4.24 × 102 s, , R=60 Ω, 15 V, C, , 10 V, , R′=40 Ω, , a. 0.8 H and 150 µF, c. 1.33 H and 250 µF, , L, , 20 V, , b. 0.8 H and 250 µF, d. 1.33 H and 150 µF, , 5. A proton, a deuteron and an α-particle are, moving with same momentum in a uniform, magnetic field. The ratio of magnetic forces, acting on them is ……… and their speed, is ……… in the ratio., a. 1 : 2 : 4 and 2 : 1 : 1, c. 4 : 2 : 1 and 2 : 1 : 1, , b. 2 : 1 : 1 and 4 : 2 : 1, d. 1 : 2 : 4 and 1 : 1 : 2, , 6. Given, below are two statements, Statement I A speech signal of 2 kHz is used, to modulate a carrier signal of 1 MHz. The, bandwidth requirement for the signal is, 4 kHz., Statement II The side band frequencies are, 1002 kHz and 998 kHz. In the light of the, above statements, choose the correct, answer from the options given below, a. Statement I is true but Statement II is false., b. Statement I is false but Statement II is true., c. Both Statement I and Statement II are true., d. Both Statement I and Statement II are false.
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24, , ONLINE, , 7. If the time period of a 2 m long simple, pendulum is 2 s, the acceleration due to, gravity at the place, where pendulum is, executing SHM is, , a. π 2 ms −2, c. 2 π 2 ms −2, , b. 9.8 ms −2, d. 16 ms −2, , 8. The pitch of the screw gauge is 1 mm and, there are 100 divisions on the circular scale., When nothing is put in between the jaws, the, zero of the circular scale lies 8 divisions, below the reference line. When a wire is, placed between the jaws, the first linear, scale division is clearly visible while 72nd, division on circular scale coincides with the, reference line. The radius of the wire is, a. 1.64 mm, c. 1.80 mm, , b. 0.82 mm, d. 0.90 mm, , 9. A 5 V battery is connected across the points X, and Y. Assume D1 and D 2 to be normal silicon, diodes. Find the current supplied by the, battery, if the positive terminal of the battery, is connected to point X., D1, , 10 Ω, , D2, , 5Ω, , 13. Match List-I with List-II, List-I, , List-II, , A., , h (Planck's constant), , 1., , [M L T −1], , B., , E (kinetic energy), , 2., , [M L2 T −1], , C., , V (electric potential), , 3., , [M L2 T −2 ], , D., , P (linear momentum), , 4., , [M L2I−1T −3 ], , Choose the correct answer from the options, given below., A B C D, a. 3, 4, 2, 1, b. 2, 3, 4, 1, c. 1, 2, 4, 3, d. 3, 2, 4, 1, , 14. Magnetic fields at two points on the axis of a, circular coil at a distance of 0.05 m and 0.2 m, from the centre are in the ratio 8 : 1. The, radius of coil is, a. 0.2 m, c. 0.15 m, , b. 0.1 m, d. 1.0 m, , 15. A solid sphere of radius R gravitationally, attracts a particle placed at 3R from its, centre with a force F1. Now, a spherical cavity, R, of radius is made in the sphere (as, 2, shown in figure) and the force becomes F 2., The value of F1 : F 2 is, , X Y, , a. ~ 0.5 A, c. ~ 0.86 A, , JEE Main 2021 ~ Solved Papers, , b. ~ 1.5 A, d. ~ 0.43 A, , 10. An α-particle and a proton are accelerated, B, , from rest by a potential difference of 200 V., After this, their de-Broglie wavelengths are, λp, is, λ α and λ p, respectively. The ratio, λα, a. 3.8, , 11., , b. 8, , c. 7.8, , b. 5 : 7 : 2, d. 3 : 5 : 2, , 12. An engine of a train moving with uniform, acceleration, passes the signal-post with, velocity u and the last compartment with, velocity v. The velocity with which middle, point of the train passes the signal post is, a., , v2 + u2, v −u, b., 2, 2, , c., , u+v, 2, , 2R, , A, m, , d. 2.8, , 7, 5, A diatomic gas having C p = R and C V = R ,, 2, 2, is heated at constant pressure. The, ratio dU : dQ : dW is, a. 5 : 7 : 3, c. 3 : 7 : 2, , O, , d., , v2 − u2, 2, , a. 25 : 36, c. 50 : 41, , b. 36 : 25, d. 41 : 50, , 16. Two radioactive substances X and Y originally, have N1 and N2 nuclei, respectively. Half-life, of X is half of the half-life of Y. After three, half-lives of Y, number of nuclei of both are, N, equal. The ratio 1 will be equal to, N2, a., , 1, 8, , b., , 3, 1, , c., , 8, 1, , d., , 1, 3
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25, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift I, 17. In an octagon ABCDEFGH of equal side, what, is the sum of, AB + AC + AD + AE + AF + AG + AH, if, AO = 2i$ + 3$j − 4k$ ?, A, , B, , O, G, , D, E, , F, , 2 2x, x+1, 2x, c., x+1, , 2x, 2x + 1, 2 2x, d., 2x + 1, , b., , Section B : Numerical Type Questions, 21. A transmitting station releases waves of, wavelength 960 m. A capacitor of 2.56 µF is, used in the resonant circuit. The, self-inductance of coil necessary for, resonance is ……… × 10−8 H., , a. −16$i − 24 $j + 32k$, b. 16 $i + 24 $j − 32k$, c. 16 $i + 24 $j + 32k$, d. 16 i$ − 24 $j + 32k$, , 18. Given below are two statements: one is, labelled as Assertion A and the other is, labelled as Reason R., Assertion A The escape velocities of planet A, and B are same. But A and B are of unequal, mass., Reason R The product of their mass and, radius must be same, M1R1 = M 2R 2, In the light of the above statements, choose, the most appropriate answer from the, options given below., (a) Both A and R are correct but R is not the, correct explanation of A., (b) A is correct but R is not correct., (c) Both A and R are correct and R is the correct, explanation of A., (d) A is not correct but R is correct., , 19. The current ( i) at time t = 0 and t = ∞, respectively for the given circuit is, 5Ω, , 5Ω, i, , 1Ω, , 4Ω, , L, , 10E 5E, ,, 33 18, 5E 10E, d., ,, 18 33, b., , 22. The electric field in a region is given, 4, 3, N, E = E 0$i + E 0$j . The ratio of flux of, 5, C, 5, reported field through the rectangular, surface of area 0.2 m2 (parallel to YZ-plane) to, that of the surface of area 0.3 m 2 (parallel to, XZ- plane) is a : b, where a = ……… ., [Here $i, $j and k$ are unit vectors along X, Y, and Z-axes, respectively], , 23. In a certain thermodynamical process, the, pressure of a gas depends on its volume as, kV 3. The work done when the temperature, changes from 100°C to 300°C will be ………, nR, where n denotes number of moles of a, gas., , 24. A small bob tied at one end of a thin string of, length 1m is describing a vertical circle, so, that the maximum and minimum tension in, the string are in the ratio 5 : 1. The velocity of, the bob at the highest position is ……… m/s., (Take, g = 10 m/s 2), , 25. In the given circuit of potentiometer, the, , E, , 18E 5E, a., ,, 55 18, 5E 18E, c., ,, 18 55, , in the ratio 2x produce an interference, I, −I, pattern. The ratio max min will be, Imax + Imin, a., , C, , H, , 20. Two coherent light sources having intensity, , potential difference E across AB (10 m length), is larger than E 1 and E 2 as well. For key, K1(closed), the jockey is adjusted to touch the, wire at point J1, so that there is no deflection, in the galvanometer. Now, the first battery, (E 1) is replaced by second battery (E 2) for, working by making K1 open and K 2 closed., The galvanometer gives then null deflection, E, a, at J 2. The value of 1 is , where a = ……… ., E2 b
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26, , JEE Main 2021 ~ Solved Papers, , ONLINE, K1, , joined to form a single drop. The potential of, this drop is ………… V., , E1, , 28. A coil of inductance 2H having negligible, , G, E2, , E, , resistance is connected to a source of supply, whose voltage is given by V = 3t V (where, t is, in second). If the voltage is applied when, t = 0, then the energy stored in the coil after, 4 s is ………… J., , K2, , A, K, J1, , 20 cm, , 29. A monoatomic gas of mass 4.0 u is kept in an, J2, , Rh, , insulated container. Container is moving with, velocity 30 m/s. If container is suddenly, stopped, then change in temperature of the, x, gas (R = gas constant) is . Value of x is …… ., 3R, , 60 cm, , 30. The potential energy (U) of a diatomic, , 1m, , B, , 26. The same size images are formed by a, convex lens when the object is placed at, 20 cm or at 10 cm from the lens. The focal, length of convex lens is ………… cm., , 27. 512 identical drops of mercury are charged, to a potential of 2 V each. The drops are, , molecule is a function dependent on r, α, β, (interatomic distance) as U = 10 − 5 − 3, r, r, where, α and β are positive constants. The, equilibrium distance between two atoms will, a, , 2α b, be , where a = ……… ., β, , CHEMISTRY, , 0, , 5, , 10, , n, l(r), , 4πr 2 R2, , (D), , 3, 2, 1, 0, , 4πr 2 R 2, , 2, 1, 5, , 10, r(A), , r(A), , (B), , 3, , 0, , n, l(r), , 4, , (C), , 5, , 10, r(A), , 4πr 2 R 2, , n, l(r), , (A), , 8, , 4πr 2 R 2, , various orbitals of hydrogen atom against ‘r’, are given below., , n, l(r), , Section A : Objective Type Questions, 1. The plots of radial distribution functions for, , 2.0, 1.5, 1.0, 0.5, 0, , 5, r(A), , 10, , The correct plot for 3s–orbital is, a. (A), b. (B), c. (C), d. (D)
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27, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift I, 2. According to molecular orbital theory, the, , 10. The hybridisation and magnetic nature of, , [Mn(CN) 6 ]4− and [Fe(CN) 6 ]3− , respectively are, , species among the following that does not, exist is, a. O 2−, 2, , b. He−2, , c. Be2, , a. d 2 sp 3 and paramagnetic, b. sp 3d 2 and diamagnetic, c. d 2 sp 3 and diamagnetic, d. sp 3d 2 and paramagnetic, , d. He2+, , 3. The solubility of AgCN in a buffer solution of, pH = 3 is x. The value of x is…… ., , [Assume : No cyano complex is formed;, K sp(AgCN) = 2.2 × 10−16 and, K a(HCN) = 6.2 × 10−10], a. 0.625 × 10−6, c. 2.2 × 10−16, , 11. Given below are two statements:, Statement I An allotrope of oxygen is an, important intermediate in the formation of, reducing smog., , b. 1.6 × 10−6, d. 1.9 × 10−5, , Statement II Gases such as oxides of, nitrogen and sulphur present in, troposphere contribute to the formation of, photochemical smog., , 4. In Freundlich adsorption isotherm at, moderate pressure, the extent of adsorption, x is directly proportional to px . The value, m, of x is, a. 1, , b. zero, , c. ∞, , In the light of the above statements, choose, the correct answer from the options given, below., , d. 1/ n, , (a), (b), (c), (d), , 5. Ellingham diagram is a graphical, representation of, a. ∆G vs T, c. ∆G vs p, , b. ∆H vs T, d. (∆G – T∆S) vs T, , 6. Which of the following equation depicts the, , 12. Complete combustion of 1.80 g of an, oxygen containing compound (C xH yOz) gave, 2.64 g of CO2 and 1.08 g of H 2O. The, percentage of oxygen in the organic, compound is, , oxidising nature of H 2O2?, , a. KIO 4 + H2O 2 → KIO 3 + H2O + O 2, b. I2 + H2O 2 + 2OH− → 2I− + 2H2O + O 2, c. 2I− + H2O 2 + 2H+ → I2 + 2H2O, d. Cl2 + H2O 2 → 2HCl + O 2, , 7. The correct statement about B 2H6 is, (a) all B—H—B angles are of 120°, (b) the two B—H—B bonds are not of same length, (c) terminal B—H bonds have less p-character, when compared to bridging bonds, (d) Its fragment, BH3 , behaves as a Lewis base, , 8. Given below are two statements:, Statement I CeO2 can be used for oxidation, of aldehydes and ketones., Statement II Aqueous solution of EuSO4 is a, strong reducing agent., In the light of the above statements, choose, the correct answer from the options given, below., (a), (b), (c), (d), , Both statement I and statement II are true., Both statement I and statement II are false., Statement I is true but statement II is false., Statement I is false but statement II is true., , Both statement I and statement II are true., Both statement I and statement II are false., Statement I is true but statement II is false., Statement I is false but statement II is true., , a. 50.33, c. 63.53, , 13. Identify A in the given chemical reaction., CH3, CH2, CH2, CH2, , CH3, CH3, , Mo2O3, , ‘ A’, , 773 K, 10-20 atm (Major product), , CH3, b., , c., , d., , CH3, , 14. Identify A and B in the chemical reaction., OCH3, HCl, , electronic configuration will be the same?, b. Cr + and Mn 2 +, d. Fe2 + and Co +, , CH, , a., , 9. In which of the following pairs, the outer most, a. V 2 + and Cr +, c. Ni2 + and Cu +, , b. 53.33, d. 51.63, , NO2, , Nal, , [A], [B], Dry acetone, (Major), (Major)
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29, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift I, Section B : Numerical Type Questions, 21. 0.4 g mixture of NaOH, Na 2CO3 and some inert, , N, HCl using, 10, phenolphthalein as an indicator, 17.5 mL of HCl, was required at the end point. After this methyl, orange was added and titrated. 1.5 mL of same, HCl was required for the next end point. The, weight percentage of Na 2CO3 in the mixture is, …………. (Rounded off to the nearest integer)., impurities was first titrated with, , 22. A car tyre is filled with nitrogen gas at 35 psi at, 27°C. It will burst if pressure exceeds 40 psi. The, temperature in °C at which the car tyre will burst, is ……… (Rounded-off to the nearest integer)., , 23. The reaction of cyanamide, NH2CN( s) with, oxygen was run in a bomb calorimeter and ∆U, was found to be –742.24 kJ mol−1. The magnitude, of ∆H 298 for the reaction, 3, NH 2CN( s) + O2( g) → N2(g) + O2(g) + H 2O( l) is, 2, ……… kJ (Rounded off to the nearest integer)., [Assume ideal gases and, R = 8.314 J mol−1 K −1], , 24. 1 molal aqueous solution of an electrolyte A2B 3 is, 60% ionised. The boiling point of the solution at, 1 atm is ………… K (Rounded off to the nearest, integer). [Given, K b for (H 2O), , The temperature at which the rate, constant of the reaction is 10−4s −1 is, ……… K, (Rounded off to the nearest integer)., [Given : The rate constant of the reaction, is 10−5s −1at 500 K], , 27. The ionisation enthalpy of Na + formation, from Na(g) is 495.8 kJ mol−1, while the, electron gain enthalpy of Br is, –325.0 kJ mol−1. Given, the lattice, enthalpy of NaBr is –728.4 kJ mol−1. The, energy for the formation of NaBr ionic, solid is (–) ………… × 10−1 kJ mol−1., , 28. Among the following, the number of, halide(s) which is/are inert to hydrolysis, is …………… ., a. BF3, b. SiCl4, c. PCl5, d. SF6, , 29. Consider the following chemical reaction., (1) Red hot Fe tube, 873 K, , CH ≡≡ CH → Product, (2) CO, HCl, AlCl 3, , The number of sp2 hybridised carbon, atom(s) present in the product is ………… ., , 30. Using the provided information in the, following paper chromatogram., , −1, , = 0.52 K kg mol ], 2−, 25. In basic medium CrO2−, 4 oxidises S 2O3 to form, , −, SO2−, 4 and itself changes into Cr(OH) 4 . The volume, of 0.154 M CrO2−, required, to, react, with 40 mL of, 4, 0.25 M S 2O2−, 3 is ………… mL, , Solvent front, 5cm, , 2cm, , (Rounded off to the nearest integer)., , 2cm, , 26. For the reaction, aA + bB → cC + dD, the plot of, log k vs, , 1, is given below, T, , Spot, , Slope = –10000K, log k, , Base line, , Paper chromatography, for compounds A and B, , The calculated R f value of A ……… × 10−1., 1/T
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30, , ONLINE, , JEE Main 2021 ~ Solved Papers, , MATHEMATICS, Section A : Objective Type Questions, 1. When a missile is fired from a ship, the, 1, and the, 3, probability that the missile hits the target,, 3, given that it is not intercepted, is . If three, 4, missiles are fired independently from the, ship, then the probability that all three hit, the target, is, probability that it is intercepted is, , 1, 27, 1, c., 8, , 3, 4, 3, d., 8, , a., , b., , π, 2, , 2. If 0 < θ, φ < , x =, and z =, , ∞, , ∞, , ∑ cos, , 2n, , θ, y =, , n=0, , ∑ cos, , 2n, , ∞, , ∑ sin, , 2n, , φ, , n=0, , θ ⋅ sin2n φ, then, b. xy + yz + zx = z, d. xy + z = (x + y ) z, , 3. Let f , g : N → N, such that, f ( n + 1) = f ( n) + f (1) ∀ n ∈ N and g be any, arbitrary function. Which of the following, statements is not true?, a. if fog is one-one, then g is one-one, b. if f is onto, then f (n ) = n ∀ n ∈ N, c. f is one-one, d. if g is onto, then fog is one-one, , 4. The equation of the line through the point, (0,1,2) and perpendicular to the line, x −1 y + 1 z −1, is, =, =, 2, 3, −2, , x y −1 z −2, =, =, 3, 4, 3, x y −1 z −2, b. =, =, 3, 3, −4, x y −1 z −2, c. =, =, 3, 4, −3, y −1 z −2, x, d., =, =, −3, 4, 3, a., , b., , 3, 8, , 3, , 7. The value of ∫ x 2e[x ] dx , where [t ] denotes, −1, , the greatest integer ≤ t, is, , a., , e−1, 3e, , b., , e+1, 3, , c., , e+1, 3e, , d., , 1, 3e, , 8. A man is observing, from the top of a tower,, a boat speeding towards the tower from a, certain point A, with uniform speed. At that, point, angle of depression of the boat with, the man's eye is 30° (ignore man's height)., After sailing for 20 s, towards the base of the, tower (which is at the level of water), the, boat has reached a point B, where the angle, of depression is 45°. Then, the time taken (in, seconds) by the boat from B to reach the, base of the tower is, a. 10, , b. 10 3, , c. 10 ( 3 + 1), , d. 10 ( 3 − 1), , which is perpendicular to the line 2x + y = 1., Which of the following points does not lie on, it?, a. (–6, 0), c. (5, 4), , direction cosines satisfy the equations, l + m − n = 0 and l 2 + m 2 − n2 = 0. Then, the, value of sin4 α + cos 4 α is, 3, 4, , 3, , 1, [ 11 − 18 sin 2 θ + 9 sin 4 θ − 2 sin 6 θ] 2 + c, 18, 3, 1, b., [ 9 − 2 cos 6 θ 3cos 4 θ − 6cos 2 θ] 2 + c, 18, 3, 1, c., [ 9 − 2 sin 6 θ − 3sin 4 θ − 6sin 2 θ] 2 + c, 18, 3, 1, d. [ 11 − 18 cos 2 θ + 9cos 4 θ − 2cos 6 θ] 2 + c, 18, , a., , 9. A tangent is drawn to the parabola y 2 = 6x ,, , 5. Let α be the angle between the lines whose, , a., , sinθ ⋅ sin2θ (sin6 θ + sin4 θ + sin2 θ) , , , , 4, 2, 2sin θ + 3sin θ + 6 , dθ is, ∫ , , 1 − cos 2θ, , , , , , , (where, c is a constant of integration), , 1, , n=0, , a. xy − z = (x + y ) z, c. xyz = 4, , 6. The value of the integral, , c., , 5, 8, , d., , 1, 2, , b. (4, 5), d. (0, 3), , 10. All possible values of θ ∈[0, 2π ] for which, sin 2θ + tan 2θ > 0 lie in, , 3π , π, a. 0, ∪ π ,, , 2 , 2 , π, π 3π 7π , b. 0, ∪ ,, ∪ π,, , 2 2 4 , 6
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31, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift I, π, π 3 π 3π 11π , c. 0, ∪ ,, ,, ∪, , 4 2 4 2, 6 , π, π 3π 5π 3π 7π , d. 0, ∪ ,, ,, ∪ π,, ∪, , 4 2 4 , 4 2 4 , , 11. Let the lines (2 − i) z = (2 + i) z and, , 19. The statement A → (B → A) is equivalent to, a. A → (A ∧ B ), c. A → (A ↔ B ), , 20. If Rolle's theorem holds for the function, , f ( x) = x 3 − ax 2 + bx + 4, x ∈[1, 2] with, 4, f ′ = 0, then ordered pair (a , b) is equal to, 3, , (2 + i) z + ( i − 2) z − 4 i = 0, (here i 2 = − 1) be, normal to a circle C . If the line, iz + z + 1 + i = 0 is tangent to this circle C ,, then its radius is, a., , 3, 2, , b., , 1, 2 2, , c. 3 2, , d., , 3, 2 2, , 12. The image of the point (3, 5) in the line, , a. (5, 8), , a. (x − 2) + ( y − 2) = 12, b. (x − 4 ) 2 + ( y + 2) 2 = 16, c. (x − 4 ) 2 + ( y − 4 ) 2 = 8, d. (x − 2) 2 + ( y − 4 ) 2 = 4, , 13., , a. a + b = c + d, , 22. The number of points at which the function, , f ( x) = |2x + 1| − 3|x + 2| + |x 2 + x − 2|, x ∈ R is, not differentiable, is ………. ., , 23. The graph of sine and cosine functions,, intersect each other at a number of points, and between two consecutive points of, intersection, the two graphs enclose the, same area A. Then A 4 is equal to ………… ., , n, , 14., , 1, 1, , 1 + + ...... + , n, 2, lim 1 + , is equal to, n→ ∞, n2, , , , , a., , 1, 2, , b. 0, , c., , 1, e, , 24. Let A1, A2 , A3 , ......… be squares, such that for, each n ≥ 1, the length of the side of Anequals, the length of diagonal of An + 1. If the length of, A1 is 12 cm, then the smallest value of n for, which area of An is less than one, is ……… ., , d. 1, , 15. The coefficients a, b and c of the quadratic, , equation, ax 2 + bx + c = 0 are obtained by, throwing a dice three times. The probability, that this equation has equal roots is, , a., , 1, 72, , b., , 5, 216, , c., , 1, 36, , d., , x, , 1, 54, , solutions ( x , y , z), such that xyz = 24 is, b. 24, , c. 45, , d. 30, , 17. The integer ‘k’, for which the inequality, , x 2 − 2 (3k − 1) x + 8k 2 − 7 > 0 is valid for every, x in R, is, , a. 3, , b. 2, , c. 0, , d. 4, , 18. If a curve passes through the origin and the, slope of the tangent to it at any point ( x , y ) is, x2 − 4x + y + 8, , then this curve also passes, x −2, through the point, a. (5, 4), , b. (4, 5), , c. (4, 4), , d. (5, 5), , y, , z, , 25. Let A = y z x , where x, y and z are real, , 16. The total number of positive integral, a. 36, , d. (–5, –8), , which the coefficient of x 6 is unity and it has, f ( x), extrema at x = − 1and x = 1. If lim 3 = 1,, x→ 0 x, then 5 f (2) is equal to …………… ., , b. a − b = c − d, c+d, d. ab =, a+ b, , c. a − c = b + d, , c. (5, –8), , 21. Let f ( x) be a polynomial of degree 6 in x, in, , 2, , x2, y2, x2, y2, If the curves,, +, = 1 and, +, = 1,, a, b, c, d, intersect each other at an angle of 90°, then, which of the following relations is true?, , b. (–5, 8), , Section B : Numerical Type Questions, , x − y + 1 = 0, lies on, 2, , b. A → (A → B ), d. A → (A ∨ B ), , 26., , , , z x y , numbers, such that x + y + z > 0 and xyz = 2., If A 2 = I3, then the value of x 3 + y 3 + z 3, is ……… ., , θ , − tan , 0, 2, If A = , and, θ, , tan , 0, 2, , , , a − b, 2, 2, (I2 + A) (I2 − A) −1 = , , then 13 (a + b ) is, b a , equal to ………… ., , 27. The total number of numbers, lying between, 100 and 1000 that can be formed with the, digits 1, 2, 3, 4, 5, if the repetition of digits is, not allowed and numbers are divisible by, either 3 or 5, is ………… .
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32, , ONLINE, , 28. Let a = $i + 2$j − k$ , b = $i − $j and c = $i − $j − k$ be, , has infinitely many solutions, then k is equal, to ……… ., , three given vectors. If r is a vector such that, r × a = c × a and r ⋅ b = 0, then r ⋅ a is equal to, ……… ., , 30. The locus of the point of intersection of the, lines, ( 3) kx + ky − 4 3 = 0 and, , 29. If the system of equations, kx + y + 2z = 1, , JEE Main 2021 ~ Solved Papers, , 3x − y − 4( 3) k = 0 is a conic, whose, eccentricity is ………… ., , 3x − y − 2z = 2, , −2 x − 2 y − 4 z = 3, , Answers, For solutions scan, the QR code, , Physics, 1. (a), , 2. (d), , 3. (a), , 4. (b), , 5. (b), , 6. (c), , 7. (c), , 8. (b), , 9. (d), , 10. (d), , 11. (b), , 12. (a), , 13. (b), , 14. (b), , 15. (c), , 16. (c), , 17. (b), , 18. (b), , 19. (d), , 20. (d), , 21. 10, , 22. 1, , 23. 50, , 24. 5, , 25. 1, , 26. 15, , 27. 128, , 28. 144, , 29. 3600, , 30. 1, , Chemistry, 1. (d), , 2. (c), , 3. (d), , 4. (d), , 5. (a), , 6. (c), , 7. (c), , 8. (a), , 9. (b), , 10. (a), , 11. (d), , 12. (b), , 13. (b), , 14. (b), , 15. (d), , 16. (b), , 17. (c), , 18. (c), , 19. (d), , 20. (a), , 21. 4, , 22. 70, , 23. 741, , 24. 375, , 25. 173, , 26. 526, , 27. 5576, , 28. 1, , 29. 7, , 30. 4, , Mathematics, 1. (c), , 2. (d), , 3. (d), , 4. (d), , 5. (c), , 6. (d), , 7. (c), , 8. (c), , 9. (c), , 10. (d), , 11. (d), , 12. (d), , 13. (b), , 14. (d), , 15. (b), , 16. (d), , 17. (a), , 18. (d), , 19. (d), , 20. (a), , 21. 144, , 22. 2, , 23. 64, , 24. 9, , 25. 7, , 26. 13, , 27. 32, , 28. 12, , 29. 21, , 30. 2
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33, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift II, , JEE Main 2021, 25 FEBRUARY SHIFT II, , PHYSICS, Section A : Objective Type Questions, 1. If e is the electronic charge, c is the speed of, , harmonic motion of P. The restoration force, per unit mass when P touches M will be, , light in free space and h is Planck's constant,, 2, 1 |e |, has dimensions of, the quantity, 4 πε 0 hc, , A, 0.1s, , b. [MLT −1], d. [LC −1], , a. [MLT 0 ], c. [M 0L0 T 0 ], , M, , 0.36 m, , 30°, , N, , P, , O, , 2. A stone is dropped from the top of a, building. When it crosses a point 5 m below, the top, another stone starts to fall from a, point 25 m below the top. Both stones reach, the bottom of building simultaneously. The, height of the building is, a. 45 m, c. 35 m, , b. 25 m, d. 50 m, , 3. A sphere of radius a and mass m rolls along, , a. 100 N, c. 50 N, , b. 9.87 N, d. 0.49 N, , 5. Thermodynamic process is shown below on, a p-V diagram for one mole of an ideal gas., T, If V2 = 2V1, then the ratio of temperature 2 is, T1, p, , a horizontal plane with constant speed v 0. It, encounters an inclined plane at angle θ and, climbs upwards. Assuming that it rolls, without slipping, how far up the sphere will, travel?, , 1(p1, V1, T1), pV1/2=constant, , 2(p2, V2, T2), , a, , a., , v 02, , 2 g sin θ, 10 v 02, c., 7 g sin θ, , V1, , v0, , θ, , b., d., , v 02, 5 g sin θ, 2 v 02, 5 g sin θ, , 4. The point A moves with a uniform speed, along the circumference of a circle of radius, 0.36 m and covers 30° in 0.1 s. The, perpendicular projection P from A on the, diameter MN represents the simple, , a., , 1, 2, , b. 2, , V2, , c., , V, , 1, 2, , d. 2, , 6. Given below are two statements:, Statement I In a diatomic molecule, the, rotational energy at a given temperature, obeys Maxwell's distribution., Statement II In a diatomic molecule, the, rotational energy at a given temperature, equals the translational kinetic energy for, each molecule.
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34, , ONLINE, In the light of the above statements, choose, the correct answer from the options given, below., a., b., c., d., , Both Statement I and Statement II are true., Both Statement I and Statement II are false., Statement I is true but Statement II is false., Statement I is false but Statement II is true., , 7. Two identical springs of spring constant 2k, are attached to a block of mass m and to, fixed support (see figure).When the mass is, displaced from equilibrium position on, either side, it executes simple harmonic, motion. The time period of oscillations of, this system is, , 2k, , a. 2 π, c. π, , m, 2k, m, k, , 2k, , m, , m, k, m, d. π, 2k, b. 2π, , equation of SHM. At t = 0, the displacement, A, and it is moving along, 2, negative x-direction. Then, the initial phase, angle φ0 will be, , of the particle is Y =, , π, 3, , b., , 5π, 6, , c., , π, 6, , 10. An electron with kinetic energy K1 enters, between parallel plates of a capacitor at an, angle α with the plates. It leaves the plates at, angle β with kinetic energy K 2. Then, the ratio, of kinetic energies K1 : K 2 will be, a., c., , cos β, cos α, sin 2 β, cos 2 α, , b., d., , cos β, sin α, cos 2 β, cos 2 α, , 11. In a ferromagnetic material, below the Curie, temperature, a domain is defined as, a. a macroscopic region with zero magnetisation, b. a macroscopic region with saturation, magnetisation, c. a macroscopic region with randomly oriented, magnetic dipoles, d. a macroscopic region with consecutive, magnetic dipoles oriented in opposite, direction, , 12. An L-C-R circuit contains resistance of 110 Ω, , 8. Y = A sin (ωt + φ0) is the time-displacement, , a., , JEE Main 2021 ~ Solved Papers, , d., , 2π, 3, , 9. A charge q is placed at one corner of a cube, as shown in figure. The flux of electrostatic, field E through the shaded area is, Z, , and a supply of 220 V at 300 rad/s angular, frequency. If only capacitance is removed, from the circuit, current lags behind the, voltage by 45°. If on the other hand, only, inductor is removed the current leads by 45°, with the applied voltage. The rms current, flowing in the circuit will be, a. 1A, c. 2A, , b. 1.5 A, d. 2.5 A, , 13. The stopping potential for electrons emitted, from a photosensitive surface illuminated by, light of wavelength 491 nm is 0.710 V. When, the incident wavelength is changed to a new, value, the stopping potential is 1.43 V. The, new wavelength is, a. 309 nm, c. 382 nm, , b. 329 nm, d. 400 nm, , 14. Consider the diffraction pattern obtained, , Y, , q, X, , a., , q, 48ε0, , b., , q, 4 ε0, , c., , q, 8ε0, , d., , q, 24 ε0, , from the sunlight incident on a pinhole of, diameter 0.1µm. If the diameter of the, pinhole is slightly increased, it will affect the, diffraction pattern such that, a. its size increases and intensity increases, b. its size increases, but intensity decreases, c. its size decreases, but intensity increases, d. its size decreases and intensity decreases
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35, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift II, 15. An electron of mass m e and a proton of, mass m p = 1836 m e are moving with the, same speed., The ratio of their de-Broglie wavelength, λ electron, will be, λ proton, a. 1, , b. 1836, , c., , 1, 1836, , Choose the correct answer from the options, given below., A B C D, a. 2, 1, 3, 4, b. 2, 4, 1, 3, b. 2, 1, 4, 3, c. 3, 4, 1, 2, , d. 918, , 20. The truth table for the followng logic circuit is, , 16. The wavelength of the photon emitted by a, , A, , hydrogen atom when an electron makes a, transition from n = 2 to n = 1state is, a. 121.8 nm, c. 490.7 nm, , b. 194.8 nm, d. 913.3 nm, , Y, B, , 17. If a message signal of frequency fm is, amplitude modulated with a carrier signal of, frequency f c and radiated through an, antenna, the wavelength of the, corresponding signal in air is, a., , c, fc − fm, , b., , c, fc + fm, , c., , c, fc, , d., , a., , c, fm, , 18. For extrinsic semiconductors when doping, level is increased,, a. Fermi level of p-type semiconductor will go, upward and Fermi level of n-type, semiconductors will go downward, b. Fermi level of p-type semiconductors will go, downward and Fermi level of n-type, semiconductor will go upward, c. Fermi level of p and n-type semiconductors, will not be affected, d. Fermi level of both p-type and n-type, semiconductors will go upward for T > TF K, and downward for T < TF K, where TF is Fermi, temperature, , b., , c., , 19. Match List-I with List-II., List-I, A., , Rectifier, , 1., , B., , Stabiliser, , C., , Transformer 3., , D. Filter, , 2., , 4., , A, , B, , Y, , 0, , 0, , 0, , 0, , 1, , 1, , 1, , 0, , 1, , 1, , 1, , 0, , A, , B, , Y, , 0, , 0, , 1, , 0, , 1, , 0, , 1, , 0, , 0, , 1, , 1, , 1, , A, , B, , Y, , 0, , 0, , 1, , 0, , 1, , 0, , 1, , 0, , 1, , 1, , 1, , 0, , A, , B, , Y, , List-II, , 0, , 0, , 0, , Used either for, stepping up or stepping, down the AC voltage, , 0, , 1, , 1, , 1, , 0, , 0, , 1, , 1, , 1, , Used to convert AC, voltage into DC voltage, Used to remove any, ripple in the rectified, output voltage, Used for constant, output voltage even, when the input voltage, or load current change, , d., , Section B : Numerical Type Questions, 21. Two particles having masses 4 g and 16 g, respectively are moving with equal kinetic, energies. The ratio of the magnitudes of, their linear momentum is n : 2. The value of, n will be ………… .
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36, , ONLINE, , 22. The initial velocity v i required to project a, body vertically upward from the surface of, the Earth to reach a height of 10R, where R is, the radius of the Earth, may be described in, terms of escape velocity v e such that, x, × v e . The value of x will be ………… ., vi =, y, , 23. The percentage increase in the speed of, transverse waves produced in a stretched, string, if the tension is increased by 4%, will, be ………… %., , 24. If P × Q = Q × P, the angle between P and Q is, θ (0° < θ < 360°). The value of θ will be, ……………°., , JEE Main 2021 ~ Solved Papers, , 0.5 m. The electrostatic force acting between, the spheres is …………… × 10 −9 N., [Given, 4 πε 0 =, , 1, SI unit], 9 × 109, , 28. The peak electric field produced by the, radiation coming from the 8 W bulb at a, x µ 0c V, distance of 10 m is, . The efficiency, π m, 10, of the bulb is 10% and it is a point source., The value of x is ………… ., , 29. A current of 6 A enters one corner P of an, equilateral triangle PQR having three wires of, resistance 2 Ω each and leaves by the corner, R. The currents i l in ampere is ………… ., 6A, , 25. A reversible heat engine converts one-fourth, of the heat input into work. When the, temperature of the sink is reduced by 52 K,, its efficiency is doubled. The temperature in, kelvin of the source will be …………… ., , 2Ω, P, , suspended from a point by threads 0.5 m, long. They are equally charged and repel, each other to a distance of 0.20 m. The, a, charge on each of the sphere is, × 10−8 C., 21, The value of a will be …………… ., [Given, g = 10 ms −2], , 27. Two identical conducting spheres with, negligible volume have 2.1 nC and – 0.1 nC, charges, respectively. They are brought into, contact and then separated by a distance of, , I2, , i1, , 26. Two small spheres each of mass 10 mg are, , 2Ω, , 2Ω, 2Ω, Q, , R, , 30. The wavelength of an X-ray beam is 10 Å., The mass of a fictitious particle having the, same energy as that of the X-ray photons is, x, h kg. The value of x is ………… ., 3, (h = Planck's constant)
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37, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift II, , CHEMISTRY, Section A : Objective Type Questions, 1. Which among the following species has, unequal bond lengths ?, a. XeF4, c. SF4, , b. SiF4, d. BF4−, , 2. The solubility of Ca(OH) 2 in water is, [Given: The solubility product of Ca(OH) 2 in, water = 5.5 × 10 −6], a. 1.11 × 10 −2, c. 1.77 × 10 −2, , b. 1.11 × 10 −6, d. 1.77 × 10 −6, , 3. Which one of the following statements is false, for hydrophilic sols ?, a., b., c., d., , They do not require electrolytes for stability., These sols are reversible in nature., Their viscosity is of the order of that of H2O., The sols cannot be easily coagulated., , 4. The correct order of bond dissociation, enthalpy of halogens is, a. F2 > Cl2 > Br2 > I2, b. I2 > Br2 > Cl2 > F2, c. Cl2 > Br2 > F2 > I2, d. Cl2 > F2 > Br2 > I2, , 5. The method used for the purification of indium, is, a. van-Arkel method, c. zone refining, , b. liquation, d. vapour phase refining, , 6. Water does not produce CO on reacting with, a. CH 4, c. CO 2, , b. C, d. C 3H8, , 7. Given below are two statements., Statement I α and β-forms of sulphur can, change reversibly between themselves with, slow heating or slow cooling., Statement II At room temperature, the stable, crystalline form of sulphur is monoclinic, sulphur., In the light of the above statements, choose the, correct answer from the options given below., a. Both statements I and II are true., b. Both statements I and II are false., c. Statement I is true but statement II is false., d. Statement I is false but statement II is true., , 8. The major components of German silver, are, a. Cu, Zn and Ag, c. Ge, Cu and Ag, , b. Cu, Zn and Ni, d. Zn, Ni and Ag, , 9. In which of the following order the given, complex ions are arranged correctly with, respect to their decreasing spin only, magnetic moment?, (i) [FeF6 ] 3−, (ii) [Co(NH3 ) 6 ]3+, (iii) [NiCl4 ]2−, (iv) [Cu(NH3 ) 4 ]2+, a. (i) > (iii) > (iv) > (ii), b. (ii) > (iii) > (i) > (iv), c. (iii) > (iv) > (ii) > (i), d. (ii) > (i) > (iii) > (iv), , 10. Given below are two statements., Statement I The pH of rain water is, normally ~5.6., Statement II If the pH of rain water drops, below 5.6, it is called acid rain., In the light of the above statements,, choose the correct answer from the, options given below., a. Both statements I and II are true., b. Both statements I and II are false., c. Statement I is true but statement II is false., d. Statement I is false but statement II is true., , 11. Which of the following compound is added, to the sodium extract before addition of, silver nitrate for testing of halogens?, a. Hydrochloric acid, c. Nitric acid, , b. Sodium hydroxide, d. Ammonia, , 12. The major product of the following, reaction is, , NO2, , H2SO4, , NO2, a., , NO2, b.
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39, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift II, 19. Which of the following is correct structure of, α-anomer of maltose?, , CH2OH, , CH2OH, O H, , H, H, H, , a., , H, , HO, OH, , H, H, , O, , OH, , HO, , H, , HO, H, , H, OH, , O, , H, , H, HO, , H, , HO, H, , d., , H, , H, , H, , H, OH, , O, , H, H, , (v) 4.4 mL, If the volume of oxalic acid taken was, 10.0 mL, then the molarity of the NaOH, solution is ……… M. (Rounded off to the, nearest integer), , face centered cube of edge length 3.596 Å, with one copper atom at each lattice point., The calculated density of copper in kg/m 3, is ……… . [Molar mass of Cu = 63.54 g ;, Avogadro number = 6.022 × 10 23], , 663 nm is just sufficient to ionise the atom, of metal A. The ionisation energy of metal A, in kJ mol −1 is ……… . (Rounded off to the, nearest integer), , NA = 602, . × 1023 mol−1], HO, , H, H, , HO, , (iv) 4.4 mL, , [h = 6.63 × 10 −34 J-s, c = 3.00 × 10 8 ms −1,, , OH, , O, , H, , (iii) 4.4 mL, , 23. Electromagnetic radiation of wavelength, , CH2OH, , HO, HO, , OH, , OH, , OH, , O H, H, H, , H, , O, H, HO, , O, , CH2OH, H, , OH, , CH2OH, H, , (ii) 4.5 mL, , 22. The unit cell of copper corresponds to a, , H, , OH, , O H, , H, , OH, , O, , H, , CH2OH, c., , H, , CH2OH, O H, , H, OH, , b., , HO, H, , CH2OH, H, , O, , H, , (i) 4.5 mL, , OH, , 20. Given below are two statements., Statement I The identification of Ni2+ is, carried out by dimethyl glyoxime in the, presence of NH 4OH., Statement II The dimethyl glyoxime is a, bidentate neutral ligand., In the light of the above statements, choose, the correct answer from the options given, below., a. Both statements I and II are true., b. Both statements I and II are false., c. Statement I is true but statement II is false., d. Statement I is false but statement II is true., , Section B : Numerical Type Questions, 21. Consider titration of NaOH solution versus, 1.25 M oxalic acid solution. At the end point, following burette readings were obtained., , 24. Five moles of an ideal gas at 293 K is, expanded isothermally from an initial, pressure of 2.1 MPa to 1.3 MPa against at, constant external pressure 4.3 MPa. The, heat transferred in this process is ……… kJ, mol −1. (Rounded off to the nearest integer), [R = 8.314 J mol −1K −1], , 25. If a compound AB dissociates to the extent, of 75% in an aqueous solution, the molality, of the solution which shows a 2.5 K rise in, the boiling point of the solution is ………, molal. (Rounded off to the nearest integer), [K b = 0.52 K kg mol −1], , 26. Copper reduces NO−3 into NO and NO2, depending upon the concentration of, HNO3 in solution. (Assuming fixed [Cu2+ ], and pNO = pNO 2 ), the HNO3 concentration at, which the thermodynamic tendency for, reduction of NO−3 into NO and NO2 by, copper is same is 10x M. The value of 2x is, ……… ., (Rounded off to the nearest integer)
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40, , ONLINE, [Given, E °, , ° –, = 0.34 V, E NO, = 0.96 V,, /NO, , Cu2 + / Cu, , ° −, E NO, /NO, 3, , 2, , 3, , RT, = 0.79 V and at 298 K,, F, (2.303) = 0.059], , 27. The rate constant of a reaction increases by, five times on increase in temperature from, 27°C to 52°C. The value of activation energy, in kJ mol −1 is ……… (Rounded off to the, nearest integer), [R = 8.314 J K −1 mol −1], , JEE Main 2021 ~ Solved Papers, , 28. Among the following, number of metal(s), which can be used as electrodes in the, photoelectric cell is ……… (Integer answer), (i) Li, , (ii) Na, , (ii) Rb, , (iv) Cs, , 29. The spin only magnetic moment of a divalent, ion in aqueous solution, (atomic number = 29) is ……… BM., , 30. The number of compound(s) given below, which contain(s) — COOH group is ……… ., (i) Sulphanilic acid, (iii) Aspirin, , (ii) Picric acid, (iv) Ascorbic acid, , MATHEMATICS, Section A : Objective Type Questions, 1, α, , 1. If for the matrix, A = , , −α , , AAT = I2, then, β , , the value of α 4 + β 4 is, a. 4, , b. 1, , c. 2, , d. 3, , 2. Let A be a 3 × 3 matrix with det (A) = 4. Let R i, denote the ith row of A. If a matrix B is, obtained by performing the operation, R 2 → 2R 2 + 5R 3 on 2A, then det (B) is equal to, a. 16, c. 64, , b. 80, d. 128, , 3. The following system of linear equations, 2x + 3 y + 2z = 9, 3x + 2 y + 2z = 9, x − y + 4z = 8, a., b., c., d., , does not have any solution, has a unique solution, has infinitely many solutions, has a solution (α , β , γ ) satisfying, α + β 2 + γ 3 = 12, , 4. If In = ∫, a., , π /2, , n, , cot x dx , then, , π /4, , 1, 1, 1, are in AP, ,, ,, I2 + I4 I3 + I5 I4 + I6, , b. I 2 + I 4 , I 3 + I 5 , I 4 + I 6 are in AP, 1, 1, 1, c., are in GP, ,, ,, I2 + I4 I3 + I5 I4 + I6, d. I 2 + I 4 , (I 3 + I 5 ) 2 , I 4 + I 6 are in GP, , 5. A function f ( x) is given by f ( x) =, , 5x, , then, 5 +5, x, , the sum of the series, 1, 2, 3, 39, f + f + f + K + f is, 20, 20, 20, 20, equal to, a., , 29, 2, , b., , 49, 2, , c., , 39, 2, , d., , 19, 2, , 6. Let α and β be the roots of x 2 − 6x − 2 = 0. If, a n = α n − β n for n ≥ 1, then the value of, a10 − 2a 8, is, 3a 9, a. 4, , b. 3, , c. 2, , d. 1, x, , x, , 7. The minimum value of f ( x) = a a + a1 − a ,, where a, x ∈ R and a > 0, is equal to, a. a + 1, , b. a +, , 8. The integral ∫, , 1, a, , c. 2 a, , e 3 log e, e 4 log e, , x, , 2x, , d. 2a, , + 5e 2 log e, , + 5e 3 log e, , x, , 2x, , − 7e 2 log e, , x > 0, is equal to, (where, c is a constant of integration), a. log e | x 2 + 5x − 7| + c, b. 4 log e | x 2 + 5x − 7| + c, 1, c. log e | x 2 + 5x − 7| + c, 4, d. log e x 2 + 5x − 7 + c, , x, , dx ,
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41, , FEBRUARY ATTEMPT~ 25 Feb 2021, Shift II, 9. If α , β ∈R are such that 1 − 2i (here i 2 = − 1) is a, root of z + αz + β = 0, then (α − β) is equal to, 2, , a. 3, , b. – 3, , c. 7, , d. –7, , found to be suffering from the chest, disorder. The probability that the selected, person is a smoker and non-vegetarian is, a., , 10. If the curve x + 2 y = 2 intersects the line, 2, , 2, , x + y = 1at two points P and Q, then the, angle subtended by the line segment PQ at, the origin is, π, 1, + tan −1 , 4, 2, π, 1, c. + tan −1 , 3, 2, , π, 1, − tan −1 , 4, 2, π, 1, d. − tan −1 , 3, 2, , a., , b., , b., , 1, 2 2, , c. 0, , d., , x2 y2, −, =1, 9, 4, 2, , B(2, 3, 1) and C (2, 4 , 2). If O is the origin and P, is (2, –1, 1), then the projection of OP on this, plane is of length, 2, 3, , 1, , 2, 11, , b., , n, , 2, 7, , c., , d., , 2, 5, , n, , n, , , , equal to, b., , 1, 2, , c., , 1, 3, , d., , 14, 45, , 2, 9, , c., , 97, 297, , d., , 122, 297, , 1, 2, 1− 3, c., 2, , 3, , then, 2, , 3, 2, 1+ 3, d., 2, , b., , 18. Let x denote the total number of one-one, functions from a set A with 3 elements to a, set B with 5 elements and y denote the total, number of one-one functions from the set A, to the set A × B. Then,, b. 2 y = 273x, d. y = 273x, , 4 , , 19. cosec 2 cot −1 (5) + cos −1 is equal to, 5 , , a., , 56, 33, , b., , 65, 33, , c., , 65, 56, , d., , 75, 56, , 20. The contrapositive of the statement; "If you, will work, you will earn money" is, , 14. lim +, +, +K+, is, n→ ∞ n, ( n + 1) 2 ( n + 2) 2, (2n − 1) 2 , , a. 1, , b., , , , 13. A plane passes through the points A(1, 2, 3),, , a., , 1, 5, , a. 2 y = 91x, c. y = 91x, , d. x − y = 9, 2, , d., , whose exactly one digit is 7. Then, the, probability that a randomly chosen element, of A leaves remainder 2 when divided by 5 is, , a., , x2, y2, +, = 1 and its transverse and, 25 16, conjugate axes coincide with major and, minor axes of the ellipse, respectively. If the, product of their eccentricities is one, then, the equation of the hyperbola is, b., , 28, 45, , sin x + cos y is equal to, , 1, 2, , ellipse, , x2 y2, −, =1, 9, 16, 2, 2, y, x, c., −, =1, 9, 25, , c., , cos x + cos y − cos ( x + y ) =, , 12. A hyperbola passes through the foci of the, , a., , 8, 45, , 17. If 0 < x , y < π and, , x − y = 1and the curve x 2 = 2 y is, 1, 2, , b., , 16. Let A be a set of all 4-digit natural numbers, , a., , 11. The shortest distance between the line, a., , 7, 45, , 1, 4, , 15. In a group of 400 people, 160 are smokers, and non-vegetarian; 100 are smokers and, vegetarian and the remaining 140 are, non-smokers and vegetarian. Their chances, of getting a particular chest disorder are, 35%, 20% and 10%, respectively. A person is, chosen from the group at random and is, , a. to earn money, you need to work, b. you will earn money, if you will not work, c. if you will not earn money, you will not work, d. if you will earn money, you will work, , Section B : Numerical Type Questions, 21. A function f is defined on [–3, 3] as, min {|x|, 2 − x 2 }, − 2 ≤ x ≤ 2, f ( x) = , , 2 < |x| ≤ 3, [|x|], where, [ x ] denotes the greatest integer ≤ x ., The number of points, where f is not, differentiable in (–3, 3) is ………. .
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42, , ONLINE, , 22. If the curve y = y ( x) represented by the, , 28. A line ‘ l ’ passing through origin is, perpendicular to the lines, , solution of the differential equation, (2xy 2 − y ) dx + xdy = 0, passes through the, intersection of the lines 2x − 3 y = 1 and, 3x + 2 y = 8, then| y (1)| is equal to ………… ., , l1 : r = (3 + t) $i + ( −1 + 2t) $j + ( 4 + 2t)k$, l 2 : r (3 + 2s) $i + (3 + 2s) $j + (2 + s)k$, , 23. The total number of two digit numbers ‘ n’,, , If the coordinates of the point in the first, octant on ‘ l 2 ’ at a distance of 17 from the, point of intersection of ‘ l ’ and ‘ l1’ are (a , b, c),, then 18 (a + b + c) is equal to ………… ., , such that 3n + 7nis a multiple of 10, is ……… ., ax − (e 4x − 1), , 24. If lim, , ax (e 4x − 1), , x→ 0, , JEE Main 2021 ~ Solved Papers, , exists and is equal to b,, , 29. A line is a common tangent to the circle, , then the value of a − 2b is ……… ., , ( x − 3) 2 + y 2 = 9 and the parabola y 2 = 4 x . If, the two points of contact (a , b) and (c , d) are, distinct and lie in the first quadrant, then, 2(a + c) is equal to ………… ., , 25. If the curves x = y 4 and xy = k cut at right, angles, then ( 4 k) 6 is equal to ………… ., 2, , 26. The value of ∫ |3x 2 − 3x − 6| dx is ………. ., , 30. Let a = $i + α$j + 3k$ and b = 3$i − α$j + k$ . If the, , −2, , area of the parallelogram whose adjacent, sides are represented by the vectors a and b, is 8 3 square units, then a ⋅ b is equal, to ………… ., , 27. If the remainder when x is divided by 4 is 3,, then the remainder when (2020 + x) 2022 is, divided by 8 is ………… ., , Answers, For solutions scan, the QR code, , Physics, 1. (c), 11. (b), 21. 1, , 2. (a), 12. (c), 22. 10, , 3. (*), 13. (c), 23. 2, , 4. (b), 14. (c), 24. 180, , 5. (b), 15. (b), 25. 104, , 6. (c), 16. (a), 26. 630, , 7. (c), 17. (c), 27. 7.56, , 8. (c), 18. (b), 28. 2, , 9. (d), 19. (b), 29. 2, , 10. (d), 20. (b), 30. 10, , 3. (c), 13. (a), 23. 180, , 4. (c), 14. (b), 24. 15, , 5. (c), 15. (c), 25. 3, , 6. (c), 16. (c), 26. 4, , 7. (c), 17. (d), 27. 52, , 8. (b), 18. (c), 28. 1, , 9. (a), 19. (c), 29. 2, , 10. (a), 20. (a), 30. 1, , 3. (b), 13. (b), 23. 45, , 4. (a), 14. (b), 24. 5, , 5. (c), 15. (c), 25. 4, , 6. (c), 16. (c), 26. 19, , 7. (c), 17. (d), 27. 1, , 8. (b), 18. (a), 28. 44, , 9. (d), 19. (c), 29. 9, , 10. (a), 20. (c), 30. 2, , Chemistry, 1. (c), 11. (c), 21. 6, , 2. (a), 12. (b), 22. 9077, , Mathematics, 1. (b), 11. (b), 21. 5, , 2. (c), 12. (a), 22. 1, , Note (*) None of the option is correct.
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43, , FEBRUARY ATTEMPT ~ 26 Feb 2021, Shift I, , JEE Main 2021, 26 FEBRUARY SHIFT I, , PHYSICS, 4. If λ 1 and λ 2 are the wavelengths of the third, , Section A : Objective Type Questions, 1. Find the gravitational force of attraction, between the ring and sphere as shown in, the figure, where the plane of the ring is, perpendicular to the line joining the centres., If 8 R is the distance between the centres, of a ring (of mass m) and a sphere (of mass, M), where both have equal radius R., m, , M, , R, , R, , a. Image is real, same side of concave mirror, b. Image is virtual, opposite side of concave, mirror, c. Image is real, same side of convex mirror, d. Image is virtual, opposite side of convex, mirror, , b., , 2. Consider the combination of two capacitors, , 6. Assume that a tunnel is dug along a chord of, , C 1 and C 2, with C 2 > C 1, when connected in, parallel, the equivalent capacitance is 15/4, time the equivalent capacitance of the same, connected in series. Calculate the ratio of, C, capacitors 2 ., C1, a., , 15, 11, , b., , 111, 80, , c., , 29, 15, , d., , R, the earth, at a perpendicular distance , 2, , from the earth's centre, where R is the radius, of the earth. The wall of the tunnel is, frictionless. If a particle is released in this, tunnel, it will execute a simple harmonic, motion with a time period?, , 15, 4, , a., , 3. In a typical combustion engine, the work, done by a gas molecule is given W = α, , b. [M 0 LT 0 ], d. [MLT −1], , − βx 2, βe kT, , 2, , where x is the displacement, k is the, Boltzmann constant and T is the, temperature. If α and β are constants,, dimensions of α will be, a. [MLT −2 ], c. [M 2 LT −2 ], , b. 7 : 108, d. 1 : 3, , before the central axis of a spherical mirror,, whose focal length has absolute value, f = 40 cm. The image of object produced by, the mirror is of height 25 cm and has the, same orientation of the object. One may, conclude from the information., , 2 2 GMm, ⋅ 2, 3, R, 8 GmM, d., ⋅, 27 R 2, , 8 GmM, ⋅, 9, R, 1 GMm, c., ⋅ 2, 3 8 R, a., , a. 1 : 9, c. 7 : 135, , 5. A short straight object of height 100 cm lies, , Y, , X, , member of Lyman and first member of the, Paschen series respectively, then the value, of λ 1 : λ 2 is, , ,, , 2πR, g, , b., , g, 2πR, , c., , 1, 2π, , g, R, , d. 2π, , 7. An alternating current is given by the, , equation i = i1 sin ωt + i 2 cos ωt. The rms, current will be, 1 2, (i1 + i 22 )1/ 2, 2, 1, c. (i12 + i 22 )1/ 2, 2, a., , 1, (i1 + i 2 ) 2, 2, 1, d., (i1 + i 2 ), 2, b., , R, g
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44, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 8. The normal density of a material is ρ and its, bulk modulus of elasticity is K. The, magnitude of increase in density of material,, when a pressure p is applied uniformly on all, sides, will be, a., , ρK, p, , b., , ρp, K, , c., , K, ρp, , d., , pK, ρ, , 9. A particle is moving with uniform speed, along the circumference of a circle of radius, R under the action of a central fictitious force, F which is inversely proportional to R 3. Its, time period of revolution will be given by, a. T ∝ R 2, c. T ∝ R 5 / 2, , b. T ∝ R 3 / 2, d. T ∝ R 4 / 3, , 10. A planet revolving in elliptical orbit has, I. a constant velocity of revolution, II. has the least velocity when it is nearest to, the Sun, III. its areal velocity is directly proportional to its, velocity, IV. areal velocity is inversely proportional to its, velocity., V. to follow a trajectory such that the areal, velocity is constant., Choose the correct answer from the options, given below., a. Only I, b. Only IV, c. Only III, d. Only V, , 12. Four identical solid spheres each of mass m, and radius a are placed with their centres on, the four corners of a square of side b. The, moment of inertia of the system about one, side of square, where the axis of rotation is, parallel to the plane of the square is, 4, ma 2 + 2mb 2, 5, 8, b. ma 2 + mb 2, 5, 8, c. ma 2 + 2mb 2, 5, 4, d. ma 2, 5, a., , 13. In a Young's double slit experiment, two slits, are separated by 2 mm and the screen is, placed one metre away. When a light of, wavelength 500 nm is used, the fringe, separation will be, a. 0.25 mm, c. 0.75 mm, , b. 0.50 mm, d. 1 mm, , 14. Find the electric field at point P (as shown in, figure) on the perpendicular bisector of a, uniformly charged thin wire of length L, carrying a charge Q. The distance of the, point P from the centre of the rod is, 3, a=, L., 2, , 11. Given below are two statements : one is, labelled as Assertion A and the other is, labelled as Reason R., L, , Assertion A Body P having mass M moving, with speed u has head-on collision elastically, with another body Q having mass m initially, at rest. If m << M, body Q will have a, maximum speed equal to 2u after collision., Reason R During elastic collision, the, momentum and kinetic energy are both, conserved., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. A is not correct but R is correct., b. Both A and R are correct but R is not the, correct explanation of A., c. Both A and R are correct and R is the correct, explanation of A., d. A is correct but R is not correct., , E, , a, O, , P, , Q, , a., c., , 3Q, 4 πε0L2, Q, 2 3 π ε0L2, , b., d., , Q, 3 πε0L2, Q, 4 πε0L2, , 15. If two similar springs each of spring constant, K1 are joined in series, the new spring, constant and time period would be changed, by a factor, 1, a. , 2, 2, 1, c. , 2 2, 4, , 1, , 2, 4, 1, d. , 2 2, 2, , b.
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45, , FEBRUARY ATTEMPT ~ 26 Feb 2021, Shift I, 16. The temperature θ at the junction of two, insulating sheets, having thermal resistances, R1 and R 2 as well as top and bottom, temperatures θ1 and θ 2 (as shown in figure) is, given by, θ2, , R2, , θ, , 2T 1 1 , − , J r R, 3T, c., rJ, , 2T, rJ, 3T 1 1 , d., − , J r R, , a., , b., , 20. Five equal resistances are connected in a, network as shown in figure. The net, resistance between the points A and B is, D, , R1, θ1, , θ 2 R 2 − θ1 R1, R 2 − R1, θ1 R 2 + θ 2R1, c., R1 + R 2, a., , b., d., , R, , θ1 R 2 − θ 2R1, R 2 − R1, θ1 R1 + θ 2R 2, , R, , E, , 17. Given below are two statements: One is, , Assertion A An electron microscope can, achieve better resolving power than an, optical microscope., Reason R The de-Broglie's wavelength of the, electrons emitted from an electron gun is, much less than wavelength of visible light., In the light of the above statements, choose, the correct answer from the options given, below., a. A is true but R is false., b. Both A and R are true and R is the correct, explanation of A., c. Both A and R are true but R is not the correct, explanation of A., d. A is false but R is true., , 18. LED is constructed from GaAsP, semiconducting material. The energy gap of, this LED is 1.9 eV. Calculate the wavelength, of light emitted and its colour., [h = 6.63 × 10−34 Js and c = 3 × 108 ms −1], a. 1046 nm and red colour, b. 654 nm and orange colour, c. 1046 nm and blue colour, d. 654 nm and red colour, , A, , R, , R1 + R 2, , labelled as Assertion A and the other is, labelled as Reason R., , R, , a. 2R, , B, C, , R, , b., , R, 2, , c., , 3R, 2, , Section B : Numerical Type Questions, 21. A person standing on a spring balance inside, a stationary lift measures 60 kg. The weight, of that person, if the lift descends with, uniform downward acceleration of 1.8 m/s 2, will be ……… N. [g = 10 m/s 2], , 22. In an electrical circuit, a battery is connected, to pass 20 C of charge through it in a certain, given time. The potential difference between, two plates of the battery is maintained at, 15 V. The work done by the battery is ……… J., , 23. The circuit contains two diodes each with a, , forward resistance of 50 Ω and with infinite, reverse resistance. If the battery voltage is, 6V, the current through the 120 Ω resistance, is ……… mA., D1, , 130Ω, , D2, , 100Ω, , 19. A large number of water drops, each of, radius r, combine to have a drop of radius R., If the surface tension is T and mechanical, equivalent of heat is J, the rise in heat energy, per unit volume will be, , d. R, , 120Ω, 6V
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46, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 24. A radiation is emitted by 1000 W bulb and it, generates an electric field and magnetic field, at P, placed at a distance of 2 m. The, efficiency of the bulb is 1.25%. The value of, peak electric field at P is x × 10−1 V/m. Value, of x is ……… ., (Rounded-off to the nearest integer), [Take, ε 0 = 8.85 × 10−12 C 2N–1m–2 ,, c = 3 × 108 ms −1], , 25. A boy pushes a box of mass 2 kg with a force, F = (20i$ + 10$j) N on a frictionless surface. If, the box was initially at rest, then ……… m is, displacement along the X-axis after 10 s., , 26. As shown in the figure, a block of mass 3 kg, is kept on a horizontal rough surface of, coefficient of friction 1/ 3 3. The critical, force to be applied on the vertical surface as, shown at an angle 60° with horizontal such, that it does not move, will be 3x. The value of, 3, x will be ……… [ g = 10 ms −2; sin 60° =, ;, 2, 1, cos 60° = ], 2, µ = 1/3√3, , 27. A container is divided into two chambers by, a partition. The volume of first chamber is, 4.5 L and second chamber is 5.5 L. The first, chamber contain 3.0 mol of gas at pressure, 2.0 atm and second chamber contain 4.0 mol, of gas at pressure 3.0 atm. After the partition, is removed and the mixture attains, equilibrium, then the common equilibrium, pressure existing in the mixture is x × 10−1, atm. Value of x is ……… ., , 28. The mass per unit length of a uniform wire is, 0.135 g/cm. A transverse wave of the form, y = − 0.21sin ( x + 30t) is produced in it, where, x is in metre and t is in second. Then, the, expected value of tension in the wire is, x × 10−2 N. Value of x is ……… (Round-off to, the nearest integer), , 29. In a series L-C-R resonant circuit, the quality, factor is measured as 100. If the inductance, is increased by two fold and resistance is, decreased by two fold, then the quality, factor after this change will be ……… ., , 30. The maximum and minimum amplitude of, an amplitude modulated wave is 16 V and, 8 V, respectively. The modulation index for, this amplitude modulated wave is x × 10−2., The value of x is ……… ., , m= √3kg, 60°, , CHEMISTRY, Section A : Objective Type Questions, 1. The structure of neoprene is, , Cl, c., , CH2, , C, , CH, , CH2, n, , a., , CH2CH, , CH, , CH2, , CH2, , CH, N, , n, , d., , NH, , NHCN2, , N, , n, , b., , CH2, , N, , CH, CN, , n, , N, NH
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47, , FEBRUARY ATTEMPT ~ 26 Feb 2021, Shift I, 2. Find A, B and C in the following reactions:, NH3 + A + CO 2 → (NH4 ) 2 CO 3, (NH4 ) 2 CO 3 + H2O + B → NH4HCO 3, NH4HCO 3 + NaCl → NH4Cl + C, a. A – O 2 , B – CO 2 , C – Na2CO 3, b. A – H2O , B – O 2 , C – Na2CO 3, c. A – H2O, B – O 2 , C – NaHCO 3, d. A – H2O, B – CO 2 , C – NaHCO 3, , 3. The presence of ozone in troposphere, a. protects us from the UV radiation, b. protects us from the X-ray radiation, c. protects us from green house effect, d. generates photochemical smog, , 6. Statements about heavy water are given below., A. Heavy water is used in exchange reactions for, the study of reaction mechanisms., B. Heavy water is prepared by exhaustive, electrolysis of water., C. Heavy water has higher boiling point than, ordinary water., D. Viscosity of H2O is greater than D2O., , Whic oc the given statement are correct., a. A, B and C, c. Only A and D, , b. Only A and B, d. Only A and C, , 7. The orbital having two radial as well as two, angular nodes is, , 4. Match List-I with List-II., , a. 3p, , List-I, (Electronic, configuration of, elements), , List-II, (∆ i in kJ mol −1), , A., , 1s 2 2s 2, , (i), , 801, , B., , 1s 2 2s 2 2p 4, , (ii), , 899, , C., , 1s 2 2s 2 2p 3, , (iii) 1314, , D., , 2, , 2, , 1, , 1s 2s 2p, , (iv) 1402, , Choose the most appropriate answer from, the options given below., A, B, C, D, a. (ii) (iii) (iv) (i), b. (i) (iv) (iii) (ii), c. (i) (iii) (iv) (ii), d. (iv) (i) (ii) (iii), , 5. Given below are two statements: One is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) Dipole-dipole interactions are, the only non-covalent interactions, resulting, in hydrogen bond formation., Reason (R) Fluorine is the most, electronegative element and hydrogen, bonds in HF are symmetrical., In the light of the above statements, choose, the most appropriate answer from the, options given below., (a) A is false but R is true., (b) Both A and R are true and R is the correct, explanation of A., (c) A is true R is false., (d) Both A and R are true but R is not the correct, explanation of A., , b. 4 f, , c. 4d, , d. 5d, , 8. Match List-I with List-II., List-I, (Ore), , List-II, (Element present), , A., , Kernite, , (i), , Tin, , B., , Cassiterite, , (ii), , Boron, , C., , Calamine, , (iii), , Fluorine, , D., , Cryolite, , (iv), , Zinc, , Choose the most appropriate answer from, the options given below., A, B, C, D, a. (i) (iii) (iv) (ii), b. (ii) (i) (iv) (iii), c. (ii) (iv) (i) (iii), d. (iii) (i) (ii) (iv), , 9. Identify the major products A and B respectively, in the following reactions of phenol., OH, , (B), , (i) CHCl3, NaOH, (ii) H3O+, , Br2 in CS2, 273K, , OH, , OH, Br, , a., , and, , CHO, OH, , OH, , CHO, b., , and, , Br, , (A)
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48, , ONLINE, OH, , OH, Br, , c., , 13. Which of the following is a false statement?, CHO, , (a) Carius tube is used in the estimation of, sulphur in an organic compound, (b) Carius method is used for the estimation of, nitrogen in an organic compound, (c) Phosphoric acid produced on oxidation of, phosphorus present in an organic compound, is precipitated as Mg 2P2O 7 by adding, magnesia mixture, (d) Kjeldahl's method is used for the estimation, of nitrogen in an organic compound, , and, OH, , d., , OH, , and, , Br, , CHO, , 14. Which of the following vitamin is helpful in, , 10. Given below are two statements :, Statement I A mixture of chloroform and, aniline can be separated by simple, distillation., Statement II When separating aniline from a, mixture of aniline and water by steam, distillation aniline boils below its boiling, point. In the light of the above statements,, choose the most appropriate answer from, the options given below., a. Statement I is false but statement II is true, b. Both statement I and statement II are false, c. Statement I is true but statement II is false, d. Both statement I and statement II are true, , 11. For the given reaction, HC, CH3, , CHBr, , (i) NaNH2, , (A ), , (ii) Red hot iron tube iron, Major product, 873 K, , a. CH3CH2CH2NH2, , b. CH, , CH, , NH2, , CH2, H 3C, c., , CH3, , delaying the blood clotting ?, a. Vitamin C, c. Vitamin E, , 15., , A, , Hydrolysis, , →, , (C 4H8 Cl 2 ), , 373 K, , b. Vitamin B, d. Vitamin K, , B, (C 4H8 O), , B reacts with hydroxyl amine but does not, give Tollen's test. Identify A and B., a. 1,1-dichlorobutane and 2-butanone, b. 2,2-dichlorobutane and butanal, c. 1,1-dichlorobutane and butanal, d. 2,2-dichlorobutane and 2-butan-one, , 16. Compound A used as a strong oxidising, agent is amphoteric in nature. It is the part, of lead storage batteries. Compound A is, a. PbO 2, c. PbSO 4, , b. PbO, d. Pb 3O 4, , 17. Which one of the following lanthanoids does, not form MO2? [M is lanthanoid metal], a. Pr, c. Nd, , b. Dy, d. Yb, , 18. Given below are two statements:, , d., CH3, , 12. On treating a compound with warm, dil. H 2SO4, gas X is evolved, which turns, K 2Cr2O7 paper acidified with dil. H 2SO4 to a, green compound Y. X and Y respectively are, a. X = SO 2 , Y = Cr2O 3, b. X = SO 3 , Y = Cr2O 3, c. X = SO 2 , Y = Cr2 (SO 4 ) 3, d. X = SO 3 , Y = Cr2 (SO 4 ) 3, , JEE Main 2021 ~ Solved Papers, , Statement I o-nitrophenol is steam volatile, due to intramolecular hydrogen bonding., Statement II o-nitrophenol has high melting, due to hydrogen bonding., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Statement I is false but statement II is true, b. Both statement I and statement II are true, c. Both statement I and statement II are false, d. Statement I is true but statement II is false
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49, , FEBRUARY ATTEMPT ~ 26 Feb 2021, Shift I, 23. An exothermic reaction X → Y has an, , 19. For the given reaction,, CH2CH3, Br2, UV light, , A, (Major product), monobrominated, , activation energy 30 kJ mol −1. If energy, change ∆E during the reaction is –20 kJ mol −1,, then the activation energy for the reverse, reaction in kJ is ………… ., , CN, , 24. Consider the following reaction,, , What is A?, CH2CH3, , MnO−4 + 8H + + 5e − → Mn2+ + 4H 2O,, E ° = 1.51 V., The quantity of electricity required in Faraday, to reduce five moles of MnO−4 is ………… ., , CH2CH3, , Br, a., , b., CN, , CN, , 25. A certain gas obeys p(Vm − b) = RT . The value, , Br, Br, , CH3, CH, , CH2CH3, , ∂Z , xb, of is, . The value of x is ………… ., ∂p T RT, (Z = compressibility factor), , c., , d., , 26. A homogeneous ideal gaseous reaction, Br, , CN, , CN, , 20. An amine on reaction with benzene, sulphonyl chloride produces a compound, insoluble in alkaline solution. This amine can, be prepared by ammonolysis of ethyl, chloride. The correct structure of amine is, NH, , CH2CH2CH3, , 27. Dichromate ion is treated with base, the, oxidation number of Cr in the product, formed is ………… ., , a., , 28. 224 mL of SO 2(g) at 298 K and 1 atm is, , b., , CH3CH2NH2, , c., , CH3CH2CH2NHCH3, , d., , H, CH3CH2CH2N, , CH2CH3, , Section B : Numerical Type Questions, 21. For a chemical reaction, A + B q, , C +D, , (∆ rH° = 80 kJ mol −1) the entropy change ∆ rS°, depends on the temperature T (in K) as, ∆ r S ° = 2T (JK –1 mol–1)., Minimum temperature at which it will, become spontaneous is ………… K., , 22. The number of significant figures in, 50000.020 × 10, , AB 2( g) q, A( g) + 2B( g) is carried out in a, 25 L flask at 27°C. The initial amount of AB 2, was 1 mole and the equilibrium pressure, was 1.9 atm. The value of K p is x × 10−2. The, value of x is ………… ., , −3, , is ………… ., , passed through 100 mL of 0.1 M NaOH, solution. The non-volatile solute produced is, dissolved in 36 g of water. The lowering of, vapour pressure of solution (assuming the, solution is dilute), (p(H2 O) = 24 mm of Hg) is, x × 10−2 mm of Hg, the value of x is ………… ., , 29. 3.12 g of oxygen is adsorbed on 1.2 g of, platinum metal. The volume of oxygen, adsorbed per gram of the adsorbent at, 1 atm and 300 K in L is ………… ., [R = 0.0821 L atm K −1 mol −1], , 30. Number of bridging CO ligands in [Mn2(CO)10 ], is ………… .
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50, , JEE Main 2021 ~ Solved Papers, , ONLINE, , MATHEMATICS, Section A : Objective Type Questions, , 1+, , 1. If a and b are perpendicular, then, a × (a × (a × (a × b))) is equal to, , a., , 1, c. |a|4 b, 2, d.|a|4 b, , a. 0, c. a × b, , If the probability of getting 7 heads is equal, to probability of getting 9 heads, then the, probability of getting 2 heads is, 15, 13, , 2, , b., , 15, , c., , 12, , 2, , 15, , d., , 8, , 2, , 15, 14, , integer entries. If the sum of the diagonal, elements of A 2 is 1, then the possible, number of such matrices is, b. 1, , 13, 4, , c. 6, , a., , d. 12, , 4, 3, , 25, and the, 2, product of the third and fifth term is 25., Then, the sum of 4th, 6th and 8th terms is, equal to, the second and the sixth term is, , 100, , 5. The value of, , c. 35, n x − [x ], , ∑ ∫n e− 1, , d. 32, , dx , where [x] is the, , n =1, , greatest integer ≤ x, is, a. 100 (e − 1), c. 100e, , b. 100 (1 − e ), d. 100 (1 + e ), , 6. In the circle given below, let OA = 1 unit,, , OB = 13 unit and PQ ⊥ OB. Then, the area of, the triangle PQB (in square units) is, y, , O, , 11, 4, , x, , b., , 2, 3, , c., , 3, 4, , d., , 2, 3, , 10 !, , b., , 3 (5 !) 2, , 2⋅ 10 !, 3 3 (5 !) 2, , c., , 2 ⋅ 10 !, 3 (5 !) 2, , d., , 10 !, 3 (5 !) 2, , 2, , k , , is equal to, log e 2, a. 4, c. 2, , b. 8, d. 16, , 11. If (1, 5, 35), (7, 5, 5), (1, λ , 7) and (2λ , 1, 2) are, coplanar, then the sum of all possible values, of λ is, , 12. If, , 39, 5, , sin−1 ( x), a, , b. −, , =, , 39, 5, , cos −1 x, b, , c., , =, , 44, 5, , tan−1 y, c, , d. −, , 44, 5, , , 0 < x < 1, then, , πc , the value of cos , is, a + b, , Q, , a. 24 2, c. 26 3, , d., , proportional to the number of bacteria, present and the bacteria count is 1000 at, initial time t = 0. The number of bacteria is, increased by 20% in 2 h. If the population of, k, h, then, bacteria is 2000 after, log e (6 /5), , P, B, , 15, 4, , 10. The rate of growth of bacteria in a culture is, , a., , A, , c., , independent of ‘t’ in the expansion of, 10, 1/5 (1 − x)1/10 , , where x ∈(0, 1) is, tx +, t, , , , 4. In an increasing geometric series, the sum of, , b. 26, , 9, 4, , 9. The maximum value of the term, , a., , a. 30, , b., , π, π, , , 3 sin + h − cos + h, 6, , 6, , , lim 2 , is, h→ 0, 3h ( 3 cos h − sin h), , , , , , 2, , 3. Let A be a symmetric matrix of order 2 with, , a. 4, , 2, 7, 12, 17 22, +, +, + 4 + 5 + ... is equal to, 3 32 33, 3, 3, , 8. The value of, , 2. A fair coin is tossed a fixed number of times., , a., , 7. The sum of the infinite series, , b. 24 3, d. 26 2, , a., , 1− y2, y y, , b. 1 − y 2, , c., , 1− y2, 1+ y, , 2, , d., , 1− y2, 2y
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51, , FEBRUARY ATTEMPT ~ 26 Feb 2021, Shift I, 13. The number of seven digit integers with sum, of the digits equal to 10 and formed by using, the digits 1, 2 and 3 only is, a. 42, , b. 82, , c. 77, , d. 35, , 14. Let f be any function defined on R and let it, , a > 0 is ……… ., , 22. The number of integral values of k for which, , 15. The maximum slope of the curve, , 1, y = x 4 − 5x 3 + 18x 2 − 19x occurs at the, 2, point, a. (2, 2), , b. (0, 0), , c. (2, 9), , 21, d. 3, , 2, , 23. The number of solutions of the equation, log 4 ( x − 1) = log 2 ( x − 3) is ……… ., equation x 3 − 2x 2 + 2x − 1 = 0 is, , x + 2 y = 3 and 2x + y = 6 is a, a. right angled triangle b. equilateral triangle, c. isosceles triangle, d. None of these, , 17. Consider the three planes, P1 : 3x + 15 y + 21z = 9,, P2 : x − 3 y − z = 5 and, P3 : 2x + 10 y + 14 z = 5, , 25. Let m , n ∈ N and gcd (2, n) = 1. If, 30, 30, 30, 30, 30 + 29 + K + 2 + 1 , 29, 28, 1, 0, n, = n ⋅ 2m , then n + m is ……… . (Here, , k, , = nC k), , 26. If y = y ( x) is the solution of the equation, dy, + e sin y cos x = cos x , y (0) = 0,, dx, π, π, 3 π, 1, then 1 + y +, y +, y is, 6, 3, 2, 2 4, ……… ., , e sin y cos y, , Then, which one of the following is true ?, a. P1 and P2 are parallel, b. P1 and P3 are parallel, c. P2 and P3 are parallel, d. P1, P2 and P3 all are parallel, , 27. Let (λ, 2, 1) be a point on the plane which, , (a + 1)(a + 2), , a+2, , 1, , 18. The value of (a + 2)(a + 3), , a+3, , 1 is, , a+4, , 1, , (a + 3) (a + 4), b. –2, d. 0, , π /2, , cos 2 x, , −π / 2, , 1 + 3x, , b. 4 π, , the equation 3 sin x + 4 cos x = k + 1 has a, solution, k ∈ R is ……… ., , 24. The sum of 162th power of the roots of the, , 16. The intersection of three lines x − y = 0,, , π, a., 4, , Section B : Numerical Type Questions, a differential equation that represents the, , a, family of curves given by y 2 = a x +, ,, , 2 , , | f (x ) − f ( y )|≤| (x − y ) |, ∀ (x , y ) ∈ R, If f (0) = 1, then, a. f (x ) can take any value in R, b. f (x ) < 0, ∀ x ∈ R, c. f (x ) = 0, ∀ x ∈ R, d. f (x ) > 0, ∀ x ∈ R, 2, , 19. The value of ∫, , y 2 = 4}, y 2 = 1}, y 2 = 2}, y 2 = 2}, , 21. The difference between degree and order of, , satisfy the condition, , a. (a + 2)(a + 3)(a + 4 ), c. (a + 1)(a + 2) (a + 3), , a. S = {(x , y )| x 2 +, b. S = {(x , y )| x 2 +, c. S = {(x , y )| x 2 +, d. S = {(x , y )| x 2 +, , passes through the point (4, –2, 2). If the, plane is perpendicular to the line joining the, points (–2, –21, 29) and (–1, –16, 23), then, 2, 4λ, λ, − 4 is ……… ., −, 11, 11, , 28. The area bounded by the lines, y = || x − 1| − 2| is ……… ., , dx is, , π, c., 2, , π, , d. 2π, , 20. Let R = {(P, Q) |, P and Q are at the same, distance from the origin} be a relation, then, the equivalence class of (1, –1) is the set, , 29. The value of the integral ∫ |sin 2x | dx is ……… ., 0, , 30. If 3 (cos 2 x) = ( 3 − 1) cos x + 1, the number, of solutions of the given equation when, π, x ∈ 0, is ……… ., 2
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52, , ONLINE, , JEE Main 2021 ~ Solved Papers, , Answers, For solutions scan, the QR code, , Physics, 1. (d), 11. (c), 21. 492, , 2. (*), 12. (c), 22. 300, , 3. (b), 13. (a), 23. 20, , 4. (c), 14. (c), 24. 137, , 5. (d), 15. (a), 25. 500, , 6. (d), 16. (c), 26. 3.33, , 7. (a), 17. (b), 27. 25.5, , 8. (b), 18. (d), 28. 1215, , 9. (a), 19. (d), 29. 400, , 10. (d), 20. (d), 30. 33.33, , 3. (d), 13. (b), 23. 50, , 4. (a), 14. (d), 24. 25, , 5. (a), 15. (d), 25. 1, , 6. (a), 16. (a), 26. 73, , 7. (d), 17. (d), 27. 6, , 8. (b), 18. (d), 28. 18, , 9. (b), 19. (c), 29. 2, , 10. (d), 20. (d), 30. 0, , 3. (a), 13. (c), 23. 1, , 4. (c), 14. (d), 24. 3, , 5. (a), 15. (a), 25. 45, , 6. (b), 16. (c), 26. 1, , 7. (a), 17. (b), 27. 8, , 8. (a), 18. (b), 28. 4, , 9. (b), 19. (a), 29. 2, , 10. (a), 20. (d), 30. 1, , Chemistry, 1. (c), 11. (d), 21. 200, , 2. (d), 12. (c), 22. 7, , Mathematics, 1. (d), 11. (c), 21. 2, , 2. (a), 12. (c), 22. 11, , Note (*) None of the option is correct.
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53, , FEBUARY ATTEMPT ~ 26 Feb 2021, Shift II, , JEE Main 2021, 26 FEBRUARY SHIFT II, , PHYSICS, Section A : Objective Type Questions, 1. If C and V represent capacity and voltage, respectively, then what are the dimensions, C, of λ , where = λ ?, V, a. [M −2L−3I2 T 6 ], c. [M −1L−3I−2 T −7 ], , b. [M −3L−4I3 T 7 ], d. [M −2L−4I3 T 7 ], , 2. The length of metallic wire is l1 when tension, in it is T1. It is l 2 when the tension is T2. The, original length of the wire will be, l1 + l 2, 2, T2 l1 − T1l 2, c., T2 − T1, , a., , T2 l1 + T1l 2, T1 + T2, T1l1 − T2 l 2, d., T2 − T1, b., , 3. An aeroplane with its wings spread 10 m, is, flying at a speed of 180 km/h in a horizontal, direction. The total intensity of Earth's field, at that part is 2.5 × 10−4 Wb/m 2 and the, angle of dip is 60°. The emf induced between, the tips of the plane wings will be, a. 108.25 mV, c. 88.37 mV, , b. 54.125 mV, d. 62.50 mV, , 4. A tuning fork A of unknown frequency, produces 5 beats/s with a fork of known, frequency 340 Hz. When fork A is filled, the, beat frequency decreases to 2 beats/s. What, is the frequency of fork A?, a. 342 Hz, c. 335 Hz, , b. 345 Hz, d. 338 Hz, , 5. A particle executes SHM, the graph of, velocity as a function of displacement is, a. a circle, c. an ellipse, , b. a parabola, d. a helix, , 6. The trajectory of a projectile in a vertical, , plane is y = αx − βx 2 , where α and β are, constants and x and y are respectively the, horizontal and vertical distances of the, projectile from the point of projection. The, angle of projection θ and the maximum, height attained H are respectively given by, α2, 4β, 4α 2, c. tan −1 α ,, β, a. tan −1 α ,, , α2, 2β, β α2, d. tan −1 ,, α β, , b. tan −1 β ,, , 7. A cord is wound round the circumference of, wheel of radius r. The axis of the wheel is, horizontal and the moment of inertia about, it is I. A weight mg is attached to the cord at, the end. The weight falls from rest. After, falling through a distance h, the square of, angular velocity of wheel will be, a., , 2mgh, I + 2mr 2, , c. 2gh, , b., d., , 2mgh, I + mr 2, 2 gh, I + mr 2, , 8. The internal energy (U), pressure (p) and, volume (V) of an ideal gas are related as, U = 3pV + 4. The gas is, a. diatomic only, b. polyatomic only, c. Either monoatomic or diatomic, d. monoatomic only, , 9. Given below are two statements: one is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) For a simple microscope, the, angular size of the object equals the angular, size of the image.
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54, , JEE Main 2021 ~ Solved Papers, , ONLINE, Reason (R) Magnification is achieved as the, small object can be kept much closer to the, eye than 25 cm and hence, it subtends a, large angle., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. A is true but R is false., b. Both A and R are true but R is not the correct, explanation of A., c. Both A and R are true and R is the correct, explanation of A., d. A is false but R is true., , a. 0.2 A and 50 Hz, c. 2 A and 100 Hz, , b. 0.2 A and 100 Hz, d. 2 A and 50 Hz, , 13. An inclined plane making an angle of 30°, with the horizontal is placed in a uniform, horizontal electric field 200 N/C as shown in, the figure. A body of mass 1kg and charge, 5 mC is allowed to slide down from rest at a, height of 1m. If the coefficient of friction is, 0.2, find the time taken by the body to reach, the bottom., 1, 3, ], [Take, g = 9.8 m/s 2, sin 30° = , cos 30° =, 2, 2, , 10. Given below are two statements:, Statement I An electric dipole is placed at, the centre of a hollow sphere. The flux of, electric field through the sphere is zero but, the electric field is not zero anywhere in the, sphere., Statement II If R is the radius of a solid, metallic sphere and Q be the total charge on, it. The electric field at any point on the, spherical surface of radius r ( < R) is zero but, the electric flux passing through this closed, spherical surface of radius r is not zero., In the light of the above statements, choose, the correct answer from the options given, below., a. Both Statement I and Statement II are true., b. Statement I is true but Statement II is false., c. Both Statement I and Statement II are false., d. Statement I is false but Statement II is true., , 11. The recoil speed of a hydrogen atom after it, emits a photon in going from n = 5 state to, n = 1state will be, a. 4.17 m/s, c. 3.25 m/s, , b. 2.19 m/s, d. 4.34 m/s, , 12. Find the peak current and resonant, frequency of the following circuit (as shown, in figure)., 100 mH, , 100 µF, , C, , 2, E=, , 0, , /, 0N, , g,, 1k, , C, , 5m, , 1m, , 30°, a. 0.92 s, c. 2.3 s, , b. 0.46 s, d. 1.3 s, , 14. Two masses A and B, each of mass M are, fixed together by a massless spring. A force, acts on the mass B as shown in figure. If the, mass A starts moving away from mass B with, acceleration a, then the acceleration of mass, B wil be, F, , B, , A, , Ma − F, a., M, F + Ma, c., M, , MF, b., F + Ma, F − Ma, d., M, , 15. Draw the output signal Y in the given, combination of gates, , A, , B, , 0, , 1, , 2, , 3, , 4, , 5 t(s), , 0, , 1, , 2, , 3, , 4, , 5 t(s), , V=30sin100 t, A, 120 Ω, , B, , Y
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55, , FEBUARY ATTEMPT ~ 26 Feb 2021, Shift II, , the correct answer from the options given, below., a., 0, , 1, , 2, , 3, , 4, , 5 t(s), , a. Both Statement I and Statement II are false., b. Statement I is false but Statement II is true., c. Statement I is true but Statement II is false., d. Both Statement I and Statement II are true., , 19. A wire of 1 Ω has a length of 1m. It is, b., , 0, , 1, , 2, , 3, , 4, , 5 t(s), , stretched till its length increases by 25%. The, percentage change in resistance to the, nearest integer is, a. 56%, c. 12.5%, , b. 25%, d. 76%, , 20. The incident ray, reflected ray and the, c., 0, , 1, , 2, , 3, , 4, , 5 t(s), , a., b., c., d., , d., 0, , 1, , 2, , 3, , 4, , 5 t(s), , 16. A radioactive sample is undergoing α-decay., At any time t1, its activity is A and another, A, time t 2 , the activity is . What is the average, 5, life time for the sample?, ln 5, t 2 − t1, t −t, c. 2 1, ln 5, , a., , t1 − t 2, ln 5, ln (t 2 + t1), d., 2, b., , 17. A scooter accelerates from rest for time t1 at, constant rate a1 and then retards at constant, rate a 2 for time t 2 and comes to rest. The, t, correct value of 1 will be, t2, a1 + a 2, a2, a, c. 1, a2, , a., , outward drawn normal are denoted by the, unit vectors a, b and c, respectively. Then,, choose the correct relation for these vectors., , a2, a1, a + a2, d. 1, a1, , b., , 18. Given below are two statements:, Statement I A second's pendulum has a time, period of 1 s., Statement II It takes precisely one second to, move between the two extreme positions., In the light of the above statements, choose, , b = a + 2c, b = 2a + c, b = a − 2(a ⋅ c )c, b=a−c, , Section B : Numerical Type Questions, 21. The volume V of a given mass of, monoatomic gas changes with temperature, T according to the relation V = kT 2/ 3. The, work done when temperature changes by, 90 K will be xR. The value of x is……… ., [R = universal gas constant], , 22. If the highest frequency modulating a carrier, is 5 kHz, then the number of AM broadcast, stations accommodated in a 90 kHz, bandwidth are ......... ., , 23. Two stream of photons, possessing energies, equal to twice and ten times the work, function of metal are incident on the metal, surface successively. The value of ratio of, maximum velocities of the photoelectrons, emitted in the two respective cases is x : y., The value of x is .............. ., , 24. A point source of light S, placed at a distance, 60 cm in front of the centre of a plane mirror, of width 50 cm, hangs vertically on a wall. A, man walks in front of the mirror along a line, parallel to the mirror at a distance 1.2 m, from it (see in the figure). The distance, between the extreme points, where he can
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56, , ONLINE, see the image of the light source in the, mirror is .......... cm., , JEE Main 2021 ~ Solved Papers, , at point B (surface of the Earth). The value of, OA : AB will be x : y. The value of x is .......... ., C, 3200 km, , 50 cm, , 60 cm, , B, , S, , A, Earth, , O, , 1.2 m, R=6400 km, , 25. A particle executes SHM with amplitude a, and time period T . The displacement of the, particle when its speed is half of maximum, xa, speed is, . The value of x is ........... ., 2, , 26. 27 similar drops of mercury are maintained, at 10 V each. All these spherical drops, combine into a single big drop. The potential, energy of the bigger drop is ............ times, that of a smaller drop., , 27. Time period of a simple pendulum is T. The, time taken to complete 5/8 oscillations, α, starting from mean position is T. The, β, value of α is ......... ., , 29. 1 mole of rigid diatomic gas performs a work, of Q/5 when heat Q is supplied to it. The, molar heat capacity of the gas during this, xR, transformation is, , The value of x is ........... ., 8, [R = universal gas constant], , 30. The Zener diode has a Vz = 30 V. The current, passing through the diode for the following, circuit is ......... mA., 4kΩ, , 90 V, , 5kΩ, , 28. In the reported figure of Earth, the value of, acceleration due to gravity is same at point A, and C but it is smaller than that of its value, , CHEMISTRY, Section A : Objective Type Questions, 1. Which of the following forms of hydrogen, emits low energy β − particles ?, a. Deuterium 12 H, c. Protium 11H, , b. Tritium 13 H, d. Proton H +, , 2. Given below are two statements: one is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) In TlI 3 , isomorphous to CsI3 , the, metal is present in + 1oxidation state., , Reason (R) Tl metal has fourteen f-electrons in, the electronic configuration., In the light of the above statements, choose, the most appropriate answer from the options, given below., a. A is correct but R is not correct., b. Both A and R are correct and R is the correct, explanation of A., c. A is not correct but R is correct, d. Both A and R are correct but R is not correct, explanation of A.
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57, , FEBUARY ATTEMPT ~ 26 Feb 2021, Shift II, 3. Match List-I with List-II., List-I, , 10. Which pair of oxides is acidic in nature?, List-II, , a. B2O 3 , CaO, c. N2O, BaO, , b. B2O 3 , SiO 2, d. CaO, SiO 2, , A., , Sucrose, , (i), , β-D-galactose and, β-D-glucose, , B., , Lactose, , (ii), , α-D-glucose and, β-D-fructose, , CH2CH2CHO, , C., , Maltose, , (iii), , α-D-glucose and, α-D-glucose, , CH2CH2CHO, , Choose the correct answer from the options, given below., a. A → (i), B → (iii), C → (ii), b. A → (iii), B → (i), C → (iii), c. A → (ii), B → (i), C → (iii), d. A → (iii), B → (ii), C → (i), , 11. Identify A in the given chemical reaction,, NaOH, A (Major product), C2H5OH, H2O, , CHO, a., CH2CH2COOH, b., CH2CH2CH2OH, , 4. A. phenyl methanamine, B. N,N-dimethylaniline, C. N-methyl aniline, D. Benzenamine, Choose the correct order of basic nature of the, above amines., a. A > C > B > D, c. D > B > C > A, , a. S > Se > Te > O, c. O > S > Se > Te, 2, , C, , 3, , O, d., , b. Te > Se > S > O, d. S > O > Se > Te, , O, , 12. Identify A in the following chemical reaction., , 4, , 6. In C H2 == C == C H — C H3 molecule,, the hybridisation of carbon 1, 2, 3 and 4, respectively are, a. sp 3 , sp , sp 3 , sp 3, c. sp 2 , sp , sp 2 , sp 3, , b. sp 2 , sp 2 , sp 2 , sp 3, d. sp 2 , sp 3 , sp 2 , sp 3, , 7. Seliwanoff test and xanthoproteic test are, used for the identification of ……… and ………, respectively., a. aldoses, ketoses, c. ketoses, proteins, , are used for the identification of functional, groups present in ……… and ………, respectively., b. amine, alcohol, d. amine, phenol, , (i) HCHO, NaOH, (ii) CH3CH2Br, NaH, DMF, (iii) HI, ∆, , CH3O, , O, C, , OCH2CH3, , a., HO, CH2OH, b., , b. aldehyde, d. halogens, , 9. Ceric ammonium nitrate and CHCl3 /alc. KOH, , a. alcohol, phenol, c. alcohol, amine, , CHO, , b. proteins, ketoses, d. ketoses, aldoses, , 8. 2,4-DNP test can be used to identify, a. amine, c. ether, , H, , c., , b. D > C > B > A, d. A > B > C > D, , 5. The correct order of electron gain enthalpy is, , 1, , O, , CH3O, , CH2I, c., HO, CH2OH, d., HO, , A
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58, , JEE Main 2021 ~ Solved Papers, , ONLINE, , CH2CH3, , 13. Calgon is used for water treatment. Which of, the following statement is not true about, Calgon?, a. Calgon contains the 2nd most abundant, element by weight in the Earth’s crust., b. It is polymeric compound and is water, soluble., c. It is also known as Graham’s salt., d. It does not remove Ca2 + ion by precipitation., , CH2CH2CH3, , a., , b., , CH3, , COCH2CH3, CH3, , c., , d., , 14. Match List-I with List-II., 16. Match List-I with List-II, , List-I, , List-I, (Molecule), , Cl, +, , N2Cl–, A., , Cu2Cl2, , + N2, Cl, , A., , Ne2, , (i), , 1, , B., , N2, , (ii), , 2, , C., , F2, , (iii), , 0, , D., , O2, , (iv), , 3, , +, , N2Cl–, , Cu,HCl, , B., , + N2, , Ether, C. 2CH3CH2Cl + 2Na →, C 2H5 — C 2H5 + 2NaCl, Ether, , D. 2C 6H5Cl + 2Na → C 6H5 — C 6H5 + 2NaCl, , List-II, (Bond order), , Choose the correct answer from the options, given below., A, B, C, D, a. (iii) (iv) (i) (ii), c. (ii) (i) (iv) (iii), , A, B, C, D, b. (i) (ii) (iii) (iv), d. (iv) (iii) (ii) (i), , 17. Identify A in the given reaction., OH, , List-II, (i), (ii), (iii), (iv), , Wurtz reaction, Sandmeyer reaction, Fittig reaction, Gattermann reaction, , SOCl3, , HO, , Choose the correct answer from the options, given below., a., b., c., d., , A, B, C, D, (iii) (i) (iv) (ii), (ii) (i) (iv) (iii), (ii) (iv) (i) (iii), (iii) (iv) (i) (ii), , 15., , A (Major product), , CH2OH, , OH, , a., , OH, , b., , HO, (1) Zn/HCl, , CH2Cl, , Cl, , CH2Cl, , Cl, , Cl, , (2) Cr2O3 773K, 10-20 atm, , O, , considering the above reaction, the major, product among the following is, , d., , c., , Cl, , CH2Cl, , OH, , CH2OH
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59, , FEBUARY ATTEMPT ~ 26 Feb 2021, Shift II, 18. Match List-I with List-II., List-I, , 22. Emf of the following cell at 298 K in V is, List-II, , A., , Siderite, , (i), , Cu, , B., , Calamine, , (ii), , Ca, , C., , Malachite, , (iii) Fe, , D. Cryolite, , Zn, , Zn, , 23. When 12.2 g of benzoic acid is dissolved in, , Chose the correct answer from the options, given below., A, a. (iii), b. (i), c. (iii), d. (i), , B, (i), (ii), (v), (ii), , C, D, (v) (ii), (v) (iii), (i) (iv), (iii) (iv), , particles when FeCl3 is added to excess of, hot water is, Positive, Sometimes positive and sometimes negative, Neutral, Negative, , 20. Match List-I with List-II, List-I, , List-II, , A., , Sodium carbonate, , (i), , Deacon, , B., , Titanium, , (ii), , Castner-Kellner, , C., , Chlorine, , (iii), , van-Arkel, , D., , Sodium hydroxide, , (iv), , Solvay, , Choose the correct answer form the options, given below., a., b., c., d., , 100 g of water, the freezing point of solution, was found to be – 0.93°C (K f (H 2O) = 1.86 K kg, mol −1). The number ( n) of benzoic acid, molecules associated, (assuming 100% association) is ……… ., , 24. The average S—F bond energy in kJ mol −1 of, , 19. The nature of charge on resulting colloidal, a., b., c., d., , / Zn, , 2.303RT, = 0.059], F, , (iv) Al, (v), , x × 10−2, Zn | Zn2+ (0.1 M) || Ag + (0.01 M) | Ag, The value of x is ……… ., (Rounded off to the nearest integer)., °+, [Given, E ° 2 +, = − 0.76 V, E Ag, = + 0.80 V,, / Ag, , A, B, C, D, (iv) (iii) (i) (ii), (i) (iii) (iv) (ii), (iv) (i) (ii) (iii), (iii) (ii) (i) (iv), , Section B : Numerical Type Questions, 21. The NaNO3 weighed out to make 50 mL of an, aqueous solution containing 70.0 mg Na +, per mL is ……… g. (Rounded off to the, nearest integer), [Given : Atomic weight in g mol −1, –Na : 23 ;, N : 14 ; O : 16]., , SF6 is ………… (Rounded off to the nearest, integer), [Given, the values of standard enthalpy of, formation of SF6( g), S( g) and F( g) are –1100,, 275 and 80 kJ mol −1 respectively. ], , 25. A ball weighing 10 g is moving with a velocity, , of 90 ms −1. If the uncertainity in its velocity is, 5%, then the uncertainty in its position is, ……… × 10−33 m (Rounded off to the nearest, integer). [Given, h = 6.63 × 10−34 J- s], , 26. The number of octahedral voids per lattice, site in a lattice is ……… ., (Rounded off to the nearest integer), , 27. In mild alkaline medium, thiosulphate ion is, , oxidised by MnO−4 to “ A ”. The oxidation state, of sulphur in “ A ” is ……… ., , 28. The number of stereoisomers possible for, [Co(ox) 2(Br)(NH 3)]2– is ……… [ox = oxalate]., , 29. If the activation energy of a reaction is, , 80.9 kJ mol −1, the fraction of molecules at, 700 K, having enough energy to react to, form products is e − x . The value of x is ………, (Rounded off to the nearest integer), [Use, R = 8.31 JK –1 mol–1]., , 30. The pH of ammonium phosphate solution, if, pK a of phosphoric acid and pK b of, ammonium hydroxide are 5.23 and 4.75, respectively, is ……… .
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60, , ONLINE, , JEE Main 2021 ~ Solved Papers, , MATHEMATICS, Section A : Objective Type Questions, 1. If vectors a1 = x $i − $j + k$ and a2 = i$ + y$j + zk$ are, collinear, then a possible unit vector parallel, to the vector x $i + y$j + zk$ is, 1, (− $j + k$ ), 2, 1 $ $ $, c., (i + j − k ), 3, , 1 $ $, (i − j ), 2, 1 $ $ $, d., (i − j + k ), 3, , a., , b., , 2. Let A = { 1, 2, 3, ..., 10} and f : A → A be defined, k + 1, if k is odd, as f ( k) = , k , if k is even, Then, the number of possible functions, g : A → A, such that gof = f is, a. 105, c. 55, , b. 10 C 5, d. 5!, , 3. Let f : R → R be defined as, πx , , ,, 2 sin −, if x < − 1, 2, , , f ( x) = | ax 2 + x + b|, if − 1 ≤ x ≤ 1, sin ( πx),, if x > 1, , , If f ( x) is continuous on R, then a + b equals, a. –3, c. 3, , b. –1, d. 1, x, , 4. For x > 0, if f ( x) = ∫, , log e t, , (1 + t), 1, , 1, dt , then f (e) + f , e, , is equal to, a. 1, 1, c., 2, , b. –1, d. 0, , x2 − x − 2, 2x 2 − x − 6, , ., , If g(2) = lim g( x), then the domain of the, x→ 2, , function fog is, , 3, a. (− ∞ , − 2] ∪ − , ∞ , , 2, b. (−∞ , − 2] ∪ [ −1, ∞ ), 4, c. (−∞ , − 2] ∪ − , ∞ , 3, , d. (−∞ , − 1] ∪ [ 2, ∞ ), , 7. The triangle of maximum area that can be, inscribed in a given circle of radius r is, a. an isosceles triangle with base equal to 2r, 2r, 3, c. an equilateral triangle having each of its side, of length 3r, d. a right angle triangle having two of its sides of, length 2r and r, , b. an equilateral triangle of height, , 8. Let L be a line obtained from the intersection, of two planes x + 2 y + z = 6 and y + 2z = 4. If, point P(α , β , γ) is the foot of perpendicular, from (3, 2, 1) on L, then the value of, 21(α + β + γ) equals, a. 142, c. 136, , b. 68, d. 102, , 9. Let F1( A , B , C ) = ( A ∧ ~ B) ∨ [~ C ∧ ( A ∨ B)] ∨ ~ A, and F 2( A , B) = ( A ∨ B) ∨ (B → ~ A) be two logical, expressions. Then,, a. F1 and F2 both are tautologies, b. F1 is a tautology but F2 is not a tautology, c. F1 is not tautology but F2 is a tautology, d. Both F1 and F2 are not tautologies, , 10. Let slope of the tangent line to a curve at any, , 5. A natural number has prime factorisation, , given by n = 2x3 y5z , where y and z are such, 5, that y + z = 5 and y −1 + z −1 = , y > z. Then,, 6, the number of odd divisors of n, including 1,, is, a. 11, c. 6x, , 6. Let f ( x) = sin−1 x and g( x) =, , b. 6, d. 12, , xy 2 + y, , . If the curve, x, intersects the line x + 2 y = 4 at x = − 2, then, the value of y, for which the point (3, y) lies, on the curve, is, point P( x , y ) be given by, , 18, 35, 18, c. −, 19, , a., , 4, 3, 18, d. −, 11, , b. −
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61, , FEBUARY ATTEMPT ~ 26 Feb 2021, Shift II, 11. If the locus of the mid-point of the line, segment from the point (3, 2) to a point on, the circle, x 2 + y 2 = 1 is a circle of radius r,, then r is equal to, a. 1, , b. 1/2, , c. 1/3, , d. 1/4, , 12. Consider the following system of equations, x + 2 y − 3z = a, 2x + 6 y − 11z = b, x − 2 y + 7z = c, where, a, b and c are real constants. Then, the, system of equations, a. has a unique solution, when 5a = 2b + c, b. has infinite number of solutions when, 5a = 2b + c, c. has no solution for all a, b and c, d. has a unique solution for all a, b and c, , 13. If 0 < a, b < 1 and tan−1 a + tan−1 b =, , π, , then, 4, , the value of, a 2 + b2 a 3 + b3 a 4 + b4 , +K, −, +, (a + b) − , 2 , 3 , 4 , , is, a. log e 2, c. e, , b. e 2 − 1, e, d. log e , 2, ∞, , 14. The sum of the series, , ∑, , n + 6n + 10, , n =1, , is, , equal to, 41, 19 −1, e+, e − 10, 8, 8, 41, 19 −1, c., e+, e + 10, 8, 8, a., , 41, 19 −1, e−, e − 10, 8, 8, 41, 19 −1, d. − e +, e − 10, 8, 8, b., , 15. Let f ( x) be a differentiable function at x = a, with f ′ (a) = 2 and f (a) = 4., xf (a) − af ( x), equals, Then, lim, x→ a, x −a, a. 2a + 4, c. 2a − 4, , b. 4 − 2a, d. a + 4, , 16. Let A(1, 4) and B(1, –5) be two points. Let P be, a point on the circle ( x − 1) 2 + ( y − 1) 2 = 1, such, that (PA) 2 + (PB) 2 have maximum value, then, the points P, A and B lie on, a. a straight line, c. an ellipse, , b. a hyperbola, d. a parabola, , respect to the plane 4 x − 5 y + 2z = 8 is, (α , β , γ), then 5(α + β + γ) equals, a. 47, c. 39, , b. 43, d. 41, x, , 18. Let f ( x) = ∫ e t f (t) dt + e x be a differentiable, 0, , function for all x ∈ R. Then, f ( x) equals, a. 2e ( e, b. e, , e, , x, , x, , − 1), , −1, , −1, x, , c. 2e e − 1, d. e ( e, , x, , − 1), , 19. Let A1 be the area of the region bounded by, the curves y = sin x , y = cos x and y-axis in, the first quadrant. Also, let A2 be the area of, the region bounded by the curves y = sin x ,, π, y = cos x , x-axis and x = in the first, 2, quadrant. Then,, a. A1 : A 2 = 1: 2 and A1 + A 2 = 1, b. A1 = A 2 and A1 + A 2 = 2, c. 2A1 = A 2 and A1 + A 2 = 1 + 2, d. A1 : A 2 = 1: 2 and A1 + A 2 = 1, , 20. A seven digit number is formed using digits, , 2, , (2n + 1) !, , 17. If the mirror image of the point (1, 3, 5) with, , 3, 3, 4, 4, 4, 5, 5. The probability, that number, so formed is divisible by 2, is, a., , 6, 7, , b., , 1, 7, , c., , 3, 7, , d., , 4, 7, , Section B : Numerical Type Questions, 21. Let z be those complex numbers which, satisfy |z + 5| ≤ 4 and z (1 + i) + z (1 − i) ≥ − 10,, i = −1. If the maximum value of| z + 1|2 is, α + β 2, then the value of (α + β) is ……… ., , 22. Let the normals at all the points on a given, curve pass through a fixed point (a , b). If the, curve passes through (3, − 3) and ( 4 , − 2 2), and given that a − 2 2b = 3, then, (a 2 + b2 + ab) is equal to ______., , 23. Let α and β be two real numbers, such that, α + β = 1and αβ = − 1. Let pn = (α ) n + (β) n ,, pn − 1 = 11and pn + 1 = 29, for some integer, n ≥ 1. Then, the value of pn2 is ______.
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62, , ONLINE, 1, , 2x 5 + 5x 4 + 10x 3 + 10x 2 + 10x + 10 lie in the, interval (a , a + 1). Then, |a| is equal to ______., , 24. If Im ⋅ n = ∫ x m − 1 (1 − x) n − 1 dx , for m , n ≥ 1and, 1x, , ∫0, , m −1, , 0, , + xn −1, , (1 + x) m +, , n, , JEE Main 2021 ~ Solved Papers, , dx = αIm ⋅ n , α ∈R , then α, , 29. Let X 1, X 2 , ..., X 18 be eighteen observations,, , equals _____ ., , such that, , 25. If the arithmetic mean and geometric mean, , greatest common divisor with 18 is 3,, is ______., , 18, , i =1, , i =1, , 2, , = 90,, , where α and β are distinct real numbers. If, the standard deviation of these observations, is 1, then the value of| α − β | is ______., , of the pth and qth terms of the sequence, –16, 8, –4, 2, ... satisfy the equation, 4 x 2 − 9x + 5 = 0, then p + q is equal to ______., , 26. The total number of 4-digit numbers whose, , 18, , ∑ (X i − α ) = 36 and ∑ (X i − β), , 0, 2 0 satisfies the, , 0 −1, 1 0 0, equation A 20 + αA19 + βA = 0 4 0 for, , , 0 0 1, some real numbers α and β, then β − α is, equal to ______., , 1, 30. If the matrix A = 0, 3, , 27. Let L be a common tangent line to the curves, 4 x 2 + 9 y 2 = 36 and (2x) 2 + (2 y ) 2 = 31. Then,, the square of the slope of the line L is ______., , 28. Let a be an integer, such that all the real, roots of the polynomial, , 0, , Answers, For solutions scan, the QR code, , Physics, 1. (d), 11. (a), 21. 60, , 2. (c), 12. (a), 22. 9, , 3. (a), 13. (d), 23. 1, , 4. (c), 14. (d), 24. 150, , 5. (c), 15. (d), 25. 3, , 6. (a), 16. (c), 26. 243, , 7. (b), 17. (b), 27. 7, , 8. (b), 18. (b), 28. 4, , 9. (c), 19. (a), 29. 25, , 10. (b), 20. (c), 30. 9, , 3. (c), 13. (a), 23. 2, , 4. (d), 14. (c), 24. 309, , 5. (a), 15. (a), 25. 1, , 6. (c), 16. (a), 26. 1, , 7. (c), 17. (b), 27. 6, , 8. (b), 18. (c), 28. 3, , 9. (c), 19. (a), 29. 14, , 10. (b), 20. (a), 30. 7, , 3. (b), 13. (a), 23. 324, , 4. (c), 14. (b), 24. 1, , 5. (d), 15. (b), 25. 10, , 6. (c), 16. (a), 26. 1000, , 9. (c), 19. (a), 29. 4, , 10. (c), 20. (c), 30. 4, , Chemistry, 1. (b), 11. (c), 21. 13, , 2. (b), 12. (c), 22. 147, , Mathematics, 1. (d), 11. (b), 21. 48, , 2. (a), 12. (b), 22. 9, , 7. (c), 17. (a), 27. 3, , 8. (d), 18. (a), 28. 2
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MARCH ATTEMPT ~ 16 March 2021, Shift I, , JEE Main 2021, 16 MARCH SHIFT I, , PHYSICS, Section A : Objective Type Questions, , a. −, , 1. One main scale division of a vernier callipers, is a cm and nth division of the vernier scale, coincide with (n − 1)th division of the main, scale. The least count of the callipers (in mm), is, 10 na, (n − 1), n − 1, c. , a, 10 n , a., , b., , 10 a, (n − 1), , d., , 10a, n, , parallel plate capacitor, a dielectric material of, dielectric constant K is used, which has the, same area as the plates of the capacitor. The, 3, thickness of the dielectric slab is d, where d, 4, is the separation between the plates of, parallel plate capacitor. The new capacitance, (C′) in terms of original capacitance (C 0) is, given by the following relation, 3+ K, C0, 4K, 4K, c. C ′ =, C0, K+3, , b., , F, F, cos θ − µ k g − sin θ, , , m, m, , c., , F, F, cos θ − µ k g + sin θ, , , m, m, , d., , F, F, cos θ + µ k g − sin θ, , , m, m, , 4. The pressure acting on a submarine is, , 2. For changing the capacitance of a given, , a. C ′ =, , F, F, cos θ − µ k g − sin θ, , , m, m, , 4+K, C0, 3, 4, d. C ′ =, C0, 3+ K, b. C ′ =, , 3 × 105 Pa at a certain depth. If the depth is, doubled, the percentage increase in the, pressure acting on the submarine would be, (Assume that atmospheric pressure is, 1× 105 Pa, density of water is 103kg m−3,, g = 10 ms −2), 200, %, 3, 5, c., %, 200, , a., , 200, %, 5, 3, d., %, 200, b., , 5. The angle of deviation through a prism is, minimum when, , 3. A block of mass m slides along a floor, while a, force of magnitude F is applied to it at an, angle θ as shown in figure. The coefficient of, kinetic friction is µ k. Then, the block's, acceleration a is given by, (g is acceleration due to gravity), F, , θ, , δ, , A. incident ray and emergent ray are, symmetric to the prism, B. the refracted ray inside the prism becomes, parallel to its base, C. angle of incidence is equal to that of the, angle of emergence, D. angle of emergence is double the angle of, incidence
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4, , ONLINE, Choose the correct answer from the options, given below., a. Statements (A), (B) and (C) are true., b. Only statement (D) is true., c. Only statements (A) and (B) are true., d. Statements (B) and (C) are true., , 11. Four equal masses, m each are placed at the, corners of a square of length (l) as shown in, the figure. The moment of inertia of the, system about an axis passing through A and, parallel to DB would be, , 500 MHz is travelling in vacuum along, y-direction. At a particular point in space and, time, B = 80, . × 10−8 z$ T . The value of electric, field at this point is, (speed of light = 3 × 108 ms −1;, $ y,, $ z$ are unit vectors along x , y and, x,, z-direction)., b. 2.6x$ V/m, d. −2.6x$ V/m, , 7. The maximum and minimum distance of a, , comet from the Sun are 16, . × 1012 m and, 10, 80, . × 10 m, respectively. If the speed of the, comet at the nearest point is 6 × 104ms −1,, then the speed at the farthest point is, a. 15, . × 103 m/s, c. 30, . × 103 m/s, , b. 60, . × 103 m/s, d. 4.5 × 103 m/s, , 8. A bar magnet of length 14 cm is placed in the, magnetic meridian with its North pole, pointing towards the geographic North pole., A neutral point is obtained at a distance of, 18 cm from the centre of the magnet. If, B H = 0.4 G, then the magnetic moment of the, magnet is, (1 G = 10−4T), a. 2.88 × 103 J T −1, b. 2.88 × 102 J T −1, c. 2.88 J T −1, d. 28.8 J T −1, , l, , b. 2ml 2, , mixture of three gases, 16 g of oxygen, 28 g, of nitrogen and 44 g of carbon dioxide at, absolute temperature T . Consider R as, universal gas constant. The pressure of the, mixture of gases is, 3RT, V, 4RT, d., V, , b., , m, B, , l, , c. 3ml 2, , d. 3ml 2, , 12. A conducting wire of length l, area of, , cross-section A and electric resistivity ρ is, connected between the terminals of a, battery. A potential difference V is developed, between its ends, causing an electric current., If the length of the wire of the same material, is doubled and the area of cross-section is, halved, the resultant current would be, 1 VA, 4 ρl, 1 ρl, c., 4 VA, , 3 VA, 4 ρl, VA, d. 4, ρl, b., , a., , 13. Time period of a simple pendulum is T inside, a lift, when the lift is stationary. If the lift, moves upwards with an acceleration g/2,, then the time period of pendulum will be, , c., , 88RT, V, 5 RT, c., 2V, , l, , T, 3, 2, d., T, 3, , a. 3T, , 9. The volume V of an enclosure contains a, , a., , C, m, , m, A, , a. 1ml 2, , l, , m, , D, , 6. A plane electromagnetic wave of frequency, , a. −24 x$ V/m, c. 24 x$ V/m, , JEE Main 2021 ~ Solved Papers, , b., , 3, T, 2, , 14. The velocity-displacement graph describing, the motion of a bicycle is shown in the, following figure., v(ms-1), 50, , 10. In thermodynamics, heat and work are, a. path functions, b. intensive thermodynamic state variables, c. extensive thermodynamic state variables, d. point functions, , 10, 0, , 200, , 400 x(m)
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5, , MARCH ATTEMPT ~ 16 March 2021, Shift I, The acceleration-displacement graph of the, bicycle’s motion is best described by, -2, , a(ms ), , 16. For an electromagnetic wave travelling in, free space, the relation between average, energy densities due to electric (U e ) and, magnetic (U m ) fields is, a. Ue = Um, , b. Ue > Um, , c. Ue < Um, , d. Ue ≠ Um, , 17. An R-C circuit as shown in the figure is driven, , a., , by an AC source generating a square wave., The output wave pattern monitored by CRO, would look close to, , 18, 2, 0, , 200, , 400, , x(m), , R, , a(ms-2), C, , CRO, , b., 18, 2, 0, , 200, , 400, , x(m), , a., , -2, , a(ms ), b., , c., 18, c., , 2, 0, , 200, , 400, , x(m), , a(ms-2), d., , d., , 18. The stopping potential in the context of, 18, 2, 0, , 200, , 400, , x(m), , 15. A 25 m long antenna is mounted on an, antenna tower. The height of the antenna, tower is 75 m. The wavelength (in m) of the, signal transmitted by this antenna would be, a. 300, b. 400, c. 200, d. 100, , photoelectric effect depends on the, following property of incident, electromagnetic radiation, a. phase, c. amplitude, , b. intensity, d. frequency, , 19. A block of 200 g mass moves with a uniform, speed in a horizontal circular groove, with, vertical side walls of radius 20 cm. If the block, takes 40 s to complete one round, the normal, force by the side walls of the groove is, a. 0.0314 N, c. 6.28 × 10−3 N, , b. 9.859 × 10−2 N, d. 9.859 × 10−4 N
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6, , ONLINE, , JEE Main 2021 ~ Solved Papers, , 20. A conducting bar of length L is free to slide, on two parallel conducting rails as shown in, the figure, C, , v, R1, , ×, , ×, B, , ×, , R2, , ×, , F = 20 N, , Two resistors R1 and R2 are connected across, the ends of the rails. There is a uniform, magnetic field B pointing into the page. An, external agent pulls the bar to the left at a, constant speed v., The correct statement about the directions of, induced currents I1 and I 2 flowing through R1, and R2 respectively is, a. both I1 and I 2 are in anti-clockwise direction., b. both I1 and I 2 are in clockwise direction., c. I1 is in clockwise direction and I 2 is in, anti-clockwise direction., d. I1 is in anticlockwise direction and I 2 is in, clockwise direction., , Section B : Numerical Type Questions, 21. In the figure given, the electric current, flowing through the 5 kΩ resistor is x mA., 3 kΩ, , 5 kΩ, , 3 kΩ, , Suppose the disc makes n number of, revolutions to attain an angular speed of, 50 rad s −1. The value of n to the nearest, integer, is ………. ., (Given, in one complete revolution, the disc, rotates by 6.28 rad.), , 24. The first three spectral lines of H-atom in the, , Balmer series are given λ 1 , λ 2 , λ 3, considering the Bohr atomic model, the, wavelengths of first and third spectral lines, λ1 , are related by a factor of approximately, λ3, x × 10−1. The value of x to the nearest integer,, is ……… ., , 25. The value of power dissipated across the, , Zener diode (Vz = 15 V) connected in the, circuit as shown in the figure is x × 10−1 W., Rs=35 Ω, , 3 kΩ, , 22 V, , Vz=15 V, , RL=90 Ω, , 21 V, 1 kΩ, , The value of x to the nearest Integer is …3… ., , 22. A fringe width of 6 mm was produced for, two slits separated by 1 mm apart. The, screen is placed 10 m away. The wavelength, of light used is x nm. The value of x to the, nearest integer is ……… ., , 23. Consider a 20 kg uniform circular disc of, radius 0.2 m. It is pin supported at its centre, and is at rest initially. The disc is acted upon, by a constant force F = 20 N through a, massless string wrapped around its, periphery as shown in the figure., , The value of x, to the nearest integer, is ……… ., , 26. A sinusoidal voltage of peak value 250 V is, applied to a series L-C-R circuit, in which, R = 8 Ω, L = 24 mH and C = 60µF. The value of, power dissipated at resonant condition is, x kW. The value of x to the nearest integer is, …… ., , 27. In the logic circuit shown in the figure, if, input A and B are 0 to 1 respectively, the, output at Y would be x. The value of x is …… .
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7, , MARCH ATTEMPT ~ 16 March 2021, Shift I, A, , Y, B, , V, I, I = (20 ± 02, . ) A. The percentage error in R is, x %. The value of x to the nearest integer, is……… ., , 28. The resistance R = , where V = (50 ± 2) V and, , 29. Consider a frame that is made up of two thin, massless rods AB and AC as shown in the, figure. A vertical force P of magnitude 100 N, is applied at point A of the frame., , A, 70°, , Suppose the force is P resolved parallel to the, arms AB and AC of the frame. The magnitude, of the resolved component along the arm AC is, x N. The value of x, to the nearest integer, is, ……… ., [Given, sin(35° ) = 0. 573,, cos(35° ) = 0.819, sin(110° ) = 0.939,, cos(110° ) = − 0. 342], , 30. A ball of mass 10 kg moving with a velocity, , 10 3 ms −1 along X-axis, hits another ball of, mass 20 kg, which is at rest. After collision,, the first ball comes to rest and the second, one disintegrates into two equal pieces. One, of the pieces starts moving along Y-axis at a, speed of 10 m/s. The second piece starts, moving at a speed of 20 m/s at an angle θ, (degree) with respect to the X-axis., The configuration of pieces after collision is, shown in the figure. The value of θ to the, nearest integer is ……… ., After collision, Y, , B, , P, , C, , θ, , X-axis, , 145°, , CHEMISTRY, Section A : Objective Type Questions, 1. Given below are two statements. One is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) Size of Bk3+ ion is less than, Np3+ ion., Reason (R) The above is a consequence of, the lanthanoid contraction., In the light of the above statements, choose, the correct answer from the options given, below, , a. A is false but R is true., b. Both A and R are true but R is not the correct, explanation of A., c. Both A and R are true and R is the correct, explanation of A., d. A is true but R is false., , 2. Which among the following pair of vitamins, is stored in our body relatively for longer, duration ?, a. Thiamine and vitamin A, b. Vitamin A and vitamin D, c. Thiamine and ascorbic acid, d. Ascorbic acid and vitamin D
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8, , ONLINE, , Choose the correct answer from the options, given below :, , 3. Given below are two statements., Statement I Both CaCl2 ⋅ 6H 2O and, MgCl2 ⋅ 8H 2O undergo dehydration on, heating., Statement II BeO is amphoteric, whereas, the oxides of other elements in the same, group are acidic., In the light of the above statements, choose, the correct answer from the options given, below., , a. A-(ii), B-(iii), C-(iv), D-(i), b. A-(iii), B-(iv), C-(i), D-(ii), c. A-(iii), B-(i), C-(iv), D-(ii), d. A-(iv), B-(i), C-(ii), D-(iii), , 6. Among the following, the aromatic, compounds are, A., , a. Statement I is false but statement II is true, b. Both statement I and statement II are false, c. Both statement I and statement II are true, d. Statement I is true but statement II is false, , 4., , JEE Main 2021 ~ Solved Papers, , CH2, , B., , D., , C., , ⊕, , O, O, , Choose the correct answer from the, following options., , i)DIBAL-H,Toluene,–78°C, , 'P', (Major product), , ii)H3O+, , The product P in the above reaction is, , a. Only (A) and (B), c. (B), (C) and (D), , 7., , b. Only (B) and (C), d. (A), (B) and (C), OH, , NH2, , COOH, a., NaNO2,HCI, 'A ', 'X', 273–278 K, , OH, , (Major product), CHO, , In the above chemical reaction, intermediate, X and reagent / condition A are, , b., , –, N+, 2 Cl, , O, O—C—H, , ; A -H2O/NaOH, , a. Xc., , NO2, CHO, , d., , –, N+, 2 Cl, , 5. Match List -I with List II., List-I, (Industrial process), , ; A -H2O/∆, , b. X-, , List-II, (Application), , A., , Haber’s process, , (i), , HNO 3 synthesis, , B., , Ostwald’s process, , (ii), , Aluminium extraction, , C., , Contact process, , (iii) NH3 synthesis, , D., , Hall-Heroult process (iv) H2SO 4 synthesis, , ; A -H2O/∆, , c. X-, , NO2, d. X-, , ; A -H2O/NaOH
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9, , MARCH ATTEMPT ~ 16 March 2021, Shift I, 8. Given below are two statements., , CH2, , Statement I The E ° value of Ce / Ce is, +174, . V., Statement II Ce is more stable in Ce 4+ state, than Ce 3+ state., In the light of the above statements, choose, the most appropriate answer from the, options given below., 4+, , a. Both statement I and statement II are correct., b. Statement I is incorrect but statement II is, correct., c. Both statement I and statement II are incorrect., d. Statement I is correct but statement II is, incorrect., , 9. The functions of antihistamine are, a. antiallergic and analgesic, b. antacid and antiallergic, c. analgesic and antacid, d. antiallergic and antidepressant, , 10. Which of the following is Lindlar catalyst ?, a. Zinc chloride and HCl, b. Cold dilute solution of KMnO 4, c. Sodium and liquid NH3, d. Partially deactivated palladised charcoal, H 3C, , 11., , OH, 20% H3PO4, 358 K, , H 3C, , 'A ', (Major product), , Cl, – +, , (CH3)3CO K, , 'B', (Major product), , The product A and B formed in above reactions, are, CH2, , a., , A-, , CH2, , BCH3, , CH3, , CH3, , 3+, , d., , A-, , B-, , 12. Given below are two statements., Statement I H 2O2 can act as both oxidising, and reducing agent in basic medium., Statement II In the hydrogen economy, the, energy is transmitted in the form of, dihydrogen. In the light of the above, statements, choose the correct answer from, the options given below :, a. Both statement I and statement II are false., b. Both statement I and statement II are true., c. Statement I is true but statement II is false., d. Statement I is false but statement II is true., , 13. The type of pollution that gets increased, during the day time and in the presence of, O3 is, a. reducing smog, c. global warming, , b. oxidising smog, d. acid rain, , 14. Assertion (A) Enol form of acetone, [CH 3COCH 3 ] exists in < 0.1% quantity., However, the enol form of acetyl acetone, [CH 3COCH 2OCCH 3 ] exists in approximately, 15% quantity., Reason (R) Enol form of acetyl acetone is, stabilised by intramolecular hydrogen, bonding, which is not possible in enol form, of acetone., Choose the correct statement., a. A is false but R is true., b. Both A and R are true and R is the correct, explanation of A., c. Both A and R are true but R is not the correct, explanation of A., d. A is true but R is false., , 15. Which of the following reaction does not, involve Hoffmann bromamide degradation?, O, , B-, , —, —, , b. A-, , CH2—C—NH2, , CH3, c., , A-, , CH2, B-, , a., , CH2—NH2, Br2,NaOH
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10, , ONLINE, CN, , 19. In chromatography technique, the, , NH2, , purification of compound is independent of, , i) KOH,H2O, , b., , a. mobility or flow of solvent system, b. solubility of the compound, c. length of the column or TLC plate, d. physical state of the pure compound, , ii) Br2,NaOH, , O, CH2—C—CH3, CH2NH2, , i)Br2,NaOH/H+, ii)NH3/∆, , c., O, d., , 20. A group 15 element, which is a metal and, forms a hydride with strongest reducing, power among group 15 hydrides. The, element is, , iii)LiAlH4/H2O, , Cl, , JEE Main 2021 ~ Solved Papers, , NH2, , a. Sb, , b. P, , c. As, , d. Bi, , i)NH2,NaOH, ii) Br2,NaOH, , 16. The process that involves the removal of, sulphur from the ores is, a. smelting, c. leaching, , b. roasting, d. refining, , 17. Match List-I with List-II., List-I, (Name of oxo acid), , List-II, (Oxidation, state of P), , A., , Hypophosphorus acid (i), , +5, , B., , Orthophosphoric acid, , (ii), , +4, , C., , Hypophosphoric acid, , (iii), , +3, , D. Orthophosphorus acid (iv), , +2, , (v), , +1, , Choose the correct answer from the options, given below :, a. A-(v), B-(i), C-(ii), D-(iii), b. A-(iv), B-(i), C-(ii), D-(iii), c. A-(iv), B-(v), C-(ii), D-(iii), d. A-(v), B-(iv), C-(ii), D-(iii), , 18. Given below are two statements : one is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) The H O H bond angle in, water molecule is 104.5°., Reason (R) The lone pair - lone pair, repulsion of electrons is higher than the, bond pair - bond pair repulsion., a. A is false but R is true., b. Both A and R are true, but R is not the correct, correct explanation of A., c. A is true but R is false., d. Both A and R are true, and R is the correct, explanation of A., , Section B : Numerical Type Questions, 21. For the reaction, A(g), B(g) at 495 K,, , -, , ∆ rG ° = − 9.478 kJ mol−1., If we start the reaction in a closed container, at 495 K with 22 millimoles of A, the amount, of B is the equilibrium mixture is ………, millimoles (Round off to the nearest integer)., [R = 8.314 J mol−1 K −1, ln10 = 2303, ], ., , 22. Complete combustion of 750 g of an organic, compound provides 420 g of CO2 and 210 g, of H 2O. The percentage composition of, carbon and hydrogen in organic compound, is 15.3 and …… respectively (Round off to the, nearest integer)., , 23. 2MnO−4 + bC 2O24− + cH+ → x Mn2++ yCO2 + zH2O, If the above equation is balanced with, integer coefficients, the value of c is ……… ., , 24. AB 2 is 10% dissociated in water to A 2+ and B − ., The boiling point of a 10.0 molal aqueous, solution of AB 2 is …… °C (Round off to the, nearest integer)., [Given, molal elevation constant of water, K b = 0.5K kg mol−1 boiling point of, pure water = 100° C], , 25. The equivalents of ethylene diamine, required to replace the neutral ligands from, the coordination sphere of the, trans-complex of COCl3 ⋅ 4NH 3 is …… (Round, off to the nearest integer)., , 26. A 6.50 molal solution of KOH (aq) has a, denisity of 1.89 g cm−3. The molarity of the, solution is …… mol dm−3 (Round off to the, nearest integer)., [Atomic masses: K : 39.0 u, O : 16.0u, H : 1.0 u]
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11, , MARCH ATTEMPT ~ 16 March 2021, Shift I, 27. When light of wavelength 248 nm falls on a, , 29. A certain element crystallises in a bcc lattice, , metal of threshold energy 3.0 eV, the, de- Broglie wavelength of emitted electrons, is …… Å., , of unit cell edge length 27Å. If the same, element under the same conditions, crystallises in the fcc lattice, the edge length, of the unit cell in Å will be ……, (Round off to the nearest integer), [Assume each lattice point has a single atom ], [Assume 3 = 173, . , 2 = 141, . ], , [Round off to the nearest integer], [Use: 3 = 173, . , h = 663, . × 10−34 Js, me = 9.1× 10−31 kg, c = 3.0 × 108ms −1,, 1eV = 16, . × 10−19 J ], , 28. Two salts A2X and MX have the same value of, −12, , solubility product of 4.0 × 10 . The ratio of, S (A2 X ), their molar solubilities i.e, = ……, S (MX ), (Round off to the nearest integer), , 30. The decomposition of formic acid on gold, surface follows first order kinetics. If the rate, constant at 300K is 10, . × 10−3s −1 and the, activation energy, E a = 11.488 kJ mol−1, the, rate constant at 200 K is …… ×10−5s −1 (Round, off to the nearest integer)., [Given, R = 8.314 J mol−1 K −1], , MATHEMATICS, Section A : Objective Type Questions, 1. The number of elements in the set, { x ∈ R: (|x| − 3)|x + 4| = 6} is equal to, a. 3, c. 4, , b. 2, d. 1, , 2. Let a vector α $i + β$j be obtained by rotating, the vector 3$i + $j by an angle 45° about the, origin in counterclockwise direction in the, first quadrant. Then the area of triangle, having vertices (α, β), (0, β) and (0,0) is equal, to, a., , 1, 2, , b. 1, , c., , 1, 2, , d. 2 2, , 3. If for a > 0, the feet of perpendiculars from, the points A(a ,–2a , 3) and B(0, 4, 5) on the, plane lx + my + nz = 0 are points C (0, – a, –1), and D respectively, then, the length of line, segment CD is equal to, a. 31, c. 55, , b. 41, d. 66, , 4. Consider three observations a , b and c, such, that b = a + c. If the standard deviation of, a + 2, b + 2, c + 2 is d, then which of the, following is true?, a. b 2 = 3(a 2 + c 2 ) + 9d 2 b. b 2 = a 2 + c 2 + 3d 2, c. b 2 = 3(a 2 + c 2 + d 2 ) d. b 2 = 3(a 2 + c 2 ) −9d 2, , π, , 5. If for x ∈ 0, , log 10 sin x + log 10 cos x = −1, 2, 1, (log 10 n − 1), n > 0,, 2, then the value of n is equal to, and log 10(sin x + cos x) =, a. 20, c. 9, , b. 12, d. 16, , −i , , i = −1. Then, the system of, i , x 8 , linear equations A 8 = has, y 64 , i, −i, , 6. Let A = , , a. a unique solution, b. infinitely many solutions, c. no solution, d. exactly two solutions, , 7. If the three normals drawn to the parabola,, y 2 = 2x pass through the point (a , 0), a ≠ 0,, then a must be greater than, a., , 1, 2, , b. −, , 1, 2, , c. −1, , d. 1, , 8. Let the position vectors of two points P and Q, be 3$i − $j + 2k$ and $i + 2$j − 4k$ , respectively. Let, R and S be two points such that the direction, ratios of lines PR and QS are (4, −1, 2) and, (−2, 1, −2), respectively. Let lines PR and, QS intersect at T . If the vector TA is, perpendicular to both PR and QS and the
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12, , JEE Main 2021 ~ Solved Papers, , ONLINE, length of vector TA is 5 units, then the, modulus of a position vector of A is, a. 482, c. 5, , b. 171, d. 227, , 9. Let the functions f :R → R and g :R → R be, defined as, x + 2, x < 0, f (x ) = 2, x≥0, x ,, , b. 1, , j=0, , c. 0, , d. 2, , a tautology?, a. (p ∧ q ) ∨ (p ∨ q ), c. (p ∧ q ) ∧ (p → q ), , b. (p ∧ q ) ∨ (p → q ), d. (p ∧ q ) → (p → q ), , 11. Let a complex number z ,|z|≠ 1,, , 2, , |z| + 11 , ≤ 2. Then, the largest, , 2, (|z| − 1) , , value of|z| is equal to, a. 8, , b. 7, , expansion of (3, divisible by, , c. 6, , a. 26, c. 8, , +5, , ) , then ( n − 1) is, , 1/ 8 60, , b. 30, d. 7, , y+4 z+2, . If plane P, =, =, 1, 2, 3, divides the line segment AB joining points, A( −3, − 6, 1) and B (2, 4 , − 3) in ratio k : 1, then, the value of k is equal to, a. 1.5, , 1− x, , b. 3, , c. 2, , d. 4, , 14. The range of a ∈ R for which the function, f ( x) = ( 4a − 3)( x + log e 5) + 2(a − 7), x, x, cot sin2 , x ≠ 2 nπ, n ∈ N, has critical, 2, 2, points, is, a. (−3, 1), c. [ 1, ∞ ), , 3n , 2 , , 3 n −1, 2 , , j=0, , j=0, , Σ a2 j + 4, , 4, b. − , 2, 3 , d. (−∞ , − 1], , Σ a2 j + 1is equal to, b. 2n − 1, d. n, , a. 2, c. 1, , 17. If y = y ( x) is the solution of the differential, equation,, π, dy, + 2 y tan x = sin x , y = 0, then the, 3, dx, maximum value of the function y ( x) over R is, equal to, b., , d. 5, , 13. Let P be a plane lx + my + nz = 0 containing, the line,, , then, , a. 8, , 12. If n is the number of irrational terms in the, 1/ 4, , 52, 867, 22, d., 425, b., , 3n, , 10. Which of the following Boolean expression is, , 1, , 3, 4, 39, c., 50, a., , equal to x. If for n ∈ N, (1 − x + x 3) n = Σ a j x j ,, , Then, the number of points in R, where ( fog )(x ), is NOT differentiable is equal to, , satisfy log, , cards are drawn randomly and are found to, be spades. The probability that the missing, card is not a spade, is, , 16. Let [ x ] denote greatest integer less than or, , x3 ,, x<1, and g (x ) = , 3x − 2, x ≥ 1, , a. 3, , 15. A pack of cards has one card missing. Two, , 1, 2, , c. −, , 15, 4, , d., , 1, 8, , 18. The locus of the mid-points of the chord of, , the circle, x 2 + y 2 = 25 which is tangent to the, x2 y2, hyperbola,, −, = 1 is, 9, 16, a. (x 2 +, b. (x 2 +, c. (x 2 +, d. (x 2 +, , y 2 ) 2 − 16x 2 + 9 y 2 = 0, y 2 ) 2 − 9x 2 + 144 y 2 = 0, y 2 ) 2 − 9x 2 − 16 y 2 = 0, y 2 ) 2 − 9x 2 + 16 y 2 = 0, , 19. The number of roots of the equation,, 2, , (81) sin, , x, , + (81) cos, , 2, , x, , = 30 in the interval [0, π ] is, , equal to, a. 3, c. 8, , b. 4, d. 2, k, , , 6r, . Then, lim S k, 2r+ 1, 2 r+ 1, k→ ∞, +3, , 2, , , 20. Let S k = Σ tan−1, r=1, , is equal to, 3, a. tan −1 , 2, 3, c. cot −1 , 2, , b., , π, 2, , d. tan −1(3)
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13, , MARCH ATTEMPT ~ 16 March 2021, Shift I, Section B : Numerical Type Questions, 21. Consider an arithmetic series and a, geometric series having four initial terms, from the set {11, 8, 21, 16, 26, 32, 4}. If the, last terms of these series are the maximum, possible four digit numbers, then the, number of common terms in these two, series is equal to……… ., , 22. Let f : (0, 2) → R be defined as, πx , , f (x ) = log 2 1 + tan ., , 4 , 2 1, 2, , Then, lim, f + f + K+ f (1) is equal, , n→ ∞ n , , , , , n, n, , to……… ., , 23. Let ABCD be a square of side of unit length., Let a circle C 1 centred at A with unit radius is, drawn. Another circle C 2, which touches C 1, and the lines AD and AB are tangent to it, is, also drawn. Let a tangent line from the point, C to the circle C 2 meet the side AB at E. If the, length of EB is α + 3 β, where α, β are, integers, then α + β is equal to …… ., , 24. If lim, , ae x − bcos x + ce − x, , x→ 0, , x sin x, equal to ……… ., , = 2 , then a + b + c is, , 25. The total number of 3 × 3 matrices A having, entries from the set (0, 1, 2, 3), such that the, sum of all the diagonal entries of AAT is 9, is, equal to ……… ., , 26. Let, , −30 20 56 , P = 90 140 112 and, , , 120 60 14 , , 2 7, ω2 , , , 1 , A = −1 −ω, 0 −ω −ω + 1, , , , where, ω =, , −1 + i 3, , , and I3 be the identity, 2, matrix of order 3. If the determinant of the, matrix (P −1AP − I3) 2 is αω 2, then the value of α, is equal to……… ., , 27. If the normal to the curve, x, , y ( x) = ∫ (2t 2 − 15t + 10)dt at a point (a , b) is, 0, , parallel to the line x + 3 y = − 5, a > 1, then the, value of|a + 6b| is equal to……… ., , 28. Let the curve y = y ( x) be the solution of the, dy, = 2( x + 1)., dx, If the numerical value of area bounded by, 4 8, the curve y = y ( x) and x-axis is, , then the, 3, value of y(1) is equal to……… ., , differential equation, , 29. Let f : R → R be a continuous function such, that f ( x) + f ( x + 1) = 2, for all x ∈ R . If, I1 =, , 8, , 3, , 0, , −1, , ∫ f (x)dx and I2 = ∫ f (x)dx, then the value of, , I1 + 2I2 is equal to……… ., , 30. Let z and w be two complex numbers, such, z + i, = 1and Re(w) has, that w = zz − 2z + 2,, z − 3i, , minimum value. Then, the minimum value of, n ∈ N for which w n is real, is equal to
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14, , ONLINE, , JEE Main 2021 ~ Solved Papers, , Answers, For solutions scan, the QR code, , Physics, 1. (d), 11. (c), 21. (3), , 2. (c), 12. (a), 22. (600), , 3. (b), 13. (d), 23. (20), , 4. (a), 14. (a), 24. (15), , 5. (a), 15. (d), 25. (5), , 6. (a), 16. (a), 26. (4), , 7. (c), 17. (c), 27. (0), , 8. (c), 18. (d), 28. (5), , 9. (c), 19. (d), 29. (82), , 10. (a), 20. (c), 30. (30), , 3. (b), 13. (b), 23. (16), , 4. (b), 14. (b), 24. (106), , 5. (c), 15. (c), 25. (2), , 6. (b), 16. (b), 26. (9), , 7. (c), 17. (a), 27. (9), , 8. (d), 18. (d), 28. (50), , 9. (b), 19. (d), 29. (33), , 10. (d), 20. (d), 30. (10), , 3. (d), 13. (c), 23. (1), , 4. (d), 14. (b), 24. (4), , 5. (b), 15. (c), 25. (766), , 6. (c), 16. (c), 26. (36), , 7. (d), 17. (d), 27. (406), , 8. (b), 18. (d), 28. (2), , 9. (b), 19. (b), 29. (16), , 10. (d), 20. (c), 30. (4), , Chemistry, 1. (d), 11. (c), 21. (20), , 2. (b), 12. (b), 22. (3), , Mathematics, 1. (b), 11. (b), 21. (3), , 2. (a), 12. (a), 22. (1)
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MARCH ATTEMPT ~ 16 March 2021, Shift II, , JEE Main 2021, 16 MARCH SHIFT II, , PHYSICS, Section A : Objective Type Questions, , a circular tap, when its flow rate increased, from 0.18 L/min to 0.48 L/min ? The radius of, the tap and viscosity of water are 0.5 cm and, 10−3 Pa-s, respectively., (Density of water = 10 3 kg/m 3 ), , 1. The following logic gate is equivalent to, A, Y, B, , a. NOR Gate, c. AND Gate, , 4. What will be the nature of flow of water from, , b. OR Gate, d. NAND Gate, , 2. A large block of wood of mass M = 599, . kg is, hanging from two long massless cords. A, bullet of mass m = 10 g is fired into the block, and gets embedded in it. The system (block +, bullet) then swing upwards, their centre of, mass rising a vertical distance h = 98, . cm, before the (block + bullet) pendulum comes, momentarily to rest at the end of its arc. The, speed of the, bullet just before collision is, (Take g = 9.8 ms −2 ), , a. Unsteady to steady flow, b. Remains steady flow, c. Remains turbulent flow, d. Steady flow to unsteady flow, , 5. A mosquito is moving with a velocity, , v = (05, . t 2i$ + 3t $j + 9k$ ) m/s and accelerating in, uniform conditions. What will be the, direction of mosquito after 2s?, 2, a. tan −1 from X-axis, 3, 2, b. tan −1 from Y-axis, 3, 5, c. tan −1 from Y-axis, 2, 5, d. tan −1 from X-axis, 2, , 6. Find out the surface charge density at the, , h, m, , M, , v, , a. 841.4 m/s, c. 831.4 m/s, , b. 811.4 m/s, d. 821.4 m/s, , intersection of point X = 3 m plane and, X-axis, in the region of uniform line charge of, 8 nC/m lying along the Z-axis in free space., a. 0.424 nC m−2, c. 0.07 nC m−2, , b. 47.88 nC m−2, d. 4.0 nC m−2, , 7. The de-Broglie wavelength associated with, , magnetic field B . Find the value of work, done by B., , an electron and a proton were calculated by, accelerating them through same potential of, 100 V. What should nearly be the ratio of, their wavelengths? (m p = 100727, ., u,, m e = 000055, ., u), , a. 1, c. Zero, , a. 1860 : 1, c. 41.4 : 1, , 3. A charge Q is moving dI distance in the, b. Infinite, d. −1, , b. (1860) 2 : 1, d. 43 : 1
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16, , ONLINE, , 8. For the given circuit, comment on the type of, transformer used., Il, , 220 V, , IL 0.11 A, p, , s, , L, O, 60 W V2, A, D, , JEE Main 2021 ~ Solved Papers, , 13. A bimetallic strip consists of metals A and B., It is mounted rigidly as shown. The metal, A has higher coefficient of expansion, compared to that of metal B. When the, bimetallic strip is placed in a cold bath, it will, , A, , a. Auxilliary transformer, b. Auto transformer, c. Step-up transformer, d. Step down transformer, , 9. The half-life of Au198 is 2.7 days. The activity, of 1.50 mg of Au198 if its atomic weight is, 198 g mol−1 is (NA = 6 × 1023 / mol), a. 240 Ci, c. 535 Ci, , b. 357 Ci, d. 252 Ci, , 10. Calculate the value of mean free path ( λ ) for, oxygen molecules at temperature 27°C and, pressure 101, . × 105 Pa. Assume the molecular, diameter 0.3 nm and the gas is ideal., (k = 138, . × 10−23 JK −1), a. 58 nm, c. 86 nm, , b. 32 nm, d. 102 nm, , 11. The refractive index of a converging lens is, 1.4. What will be the focal length of this lens, if it is placed in a medium of same refractive, index ? (Assume the radii of curvature of the, faces of lens are R1 and R 2 respectively), a. 1, RR, c. 1 2, R1 − R 2, , b. Infinite, d. Zero, , 12. In order to determine the Young's modulus, of a wire of radius 0.2 cm (measured using, a scale of least count = 0001, cm) and length, ., 1m (measured using a scale of least count, = 1mm), a weight of mass 1kg (measured, using a scale of least count = 1g) was hanged, to get the elongation of 0.5 cm (measured, using a scale of least count 0.001 cm). What, will be the fractional error in the value of, Young's modulus determined by this, experiment ?, a. 0.14%, c. 9%, , b. 0.9%, d. 1.4%, , B, , a. bend towards the right, b. not bend but shrink, c. Neither bend nor shrink, d. bend towards the left, , 14. A resistor develops 500 J of thermal energy, in 20 s, when a current of 1.5 A is passed, through it. If the current is increased from, 1.5 A to 3 A, what will be the energy, developed in 20 s?, a. 1500 J, c. 500 J, , b. 1000 J, d. 2000 J, , 15. Statement I A cyclist is moving on an, , unbanked road with a speed of 7 kmh−1 and, takes a sharp circular turn along a path of, radius of 2 m without reducing the speed., The static friction coefficient is 0.2. The, cyclist will not slip and pass the curve, (g = 9.8 m / s 2 ), Statement II If the road is banked at an angle, of 45°, cyclist can cross the curve of 2 m radius, with the speed of 18.5 kmh−1 without slipping., In the light of the above statements, choose, the correct answer from the options given, below., a. Statement I is false and statement II is true., b. Statement I is true and statement II is false., c. Both statement I and statement II are false., d. Both statement I and statement II are true., , 16. Two identical antennas mounted on identical, towers are separated from each other by a, distance of 45 km. What should nearly be the, minimum height of receiving antenna to, receive the signals in line of sight ?, (Assume, radius of earth is 6400 km.), a. 19.77 m, c. 79.1 m, , b. 39.55 m, d. 158.2 m
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17, , MARCH ATTEMPT ~ 16 March 2021, Shift II, 17. The magnetic field in a region is given by, , (Round off to the nearest integer), , x, B = B 0 k$ . A square loop of side d is placed, a, with its edges along the X and Y-axes. The, loop is moved with a constant velocity, v = v 0$i . The emf induced in the loop is, Y, , d, , K, , Z, d, , d/2, d, , B v 2d, a. 0 0, 2a, B0v 0d 2, c., a, , X, , Bv d, b. 0 0, 2a, B0v 0d 2, d., 2a, , 18. Amplitude of a mass-spring system, which is, executing simple harmonic motion, decreases with time. If mass = 500 g, decay, constant = 20 g/s, then how much time is, required for the amplitude of the system to, drop to half of its initial value ? (ln 2 = 0.693), a. 34.65 s, c. 0.034 s, , b. 17.32 s, d. 15.01 s, , 19. Calculate the time interval between 33%, decay and 67% decay if half-life of a, substance is 20 min., a. 60 min, c. 40 min, , b. 20 min, d. 13 min, , 20. Red light differs from blue light as they have, a. different frequencies and different, wavelengths, b. different frequencies and same wavelengths, c. same frequencies and same wavelengths, d. same frequencies and different wavelengths, , Section B : Numerical Type Questions, 21. The energy dissipated by a resistor is 10 mJ, in 1s when an electric current of 2 mA flows, through it. The resistance is ……… Ω., (Round off to the nearest integer), , 22. In a parallel plate capacitor set up, the plate, area of capacitor is 2 m2 and the plates are, separated by 1m. If the space between the, plates are filled with a dielectric material of, thickness 0.5 m and area 2 m2 (see figure), the capacitance of the set-up will be …… ε 0., (Dielectric constant of the material = 3.2), , 23. A force F = 4 i$ + 3$j + 4k$ is applied on an, intersection point of x = 2 plane and X-axis., The magnitude of torque of this force about, a point (2, 3, 4) is …… ., (Round off to the nearest integer), , 24. If one wants to remove all the mass of the, earth to infinity in order to break it up, completely. The amount of energy that, x GM 2, needs to be supplied will be, , where x, 5 R, is ……… ., (Round off to the nearest integer), (M is the mass of earth, R is the radius of earth, and G is the gravitational constant.), , 25. A deviation of 2° is produced in the yellow, ray when prism of crown and flint glass are, achromatically combined. Taking dispersive, powers of crown and flint glass are 0.02 and, 0.03 respectively and refractive index for, yellow light for these glasses are 1.5 and 1.6,, respectively. The refracting angles for crown, glass prism will be ……° (in degree)., (Round off to the nearest integer), , 26. A body of mass 2 kg moves under a force of, , (2i$ + 3$j + 5k$ )N. It starts from rest and was at, the origin initially. After 4 s, its new, coordinates are (8, b, 20). The value of b is, ……… ., (Round off to the nearest integer), , 27. A swimmer can swim with velocity of 12 km/h, in still water. Water flowing in a river has, velocity 6 km/h. The direction with respect to, the direction of flow of river water he should, swim in order to reach the point on the, other bank just opposite to his starting point, is ………° (in degree)., (Round off to the nearest integer)
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18, , ONLINE, , 28. A closed organ pipe of length L and an open, , JEE Main 2021 ~ Solved Papers, , (Round off to the nearest integer), (g = acceleration due to gravity), (θ = angle as shown in figure), , organ pipe contain gases of densities ρ1 and, ρ2 respectively. The compressibility of gases, are equal in both the pipes. Both the pipes, are vibrating in their first overtone with, same frequency. The length of the open pipe, x ρ, is L 1 where x is …… ., 3 ρ2, , a, P, , θ, , (Round off to the nearest integer), , 29. A solid disc of radius a and mass m rolls, down without slipping on an inclined plane, making an angle θ with the horizontal. The, 2, acceleration of the disc will be gsinθ, where, b, b is ……… ., , 30. For an ideal heat engine, the temperature of, the source is 127°C. In order to have 60%, efficiency the temperature of the sink should, be …… °C., (Round off to the nearest integer), , CHEMISTRY, Section A : Objective Type Questions, , 4. Identify the elements X and Y using the, ionisation energy values given below., , 1. The green house gas/es is (are), (A), (B), (C), (D), , carbon dioxide, oxygen, water vapour, methane, , Ionisation energy (Ist), , Choose the most appropriate answer from the, options given below., a. Only (A) and (C), b. Only (A), c. (A), (C) and (D), d. Only (A) and (B), , 2., , CH3, , kJ/mol (IInd), , X, , 495, , 4563, , Y, , 731, , 1450, , a. X = Na, Y = Mg, c. X = Mg, Y = Na, , b. X = Mg, Y = F, d. X = F, Y = Mg, , 5., , Cl, ′A ′, , COOH, ′A′, Cl, , OCH3, , OCH3, , In the above reaction, the reagent ‘A’ is, +, , a. NaBH4 , H3O, b. LiAIH4, c. Alkaline KMNO 4 ,H +, d. HCl, Zn - Hg, , a. A = HCl, anhydrous AlCl3, b. A = HCl, ZnCl2, c. A = Cl2 , UV light, d. A = Cl2 , dark, anhydrous AlCl3, , 6. The secondary structure of protein is, , 3. Which of the following reduction reaction, cannot be carried out with coke?, a. Al2O 3 → Al, c. Fe2O 3 → Fe, , Identify the reagent(s) ‘A’ and condition(s) for, the reaction:, , b. ZnO → Zn, d. Cu 2O → Cu, , stabilised by, a. peptide bond, b. glycosidic bond, c. hydrogen bonding, d. van der Waals’ forces
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19, , MARCH ATTEMPT ~ 16 March 2021, Shift II, 7. Fex 2 and Fey 3 are known when x and y are, a. x = F, Cl, Br, I and y = F, Cl and Br, b. x = F, Cl, Br and y = F, Cl, Br and I, c. x = Cl, Br, I and y = F, Cl, Br and I, d. x = F, Cl, Br, I and y = F, Cl, Br and I, , 8. Which of the following polymer is used in the, manufacture of wood laminates ?, a. cis-polyisoprene, b. Melamine formaldehyde resin, c. Urea formaldehyde resin, d. Phenol and formaldehyde resin, , 9. Statement I Sodium hydride can be used as, an oxidising agent., Statement II The lone pair of electrons on, nitrogen in pyridine makes it basic., Choose the correct answer from the options, given below., a. Both statement I and statement II are true, b. Both statement I and statement II are false, c. Statement I is true but statement II is false, d. Statement I is false but statement II is true, , 10. The incorrect statement regarding the, structure of C 60 is, a. the six-membered rings are fused to both six, and five-membered rings, b. each carbon atom forms three sigma bonds, c. the five-membered rings are fused only to, six-membered rings, d. it contains 12 six-membered rings and, 24 five-membered rings, , 11. The correct statements about H2O2 are, a. used in the treatment of effluents., b. used as both oxidising and reducing agents., c. the two hydroxyl groups lie in the same, plane., d. miscible with water., , 13. An unsaturated hydrocarbon X on ozonolysis, gives A. Compound A when warmed with, ammonical silver nitrate forms a bright silver, mirror along the sides of the test tube. The, unsaturated hydrocarbon X is, CH3, |, b. CH3 C ==, , a. CH 3 C === C CH 3, , , CH3 CH3, c. HC ≡≡ C CH2 CH3 d. CH3 C ≡≡ C CH3, , 14. Which of the following is least basic?, ••, , ••, , a. (CH3CO) NHC 2H5, , b. (C 2H5 ) 3 N, , c. (CH3CO) 2 NH, , d. (C 2H5 ) 2 NH, , ••, , ••, , 15. The characteristics of elements X , Y and Z, with atomic numbers, respectively, 33, 53, and 83 are, a. X and Y are metalloids and Z is a metal, b. X is a metalloid, Y is a non-metal and Z is a, metal, c. X , Y and Z are metals, d. X and Z are non-metals and Y is a metalloid, , 16. Match List-I with List-II., List-I, (Test / Reagents /, Observation(s)), , List-II, (Species detected), , A., , Lassaigne’s test, , (i), , Carbon, , B., , Cu(II) oxide, , (ii), , Sulphur, , C., , Silver nitrate, , (iii) N, S, P, and, halogen, , D., , The sodium fusion (iv) Halogen, extract gives black, specifically, precipitate with, acetic acid and lead, acetate, , Choose the correct answer from the options, given below., , The correct match is, , a. (A), (B), (C) and (D), c. (B), (C) and (D), , a. A-(iii), B-(i), C-(ii), D-(iv) b. A-(i), B-(iv), C-(iii), D-(ii), c. A-(iii), B-(i), C-(iv), D-(ii) d. A-(i), B-(ii), C-(iv), D-(iii), , b. (A), (B) and (D), d. (A), (C) and (D), , 12. Ammonolysis of alkyl halides followed by the, treatment with NaOH solution can be used, to prepare primary, secondary and tertiary, amines. The purpose of NaOH in the, reaction is, a. to remove basic impurities, b. to activate NH 3 used in the reaction, c. to remove acidic impurities, d. to increase the reactivity of alkyl halide, , 17. The incorrect statements below regarding, colloidal solutions is, a. a colloidal solution shows colligative properties, b. an ordinary filter paper can stop the flow of, colloidal particles, c. the flocculating power of Al3 + is more than, that of Na +, d. a colloidal solution shows Brownian motion of, colloidal particles
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20, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 18. Arrange the following metal, , 23. A and B decompose via first order kinetics, , complex/compounds in the increasing order, of spin only magnetic moment. Presume all, the three, high spin system., (Atomic numbers Ce = 58, Gd = 64 and Eu = 63.), A. (NH4 ) 2 [Ce(NO3 ) 6 ], B. Gd(NO3 ) 3 and, C. Eu(NO3 ) 3, a. (B) < (A) < (C), c. (A) < (B) < (C), , b. (C) < (A) < (B), d. (A) < (C) < (B), , 19. The exact volumes of 1 M NaOH solution, required to neutralise 50 mL of 1 M H 3PO3, solution and 100 mL of 2 M H 3PO2 solution,, respectively, are, a. 100 mL and 100 mL, c. 100 mL and 200 mL, , b. 100 mL and 50 mL, d. 50 mL and 50 mL, , CN, , 20., , (i)C6H5MgBr, (1.0 equivalent), Dry ether, , OCH3, NH2, , a., , 24. In Duma's method of estimation of nitrogen,, 0.1840 g of an organic compound gave 30 mL, of nitrogen collected at 287 K and 758 mm of, Hg pressure. The percentage composition of, nitrogen in the compound is ……… ., (Round off to the nearest integer)., [Given: Aqueous tension at 287 K = 14 mm of Hg], , 25. The number of orbitals with n = 5, m l = +2 is, ……… . (Round off to the nearest integer)., , 26. At 363 K, the vapour pressure of A is 21 kPa, , X, (Major product), , (ii)H3O+, , with half-lives 54.0 min and 18.0 min, respectively. Starting from an equimolar, non-reactive mixture of A and B, the time, taken for the concentration of A to become 16, times that of B is ……… min., (Round off to the nearest integer)., , NH2, , b., , and that of B is 18 kPa. One mole of A and, 2 moles of B are mixed. Assuming that this, solution is ideal, the vapour pressure of the, mixture is ……… kPa. (Round off to the, nearest integer)., , 27. Sulphurous acid (H2SO3) has K a1 = 17, . × 10−2, , and K a = 6.4 × 10−8 . The pH of 0.588 M is ……, 2, , c., , C6H5, , OCH3, , O, , O, C6H5, , d., , (Round off to the nearest integer), , 28. When 35 mL of 0.15 M lead nitrate solution, C6H5, , C6H5, OCH3, , Section B : Numerical Type Questions, 21. Ga (atomic mass 70 u) crystallises in a, hexagonal close packed structure. The total, number of voids in 0.581 g of Ga is ……, × 10 21. (Round off to the nearest integer)., , 22. A 5.0 m mol dm−3 aqueous solution of KCl, has a conductance of 0.55 mS when, measured in a cell constant 1.3 cm−1., The molar conductivity of this solution is ……, mSm2 mol−1., (Round off to the nearest integer), , is mixed with 20 mL of 0.12 M chromic, sulphate solution, ……… ×10–5 moles of lead, sulphate precipitate out. (Round off to the, nearest integer)., , 29. At 25°C, 50 g of iron reacts with HCl to form, FeCl2. The evolved hydrogen gas expands, against a constant pressure of 1 bar. The, work done by the gas during this expansion, is …… J. (Round off to the nearest integer), [Given, R = 8.314 J mol–1 K –1. Assume, hydrogen, is an ideal gas], [Atomic mass off Fe is 55.85 u], , 30. [Ti(H2O) 6 ]3+ absorbs light of wavelength, 498 nm during a d-d transition. The, octahedral splitting energy for the above, complex is ……… × 10−9 J (Round off to the, nearest intger). [h = 6626, ., × 10−34 Js,, 8, −1, c = 3 × 10 ms ]
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21, , MARCH ATTEMPT ~ 16 March 2021, Shift II, , MATHEMATICS, Section A : Objective Type Questions, , 5. Consider the integral, 10, , 1. The maximum value of, sin2 x, 1 + cos 2 x cos 2x, 2, f (x ) = 1 + sin x, cos 2 x, cos 2x , x ∈ R is, 2, sin x, cos 2 x, sin2x, a. 7, c. 5, , 3, 4, d. 5, b., , 2. Let A denote the event that a 6-digit integer, formed by 0, 1, 2, 3, 4, 5, 6 without, repetitions, be divisible by 3. Then,, probability of event A is equal to, 9, 56, 3, c., 7, a., , 4, 9, 11, d., 27, , b., , 3. Let α ∈R be such that the function, cos −1(1 − { x } 2)sin−1(1 − { x }), , x ≠0, , f ( x) = , {x} − {x}3, , α, , x =0, , is continuous at x = 0, where { x } = x − [ x ],[ x ] is, the greatest integer less than or equal to x., Then,, π, 2, b. α = 0, c. no such α exists, π, d. α =, 4, , a. α =, , [ x ]e[x ], ∫ e x − 1 dx,, 0, , where [ x ] denotes the greatest integer less than, or equal to x . Then, the value of I is equal to, a. 9(e − 1), c. 45(e − 1), , b. 45(e + 1), d. 9(e + 1), , 6. Let C be the locus of the mirror image of a, , point on the parabola y 2 = 4 x with respect to, the line y = x . Then, the equation of tangent, to C at P(2, 1) is, a. x − y = 1, b. 2x + y = 5, c. x + 3 y = 5, d. x + 2 y = 5, , 7. If y = y ( x) is the solution of the differential, , π, dy, + (tan x) y = sin x , 0 ≤ x ≤ , with, 3, dx, π, y(0) = 0, then y is equal to, 4, , equation, , a., , 1, log e 2, 4, , c. log e 2, , 1 , b. , log e 2, 2 2, 1, d. log e 2, 2, , 8. Let A = {2, 3, 4, 5, .... , 30} and ‘−~’ be an, equivalence relation on A × A, defined by, (a , b) −~ (c , d), if and only if ad = bc. Then, the, number of ordered pairs, which satisfy this, equivalence relation with ordered pair (4, 3), is equal to, , 4. If ( x , y , z) be an arbitrary point lying on a, plane P, which passes through the points, (42, 0, 0), (0, 42, 0) and (0, 0, 42), then the, value of expression, y − 19, x − 11, +, 3+, ( y − 19) 2 (z − 12) 2 (x − 11) 2 (z − 12) 2, x+ y+ z, z − 12, is, −, +, (x − 11) 2 ( y − 19) 2 14 (x − 11)( y − 19)(z − 12), equal to, a. 0, c. 39, , I=, , b. 3, d. –45, , a. 5, c. 8, , b. 6, d. 7, , 9. Let the lengths of intercepts on x-axis and, y-axis made by the circle, x 2 + y 2 + ax + 2ay + c = 0, (a < 0) be 2 2 and, 2 5, respectively. Then, the shortest distance, from origin to a tangent to this circle which, is perpendicular to the line x + 2 y = 0, is, equal to, a. 11, c. 6, , b. 7, d. 10
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22, , ONLINE, , 10. The least value of|z|, where z is a complex, number which satisfies the inequality, (|z| + 3)(|z| − 1), , exp , log e 2 ≥ log 2|5 7 + 9i|., (|z| + 1), , , i=, , −1, is equal to, , a. 3, c. 2, , b. 5, d. 8, , 11. Consider a rectangle ABCD having 5, 7, 6, 9, points in the interior of the line segments AB,, CD , BC , DA, respectively. Let α be the number, of triangles having these points from, different sides as vertices and β be the, number of quadrilaterals having these, points from different sides as vertices. Then,, (β − α ) is equal to, a. 795, c. 1890, , b. 1173, d. 717, , x, y, +, = 1 and the circle x 2 + y 2 = 4 b, b > 4,, 16 b2, lie on the curve y 2 = 3x 2, then b is equal to, b. 5, d. 10, , functions take principal values only. Then,, the number of real values of x which satisfy, 3x , 4x, sin−1 + sin−1 = sin−1 x is equal to, 2, 5, b. 1, d. 0, , points. A line y = mx , m > 0 intersects lines AC, and BC at point P and Q, respectively. Let A1, and A2 be the areas of ∆ABC and ∆PQC ,, respectively, such that A1 = 3A2, then the, value of m is equal to, 4, 15, , b. 1, , c. 2, , differentiable function, such that, f ( x + 1) = x f ( x). If g : S → R be defined as, g( x) = log e f ( x), then the value of, | g′′ (5) − g′′ (1)| is equal to, a., , 205, 144, , b., , 197, 144, , c., , 187, 144, , d. 1, , 17. Let P( x) = x 2 + bx + c be a quadratic, , ∫ P(x)dx = 1and P(x) leaves remainder 5 when, 0, , it is divided by ( x − 2). Then, the value of, 9( b + c) is equal to, a. 9, , b. 15, , c. 7, , d. 11, , y − 2 z −b, ,, =, =, l, 3, 4, l ≠ 0 is (3, 5, 7), then the shortest distance, between the line L1 and line, x −2 y − 4 z −5, is equal to, L2 :, =, =, 3, 4, 5, (4, 3, 8) on the line L1 :, , a. 1/2, , 14. Let A( −1, 1,) B(3, 4) and C(2 , 0) be given three, , a., , 16. Let f : S → S, where S = (0, ∞) be a twice, , 18. If the foot of the perpendicular from point, , 13. Given that the inverse trigonometric, , a. 2, c. 3, , b. (−∞ , ∞ ) − { −1, 1}, 1, c. −1, , , 2 , 1, d. −∞ , −[ −1], , 2 , , 1, , 2, , a. 12, c. 6, , 1, , a. (−∞ , − 1) ∪ , ∞ − {1}, 2 , , , polynomial with real coefficients, such that, , 12. If the point of intersections of the ellipse, 2, , JEE Main 2021 ~ Solved Papers, , d. 3, , Then, in which of the following intervals,, function f (x ) is increasing?, , c. 2/ 3, , d. 1/ 3, , 19. Let C 1 be the curve obtained by the solution, , dy, = y 2 − x 2, x > 0., dx, Let the curve C 2 be the solution of, 2xy, dy, = . If both the curves pass through, x 2 − y 2 dx, of differential equation 2xy, , (1, 1), then the area enclosed by the curves, C 1 and C 2 is equal to, a. π − 1, , 15. Let f be a real valued function, defined on, R − { −1, 1} and given by, x − 1, 2, ., f (x ) = 3log e, −, +, x, x, 1, −1, , , , b. 1/ 6, , x −a, , b., , π, −1, 2, , c. π + 1, , d., , π, +1, 4, , 20. Let a = $i + 2$j − 3k$ and b = 2$i − 3$j + 5k$ . If, r × a = b × r, r.(α i$ + 2$j + k$ ) = 3 and, r.(2$i + 5$j − ak$ ) = − 1, α ∈R, then the value of, α + |r|2 is equal to, a. 9, , b. 15, , c. 13, , d. 11
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23, , MARCH ATTEMPT ~ 16 March 2021, Shift II, Section B : Numerical Type Quesions, , 25. Let f : R → R and g : R → R be defined as, , 21. If the distance of the point (1, −2, 3) from the, , x + a, x < 0, f ( x) = , |x − 1|, x ≥ 0, , plane x + 2 y − 3z + 10 = 0 measured parallel, x −1 2− y z + 3, 7, , then, to the line,, is, =, =, 2, 3, m, 1, the value of|m| is equal to……… ., , x <0, x + 1,, andg( x) = , 2, 1, −, +, ≥0, (, ), ,, x, b, x, , , 22. Consider the statistics of two sets of, , where a , b are non-negative real numbers. If, (gof) ( x) is continuous for all x ∈ R , then a + b, is equal to……… ., , observations as follows, Size, , Mean, , Variance, , Observation I, , 10, , 2, , 2, , Observation II, , n, , 3, , 1, , If the variance of the combined set of these, two observations is 17/9, then the value of n, is equal to ……… ., a , , 26. Let, , be in A. P., where a , b > 0. Then, 72(a + b) is, equal to ……… ., , 27. In ∆ABC , the lengths of sides AC and AB are, 12 cm and 5 cm, respectively. If the area of, ∆ABC is 30 cm2 and R and r are respectively, the radii of circumcircle and incircle of ∆ABC ,, then the value of 2R + r (in cm) is equal to, ……… ., , b , , 23. Let A = 1 and B = 1 be two 2 × 1 matrices, a 2 , b2 , with real entries such that A = XB, where, 1 1 −1, and k ∈ R . If, X =, 3 1 k , 2, a12 + a 22 = ( b12 + b22) and ( k 2 + 1) b22 ≠ −2b1b2,, 3, then the value of k is ……… ., , 28. Let n be a positive integer. Let, , , x2 +, = α log e tan−1 , x, , 2, , γ (x – 1) , , + β tan−1 , x, , , , 29., , r r r, r, If c .( $i + $j + 3k$ ) = 8 then the value of c .(a × b) is, , 1 , , , x2 +, + δ tan−1 , x, , 1 k 3 k 7 k , + + , 2, 4, 8 , A = Σ (−1) knC k , k, k, , , k, + 15 + 31, , 32, 16, , 1, If 63A = 1 − 30 , then n is equal to ……… ., 2, r, Let c be a vector rperpendicular to the vectors, r, a = $i + $j − k$ and b = $i + 2 $j + k$, n, , 24. For real numbers α, β, γ and δ, if, x 2 + 1, , (x 2 − 1) + tan−1 , x , dx, ∫ 4, 2, 2, −1 x + 1, , (x + 3x + 1) tan , x , , 1, 1 1, , a and b be in G. P. and , , 6, 16, a b, , equal to ……… ., 1, + C, , , where C is an arbitrary constant, then the value, of 10(α + βγ + δ) is equal to……… ., , 30. Let S n( x) = log a1/ 2 x + log a1/ 3 x + log a1/ 6 x, + log, , a1/ 11, , x + log, , a1/ 18, , x + log, , a1/ 27, , x + ...., , up to n-terms, where a > 1. If S 24( x) = 1093, and S12(2x) = 265, then value of a is equal to, ……… .
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24, , ONLINE, , JEE Main 2021 ~ Solved Papers, , Answers, For solutions scan, the QR code, , Physics, 1. (a), 11. (b), 21. 2500, , 2. (c), 12. (d), 22. 3, , 3. (c), 13. (d), 23. 20, , 4. (d), 14. (d), 24. 3, , 5. (*), 15. (d), 25. 12, , 6. (a), 16. (b), 26. 12, , 7. (d), 17. (c), 27. 120, , 8. (c), 18. (a), 28. 4, , 9. (b), 19. (b), 29. 3, , 10. (d), 20. (a), 30. 113, , Chemistry, 1. (c), 11. (b), 21. 15, , 2. (c), 12. (c), 22. 14, , 3. (a), 13. (c), 23. 108, , 4. (a), 14. (c), 24. 19, , 3. (c), 13. (c), 23. 1, , 4. (b), 14. (b), 24. 6, , 5. (c), 15. (b), 25. 3, , 6. (c), 16. (c), 26. 19, , 7. (a), 17. (b), 27. 1, , 8. (c), 18. (d), 28. 525, , 9. (c), 19. (c), 29. 2218, , 10. (d), 20. (d), 30. 4, , 8. (d), 18. (b), 28. 6, , 9. (c), 19. (b), 29. 28, , 10. (a), 20. (b), 30. 16, , Mathematics, 1. (c), 11. (d), 21. 2, , 2. (b), 12. (a), 22. 5, , Note (*) None of the option is correct., , 5. (c), 15. (a), 25. 1, , 6. (a), 16. (a), 26. 14, , 7. (b), 17. (c), 27. 15
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MARCH ATTEMPT ~ 17 March 2021, Shift I, , JEE Main 2021, 17 MARCH SHIFT I, , PHYSICS, Section A : Objective Type Questions, 1. A triangular plate is shown below. A force, , F = 4 i$ − 3$j is applied at point P. The torque at, point P with respect to point O and Q are, Y, , 5. An electron of mass m and a photon have, same energy E. The ratio of wavelength of, electron to that of photon is, (c being the velocity of light), 1/ 2, , 1 2m , a. , , c E , 1/ 2, E , c. , , 2m , , 1 E , b. , , c 2m , , 1/ 2, , d. c (2mE )1/ 2, , P, , F, , 6. Two identical metal wires of thermal, 10, , cm, , cm, , 10, , 60°, O, , conductivities K1 and K 2 respectively are, connected in series. The effective thermal, conductivity of the combination is, , 60°, 10 cm, , Q, , X, , a. −15 − 20 3 , 15 − 20 3, b. 15 + 20 3 , 15 − 20 3, c. 15 − 20 3 , 15 + 20 3, d. −15 + 20 3 , 15 + 20 3, , b( b > a) coalesce, the radius of curvature of, common surface is, a+ b, ab, ab, d., a+ b, , ab, b −a, b −a, c., ab, , b., , c. 1.37, , d. 10.3, , 4. If an electron is moving in the nth orbit of the, hydrogen atom, then its velocity v n for the, nth orbit is given as, a. v n ∝ n, , b. v n ∝, , c. v n ∝ n 2, , d. v n ∝, , 1, n, 1, n, , b. 8.54, d. 8.56, , 8. An AC current is given by I = I1sinωt + I2 cos ωt., , modes. What is the value of γ?, b. 1.30, , K1 + K 2, 2K 1K 2, K K, d. 1 2, K1 + K 2, b., , a positive zero error of 0.2 mm. If while, taking a measurement, it was noted that '0', on the vernier scale lies between 8.5 cm and, 8.6 cm, vernier coincidence is 6, then the, correct value of measurement is ……… cm., a. 8.36, c. 8.58, , 3. A polyatomic ideal gas has 24 vibrational, a. 1.03, , 2K 1K 2, , K1 + K 2, K1 + K 2, c., K 1K 2, , 7. The vernier scale used for measurement has, , 2. When two soap bubbles of radii a and, , a., , a., , 2, , A hot wire ammeter will give a reading, a., c., , I12 − I 22, 2, I1 + I 2, 2, , b., d., , I12 + I 22, 2, I1 + I 2, 2 2, , 9. A modern grand-prix racing car of mass m is, travelling on a flat track in a circular arc of, radius R with a speed v. If the coefficient of, static friction between the tyres and the
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26, , JEE Main 2021 ~ Solved Papers, , ONLINE, , z ω, , track is µ s , then the magnitude of negative, lift f L acting downwards on the car is, (Assume forces on the four tyres are identical, and g = acceleration due to gravity), , B, , α, , v, , I, , R, A, , v2, , a. m , + g, R, µ, s, , , v2 , c. m g −, , µ sR , , , v2, , b. m , − g, R, µ, s, , , v2 , d. − m g +, , µ sR , , , 10. A car accelerates from rest at a constant rate, α for some time after which it decelerates at, a constant rate β to come to rest. If the total, time elapsed is t seconds, the total distance, travelled is, 4αβ 2, t, (α + β), αβ, c., t2, 2(α + β), , a., , 2αβ 2, t, (α + β), αβ, d., t2, 4(α + β), , b., , 11. A solenoid of 1000 turns per metre has a, core with relative permeability 500. Insulated, windings of the solenoid carry an electric, current of 5 A. The magnetic flux density, produced by the solenoid is, (Permeability of free space = 4 π × 10−7 H/m), a. πT, b. 2 × 10−3 πT, π, c. T, 5, d. 10−4 πT, , 12. A mass M hangs on a massless rod of length l, which rotates at a constant angular, frequency. The mass M moves with steady, speed in a circular path of constant radius., Assume that the system is in steady circular, motion with constant angular velocity ω. The, angular momentum of M about point A is LA, which lies in the positive z-direction and the, angular momentum of M about B is LB . The, correct statement for this system is, , r, , M, , a. L A and L B are both constant in magnitude and, direction, b. L B is constant in direction with varying, magnitude, c. L B is constant, both in magnitude and, direction, d. L A is constant, both in magnitude and, direction, , 13. For what value of displacement the kinetic, energy and potential energy of a simple, harmonic oscillation become equal?, a. x = 0, A, c. x = ±, 2, , b. x = ± A, A, d. x =, 2, , 14. A Carnot's engine working between 400 K, and 800 K has a work output of 1200 J per, cycle. The amount of heat energy supplied to, the engine from the source in each cycle is, a. 3200 J, , b. 1800 J, , c. 1600 J, , d. 2400 J, , 15. The thickness at the centre of a plano convex, lens is 3 mm and the diameter is 6 cm. If the, speed of light in the material of the lens is, 2 × 108ms −1, then the focal length of the lens, is, a. 0.30 cm b. 15 cm, , c. 1.5 cm, , d. 30 cm, , 16. The output of the given combination gates, represents, A, Y, B, , a. XOR gate, c. AND gate, , b. NAND gate, d. NOR gate
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27, , MARCH ATTEMPT ~ 17 March 2021, Shift I, 17. A boy is rolling a 0.5 kg ball on the, , frictionless floor with the speed of 20 ms −1., The ball gets deflected by an obstacle on the, way. After deflection it moves with 5% of its, initial kinetic energy. What is the speed of, the ball now ?, a. 19.0 ms −1, b. 4.47 ms −1, c. 14.41 ms −1, d. 1.00 ms −1, , combination of two resistors is s. When they, are connected in parallel, the equivalent, resistance is p. If s = np, then the minimum, value for n is ……… ., (Round off to the nearest integer), , 24. Four identical rectangular plates with length,, 3, cm are arranged, 2, as shown in figure. The equivalent, xε, capacitance between A and C is 0 . The, d, value of x is ……… ., (Round off to the nearest integer), l = 2 cm and breadth, b =, , 18. Which level of the single ionized carbon has, the same energy as the ground state energy, of hydrogen atom?, a. 1, c. 4, , 23. The equivalent resistance of series, , b. 6, d. 8, , 19. Two ideal polyatomic gases at temperatures, , A, , B, , C, D, , T1 and T2 are mixed so that there is no loss of, energy. If f1 and f 2, m1 and m 2 , n1 and n2 be, the degrees of freedom, masses, number of, molecules of the first and second gas, respectively, the temperature of mixture of, these two gases is, a., , n1T1 + n 2T2, n1 + n 2, , b., , n1 f1T1 + n 2 f 2T2, n1 f1 + n 2 f 2, , c., , n1 f1T1 + n 2 f 2T2, f1 + f 2, , d., , n1 f1T1 + n 2 f 2T2, n1 + n 2, , 20. A current of 10 A exists in a wire of cross, , sectional area of 5 mm2 with a drift velocity, of 2 × 10−3 ms −1. The number of free electrons, in each cubic metre of the wire is, a. 2 × 106, c. 2 × 1025, , b. 625 × 1025, d. 1 × 1023, , Section B : Numerical Type Questions, 21. For VHF signal broadcasting, ……… km 2 of, maximum service area will be covered by an, antenna tower of height 30 m, if the, receiving antenna is placed at ground. Let, radius of the Earth be 6400 km., (Round off to the nearest integer)., (Take π as 3.14), , d, , d, , d, , 25. The radius in kilometre to which the present, radius of Earth (R = 6400 km) to be, compressed so that the escape velocity is, increased 10 times is ……… ., , 26. Consider two identical springs each of spring, constant k and negligible mass compared to, the mass M as shown. Fig.1 shows one of, them and Fig.2 shows their series, combination. The ratios of time period of, T, oscillation of the two SHM is b = x , where, Ta, value of x is ……… ., (Round off to the nearest integer), , Ta, , Tb, M, , 22. The angular speed of truck wheel is, increased from 900 rpm to 2460 rpm in, 26 s. The number of revolutions by the truck, engine during this time is ……… ., (Assuming the acceleration to be uniform)., , Fig. 1, , M, Fig. 2
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28, , ONLINE, , 27. The following bodies,, , JEE Main 2021 ~ Solved Papers, , the plates with a constant mechanical, energy of ……… pJ., (Assume no friction), , 1. a ring, 2. a disc, 3. a solid cylinder, 4. a solid sphere, , 29. Two blocks ( m = 0.5 kg and M = 4 .5 kg) are, , of same mass m and radius R are allowed to, roll down without slipping simultaneously, from the top of the inclined plane. The body, which will reach first at the bottom of the, inclined plane is ……… ., (Mark the body as per their respective, numbering given in the question), , S, , arranged on a horizontal frictionless table as, shown in figure. The coefficient of static, 3, friction between the two blocks is . Then,, 7, the maximum horizontal force that can be, applied on the larger block so that the blocks, move together is …… N., (Round off to the nearest integer. Take,, g = 9.8 ms −2), m, F, , h, , M, , 30. If 2.5 × 10−6 N average force is exerted by a, , θ, , 28. A parallel plate capacitor whose capacitance, C is 14 pF is charged by a battery to a, potential difference V = 12 V between its, plates. The charging battery is now, disconnected and a porcelain plate with, K = 7 is inserted between the plates, then the, plate would oscillate back and forth between, , light wave on a non-reflecting surface of, 30 cm2 area during 40 min of time span, the, energy flux of light just before it falls on the, surface is …… W / cm2., (Round off to the nearest integer. Assume, complete absorption and normal incidence, conditions are there.), , CHEMISTRY, Section A : Objective Type Questions, 1. With respect to drug-enzyme interaction,, , 2. Which of the following is an aromatic, compound?, , identify the wrong statement, a. Non-competitive inhibitor binds to the, allosteric site., b. Allosteric inhibitor changes the enzyme's, active site., c. Allosteric inhibitor competes with the, enzyme's active site., d. Competitive inhibitor binds to the enzyme's, active site., , a., , b., , c., , d., , ⊕, , ⊕
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29, , MARCH ATTEMPT ~ 17 March 2021, Shift I, 3., , O, , O, , 6. Which of the following is correct structure of, OC2H5, , Ethylene glycol, , H+, , tyrosine?, A, (Major product), , COOH, a., , The product A in the above reaction is, , H 2N, , OH, O O, OH, , a., , OH, , OC2H5, b., , H, , O, , O, , COOH, H 2N, , O, , H, , OH, , b., , OC2H5, , O, , COOH, , OC2H5, , c., , c., , H2N, , H, , OH, , OH, d., , O, , O, , O, COOH, , OH, d., , H 3N, , H, , 4. A central atom in a molecule has two lone, , OH, , pairs of electrons and forms three single, bonds. The shape of this molecule is, a. see-saw, b. planar triangular, c. T-shaped, d. trigonal pyramidal, , 7., , O–Na+, , Cl, , +NaOH, , 5. Given below are two statements., Statement I Potassium permanganate on, heating at 573 K forms potassium manganate., Statement II Both potassium permanganate, and potassium manganate are tetrahedral and, paramagnetic in nature., In the light of the above statements, choose, the most appropriate answer from the options, given below, a. Statement I is true but statement II is false, b. Both statement I and statement II are true, c. Statement I is false but statement II is true, d. Both statement I and statement II are false, , The above reaction requires which of the, following reaction conditions?, a. 573 K, Cu, 300 atm, c. 573 K, 300 atm, , b. 623 K, Cu, 300 atm, d. 623 K, 300 atm, , 8. The absolute value of the electron gain, enthalpy of halogens satisfies, a. I > Br > Cl > F, c. Cl > F > Br > I, , b. Cl > Br > F > I, d. F > Cl > Br > I, , 9. Which of the following compound cannot act, as a Lewis base?, a. NF3, c. SF4, , b. PCl5, d. ClF3
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30, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 10. Reducing smog is a mixture of, , 14., , a. smoke, fog and O 3, b. smoke, fog and SO 2, c. smoke, fog and CH2 == CH CHO, d. smoke, fog and N2O 3, , Br, , CH3, , Product A is, , 11. Hofmann bromamide degradation of, benzamide gives product A, which upon, heating with CHCl3 and NaOH gives product, B. The structures of A and B are, NH2, , A, (Major product), , CCI4, , Br, , a., , Br CH, 3, , b., , CH3, Br, , NH2, , Br, , CHO, a., , A=, , CH3, , c., , B=, , d., , Br, , NH2, , NC, , b. A =, , CH3, , CH3, , CH3, , Br, , CH3, , 15. A colloidal system consisting of a gas, dispersed in a solid is called a/an, a. solid sol, c. aerosol, , B=, , b. gel, d. foam, , 16. The incorrect statement(s) about heavy, water is (are), , NH2, , NH2, CHO, , c., , A=, , B=, , O, , O, , NH2, , d. A =, , NH2, CHO, , B=, , Br, , Br, , (A), (B), (C), (D), , used as a moderator in nuclear reactor., obtained as a by-product in fertiliser industry., used for the study of reaction mechanism., has a higher dielectric constant than water., , Choose the correct answer from the options, given below :, a. (B) only, b. (C) only, c. (D) only, d. (C) and (D) only, , 17. The correct order of conductivity of ions in, water is, , 12. Mesityl oxide is a common name of, a. 2,4-dimethyl pentan-3-one, b. 3-methyl cyclohexane carbaldehyde, c. 2-methyl cyclohexanone, d. 4-methyl pent-3-en-2-one, , a. Na+ > K + >Rb + >Cs +, b. Cs + > Rb + > K + > Na+, c. K + > Na+ > Cs + > Rb +, d. Rb + > Na+ > K + > Li+, , 18. What is the spin-only magnetic moment, 13. Which of the following reaction is an, example of ammonolysis?, a. C 6H5COCl + C 6H5NH2 → C 6H5CONHC 6H5, [H], , b. C 6H5CH2CN → C 6H5CH2CH2NH2, +, , HCl, c. C 6H5NH2 →, C 6H5 NH3Cl−, , d. C 6H5CH2Cl + NH3 → C 6H5CH2NH2, , value (BM) of a divalent metal ion with, atomic number 25, in it's aqueous solution?, a. 5.92, c. zero, , b. 5.0, d. 5.26, , 19. Given below are two statements., Statement I Retardation factor (R f ) can be, measured in metre/centimetre.
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31, , MARCH ATTEMPT ~ 17 March 2021, Shift I, Statement II R f value of a compound remains constant in all solvents., Choose the most appropriate answer from the options given below, a. Statement I is true but statement II is false., b. Both statement I and statement II are true., c. Both statement I and statement II are false., d. Statement I is false but statement II is true., , 20. The point of intersection and sudden increase in the slope, in the diagram given below,, respectively, indicates., 0, 100, , Cu 2O, O →2, 4Cu+ 2 FeO, O →2, 2Fe+ 2, , 200, 300, , ∆G°/kJmol–1 of O2, , 400, , C+O2→CO2, 2C, +O, , 2CO 2, O 2→, +, O, C, O, 2Zn, 600 2, O 2→, +, n, Z, 700 2, , 2 →2, , 500, , CO, , 800, , l O3, 2/3A 2, , 900, 1000, 1100, , 4/3A, , →, +O 2, , A, , l, , 2MgO, O 2→, 2Mg+, , 1200, , 0°C, 273K, , 400°C, 673K, , 800°C, 1200°C 1600°C 2000°C, 1073K, 1473K 1873K 2273K, Temperature, , a. ∆G = 0 and melting or boiling point of the metal oxide, b. ∆G > 0 and decomposition of the metal oxide, c. ∆G < 0 and decomposition of the metal oxide, d. ∆G = 0 and reduction of the metal oxide, , Section B : Numerical Type Questions, 21. The reaction of white phosphorus on boiling with alkali in inert atmosphere resulted in the, formation of product A. The reaction of 1 mol of A with excess of AgNO3 in aqueous medium gives, …… mol(s) of Ag (Round off to the nearest integer)., , 22. 0.01 moles of a weak acid HA (K a = 2.0 × 10–6) is dissolved in 10, . L of 0.1 M HCl solution. The degree of, dissociation of HA is …… × 10−5 (Round off to the nearest integer)., [Neglect volume change on adding HA. Assume degree of dissociation << 1], , 23. A certain orbital has n = 4 and m l = − 3. The number of radial nodes in this orbital is …… (Round off, to the nearest integer).
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32, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 24., , NO2, HNO3, H2SO4, , In the above reaction 3.9 g of benzene on, nitration gives 4.92 g of nitrobenzene. The, percentage yield of nitrobenzene in the, above reaction is ……… % (Round off to the, nearest integer)., (Given, atomic mass C : 12.0 u, H : 1.0 u,, O : 16.0 u, N : 14.0 u), , 25. The mole fraction of a solute in a 100 molal, aqueous solution ……… ×10−2, (Round off to the nearest integer)., [Given, atomic masses H : 1.0 u, O : 16.0 u], , 26. For a certain first order reaction 32% of the, reactant is left after 570 s. The rate constant, of this reaction is …… ×10−3s −1. (Round off to, the nearest integer)., [Given, log10 2 = 0.301, In 10 = 2.303], , 27. The standard enthalpies of formation of, Al2O3 and CaO are −1675 kJ mol−1 and, , −625 kJ mol−1 respectively., , For the reaction,, 3CaO + 2Al → 3Ca + Al2O3 the standard, reaction enthalpy ∆ rH° ……… kJ., (Round off to the nearest integer)., , 28. 15 mL of aqueous solution of Fe 2+ in acidic, medium completely reacted with 20 mL of, 0.03 M aqueous Cr2O2−, 7 . The molarity of the, Fe 2+ solution is …… × 10−2 M (Round off to, the nearest integer)., , 29. The oxygen dissolved in water exerts a, partial pressure of 20 kPa in the vapour, above water. The molar solubility of oxygen, in water is …… × 10−5 mol dm−3., (Round off to the nearest integer)., [Given, Henry’s law constant (KH ), = 8.0 × 104 kPa for O2 , density of water with, dissolved oxygen = 10, . kg dm−3 ]., , 30. The pressure exerted by a non-reactive, gaseous mixture of 6.4 g of methane and, 8.8 g of carbon dioxide in a 10L vessel at, 27°C is …… kPa (Round off to the nearest, integer), (Assume gases are ideal, R = 8.314 J mol−1 K −1, Atomic mass, C : 12.0 u, H : 1.0 u, O : 16.0 u), , MATHEMATICS, Section A : Objective Type Questions, 1. The inverse of y = 5, , logx, , b. x = ylog 5, , c. x = y, , d. x = 5log y, , 1, log 5, , x + ky + z = k and x + y + zk = k 2 has no, solution, if k is equal to, , is, , a. x = 5log y, , a. 0, , 1, , b. 8, d. 10, , and Q are (−2, 4) and (4, −2), respectively. If, the equation of the perpendicular bisector of, PR is 2x − y + 2 = 0, then the centre of the, circumcircle of the ∆PQR is, c. (0, 2), , c. −1, −1, , d. −2, −1, , + cot −132 + ..... upto 100 terms, then α is, a. 1.01, , b. 1.00, , c. 1.02, , d. 1.03, , 6. The equation of the plane which contains the, Y-axis and passes through the point (1, 2, 3) is, , 3. In a ∆PQR, the coordinates of the points P, , b. (−2, − 2), , −1, , 5. If cot (α ) = cot 2 + cot 8 + cot 18, , r × a = r × b, r ⋅ ( $i + 2$j + k$ ) = − 3, then., r ⋅ (2i$ − 3$j + k$ ) is equal to, , a. (−1, 0), , b. 1, −1, , 2. Let a = 2i$ − 3$j + 4k$ and b = 7$i + $j − 6k$ . If, , a. 12, c. 13, , 4. The system of equations kx + y + z = 1,, , d. (1, 4), , a. x + 3z = 10, c. 3x + z = 6, , b. x + 3z = 0, d. 3x − z = 0, , sinα , 0, 2 1, and det A − I = 0, then, , 0 , sinα, 2, , 7. If A = , , a possible value of α is, a., , π, 2, , b., , π, 3, , c., , π, 4, , d., , π, 6
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33, , MARCH ATTEMPT ~ 17 March 2021, Shift I, 8. If the Boolean expression ( p ⇒ q) ⇔ (q * (~ p)), is a tautology, then the Boolean expression, ( p * (~ q)) is equivalent to, a. q ⇒ p, c. p ⇒~ q, , b. ~q ⇒ p, d. p ⇒ q, , boy and a girl plays against a girl, then n is, equal to, a. 5, , b. 2, , 16. The value of 4 +, , 9. Two dices are rolled. If both dices have six, faces numbered 1, 2, 3, 5, 7 and 11, then the, probability that the sum of the numbers on, the top faces is less than or equal to 8 is, a., , 4, 9, , b., , 17, 36, , c., , 5, 12, , d., , 1, 2, , 10. If the fourth term in the expansion of, , ( x + x log 2 x ) 7 is 4480, then the value of x,, where x ∈ N is equal to, a. 2, , b. 4, , c. 3, , c. 4, , d. 1, , 11. In a school, there are three types of games, to be played. Some of the students play two, types of games, but none play all the three, games. Which Venn diagram can justify the, above statement?, , d. 6, , 1, 5+, , is, , 1, 4+, , 2, 30, 5, 4, c. 4 +, 30, 5, , 1, 5+, , 1, 4 + .... ∞, , 4, 30, 5, 2, d. 5 +, 30, 5, , a. 2 +, , b. 2 +, , 17. Choose the incorrect statement about the, two circles whose equations are given below, x 2 + y 2 − 10x − 10 y + 41 = 0, and x 2 + y 2 − 16x − 10 y + 80 = 0, a. Distance between two centres is the average, of radii of both the circles., b. Both circles' centres lie inside region of one, another., c. Both circles pass through the centre of each, other., d. Circles have two intersection points., , 18. Which of the following statements is correct, (P), , (Q), , a. P and Q, c. None of these, , (R), , b. P and R, d. Q and R, , 12. The sum of possible values of x for, , 1 , 8, tan−1( x + 1) + cot −1, = tan−1 is, 31, −, x, 1, , , a., , −32, 4, , b. −, , 31, 4, , c. −, , 30, 4, , d. −, , 33, 4, , 13. The area of the triangle with vertices, A( z), B( iz) and C ( z + iz) is, a. 1, , 1, b. |z|2, 2, , c., , 1, 2, , 1, d. |z + iz|2, 2, , for the function g(α) for α ∈R, such that, π /3, sinα x, g (α ) = ∫, dx, α, cos x + sinα x, π /6, a. g (α ) is a strictly increasing function, 1, b. g (α ) has an inflection point at α = −, 2, c. g (α ) is a strictly decreasing function, d. g (α ) is an even function, , 19. Which of the following is true for y ( x) that, satisfies the differential equation, dy, = xy − 1 + x − y ; y (0) = 0, dx, a. y (1) = e, , −, , 1, 2, , 1, , −1, , b. y (1) = e 2 − e, , −, , 1, 2, , 1, , 14. The line 2x − y + 1 = 0 is a tangent to the, circle at the point (2, 5) and the centre of the, circle lies on x − 2 y = 4. Then, the radius of, the circle is, a. 3 5, , b. 5 3, , c. 5 4, , d. 4 5, , 15. Team A consists of 7 boys and n girls and, Team B has 4 boys and 6 girls. If a total of 52, single matches can be arranged between, these two teams, when a boy plays against a, , d. y (1) = e 2 − 1, , c. y(1) = 1, , 20. The value of, lim+, , x→ 0, , cos −1( x − [ x ]2).sin−1( x − [ x ]2), x − x3, , , where [ x ], , denotes the greatest integer ≤ x is, a. π, π, c., 4, , b. 0, π, d., 2
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34, , ONLINE, , 25. If a = α$j + β$j + 3k$ , b = − β i$ − α$j − k$ and, , Section B : Numerical Type Questions, , c = i$ − 2$j − k$ ,, , 21. The maximum value of z in the following, , equation z = 6xy + y 2, where 3x + 4 y ≤ 100, and 4 x + 3 y ≤ 75 for x ≥ 0 and y ≥ 0 is ……… ., , 22. If the function f ( x) =, , 1, such that a. b = 1and b. c = − 3, then [(a × b) ⋅ c ], 3, is equal to ……… ., , cos(sin x) − cos x, , is, x4, continuous at each point in its domain and, 1, f (0) = ,then k is ……… ., k, , 2 3 , , then the value of, 0 −1, det ( A 4) + det[ A10 − Adj(2A)10 ] is equal to …… ., , 26. If A = , , , , 1 − 2 2x , and its first, 2x, 1 + 2 , , b, derivative with respect to x is − log e 2 when, a, x = 1, where a and b are integers, then the, minimum value of|a 2 − b2| is ……… ., , 23. If f ( x) = sin cos −1, , 27. If [⋅] represents the greatest integer function,, π /2, , and E 3. The probability that only E 1 occurs is, α, only E 2 occurs is β and only E 3 occurs is γ., Let p denote the probability of none of, events occur that satisfies the equations, (α − 2β) p = αβ and (β − 3γ) p = 2βγ. All the given, probabilities are assumed to lie in the, interval (0, 1)., probability of occurrence of E 1, is equal, probability of occurrence of E 3, , ∫[x, , then the value of, , 2, , − cos x ]dx is ……… ., , 0, , 28. The minimum distance between any two, points P1 and P2 while considering point P1 on, one circle and point P2 on the other circle for, the given circles equations, x 2 + y 2 − 10x − 10 y + 41 = 0, x 2 + y 2 − 24 x − 10 y + 160 = 0 is ……… ., , 24. Let there be three independent events E 1, E 2, , Then,, , JEE Main 2021 ~ Solved Papers, , 29. If the equation of the plane passing through, the line of intersection of the planes, 2x − 7 y + 4 z − 3 = 0, 3x − 5 y + 4 z + 11 = 0 and, the point (−2, 1, 3) is ax + by + cz − 7 = 0, then, the value of 2a + b + c − 7 is ……… ., , 30. If (2021) 3762 is divided by 17, then the, , to ……… ., , remainder is ……… ., , Answers, For solutions scan, the QR code, , Physics, 1. (b), 11. (a), 21. 1206, , 2. (a), 12. (d), 22. 728, , 3. (a), 13. (c), 23. 4, , 4. (b), 14. (d), 24. 2, , 5. (b), 15. (d), 25. 64, , 6. (a), 16. (b), 26. 2, , 7. (b), 17. (b), 27. 4, , 8. (b), 18. (b), 28. 864, , 9. (b), 19. (b), 29. 21, , 10. (c), 20. (b), 30. 25, , Chemistry, 1. (c), 11. (b), 21. 4, , 2. (a), 12. (d), 22. 2, , 3. (b), 13. (d), 23. 0, , 4. (c), 14. (d), 24. 80, , 5. (a), 15. (a), 25. 64, , 6. (d), 16. (c), 26. 2, , 7. (d), 17. (b), 27. 230, , 8. (c), 18. (a), 28. 24, , 9. (b), 19. (c), 29. 25, , 10. (b), 20. (a), 30. 150, , 3. (b), 13. (b), 23. 481, , 4. (d), 14. (a), 24. 6, , 5. (a), 15. (c), 25. 2, , 6. (d), 16. (a), 26. 16, , 7. (c), 17. (b), 27. 1, , 8. (a), 18. (d), 28. 1, , 9. (b), 19. (a), 29. 4, , 10. (a), 20. (d), 30. 4, , Mathematics, 1. (c), 11. (c), 21. 904, , 2. (a), 12. (a), 22. 6
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MARCH ATTEMPT ~ 17 March 2021, Shift II, , JEE Main 2021, 17 MARCH SHIFT II, , PHYSICS, Section A : Objective Type Questions, 1. A rubber ball is released from a height of, , 5. An object is located at 2 km beneath the, , 5 m above the floor. It bounces back, 81, of the height, repeatedly, always rising to, 100, through which it falls. Find the average, speed of the ball., (Take, g = 10 ms −2), a. 3.0 ms −1, c. 2.0 ms −1, , b. 3.5 ms −1, d. 2.5 ms −1, , 2. If one mole of the polyatomic gas is having, two vibrational modes and β is the ratio of, molar specific heats for polyatomic gas, C p, , , then the value of β is, β =, CV , , a. 1.02, c. 1.25, , b. 1.2, d. 1.35, , surface of the water. If the fractional, ∆V, compression, is 1.36% , the ratio of, V, hydraulic stress to the corresponding, hydraulic strain will be …………… ., (Take, density of water is 1000 kg m −3 and, g = 981, . ms −2), a. 196, . × 107 Nm−2, c. 226, . × 109 Nm−2, , 6. A geostationary satellite is orbiting around, an arbitrary planet P at a height of 11R above, the surface of P, R being the radius of P. The, time period of another satellite in hours at a, height of 2R from the surface of P is ………… ., P has the time period of 24 h., a. 6 2, , 3. A block of mass 1 kg attached to a spring is, made to oscillate with an initial amplitude of, 12 cm. After 2 min, the amplitude decreases, to 6 cm. Determine the value of the damping, constant for this motion., (Take, ln 2 = 0693, ., ), a. 069, . × 102 kg/s, b. 3.3 × 102 kg/s, c. 116, . × 10−2 kg/s, d. 5.7 × 10−3 kg/s, , b. 144, . × 107 Nm−2, d. 144, . × 109 Nm−2, , b. 6/ 2, , c. 3, , d. 5, , 7. A sound wave of frequency 245 Hz travels, , with the speed of 300 ms −1 along the, positive X-axis. Each point of the wave moves, to and fro through a total distance of 6 cm., What will be the mathematical expression of, this travelling wave ?, a. y (x , t ) = 003, . [sin 51, . x–, b. y (x , t ) = 006, . [sin 51, . x–, c. y (x , t ) = 006, . [sin 08, . x–, d. y (x , t ) = 003, . [sin 51, . x–, , (02, . × 103 )t ], (15, . × 103 )t ], (05, . × 103 )t ], (15, . × 103 )t ], , 8. Which one is the correct option for the two, , 4. Which one of the following will be the output, , different thermodynamic processes ?, , of the given circuit ?, A, , Adiabatic, , p, Y, , (A), , B, , a. NOR Gate, c. AND Gate, , b. NAND Gate, d. XOR Gate, , Isothermal, , V
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36, , ONLINE, , JEE Main 2021 ~ Solved Papers, E, , 2E, , Isothermal, p, (B), Adiabatic, , R, , T, , a. r1 + r2, , Isothermal, , V, (C), , Adiabatic, , b., , r1, − r2, 2, , c., , r1, + r2, 2, , d. r1 − r2, , 12. A hairpin like shape as shown in figure is, made by bending a long current carrying, wire. What is the magnitude of a magnetic, field at point P which lies on the centre of the, semicircle?, I, , T, P, , Isothermal, , r, , I, , p, (D), Adiabatic, , a. C and A, c. Only A, , I, , µ 0I, (2 − π ), 4 πr, µ 0I, c., (2 + π ), 2 πr, , T, b. C and D, d. B and C, , 9. The velocity of a particle is v = v 0 + gt + Ft 2., Its position is x = 0 at t = 0, then its, displacement after time (t = 1) is, , b., , 13. The four arms of a Wheatstone bridge have, resistances as shown in the figure. A, galvanometer of 15 Ω resistance is, connected across BD. Calculate the current, through the galvanometer when a potential, difference of 10 V is maintained across AC ., , a. v 0 + g + F, g F, b. v 0 + +, 2 3, g, c. v 0 + + F, 2, d. v 0 + 2 g + 3F, , A, , 1, 60, , amplitude modulated by a message signal, m(t) = 5sin(157, . × 108t) and transmitted, through an antenna. What will be the, bandwidth of the modulated signal ?, b. 2.01 GHz, d. 50 MHz, , 11. Two cells of emf 2E and E with internal, resistance r1 and r2 respectively are, connected in series to an external resistor R, (see figure). The value of R, at which the, potential difference across the terminals of, the first cell becomes zero is, , 00, , Ω, , B, , 10, , Ω, , C, G, , Ω, , 5, , Ω, , D, , 10. A carrier signal C (t) = 25sin(2512, ., × 1010t) is, , a. 8 GHz, c. 1987.5 MHz, , µ 0I, (2 + π ), 4 πr, µ 0I, d., (2 − π ), 2 πr, , a., , 10V, , a. 2.44 µA, , b. 2.44 mA c. 4.87 mA d. 4.87 µA, , 14. Two particles A and B of equal masses are, suspended from two massless springs of, spring constants k1 and k 2, respectively. If, the maximum velocities during oscillations, are equal, the ratio of the amplitude of A and, B is, a., , k2, k1, , b., , k1, k2, , c., , k1, k2, , d., , k2, k1
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37, , MARCH ATTEMPT ~ 17 March 2021, Shift II, a. v12 − v 22 =, , 15. Match List-I with List-II, List-I, A., , B., , C., , D., , List-II, , Phase difference, between current and, voltage in a purely, resistive AC circuit, Phase difference, between current and, voltage in a pure, inductive AC circuit, Phase difference, between current and, voltage in a pure, capacitive AC circuit, Phase difference, between current and, voltage in an L-C-R, series circuit, , 1. π ; current leads, 2, voltage, , B, , C, , D, , a., , 1, , 3, , 4, , 2, , c., , 2, , 3, , 4, , 1, , b. v12 + v 22 =, 1, , 2h, [ f1 + f 2 ], m, , 19. What happens to the inductive reactance and, , a. Both inductive reactance and current will be, halved., 3. π ; current lags, 2, voltage, , b. Inductive reactance will be halved and current, will be doubled., , 4. tan −1 XC − X L , , , R , , d. Both inductive reactance and current will be, doubled., , c. Inductive reactance will be doubled and, current will be halved., , 20. A sphere of mass 2 kg and radius 0.5 m is, , A, , B, , C, , D, , b., , 2, , 4, , 3, , 1, , d., , 2, , 3, , 1, , 4, , rolling with an initial speed of 1 ms −1 goes up, an inclined plane which makes an angle of, 30° with the horizontal plane, without, slipping. How long will the sphere take to, return to the starting point A ?, , 16. Two identical blocks A and B each of mass m, resting on the smooth horizontal floor are, connected by a light spring of natural length, L and spring constant k. A third block C of, mass m moving with a speed v along the line, joining A and B collides with A. The maximum, compression in the spring is, C, , A, , B, , m, , m, , m, , a. v, , m, 2k, , b., , mv, 2k, , c., , mv, k, , d., , m, 2k, , 17. The atomic hydrogen emits a line spectrum, consisting of various series. Which series of, hydrogen atomic spectra is lying in the visible, region ?, a. Brackett series, c. Lyman series, , 1, , 2h, 2h, 2, 2, c. v1 − v 2 = , ( f + f 2 ) d. v1 − v 2 = , (f − f ), , m 1, m 1 2 , , the current in a purely inductive circuit, if the, frequency is halved ?, , 2. zero, , Choose the most appropriate answer from, the options given below., A, , 2h, [ f1 − f 2 ], m, , b. Paschen series, d. Balmer series, , 18. Two identical photocathodes receive the light, of frequencies f1 and f 2, respectively. If the, velocities of the photoelectrons coming out, are v1 and v 2 respectively, then, , A, , a. 0.60 s, , 30°, , b. 0.52 s, , c. 0.57 s, , d. 0.80 s, , Section B : Numerical Type Questions, 21. The electric field intensity produced by the, radiation coming from a 100 W bulb at a, distance of 3 m is E. The electric field, intensity produced by the radiation coming, x, from 60 W at the same distance is, E,, 5, where the value of x is …………… ., , 22. A body of mass 1 kg rests on a horizontal, floor with which it has a coefficient of static, 1, friction, . It is desired to make the body, 3, move by applying the minimum possible, force F newton. The value of F will be, ……………… ., (Round off to the nearest integer), (Take, g = 10 ms −2)
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38, , ONLINE, , JEE Main 2021 ~ Solved Papers, , 23. A boy of mass 4 kg is standing on a piece of, , Y, , wood having mass 5 kg . If the coefficient of, friction between the wood and the floor is, 0.5, the maximum force that the boy can, exert on the rope, so that the piece of wood, does not move from its place is …………… N., (Round off to the nearest integer), (Take, g = 10 ms −2), , a, θ, , X, , T, , 28. The image of an object placed in air formed, , T, f, , T, , R, T, , 24. Suppose you have taken a dilute solution of, oleic acid in such a way that its, concentration becomes 0.01 cm 3 of oleic, acid per cm 3 of the solution. Then, you make, a thin film of this solution (monomolecular, thickness) of area 4 cm 2 by considering, 1, , 3 3, −3, 100 spherical drops of radius , × 10, 40π , cm 2. Then, the thickness of oleic acid layer, will be x × 10–14 m,, where x is ……………… ., , by a convex refracting surface is at a, distance of 10 m behind the surface. The, 2, image is real and is at of the distance of, 3, the object from the surface .The wavelength, 2, of light inside the surface is times the, 3, wavelength in air. The radius of the curved, x, surface is, m. The value of x is ……………… ., 13, , 29. A 2 µF capacitor C 1 is first charged to a, potential difference of 10 V using a battery., Then, the battery is removed and the, capacitor is connected to an uncharged, capacitor C 2 of 8 µF. The charge in C 2 on, equilibrium condition is ………… µC., (Round off to the nearest integer), S1, , 25. A particle of mass m moves in a circular orbit, in a central potential field U( r) = U 0r 4. If, Bohr's quantisation conditions are applied,, radii of possible orbitals rn vary with n1/ α ,, where α is ………………… ., , S2, , 2 µF, 10V, , C1, , 8 µF, C2, , 26. The electric field in a region is given by, , 2, 3, E = E 0 i$ + E 0$j with E 0 = 4.0 × 103 N/C. The, 5, 5, flux of this field through a rectangular, surface area 0.4 m 2 parallel to the, yz-plane is ………… N-m 2 C −1., , 27. The disc of mass M with uniform surface, , mass density σ is shown in the figure. The, centre of mass of the quarter disc (the, xa x a, shaded area) is at the position, ,, ,, 3π 3 π, where x is ………… ., (Round off to the nearest integer), (a is an area as shown in the figure), , 30. Seawater at a frequency f = 9 × 102 Hz, has, permittivity ε = 80ε 0 and resistivity, r = 0 . 25 Ω-m. Imagine a parallel plate, capacitor is immersed in seawater and is, driven by an alternating voltage source, V (t) = V0 sin(2πft). Then, the conduction, current density becomes 10x times the, displacement current density after time, 1, s. The value of x is …………… ., t=, 800, , , 1, = 9 × 109 N- m2C −2 , Take,, 4 πε0, ,
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39, , MARCH ATTEMPT ~ 17 March 2021, Shift II, , CHEMISTRY, Section A : Objective Type Questions, , 7. Match List-I and List-II., , 1. Fructose is an example of, a. pyranose, c. aldohexose, , List-I, , b. ketohexose, d. heptose, , 2. The set of elements that differ in mutual, relationship from those of the other sets is, a. Li-Mg, , b. B-Si, , c. Be-Al, , List-II, , [Co(NH3 ) 6 ], , A., , 1., , Linkage isomerism, , 2., , Solvate isomerism, , 3., , Co-ordination, isomerism, , [Cr(CN) 6 ], [Co(NH3 ) 3, , B., , (NO 2 ) 3 ], , d. Li-Na, C., , [Cr(H2O) 6 ] Cl3, , D., , cis-[CrCl2 (ox) 2 ] 3− 4., , 3. The functional groups that are responsible, for the ion-exchange property of cation and, anion exchange resins, respectively, are, a. SO 3H and NH2, b. SO 3H and COOH, c. NH2 and COOH, d. NH2 and SO 3H, , Choose the correct answer from the options, given below., , 4. Match List-I and List-II., List-I, , List-II, , A., , Haematite, , 1., , Al2O 3 ⋅ x H2O, , B., , Bauxite, , 2., , Fe2O 3, , C., , Magnetite, , 3., , CuCO 3 ⋅ Cu(OH) 2, , D., , Malachite, , 4., , Fe3O 4, , Choose the correct answer from the options, given below., A, , B, , C, , D, , (a) 2, , 3, , 1, , 4, , (b) 4, , 1, , 2, , 3, , (c), , 1, , 3, , 2, , 4, , (d) 2, , 1, , 4, , 3, , A, , B, , C, , D, , A, , B, , C, , D, , (a) 3, , 1, , 2, , 4, , (b) 4, , 2, , 3, , 1, , (c), , 1, , 3, , 4, , (d) 1, , 2, , 3, , 4, , be separated using, a. para-toluene sulphonyl chloride, b. chloroform and KOH, c. benzene sulphonic acid, d. acetyl amide, , 9. The common positive oxidation states for an, element with atomic number 24, are, a. + 2 to + 6, c. + 1and + 3, , b. + 1and + 3 to + 6, d. + 1to + 6, , 10. Match List-I and List-II., List-I, , List-II, , (Chemical, , (Used as), , compound), , nucleophiles is(are), A. AgCN/KCN, B. RCOOAg/RCOOK, C. AgNO2/KNO2, D. AgI/KI, b. Only A, d. Only B, , 6. The set that represents the pair of neutral, , A., , Sucralose, , 1., , Synthetic, detergent, , B., , Glyceryl ester of, stearic acid, , 2., , Artificial, sweetener, , C., , Sodium benzoate 3., , Antiseptic, , D., , Bithionol, , Food, preservative, , b. N2O and N2O 3, d. NO and NO 2, , 4., , Choose the correct match., A, , B, , C, , D, , a., , 4, , 3, , 2, , 1, , c., , 3, , 2, , 4, , 1, , oxides of nitrogen is, a. NO and N2O, c. N2O and NO 2, , 2, , 8. Primary, secondary and tertiary amines can, , 5. The correct pair(s) of the ambident, , a. B and C, c. A and C, , Optical isomerism, , A, , B, , C, , D, , b., , 2, , 1, , 4, , 3, , d., , 1, , 2, , 4, , 3
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40, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 11. Given below are two statements., , N2+Cl–, , Statement-I 2-methylbutane on oxidation, with KMnO 4 gives 2-methylbutan-2-ol., Statement-II n-alkanes can be easily oxidised, to corresponding alcohols with KMnO 4., Choose the correct option., , O, , –, , N2+OCH3, , (b) Both statements I and II are incorrect., , (d) Statement I is incorrect but statement II is, correct., , CH3––C––H, HCl, , OCH3, , (a) Both statements I and II are correct., , (c) Statement I is correct but statement II is, incorrect., , ,, , a., , H, b., , ,, , H, H, , ,, , HCl, , CH3––C––H, , ,, , H 2O, , ,, , H 2O, , H, , O, , Cl, , 12. Nitrogen can be estimated by Kjeldahl's, method for which of the following, compound ?, , –, , N2+OCH3, O, , a., , b., +, , N≡≡ NCl–, , CH2NH2, , c., , ,, , c., , Cl, N2+Cl–, , d., , H, , N, NO2, , ,, , d., , H, , H, O, , H, , 13. Amongst the following, the linear species is, a. NO 2, , b. Cl2O, , d. N−3, , c. O 3, , Enzyme A, , 14. C 12H22O11 + H2O → C 6H12O6 + C 6H12O6, Glucose, , Sucrose, , Fructose, , Enzyme B, , C 6H12O 6 → 2C 2H5OH + 2CO 2, Glucose, , Ethanol, , In the above reactions, the enzyme A and enzyme, B respectively are, a. amylase and invertase, b. invertase and amylase, c. invertase and zymase, d. zymase and invertase, , 15. One of the by-products formed during the, recovery of NH 3 from solvay process is, a. Ca(OH)2 b. NaHCO3 c. CaCl2, , d. NH4Cl, , OCH3, , 16., C7H7N2OCl+C2H5OH, , +N2+X+Y, , (A ), , In the above reaction, the structural formula of, (A), X and Y respectively are, , OCH3, , 17. For the coagulation of a negative sol, the, species below, that has the highest, flocculating power is, a. SO 2−, 4, c. Na +, , b. Ba2 +, d. PO 3−, 4, , 18. Which of the following statement(s) is (are), incorrect reason for eutrophication ?, A. Excess usage of fertilisers., B. Excess usage of detergents., C. Dense plant population in water bodies., D. Lack of nutrients in water bodies that, prevent plant growth., Choose the most appropriate answer, from the options given below., a. Only A, b. Only C, c. B and D, d. Only D
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41, , MARCH ATTEMPT ~ 17 March 2021, Shift II, 19. Choose the correct statement regarding the, , 24. The total number of CC sigma bond/s in, , formation of carbocations A and B., +, , mesityl oxide (C 6H10O) is ........ . (Round off to, the nearest integer)., , –, , CH3––CH2––CH2––CH2+Br, CH3CH2CH, , (A), , CH2+HBr, , 25. A 1 molal K 4Fe(CN) 6 solution has a degree of, , +, , –, , dissociation of 0.4. Its boiling point is equal, to that of another solution which contains, 18.1 weight per cent of a non- electrolytic, solute A. The molar mass of A is ....... u., (Round off to the nearest integer)., [Density of water = 1.0 g cm −3], , CH3––CH2––CH––CH3+Br, (B), , (a) Carbocation B is more stable and formed, relatively at faster rate., (b) Carbocation A is more stable and formed, relatively at slow rate., (c) Carbocation B is more stable and formed, relatively at slow rate., , 26. In the ground state of atomic Fe( Z = 26), the, spin-only magnetic moment is ………… × 10−1, BM. (Round off to the nearest integer)., , (d) Carbocation A is more stable and formed, relatively at faster rate., , 20. During which of the following processes,, , [Given : 3 = 173, . , 2 = 141, . ], , 27. The number of chlorine atoms in 20 mL of, chlorine gas at STP is _____ 1021. (Round off to, the nearest integer)., [Assume chlorine is an ideal gas at STP, L bar mol −1 K −1, NA = 6023, R = 0083, ., ., × 1023], , does entropy decrease ?, A. Freezing of water to ice at 0°C., B. Freezing of water to ice at −10°C., C. N 2 (g) + 3H 2 (g) → 2NH 3 (g), D. Adsorption of CO(g) and lead surface., E Dissolution of NaCl in water., a. A, B, C and D, b. B and C, c. A and E, d. A, C and E, , 28. KBr is doped with 10 −5 mole per cent of SrBr, 2 . The number of cationic vacancies in 1 g of, KBr crystal is ……… 1014 (Round off to the, nearest integer). [Atomic mass : K = 39.1 u,, Br = 79.9 u, NA = 6023, ., × 1023 ], , Section B : Numerical Type Questions, 21. A KCl solution of conductivity 0.14 S m, , 29. Consider the reaction, N2O4( g), , shows a resistance of 4.19 Ω in a, conductivity cell. If the same cell is filled with, an HCl solution, the resistance drops to 1.03, Ω. The conductivity of the HCl solution is, ……… × 10−2 S m −1 (Round off to the nearest, integer), , O, , 30, , C, , 22. On complete reaction of FeCl3 with oxalic, acid in aqueous solution containing KOH,, resulted in the formation of product A. The, secondary valency of Fe in the product A is, ........ . (Round off to the nearest integer)., , 23. The reaction 2A + B 2 → 2AB is an, elementary reaction. For a certain quantity, of reactants, if the volume of the reaction, vessel is reduced by a factor of 3, the rate of, the reaction increases by a factor of ........... ., (Round off to the nearest integer)., , 2NO2( g)., , =, , The temperature at which KC = 20.4 and, K p = 6001, . , is ………… K. (Round off to the, nearest integer)., [Assume all gases are ideal and R = 00831, L, ., bar, K −1 mol −1]., , −1, , Cl, 0.140 g, , + C6H5NHC6H5, 0.388 g, , O, C6H5CN(C6H5)2, 0.210 g, , Consider the above reaction. The percentage, yield of amide product is .......... . (Round off to the, nearest integer)., (Given : Atomic mass : C : 12.0 u, H : 1.0 u,, N : 14.0 u, O : 16.0 u, Cl : 35.5 u)
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42, , ONLINE, , JEE Main 2021 ~ Solved Papers, , MATHEMATICS, Section A : Objective Type Questions, −x, , 1. Let f : R → R be defined as f ( x) = e sin x . If, F : [0, 1] → R is a differentiable function, such, x, , that F ( x) =, 1, , ∫ [F ′ ( x ) +, , ∫ f (t) dt, then the value of, 0, , f ( x)] e x dx lies in the interval, , 0, , 327 329 , a. , ,, 360 360 , 331 334 , c. , ,, 360 360 , , 330, b. , ,, 360, 335, d. , ,, 360, , 331, 360 , 336 , 360 , , 10, , 2. If the integral, , a., , 1, , −, [sin2πx ], −1, ∫ e x −[x ] dx = αe + βe 2 + γ,, 0, , where α , β , γ are integers and [ x ] denotes the, greatest integer less than or equal to x, then, the value of α + β + γ is equal to, a. 0, , b. 20, , c. 25, , d. 10, , 3. Let y = y ( x) be the solution of the differential, equation cos x (3sin x + cos x + 3)dy =, [1 + y sin x (3sin x + cos x + 3)]dx,, π, π, 0 ≤ x ≤ , y (0) = 0. Then, y is equal to, , 2, 3, 2 3 + 9, a. 2log e , , 6, , , 3 + 7, c. 2log e , , 2 , , 2, b. 2log e , , 3, d. 2log e , , , 3 + 10 , , 11 , 3 − 8, , 4, , , 6, , 4. The value of, , ∑ ( 6C r ⋅6 C 6 − r) is equal to, , r= 0, , a. 1124, , b. 1324, , 5. The value of lim, , c. 1024, , d. 924, , [ r ] + [2r ] + …… + [ nr ], , ,, n2, where r is non-zero real number and [ r ], denotes the greatest integer less than or, equal to r, is equal to, n→ ∞, , a. r /2, , b. r, , c. 2r, , d. 0, , 6. The number of solutions of the equation, 1, 2, , , = x 2, for, + cos −1 x 2 −, sin−1 x 2 +, 3 , 3 , , , x ∈ [ −1, 1], and [ x ] denotes the greatest integer, less than or equal to x, is, a. 2, , b. 0, , c. 4, , 7. Let a computer program generate only the, digits 0 and 1 to form a string of binary, numbers with probability of occurrence of 0, 1, at even places be and probability of, 2, 1, occurrence of 0 at the odd place be . Then,, 3, the probability that '10' is followed by ‘01’ is, equal to, , d. infinite, , 1, 18, , b., , 1, 3, , c., , 1, 6, , d., , 1, 9, , 8. The number of solutions of the equation, π, x + 2 tan x = in the interval [0, 2π ] is, 2, a. 3, , b. 4, , c. 2, , d. 5, , 9. Let S1, S 2 and S 3 be three sets defined as, S1 = { z ∈ C :|z − 1| ≤ 2 }, S 2 = { z ∈ C : Re[(1 − i) z ] ≥ 1}, S 3 = { z ∈ C : Im( z) ≤ 1}, Then, the set S1 ∩ S 2 ∩ S 3, a. is a singleton, b. has exactly two elements, c. has infinitely many elements, d. has exactly three elements, , 10. If the curve y = y ( x) is the solution of the, differential equation, 2( x 2 + x 5/ 4) dy − y ( x + x 1/ 4) dx = 2x 9/ 4 dx , x > 0, which passes through the point, 4, , , 1, 1 − log e 2 , then the value of y(16) is, , , 3, equal to, 31 8, a. 4 , + log e 3, 3, , 3, 31 8, , , b. , + log e 3, 3, , 3, 31 8, c. 4 , − log e 3, 3 3, , 31 8, , , d. , − log e 3, 3 3, , , 11. If the sides AB , BC and CA of a ∆ABC have 3, 5, and 6 interior points respectively, then the, total number of triangles that can be, constructed using these points as vertices,, is equal to, a. 364, , b. 240, , c. 333, , d. 360
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43, , MARCH ATTEMPT ~ 17 March 2021, Shift II, 12. If x , y , z are in arithmetic progression with, common difference d , x ≠ 3d, and the, 3 4 2 x , determinant of the matrix 4 5 2 y is, , , k, z , 5, zero, then the value of k 2 is, a. 72, , b. 12, , c. 36, , d. 6, , 13. Let O be the origin. Let OP = x $i + y$j − k$ and, OQ = − $i + 2$j + 3xk$ , x , y ∈ R , x > 0, be such, that|PQ| = 20 and the vector OP is, perpendicular to OQ. If OR = 3i$ + z$j − 7k$ ,, z ∈ R , is coplanar with OP and OQ, then the, value of x 2 + y 2 + z 2 is equal to, a. 7, , b. 9, , c. 2, , d. 1, , 14. Two tangents are drawn from a point P to, the circle x 2 + y 2 − 2x − 4 y + 4 = 0, such that, the angle between these tangents is, 12, 12, tan−1 , where tan−1 ∈ (0, π ). If the, 5, 5, centre of the circle is denoted by C and these, tangents touch the circle at points A and B,, then the ratio of the areas of ∆PAB and ∆CAB, is, a. 11: 4, , b. 9 : 4, , c. 3 : 1, , d. 2 : 1, , 15. Consider the function f : R → R defined by, , , 1 , 2 − sin |x|, x ≠ 0 , f ( x) = , x, . Then, f is, , 0, , x = 0, a. monotonic on (−∞ , 0) ∪ (0, ∞ ), b. not monotonic on (−∞ , 0) and (0, ∞ ), c. monotonic on (0, ∞ ) only, d. monotonic on (− ∞ , 0) only, , b. 14, , c. 16, , θ → 0 sin (2π, , equal to, a. −, c. 0, , 1, 2, , b. −, d., , d. 20, , tan( π cos 2 θ), , 17. The value of the limit lim, , 1, 4, , 1, 4, , sin2 θ), , 529, 64, 625, c., 72, , is, , 125, 72, 585, d., 66, , a., , b., , 19. If the Boolean expression ( p ∧ q) * ( p ⊗ q) is a, tautology, then * and ⊗ are respectively,, given by, a. → , →, , b. ∧ , ∨, , c. ∨ , →, , d. ∧ , →, , 20. If the equation of plane passing through the, mirror image of a point (2, 3, 1) with respect, x + 1 y −3 z + 2, to line, and containing, =, =, 2, 1, −1, x − 2 1− y z + 1, is, the line, =, =, 3, 2, 1, αx + βy + γz = 24, then α + β + γ is equal to, a. 20, , b. 19, , c. 18, , d. 21, , Section B : Numerical Type Questions, 18, , 21. If 1, log 10( 4 x − 2) and log 10 4 x +, are in, , 5, arithmetic progression for a real number x,, then the value of the determinant, 1, , 2x − , , 2, 1, x, , 16. Let L be a tangent line to the parabola, y 2 = 4 x − 20 at (6, 2). If L is also a tangent to, x2, y, the ellipse, + = 1, then the value of b is, 2, b, equal to, a. 11, , 18. Let the tangent to the circle x 2 + y 2 = 25 at, the point R(3, 4) meet x-axis and y-axis at, point P and Q, respectively. If r is the radius, of the circle passing through the origin O and, having centre at the incentre of the triangle, OPQ, then r 2 is equal to, , x − 1 x2, 0, , x is equal to ……… ., , 1, , 0, , 22. Let f : [ −1, 1] → R be defined as, f ( x) = ax 2 + bx + c for all x ∈ [ −1, 1], where, a , b, c ∈ R , such that f ( −1) = 2, f ′ ( −1) = 1and for, 1, x ∈ ( −1, 1) the maximum value of f ′′( x) is . If, 2, f ( x) ≤ α, x ∈ [ −1, 1], then the least value of α is, equal to …………… ., 23. Let f : [ −3, 1] → R be given as, min {( x + 6), x 2 } , − 3 ≤ x ≤ 0, f ( x) = , ., 2, 0≤ x ≤1 , max{ x , x } ,, If the area bounded by y = f ( x) and x -axis is, A, then the value of 6A is equal to ………… .
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44, , ONLINE, , 24. Let tanα, tanβ and tanγ; α , β , γ ≠, , (2n − 1) π, , ,, 2, n ∈ N be the slopes of three line segments, OA , OB and OC , respectively, where O is, origin. If circumcentre of ∆ABC coincides with, origin and its orthocentre lies on y-axis, then, 2, cos 3α + cos 3β + cos 3γ , the value of , is, cos α cos β cos γ, , , , a b, α 0, 27. Let A = , and B = β ≠ 0, such that, c, d, , , , AB = B and a + d = 2021, then the value of, ad − bc is equal to …………… ., →, , 28. Let x be a vector in the plane containing, →, →, vectors a = 2$i − $j + k$ and b = $i + 2 $j − k$ . If the, →, vector x is perpendicular to (3$i + 2 $j − k$ ) and, →, 17 6, its projection on a is, , then the value of, 2, →, |x|2 is equal to ………… ., , equal to ……… ., 25. Consider a set of 3n numbers having, variance 4. In this set, the mean of first 2n, numbers is 6 and the mean of the remaining, n numbers is 3. A new set is constructed by, adding 1 into each of first 2n numbers and, subtracting 1 from each of the remaining n, numbers. If the variance of the new set is k,, then 9k is equal to ……… ., 26. Let the coefficients of third, fourth and fifth, a n, terms in the expansion of x + 2 , x ≠ 0, be, , x , in the ratio 12 : 8 : 3. Then, the term, independent of x in the expansion, is equal, to …………… ., , JEE Main 2021 ~ Solved Papers, , e, , 29. Let In = ∫ x 19( log |x|) n dx , where n ∈ N. If, 1, , (20) I10 = αI9 + βI8, for natural numbers α and, β, then α − β is equal to …………… ., 30. Let P be an arbitrary point having sum of the, squares of the distance from the planes, x + y + z = 0, lx − nz = 0 and x − 2 y + z = 0,, equal to 9. If the locus of the point P is, x 2 + y 2 + z 2 = 9, then the value of l − n is, equal to ……………… ., , Answers, For solutions scan, the QR code, , Physics, 1. (d), 11. (b), 21. 3, , 2. (b), 12. (b), 22. 5, , 3. (c), 13. (c), 23. 30, , 4. (d), 14. (d), 24. 25, , 5. (d), 15. (d), 25. 3, , 6. (c), 16. (a), 26. 640, , 7. (d), 17. (d), 27. 4, , 8. (b), 18. (a), 28. 30, , 9. (b), 19. (b), 29. 16, , 10. (d), 20. (c), 30. 6, , 3. (a), 13. (d), 23. 27, , 4. (d), 14. (c), 24. 5, , 5. (c), 15. (c), 25. 85, , 6. (a), 16. (a), 26. 49, , 7. (a), 17. (b), 27. 1, , 8. (a), 18. (d), 28. 5, , 9. (a), 19. (a), 29. 354, , 10. (b), 20. (a), 30. 77, , 3. (b), 13. (b), 23. 41, , 4. (d), 14. (b), 24. 144, , 8. (a), 18. (c), 28. 486, , 9. (c), 19. (a), 29. 1, , 10. (c), 20. (b), 30. 0, , Chemistry, 1. (b), 11. (c), 21. 57, , 2. (d), 12. (b), 22. 6, , Mathematics, 1. (b), 11. (c), 21. 2, , 2. (a), 12. (a), 22. 5, , 5. (a), 15. (b), 25. 68, , 6. (b), 16. (b), 26. 4, , 7. (d), 17. (a), 27. 2020
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45, , MARCH ATTEMPT ~ 18 March 2021, Shift I, , JEE Main 2021, 18 MARCH SHIFT I, , PHYSICS, Section A : Objective Type Questions, 1. An oil drop of radius 2 mm with a density, −3, , 3 g cm is held stationary under a constant, electric field 355, . × 105 Vm −1 in the Millikan’s, oil drop experiment. What is the number of, excess electrons that the oil drop will, possess? (Take, g = 981, . m/s 2), a. 48.8 × 1011, c. 17.3 × 1010, , b. 1.73 × 1010, d. 1.73 × 1012, , 2. Match List-I with List-II., List-I, , List-II, , A., , 10 km height over, Earth’s surface, , (i), , Thermosphere, , B., , 70 km height over, Earth’s surface, , (ii), , Mesosphere, , C., , 180 km height over (iii) Stratosphere, Earth’s surface, , D., , 270 km height over (iv) Troposphere, Earth’s surface, , A, B, C, D, a. (iv) (iii) (ii) (i), b. (i) (iv) (iii) (ii), c. (iii) (ii) (i) (iv), d. (ii) (i) (iv) (iii), , 4. A plane electromagnetic wave of frequency, 100 MHz is travelling in vacuum along the, x-direction. At a particular point in space and, $ (where, k$ is unit vector, time, B = 20, . × 10−8 kT, along z-direction). What is E at this point?, a. 0.6 $j V/m, c. 6.0 $j V/m, , 5. A thin circular ring of mass M and radius r is, rotating about its axis with an angular speed, ω. Two particles having mass m each are now, attached at diametrically opposite points., The angular speed of the ring will become, M, M+ m, M, c. ω, M + 2m, a. ω, , M + 2m, M, M − 2m, d. ω, M + 2m, b. ω, , 6. Four identical long solenoids A, B, C and D, are connected to each other as shown in the, figure. If the magnetic field at the centre of A, is 3T, the field at the centre of C would be, (Assume that, the magnetic field is confined, with in the volume of respective solenoid), B, , 3. Imagine that the electron in a hydrogen, atom is replaced by a muon (µ). The mass of, muon particle is 207 times that of an, electron and charge is equal to the charge of, an electron. The ionisation potential of this, hydrogen atom will be, a. 13.6 eV, c. 331.2 eV, , b. 6.0 k$ V/m, d. 0.6 k$ V/m, , b. 2815.2 eV, d. 27.2 eV, , C, , A, i, , D, , a. 12T, c. 9T, , b. 6T, d. 1T
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46, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 7. The time period of a simple pendulum is, given by T = 2π l / g . The measured value, of the length of pendulum is 10 cm known, to a 1mm accuracy. The time for 200, oscillations of the pendulum is found to be, 100 s using a clock of 1s resolution. The, percentage accuracy in the determination, of g using this pendulum is x. The value of, x to the nearest integer is, a. 2%, , b. 3%, , c. 5%, , d. 4%, , 8. A constant power delivering machine has, towed a box, which was initially at rest,, along a horizontal straight line. The, distance moved by the box in time t is, proportional to, a. t 2 / 3, , b. t 3 / 2, , d. t 1/ 2, , c. t, , 9. What will be the average value of energy, along one degree of freedom for an ideal, gas in thermal equilibrium at a, temperature T ? (k B is Boltzmann constant), 1, a. kBT, 2, , b., , 2, kBT, 3, , c., , 3, kBT, 2, , d. kBT, , 12. In Young’s double slit arrangement, slits are, separated by a gap of 0.5 mm, and the screen, is placed at a distance of 0.5 m from them. The, distance between the first and the third bright, fringe formed when the slits are illuminated by, a monochromatic light of 5890 Å is, a. 1178 × 10−9 m, b. 1178 × 10−6 m, c. 1178 × 10−12 m, d. 5890 × 10−7 m, , 13. A particle is travelling 4 times as fast as an, electron. Assuming the ratio of de-Broglie, wavelength of a particle to that of electron is, 2 : 1, the mass of the particle is, 1, times the mass of electron, 16, b. 8 times the mass of electron, c. 16 times the mass of electron, 1, d. times the mass of electron, 8, , a., , 14. The position, velocity and acceleration of a, particle moving with a constant acceleration, can be represented by, , d. None of these, b., , 11. The p-V diagram of a diatomic ideal gas, system going under cyclic process as, shown in figure. The work done during an, adiabatic process CD is (use, γ = 14, . ), , Acceleration, , v(t), , t, , b. − 400 J, , a(t), , c. 400 J, , d. 200 J, , Velocity, , Position, , d., , 3 4, V(m3), , x(t), , t, , t, , t, , p, , a. − 500 J, , t, , C, , B, , 1, , a(t), , t, , Acceleration, , x(t), , t, , v(t), , t, , c., , D, , x(t), , a(t), , t, , Acceleration, , 100N/m2, , A, , Velocity, t, , Position, , T (1) T ( 2 ), c. T1/ 2 = (11/) 2 1/ 2( 2 ), T1/ 2 + T1/ 2, , v(t), , Acceleration, , b. T1/ 2 = T1(/12) + T1(/22), , T1(/12) − T1(/22), , 200N/m2, , x(t), , Velocity, , T1(/12) + T1(/22), , Position, , a. T1/ 2 =, , a., , Velocity, , two independent decay processes having, half-lives T1(/12) and T1(/22) , respectively. The, effective half-life T1/ 2 of the nuclei is, , Position, , 10. A radioactive sample disintegrates via, , v(t), , t, , a(t), , t
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47, , MARCH ATTEMPT ~ 18 March 2021, Shift I, 15. In the experiment of Ohm’s law, a potential, difference of 5.0 V is applied across the end, of a conductor of length 10.0 cm and, diameter of 5.00 mm. The measured current, in the conductor is 2.00 A. The maximum, permissible percentage error in the, resistivity of the conductor is, a. 3.9, , b. 8.4, , c. 7.5, , d. 3.0, , 16. In a series L-C-R resonance circuit, if we, change the resistance only, from a lower to, higher value,, a. the bandwidth of resonance circuit will, increase, b. the resonance frequency will increase, c. the quality factor will increase, d. the quality factor and the resonance, frequency will remain constant, , Section B : Numerical Type Questions, 21. A particle performs simple harmonic motion, with a period of 2 s. The time taken by the, particle to cover a displacement equal to half, of its amplitude from the mean position is, 1/ a s. The value of a to the nearest integer is, ……… ., , 22. The circuit shown in the figure consists of a, , charged capacitor of capacity 3 µF and a, charge of 30 µC. At time t = 0, when the key is, closed, the value of current flowing through, the 5 MΩ resistor is x µA. The value of x to, the nearest integer is ……… ., C = 3 µF, , 5MΩ, , q = 30µC, , 17. An AC source rated 220 V, 50 Hz is connected, to a resistor. The time taken by the current, to change from its maximum to the rms, value is, a. 2.5 ms, , b. 25 ms, , c. 2.5 s, , d. 0.25 ms, , 23. The voltage across the 10Ω resistor in the, given circuit is x volt., , 18. Your friend is having eye sight problem. She, is not able to see clearly a distant uniform, window mesh and it appears to her as, non-uniform and distorted. The doctor, diagnosed the problem as, a. astigmatism, b. myopia with astigmatism, c. presbyopia with astigmatism, d. myopia and hypermetropia, , carrying current is placed in an external, magnetic field., Identify the effect of the field on the wire., a. Loop assumes circular shape with its plane, normal to the field., b. Loop assumes circular shape with its plane, parallel to the field., c. Wire gets stretched to become straight., d. Shape of the loop remains unchanged., , 20. The time period of a satellite in a circular, orbit of radius R is T . The period of another, satellite in a circular orbit of radius 9R is, b. 27 T, , c. 12 T, , 10Ω, , 20Ω, , 170 V, , The value of x to the nearest integer is …… ., , 19. A loop of flexible wire of irregular shape, , a. 9 T, , 50Ω, , d. 3 T, , 24. Two separate wires A and B are stretched by, 2 mm and 4 mm respectively, when they are, subjected to a force of 2 N. Assume that, both the wires are made up of same material, and the radius of wire B is 4 times that of the, radius of wire A. The length of the wires A, and B are in the ratio of a : b. Then, a / b can, be expressed as 1/ x , where x is ……… ., , 25. A person is swimming with a speed of 10 m/s, at an angle of 120° with the flow and reaches, to a point directly opposite on the other side, of the river. The speed of the flow is x m/s., The value of x to the nearest integer, is ……… .
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48, , ONLINE, , 26. A parallel plate capacitor has plate area, 100 m2 and plate separation of 10 m. The, space between the plates is filled upto a, thickness 5 m with a material of dielectric, constant of 10. The resultant capacitance of, the system is x pF., The value of ε 0 = 885, . × 10−12 fm −1., The value of x to the nearest integer is …… ., , 28. As shown in the figure, a particle of mass, 10 kg is placed at a point A. When the particle, is slightly displaced to its right, it starts, moving and reaches the point B. The speed of, the particle at B is x m/s. (Take, g = 10 m/s 2), The value of x to the nearest integer is ….… ., A, , 27. A ball of mass 10 kg moving with a velocity, 10 3 m/s along the X-axis, hits another ball, of mass 20 kg which is at rest. After the, collision, first ball comes to rest while the, second ball disintegrates into two equal, pieces. One piece starts moving along Y-axis, with a speed of 10 m/s., The second piece starts moving at an angle, of 30° with respect to the X-axis. The, velocity of the ball moving at 30° with X-axis, is x m/s. The configuration of pieces after, collision is shown in the figure below. The, value of x to the nearest integer is .......... ., Y-axis, , C, B, , Horizontal, surface, , 10 m, , 5m, , 29. An n-p-n transistor operates as a common, emitter amplifier with a power gain of 10 6., The input circuit resistance is 100Ω and the, output load resistance is 10 kΩ. The common, emitter current gain β will be ......... . (Round, off to the nearest integer), , 30. A bullet of mass 0.1 kg is fired on a wooden, block to pierce through it, but it stops after, moving a distance of 50 cm into it. If the, velocity of bullet before hitting the wood is, 10 m/s and it slows down with uniform, deceleration, then the magnitude of effective, retarding force on the bullet is x N. The value, of x to the nearest integer is ......... ., , Piece-1, v1 = 10 m/s, X-axis, , 30°, , JEE Main 2021 ~ Solved Papers, , v2, , CHEMISTRY, Section A : Objective Type Questions, 1., , + –, , N2Cl, , CH3, , H 3C, N, , NH2, , N, b., , NaNO2, HCl, , X, 273 K- 278 K (Major product), , +, , N, , N, , N, , and, , CH3, CH3, , Y, (Major product), , Cl, , –, , N2Cl, N, a., , N, , N==, , N, , c., , and, N—CH3, CH3, , and, , CH3, CH3
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49, , MARCH ATTEMPT ~ 18 March 2021, Shift I, Cl, N==, d., , N, , and, N, H 3C, , A, B, C, (ii) (iv) (i), (iv) (i) (ii), (iv) (iii) (i), (ii) (iv) (iii), , a., b., c., d., CH3, , C≡≡ N, , 7., , 2. The ionic radius of Na + ions is 1.02 Å. The, ionic radii (in Å) of Mg, respectively, are, a. 1.05 and 0.99, c. 0.85 and 0.99, , 2+, , D, (iii), (iii), (ii), (i), , COOH, H 2O, , 3+, , and Al ,, , H+, , b. 0.72 and 0.54, d. 0.68 and 0.72, , H2O, , ''A'', , +, (Major product) H , ∆, , Consider the above chemical reaction and, identify product “A”., , C 8H 8O followed by hydrolysis gives, compound ‘A’ which reacts instantly with, Lucas reagent to give compound B, C 10H13Cl., , CH2NO2, , CH2NH2, , 3. Reaction of Grignard reagent, C 2H5MgBr with, , b., , a., , H, C==N—OH, , CONH2, , The compound B is, , d., , c., , Cl, CH3, , 8. Match the list-I with list- II, CH3, , a., , List-I, , b., , Cl, Cl, , CH3, Cl, CH3, , c., , CH3, CH3, , d., , 4. Reagent, 1-naphthylamine and sulphanilic, acid in acetic acid is used for the detection of, b. NO −3, d. NO −2, , a. N2O, c. NO, , 5. A non-reducing sugar “A” hydrolyses to give, two reducing monosaccharides. Sugar A is, a. fructose, c. glucose, , List-I, , Antacid, , (i), , Ruthenium, , (B), , Vitamin-B12, , (ii), , Platinum, , (C), , Anticancer drug, , (iii), , Cobalt, , (D), , Grubbs catalyst, , (iv), , Magnesium, , Choose the most appropriate answer from, the options given below, a., b., c., d., , Novestrol, Cimetidine, , (B), , Artificial sweetener, , (ii), , (C), , Antifertility, , (iii) Valium, , (D), , Tranquilizers, , (iv) Alitame, , D, (i), (i), (ii), (i), , List-I, (Chemicals), , List-II, (Use / Preparation /, Constituent), , (A), , Alcoholic, potassium, hydroxide, , (i), , Electrodes in batteries, , (B), , Pd/BaSO4, , (ii), , Obtained by addition, reaction, , (C), , BHC (Benzene, hexachloride), , (iii) Used for β-elimination, reaction, , (Example), (i), , A, B, C, (iii) (ii) (iv), (iv) (iii) (ii), (iv) (iii) (i), (iv) (ii) (iii), , 9. Match List-I with List-II., , List-II, , (Class of drug), (A), , Chlorophyll, , b. galactose, d. sucrose, , 6. Match the List-I with List- II., , List-II, , (A), , (D) Polyacetylene, , (iv) Lindlar catalyst
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50, , JEE Main 2021 ~ Solved Papers, , ONLINE, Choose the most appropriate match, A, a. (ii), c. (iii), , B, (i), (i), , C, (iv), (iv), , D, (iii), (ii), , A, B, b. (iii) (iv), d. (ii) (iv), , NO3, , C, (ii), (i), , D, (i), (iii), , Ph3P, b., , Ph3P, , Br, , Ni, , O2N, , and, , O2N, , Br, , Co, , NH3, , (A) Methane leads to both global warming, and photochemical smog., (B) Methane is generated from paddy fields., (C) Methane is a stronger global warming, gas than CO2., , c., , Ni, , d., , Co, , O2N, , NH3, NO2, , Ph3P, Br, , Br, , Ni, , and, , H 3N, O2N, , PPh3, , Co, , NO2, NO2, , two radial nodes. The orbital is, a. 2s, b. 3s, c. 3p, c. 2p, , (i), , Antacid, , (B), , (ii), , Cement, , (C), , CaO, , (iii), , Bleach, , (D), , CaCO 3, , (iv), , Plaster of Paris, , 15., , CH3, Alkaline KMnO4, H+, , Choose the most appropriate answer from, the options given below., D, (ii), (i), , and, , Br, , NH3, , List-II, , A, B, C, a. (i) (iv) (iii), c. (iii) (iv) (ii), , O2N, , 14. A certain orbital has no angular nodes and, , Ca(OCl) 2, 1, CaSO 4 ⋅ H2O, 2, , (A), , Ph3P, , Br, , NH3, , 11. Match List-I with List-II., List-I, , Ph3P, , NH3, , (D) Methane is a part of reducing smog., Choose the most appropriate answer, from the options given below, b. (A) and (B) only, d. (A), (B), (D) only, , NH3, , NH3, , 10. The statements that are true., , a. (A), (B), (C) only, c. (B), (C), (D) only, , NH3, , A, b. (iii), d. (iii), , B, (ii), (ii), , C, (iv), (i), , D, (i), (iv), , 'X', , OCH3, , Considering the above chemical reaction,, identify the product ‘X’., CHO, , 12. Compound with molecular formula C 3H6O, , CH2OH, , can show, a., b., c., d., , positional isomerism, both positional isomerism and metamerism, metamerism, functional group isomerism, , a., , 13. The correct structures of trans-[NiBr2(PPh3) 2 ], and meridonial-[Co(NH 3) 3(NO2) 3 ],, respectively are, NO2, Ph3P, a., , Br, , Br, Ni, PPh3, , and, , H 3N, , Co, , H3N, , c., NO2, NO2, , NH3, , b. X-, , X-, , OCH3, , OCH3, , COOH, , CH3, , d. X-, , X-, , OCH3, , OH
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51, , MARCH ATTEMPT ~ 18 March 2021, Shift I, 16. Match List-I with List-II., , 20. The chemical that is added to reduce the, , List-I, (Process), , List-II, (Catalyst), , melting point of the reaction mixture during, the extraction of aluminium is, a. cryolite, c. calamine, , (A), , Deacon’s process, , (i), , ZSM-5, , (B), , Contact process, , (ii), , CuCl2, , (C), , Cracking of, hydrocarbons, , (iii), , Particles ‘Ni’, , (D), , Hydrogenation of, vegetable oils, , (iv), , V 2O 5, , Choose the most appropriate answer from, the options given below, a., b., c., d., , A, B, C, (ii) (iv) (i), (i) (iii) (ii), (iii) (i) (iv), (iv) (ii) (i), , D, (iii), (iv), (ii), (iii), , labelled as Assertion A and the other, labelled as Reason R., Assertion A During the boiling of water, having temporary hardness, Mg(HCO3) 2 is, converted to MgCO3., Reason R The solubility product of Mg(OH) 2, is greater than that of MgCO3., In the light of the above statements, choose, the most appropriate answer from the, options given below, a. Both A and R are true but R is not the correct, explanation of A., b. A is true but R is false., c. Both A and R are true and R is the correct, explanation of A., d. A is false but R is true., , 18. The number of ionisable hydrogens present, in the product obtained from a reaction of, phosphorus trichloride and phosphonic acid, is, b. 0, , c. 2, , d. 1, , 19. In a binary compound, atoms of element A, form a hcp structure and those of element M, occupy 2/3 of the tetrahedral voids of the, hcp structure. The formula of the binary, compound is, a. M 2 A 3, , b. M 4 A 3, , Section B : Numerical Type Questions, 21. AX is a covalent diatomic molecule, where A, and X are second row elements of periodic, table. Based on molecular orbital theory, the, bond order of AX is 2.5. The total number of, electrons in AX is ……… . (Round off to the, nearest integer)., , 22. In order to prepare a buffer solution of pH, , 17. Given below are two statements : One is, , a. 3, , b. bauxite, d. kaolite, , c. M 4 A, , d. MA 3, , 5.74, sodium acetate is added to acetic acid., If the concentration of acetic acid in the, buffer is 1.0 M, the concentration of sodium, acetate in the buffer is ………… M. (Round off, to the nearest integer)., [Given : pK a (acetic acid = 4.74], , 23. 2 NO( g) + Cl2( g) q, , 2 NOCl( s), , This reaction was studied at − 10°C and the, following data was obtained run, [NO]0 [Cl2 ]0, r0, 1, 2, 3, , 0.10, 0.10, 0.20, , 0.10, 0.20, 0.20, , 0.18, 0.35, 1.40, , [NO]0 and [Cl2 ]0 are the initial concentrations, and r0 is the initial reaction rate., The overall order of the reaction is ....... ., (Round off to the nearest integer)., , 24. For the reaction,, C 2H 6 → C 2H 4 + H 2, the reaction enthalpy ∆ rH = .......... kJ mol −1, (Round off to the nearest integer)., [Given : Bond enthalpies in kJ mol −1 :, C C = 347, C == C = 611; C H = 414; H H =, 436], , 25. ......... grams of 3-hydroxy propanal (MW = 74), must be dehydrated to produce 7.8 g of, acrolein (MW= 56) (C 3H 4O), if the percentage, yield is 64 (Round off to the nearest integer)., [Given : Atomic masses : C = 12.0 u, H = 1.0 u,, O = 16.0 u]
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52, , ONLINE, , 26. A reaction of 0.1 mole of benzylamine with, bromomethane gave 23 g of benzyl trimethyl, ammonium bromide. The number of moles, of bromomethane consumed in this reaction, are n × 10−1, when n = ......... (Round off to the, nearest integer)., (Given : Atomic masses : C = 12.0 u, H = 1.0 u,, N = 14.0 u, Br = 80.0 u], , 27. The total number of unpaired electrons, present in the complex K 3 [Cr(oxalate) 3] is, ........... ., , JEE Main 2021 ~ Solved Papers, , [Given : Molal depression constant of water, = 1.85 K kg mol −1, freezing point of pure, water = 0°C ], , 29. For the reaction,, 2Fe 3+ (aq ) + 2I− (aq ) → 2Fe 2+(aq ) + I2 (s ), The magnitude of the standard molar Gibbs, °, free energy change, ∆ rG m, = − ........... kJ, (Round off to the nearest integer)., E ° 2 +, = − 0.440 V ; E ° 3 +, = − 0036, ., V, Fe, /Fe ( s ), , Fe ° /Fe(s), ., V;, F = 96500 C , E I 2 / 2I − = 0539, , , 30. Complete combustion of 3 g of ethane gives, 28. 2 molal solution of a weak acid HA has a, freezing point of 3.885°C. The degree of, dissociation of this acid is ……… × 10−3., (Round off to the nearest integer)., , x × 1022 molecules of water. The value of x is, .......... . (Round off to the nearest integer)., [Use : NA = 6023, ., × 1023; Atomic masses in u :, C = 12.0 ; O = 16.0 ; H = 1.0], , MATHEMATICS, Section A : Objective Type Questions, 1. The differential equation satisfied by the, system of parabolas y = 4a( x + a) is, 2, , 2, , dy, dy, a. y − 2x − y = 0, dx , dx , 2, , dy, dy, b. y − 2x + y = 0, dx , dx , 2, , dy, dy, c. y + 2x − y = 0, dx , dx , dy, dy, d. y + 2x − y = 0, dx , dx , , 2. The number of integral values of m, so that, the abscissa of point of intersection of lines, 3x + 4 y = 9 and y = mx + 1is also an integer,, is, a. 1, c. 3, , b. 2, d. 0, , 3. Let (1+ x + 2x 2) 20 = a 0 + a1x + a 2x 2 + ... + a 40x 40,, then a1 + a 3 + a5 + ... + a 37 is equal to, a. 220 (220 − 21), b. 219 (220 − 21), c. 219 (220 + 21), d. 220 (220 + 21), , 4. The solutions of the equation, sin2 x, 1 + sin2 x, 2, cos x, 1 + cos 2 x, 4 sin2x, , 4 sin2x, , π π, a., ,, 12 6, , π 5π, b. ,, 6 6, , sin2 x, cos 2 x, 1+ 4 sin2x, = 0, (0 < x < π ), are, 5π 7π, c., ,, 12 12, , d., , 7 π 11π, ,, 12 12, , 5. Choose the correct statement about two, circles whose equations are given below., x 2 + y 2 − 10x − 10 y + 41 = 0, x 2 + y 2 − 22x − 10 y + 137 = 0, a. circles have same centre, b. circles have no meeting point, c. circles have only one meeting point, d. circles have two meeting points, , 6. Let α , β , γ be the real roots of the equation,, x 3 + ax 2 + bx + c = 0, (a , b, c ∈R and a , b ≠ 0)., If the system of equations (in u,v ,w ) given by, αu + βv + γw = 0, βu + γv + αw = 0;, γu + αv + βw = 0 has non-trivial solution, then, a2, the value of, is, b, a. 5, c. 1, , b. 3, d. 0
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53, , MARCH ATTEMPT ~ 18 March 2021, Shift I, 7. The integral ∫, , (2x − 1)cos (2x − 1) 2 + 5, 4x −4x + 6, 2, , dx is, , 12. For the four circles M, N, O and P, following, four equations are given, Circle M : x 2 + y 2 = 1, Circle N : x 2 + y 2 − 2x = 0, Circle O : x 2 + y 2 − 2x − 2 y + 1 = 0, Circle P : x 2 + y 2 − 2 y = 0, , equal to (where, c is a constant of, integration), 1, a. sin, 2, 1, b. cos, 2, 1, c. cos, 2, 1, d. sin, 2, , (2x − 1) 2 + 5 + c, (2x + 1) 2 + 5 + c, , If the centre of circle M is joined with centre, of the circle N, further centre of circle N is, joined with centre of the circle O, centre of, circle O is joined with the centre of circle P, and lastly, centre of circle P is joined with, centre of circle M, then these lines form the, sides of a, , (2x − 1) 2 + 5 + c, (2x + 1) 2 + 5 + c, , 8. The equation of one of the straight lines, which passes through the point (1,3) and, makes an angle tan−1( 2) with the straight, line, y + 1 = 3 2x is, a. 4 2x + 5 y − (15 + 4 2 ) = 0, , a. rhombus, c. rectangle, , 13. If α , β are natural numbers, such that, 100α − 199β = (100) (100) + (99) (101) +, (98) (102) + ... + (1)(199), then the slope of the, line passing through (α ,β) and origin is, , b. 5 2 x + 4 y − (15 + 4 2 ) = 0, c. 4 2 x + 5 y − 4 2 = 0, d. 4 2 x − 5 y − (5 + 4 2 ) = 0, −1, , 9. If lim, , sin x − tan x, , 3x 3, value of (6L + 1) is, a., , 1, 6, , a. 540, c. 530, , −1, , x→ 0, , b., , 1, 2, , 14. The real valued function f ( x) =, c. 6, , d. 2, , respect to rectangular cartesian system. This, system is rotated through a certain angle, about the origin in the counter clockwise, sense. If, with respect to new system, a has, components p + 1and 10, then a value of p, is equal to, 5, b. −, 4, d. − 1, , a. 1, 4, 5, , 11. If the equation a|z|2 + αz + αz + d = 0, represents a circle, where a,d are real, constants, then which of the following, condition is correct ?, a.|α|2 − ad ≠ 0, b.|α|2 − ad > 0 and a ∈ R − {0}, c.|α|2 − ad ≥ 0 and a ∈ R, d. α = 0, a , d ∈ R, , +, , b. 550, d. 510, , is equal to L, then the, , cosec −1x, x − [x], , ,, , where [ x ] denotes the greatest integer less, than or equal to x, is defined for all x, belonging to, , 10. A vector a has components 3p and 1 with, , c., , b. square, d. parallelogram, , a. all reals except integers, b. all non-integers except the interval [− 1,1], c. all integers except 0, − 1, 1, d. all reals except the interval [ − 1, 1], , 15., , 1, 1, 1, 1, is equal, +, +, + ... +, 32 − 1 52 − 1 72 − 1, (201) 2 − 1, to, a., , 101, 404, , b., , 25, 101, , c., , 101, 408, , d., , 99, 400, , 16. If the functions are defined as f ( x) = x and, g( x) = 1 − x , then what is the common, domain of the following functions?, f + g , f − g , f / g , g / f , g − f , where, f (x ), ( f ± g ) (x ) = f (x ) ± g (x ), ( f / g )(x ) =, g (x ), a. 0 ≤ x ≤ 1, c. 0 < x < 1, , b. 0 ≤ x < 1, d. 0 < x ≤ 1
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54, , ONLINE, , , 1, , , 17. If f ( x) = |x|, , 23. Let f ( x) and g( x) be two functions satisfying, , ; |x| ≥ 1, , ax 2 + b ; |x| < 1, , is differentiable at every point of the domain,, then the values of a and b are respectively, 1 1, a. ,, 2 2, 5, 3, c. , −, 2, 2, , b. 2, d. 3, , 19. The sum of all the 4-digit distinct numbers, that can be formed with the digits 1, 2, 2 and, 3 is, , 20. The value of 3 +, , b. 122664, d. 22264, , 1, 4+, , is equal, , 1, 3+, , 1, 4+, , 1, 3 + ... ∞, , to, a. 15, . + 3, c. 3 + 2 3, , 4, , then the value of, , ∫ ∫ (x) dx is ……… ., 2, , −4, , 2, , 1 2 0, 18. Let A + 2B = 6 −3 3 and, , , −5 3 1, 2 −1 5, 2A − B = 2 −1 6. If Tr( A) denotes the sum, , , 0 1 2, of all diagonal elements of the matrix A, then, Tr( A) − Tr(B) has value equal to, , a. 26664, c. 122234, , f ( x 2) + g( 4 − x) = 4 x 3 and g( 4 − x) + g( x) = 0,, , 24. The missing value in the following figure is, , 1, 3, b. , −, 2, 2, 1 3, d. − ,, 2 2, , a. 1, c. 0, , JEE Main 2021 ~ Solved Papers, , b. 2 + 3, d. 4 + 3, , Section B : Numerical Type Questions, 21. The number of times the digit 3 will be, written when listing the integers from 1 to, 1000 is ……… ., , 22. Let the plane, ax + by + cz + d = 0 bisect the, line joining the points ( 4 , − 3, 1) and (2, 3, − 5), at the right angles. If a , b, c , d are integers,, then the minimum value of (a 2 + b2 + c 2 + d 2), is ……… ., , 1, , 12, , 3, , 1, , ?, , 424, , 36, , 8, , 5, , 4, , 7, , 25. Let z1, z 2 be the roots of the equation, z 2 + az + 12 = 0 and z1, z 2 form an equilateral, triangle with origin. Then, the value of|a| is, ……… ., , 26. The equation of the planes parallel to the, , plane x − 2 y + 2z − 3 = 0 which are at unit, distance from the point (1, 2, 3) is, ax + by + cz + d = 0. If ( b − d) = K (c − a), then, the positive value of K is ……… ., , 27. The mean age of 25 teachers in a school is, 40 yr. A teacher retires at the age of 60 yr, and a new teacher is appointed in his place., If the mean age of the teachers in this school, now is 39 yr, then the age (in years) of the, newly appointed teacher is ……… ., , 28. If f ( x) = ∫, , 5x 8 + 7x 6, ( x 2 + 1 + 2x 7) 2, , dx , ( x ≥ 0),f (0) = 0 and, , 1, f (1) = , then the value of K is ………… ., K, , 29. A square ABCD has all its vertices on the, , curve x 2 y 2 = 1. The mid-points of its sides, also lie on the same curve. Then, the square, of area of ABCD is ………… ., , 30. The number of solutions of the equation, |cot x| = cot x +, ………… ., , 1, in the interval [0, 2π] is, sin x
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55, , MARCH ATTEMPT ~ 18 March 2021, Shift I, , Answers, For solutions scan, the QR code, , Physics, 1. (b), 11. (a), 21. 6, , 2. (a), 12. (b), 22. 2, , 3. (b), 13. (d), 23. 70, , 4. (c), 14. (b), 24. 32, , 5. (c), 15. (a), 25. 5, , 6. (d), 16. (a), 26. 161, , 7. (b), 17. (a), 27. 20, , 8. (b), 18. (b), 28. 10, , 9. (a), 19. (a), 29. 100, , 10. (c), 20. (b), 30. 10, , 3. (c), 13. (d), 23. 3, , 4. (d), 14. (b), 24. 128, , 5. (d), 15. (c), 25. 16, , 6. (a), 16. (a), 26. 3, , 7. (c), 17. (d), 27. 3, , 8. (b), 18. (c), 28. 50, , 9. (b), 19. (b), 29. 45, , 10. (a), 20. (a), 30. 18, , 3. (b), 13. (b), 23. 512, , 4. (d), 14. (b), 24. 4, , 5. (c), 15. (b), 25. 6, , 6. (b), 16. (c), 26. 4, , 7. (a), 17. (d), 27. 35, , 8. (a), 18. (b), 28. 4, , 9. (d), 19. (a), 29. 80, , 10. (d), 20. (a), 30. 1, , Chemistry, 1. (b), 11. (c), 21. 15, , 2. (b), 12. (d), 22. 10, , Mathematics, 1. (c), 11. (b), 21. 300, , 2. (b), 12. (b), 22. 28
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ONLINE, , JEE Main 2021 ~ Solved Papers, , JEE Main 2021, 18 MARCH SHIFT II, , PHYSICS, Section A : Objective Type Questions, 1. Which of the following statements are, correct?, A. Electric monopoles do not exist, whereas, magnetic monopoles exist., B. Magnetic field lines due to a solenoid at its, ends and outside cannot be completely, straight and confined., C. Magnetic field lines are completely confined, within a toroid., D. Magnetic field lines inside a bar magnet are, not parallel., E. χ = − 1is the condition for a perfect, diamagnetic material, where χ is its magnetic, susceptibility., , Choose the correct answer from the options, given below., , 2. An object of mass m1 collides with another, object of mass m 2, which is at rest. After the, collision, the objects move with equal speeds, in opposite direction. The ratio of the, masses m 2 : m1 is, b. 2 : 1, d. 1 : 1, , 3. For an adiabatic expansion of an ideal gas,, the fractional change in its pressure is equal, to (where, γ is the ratio of specific heats), dV, V, 1 dV, c. −, γ V, , a. − γ, , energies K p and K α , respectively, enter into a, magnetic field at right angles., The ratio of the radii of trajectory of proton to, that of α-particle is 2 : 1. The ratio of K p : K α is, b. 8 : 1, d. 4 : 1, , a. 1: 8, c. 1 : 4, , 5. A plane electromagnetic wave propagating, along y-direction can have the following pair, of electric field (E) and magnetic field (B), components., a. E y , B y or E z , Bz, b. E y , Bx or E x , B y, c. E x , Bz or E z , Bx, d. E x , B y or E y , Bx, , 6. Consider a uniform wire of mass M and, , a. C and E, b. B and D, c. A and B, d. B and C, , a. 3 : 1, c. 1 : 2, , 4. A proton and an α-particle, having kinetic, , b. − γ, d., , dV, V, , length L. It is bent into a semicircle. Its, moment of inertia about a line perpendicular, to the plane of the wire passing through the, centre is, a., c., , 1 ML2, 4 π2, ML2, , 2 ML2, 5 π2, 1 ML2, d., 2 π2, b., , π2, , 7. The velocity-displacement graph of a particle, is shown in the figure., v, v0, , V, dV, O, , x0, , x
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57, , MARCH ATTEMPT ~ 18 March 2021, Shift II, The acceleration-displacement graph of the, same particle is represented by, a, , The refractive indices of the material of the, prism for red, green and blue wavelength are, 1.27, 1.42 and 1.49, respectively. The colour, of the ray(s) emerging out of the face PR is, a. green, c. blue and green, , a., , b. red, d. blue, , x, , O, , 10. If the angular velocity of Earth’s spin is, increased such that the bodies at the, equator start floating, the duration of the, day would be approximately, (Take 2 g = 10 ms −2, the radius of Earth,, R = 6400 × 103 m, take π = 314, . ), , a, b., x, , O, , a. 60 min, c. 1200 min, , 11. The decay of a proton to neutron is, , a, c., , b. does not change, d. 84 min, , a. not possible as proton mass is less than the, neutron mass, b. possible only inside the nucleus, c. not possible but neutron to proton, conversion is possible, d. always possible as it is associated only with, β + decay, , x, , O, , a, d., , 12. In a series L-C -R circuit, the inductive, x, , O, , 8. The correct relation between α (ratio of, , collector current to emitter current) and β, (ratio of collector current to base current) of, a transistor is, α, 1+ α, 1, c. β =, 1− α, , β, 1− α, β, d. α =, 1+ β, , a. β =, , b. α =, , reactance ( X L) is 10 Ω and the capacitive, reactance ( X C ) is 4 Ω. The resistance (R) in the, circuit is 6 Ω. The power factor of the circuit, is, 1, 2, 1, c., 2, , a., , 1, 2 2, 3, d., 2, , b., , 13. The angular momentum of a planet of mass, , 9. Three rays of light, namely red (R), green (G), and blue (B) are incident on the face PQ of a, right angled prism PQR as shown in figure, P, , M moving around the Sun in an elliptical, orbit is L . The magnitude of the areal, velocity of the planet is, 4L, M, 2L, c., M, a., , L, M, L, d., 2M, , b., , 14. The function of time representing a simple, B, , harmonic motion with a period of, , G, , a. sin (ωt ) = cos (ωt ), b. cos (ωt ) + cos (2ωt ) + cos (3ωt ), c. sin 2 (ωt ), π, d. 3cos − 2ωt , 4, , , R, , Q, , R, , π, is, ω
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58, , ONLINE, , 15. A solid cylinder of mass m is wrapped with, an inextensible light string and, is placed on, a rough inclined plane as shown in the, figure. The frictional force acting between, the cylinder and the inclined plane is, , JEE Main 2021 ~ Solved Papers, , 18. An ideal gas in a cylinder is separated by a, piston in such a way that the entropy of one, part is S1 and that of the other part is S 2., Given that S1 > S 2. If the piston is removed,, then the total entropy of the system will be, a. S1 × S 2, S, c. 1, S2, , b. S1 − S 2, d. S1 + S 2, , 19. Consider a sample of oxygen behaving like, an ideal gas. At 300 K, the ratio of root mean, square (rms) velocity to the average velocity, of gas molecule would be, (Molecular weight of oxygen is 32 g/mol;, R = 8. 3 J K −1 mol −1), a., , 60°, , (The coefficient of static friction, µ s , is 0.4), 7, a. mg, 2, mg, c., 5, , 20. The speed of electrons in a scanning, , d. 0, , reach 25% of its maximum value, when a, solenoid of resistance R, inductance L is, connected to a battery, is, L, a. ln 5, R, L, c. ln 2, R, , b. infinite, , where C is a positive constant., The correct radius-velocity graph of the, particle’s motion is, r, , a., , b., v, , O, , r, , v, , r, , c., , O, , b., , −C, ,, r, , 21. The projectile motion of a particle of mass, 5 g is shown in the figure., , 45°, A, , 45°, B, , The initial velocity of the particle is 5 2 ms −1, and the air resistance is assumed to be, negligible. The magnitude of the change in, momentum between the points A and B is, x × 10–2 kg-ms −1. The value of x to the nearest, integer, is ……………… ., , 22. A ball of mass 4 kg, moving with a velocity of, , d., v, , 1, 1837, 1, d., 1837, , a. 1837, , Section B : Numerical Type Questions, , under the central potential field, U( r) =, , r, , electron microscope is 1 × 107 ms −1. If the, protons having the same speed are used, instead of electrons, then the resolving, power of scanning proton microscope will be, changed by a factor of, , c. 1837, , L, d. ln 10, R, , 17. A particle of mass m moves in a circular orbit, , O, , 8, 3, 8π, d., 3, , b., , b. 5 mg, , 16. The time taken for the magnetic energy to, , O, , c., , 3, 3, 3π, 8, , v, , 10 ms −1, collides with a spring of length 8 m, and force constant 100 Nm −1. The length of, the compressed spring is x m. The value of x, to the nearest integer, is ………… .
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59, , MARCH ATTEMPT ~ 18 March 2021, Shift II, 23. The typical output characteristics curve for a, transistor working in the common-emitter, configuration is shown in the figure., Ic(mA), 8, , IB=40 µA, , 6, , IB=30 µA, , 4, , IB=20 µA, , 2, , IB=10 µA, , 0, , VCE(V), , The estimated current gain from the figure is, ……… ., , 24. Consider a water tank as shown in the, , figure. It’s cross-sectional area is 0.4 m 2. The, tank has an opening B near the bottom, whose cross-section area is 1 cm 2. A load of, 24 kg is applied on the water at the top when, the height of the water level is 40 cm above, the bottom, the velocity of water coming out, the opening B is v ms −1. The value of v, to the, nearest integer, is …………… ., (Take value of g to be 10 ms −2), , The value of n, to the nearest integer, is ……… ., , 26. The radius of a sphere is measured to be, , (7.50 ± 0.85) cm. Suppose the percentage, error in its volume is x. The value of x to the, nearest x, is …………… ., , 27. An infinite number of point charges, each, , carrying 1 µC charge, are placed along the, Y-axis at y = 1m, 2m, 4 m, 8m., The total force on a 1 C point charge, placed at, the origin, is x × 103 N. The value of x to the, nearest integer, is …………… ., 1, (Take,, = 9 × 109 N-m 2 /C 2 ), 4 πε0, , 28. Consider a 72 cm long wire AB as shown in, the figure. The galvanometer jockey is placed, at P on AB at a distance x cm from A. The, galvanometer shows zero deflection., 12 Ω, , G, x, A, , 24 kg, , 6Ω, , C, , P, , B, , A, , The value of x, to the nearest integer, is ……… ., , 29. Two wires of same length and thickness, , B, , 25. A TV transmission tower antenna is at a, height of 20 m. Suppose that the receiving, antenna is at, (i) ground level, (ii) a height of 5 m., The increase in antenna range in case (ii), relative to case (i) is n%., , having specific resistances 6 Ω- cm and 3 Ω-cm, respectively are connected in parallel. The, effective resistivity is ρ Ω-cm. The value of ρ to, the nearest integer, is …………… ., , 30. A galaxy is moving away from the Earth at a, speed of 286 kms −1. The shift in the, wavelength of a red line at 630 nm is, x × 10–10 m. The value of x to the nearest, integer, is ………… ., (Take the value of speed of light c, as, 3 × 108 ms −1)
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60, , ONLINE, , JEE Main 2021 ~ Solved Papers, , CHEMISTRY, Section A : Objective Type Questions, 1. The oxidation states of nitrogen in NO, NO2,, N2O and, , NO –3, , are in the order of, , a. NO 3− > NO 2 > NO > N2O, b. NO 2 > NO −3 > NO > N2O, c. N2O > NO 2 > NO > NO 3−, d. NO > NO 2 > N2O > NO 3−, , following reactions ?, A. Mn 2+ → Mn 4 +, B. I2 → I–, C. PbS → PbSO 4, , Choose the most appropriate answer from, the options given below., b. Only A, d. A and B, , the carbonyl carbon is lost as, b. HCO −3, , c. CO 2, , d. CO, , 4. The oxide that shows magnetic property is, a. SiO 2, , b. Mn 3O 4, , c. Na2O, , d. MgO, , 5. Main products formed during a reaction of, 1-methoxy naphthalene with hydroiodic acid, are, I, and CH3OH, , a., , and CH3I, OH, and CH3OH, , c., I, d., , a. C 6H5 N (CH3 ) 2, b. C 6H5 NHCH2CH3, c. C 6H5 CH2NHCH3, d. C 6H5 C H NH2, , CH3, , smaller as compared to that of elements X, and Y, but higher than that of Z. The, elements X, Y and Z, respectively, are, a. chlorine, lithium and sodium, b. argon, lithium and sodium, c. argon, chlorine and sodium, d. neon, sodium and chlorine, , 9. The secondary valency and the number of, hydrogen bonded water molecule(s) in, CuSO4 ⋅ 5H 2O, respectively, are, a. 6 and 4, b. 4 and 1, c. 6 and 5, d. 5 and 1, , 10. Given below are two statements., , OH, , b., , benzene sulphonyl chloride gives compound, B. B is soluble in dil. NaOH solution., Compound A is, , 8. The first ionisation energy of magnesium is, , 3. In the reaction of hypobromite with amide,, a. CO 2−, 3, , a. increase in blood clotting time, b. increase in fragility of RBC’s, c. cheilosis, d. decrease in blood clotting time, , 7. An organic compound “A” on treatment with, , 2. In basic medium, H2O2 exhibits which of the, , a. A and C, c. B Only, , 6. Deficiency of vitamin K causes, , and CH3I, , Statement I Bohr’s theory accounts for the, stability and line spectrum of Li + ion., Statement II Bohr’s theory was unable to, explain the splitting of spectral lines in the, presence of a magnetic field., In the light of the above statements, choose, the most appropriate answer from the options, given below :, a. Both statements I and II are true., b. Statement I is false but statement II is true., c. Both statements I and II are false., d. Statement I is true but statement II is false.
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61, , MARCH ATTEMPT ~ 18 March 2021, Shift II, 11., , NH2, , OH, , NH2, , O, , NO2, HNO3, H2SO4, , ,, a., , 288 K, , O, , (A ), NH2, , NH2, , +, , O, ,, , b., , +, , OH, , NO2, , (B), , NO2, (C), , O, , Consider the given reaction, percentage yield, of, a. (C) > (A) > (B), c. (A) > (C) > (B), , ,, OH, , b. (B) > (C) > (A), d. (C) > (B) > (A), O, , d., , List-I, , 14., , List-I, , List-II, , (Class of chemicals), , (Example), , A., , Antifertility drug, , 1. Meprobamate, , B., , Antibiotic, , 2. Alitame, , C., , Tranquilizer, , 3. Norethindrone, , D., , Artificial sweetener, , 4. Salvarsan, , C, 4, 2, 1, 1, , OH, , 15. Match List-I with List-II, , 13. Match List-I with List-II., , B, 3, 3, 4, 4, , O, ,, , sol are, respectively, a. positive and positive, b. positive and negative, c. negative and negative, d. negative and positive, , A, 2, 4, 3, 2, , O, , c., , 12. The charges on the colloidal CdS sol and TiO2, , a., b., c., d., , O, , D, 1, 1, 2, 3, , List-II, , A., , Be, , 1., , Treatment of cancer, , B., , Mg, , 2., , Extraction of metals, , C., , Ca, , 3., , Incendiary bombs and, signals, , D., , Ra, , 4., , Windows of X-ray tubes, , 5., , Bearings for motor, engines., , Choose the most appropriate answer the, option given below., a., c., , O, , A, 4, 3, , B, 3, 4, , C, 1, 5, , D, 2, 2, , b., d., , A, 4, 3, , B, 3, 4, , C, 2, 2, , D, 1, 5, , 16. Given below are two statements., dil. NaOH, , +, , ‘‘X’’, , H , Heat, , ‘‘Y’’, , Consider the above reaction, the product ‘X’, and ‘Y’ respectively are, , Statement I C 2H5OH and AgCN both can, generate nucleophile., Statement II KCN and AgCN both will, generate nitrile nucleophile with all reaction, conditions.
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62, , ONLINE, Choose the most appropriate option., a. Statement I is true but statement II is false., b. Both statements I and II are true., c. Statement I is false but statement II is true., d. Both statements I and II are false., , 17. Given below are two statements, Statement I Non-biodegradable wastes are, generated by the thermal power plants., Statement II Bio-degradable detergents leads, to eutrophication., In the light of the above statements, choose, the most appropriate answer from the option, given below., a. Both statements I and II are false., b. Statement I is true but statement II is false., c. Statement I is false but statement II is true., d. Both statements I and II are true., , 18. Match List-I with List-II., List-I, , List-II, , A. Mercury, , 1. Vapour phase refining, , B. Copper, , 2. Distillation refining, , C. Silicon, , 3. Electrolytic refining, , D. Nickel, , 4. Zone refining, , Choose the most appropriate answer the, option given below, a., b., c., d., , A, 1, 2, 2, 2, , B, 4, 3, 3, 4, , C, 2, 1, 4, 3, , D, 3, 4, 1, 1, , 19. In the following molecules,, a, , H3C, H, , b, , C, , C, , O, , c, , H, , hybridisation of carbon a , b and c respectively, are, a. sp 3 , sp , sp, c. sp 3 , sp 2 , sp 2, , b. sp 3 , sp 2 , sp, d. sp 3 , sp , sp 2, , 20. A hard substance melts at high temperature, and is an insulator in both solid and in, molten state., This solid is most likely to be a/an, a. ionic solid, c. metallic solid, , b. molecular solid, d. covalent solid, , JEE Main 2021 ~ Solved Papers, , Section B : Numerical Type Questions, 21. A reaction has a half-life of 1 min. The time, required for 99.9% completion of the, reaction is ……… min (Round off to the, nearest integer)., [Use : ln 2 = 069, . , ln 10 = 2.3], , 22. The molar conductivities at infinite dilution, of barium chloride, sulphuric acid and, hydrochloric acid are 280, 860 and 426 Scm 2, mol −1 respectively. The molar conductivity at, infinite dilution of barium sulphate is ………, S cm 2 mol −1 (Round off to the nearest, Integer)., , 23. The number of species below that have two, lone pairs of electrons in their central atom, is ……… . (Round off to the nearest integer), SF4 , BF4− , CIF3 , AsF3 , PCl5 , BrF5, XeF4 , SF6, , 24. A xenon compound ‘A’ upon partial, hydrolysis gives XeO2F2. The number of lone, pair of electrons present in compound A is, ……… (Round off to the nearest integer)., , 25. The gas phase reaction, 2A( g), , A2 ( g ), , =, , at 400 K has ∆G° = + 25.2 kJ mol −1., The equilibrium constant KC for this reaction, is ……… × 10−2. (Round off to the nearest, integer)., [Use : R = 8.3 J mol −1 K −1, In 10 = 2.3], log 10 2 = 0.30, 1 atm = 1bar], [antilog ( − 0.3) = 0501], ., , 26. In Tollen’s test for aldehyde, the overall, number of electron(s) transferred to the, Tollen’s reagent formula [Ag(NH 3) 2 ]+ per, aldehyde group to form silver mirror is ………, (Round off to the nearest integer)., , 27. The solubility of CdSO 4 in water is, 80, . × 10–4 mol L −1. Its solubility in 0.01 M, H 2SO4 solution is ……… × 10–6 mol L −1. (Round, off to the nearest integer) (Assume that,, solubility is much less than 0.01 M), , 28. A solute a dimerises in water. The boiling, point of a 2 molar solution of A is 100.52ºC.
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63, , MARCH ATTEMPT ~ 18 March 2021, Shift II, 30., , The percentage association of A is ……… ., (Round off to the nearest integer), [Use : K b for water = 052, . K kg mol −1,, boiling point of water = 100°C], , COOH, , COOH, , + Br2, , FeBr3, , + HBr, Br, , 29. 10.0 mL of Na2CO3 solution is titrated against, 0.2 M HCl solution. The following titre values, were obtained in 5 readings. 4.8 mL, 4.9 mL,, 5.0 mL, 5.0 mL and 5.0 mL based on these, readings and convention of titrimetric, estimation of concentration of Na2CO3, solution is ……… mM (Round off to the, nearest integer)., , Consider the above reaction where 6.1 g of, benzoic acid is used to get 7.8 g of m-bromo, benzoic acid. The percentage yield of the, product is ……… ., (Round off to the nearest integer)., [Given : Atomic masses : C = 120, . u, H = 1.0 u,, O = 16.0u, Br = 80.0 u], , MATHEMATICS, 4. Let f : R − { 3} → R − { 1} be defined by, , Section A : Objective Type Questions, 1. Let y = y ( x) be the solution of the differential, 2, dy, equation, = ( y + 1)[( y + 1)e x / 2 − x ],, dx, , dy, 0 < x < 2. 1, with y(2) = 0. Then the value of, dx, at x = 1is equal to, a., c., , − e3/ 2, , b. −, , (e 2 + 1) 2, e5/ 2, , d., , (1 + e 2 ) 2, , 2e 2, , (e 2 + 1) 2, , →, , →, , →, , →, , |AB| = 10, then the projection of the vector AB, →, , on AC is equal to, 25, 4, 127, c., 20, a., , 85, 14, 115, d., 16, b., , 3. Let the system of linear equations, 4 x + λy + 2 z = 0, 2x − y + z = 0, µx + 2 y + 3z = 0, λ , µ ∈ R., has a non-trivial solution. Then which of the, following is true ?, a. µ = 6, λ ∈ R, b. λ = 2, µ ∈R, c. λ = 3, µ ∈ R, d. µ = − 6, λ ∈ R, , x −2, x −3, , . Let g : R → R be given as, , g( x) = 2x − 3. Then, the sum of all the values, 13, of x for which f −1( x) + g −1( x) =, is equal to, 2, a. 7, , b. 2, , c. 5, , d. 3, , 5. Let the centroid of an equilateral triangle, , (1 + e 2 ) 2, 5e1/ 2, , 2. In a triangle ABC , if|BC | = 8, |CA | = 7,, , f ( x) =, , ∆ABC be at the origin. Let one of the sides of, the equilateral triangle be along the straight, line x + y = 3. If R and r be the radius of, circumcircle and incircle, respectively of, ∆ABC, then (R + r) is equal to, a., , 9, 2, , b. 7 2, , c. 2 2, , d. 3 2, , 6. Consider a hyperbola H : x 2 − 2 y 2 = 4. Let the, tangent at a point P(4, 6 ) meet the x-axis at, Q and latus rectum at R( x1, y1), x1 > 0. If F is a, focus of H which is nearer to the point P,, then the area of ∆QFR is equal to, a. 4 6, , b. 6 − 1, , c., , 7, −2, 6, , d. 4 6 − 2, , 7. If P and Q are two statements, then which of, the following compound statement is a, tautology ?, a. (P ⇒ Q ) ∧ ~ Q ] ⇒ Q, b. (P ⇒ Q ) ∧ ~ Q ] ⇒ ~ P, c. (P ⇒ Q ) ∧ ~ Q ] ⇒ P, d. (P ⇒ Q ) ∧ ~ Q ] ⇒ (P ∧ Q )
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64, , ONLINE, x, , 8. Let g( x) = ∫ f (t) dt, where f is continuous, 0, , 1, function in [0, 3] such that ≤ f (t) ≤ 1 for all, 3, 1, t ∈[0, 1] and 0 ≤ f (t) ≤ for all t ∈(1, 3]. The, 2, largest possible interval in which g (3) lies is, 1, a. −1, − , 2 , , 1, c. , 2, 3 , , 3, b. − , − 1, 2, , d. [ 1, 3], , 9. Let S1 be the sum of first 2n terms of an, arithmetic progression. Let S 2 be the sum of, first 4 n terms of the same arithmetic, progression. If ( S 2 − S1) is 1000, then the sum, of the first 6n terms of the arithmetic, progression is equal to, a. 1000, c. 5000, , b. 7000, d. 3000, , 10. Let a complex number be w = 1 − 3 i. Let, another complex number z be such that, π, |zw| = 1and arg(z) − arg(w) = . Then the area, 2, of the triangle with vertices origin, z and w, is, equal to, 1, b., 2, d. 2, , a. 4, c., , 1, 4, , 13. Let a and b be two non-zero vectors, , perpendicular to each other and|a| = |b|. If, |a × b| = |a|, then the angle between the, vectors [ a + b + ( a × b)] and a is equal to, 1 , a. sin −1, , 3, 1, , c. cos −1, , 2, , 1 , b. cos −1, , 3, 1, , d. sin −1, , 6, , 14. Let in a Binomial distribution, consisting of 5, independent trials, probabilities of exactly 1, and 2 successes be 0.4096 and 0.2048,, respectively. Then the probability of getting, exactly 3 successes is equal to, 32, 625, 40, c., 243, a., , 80, 243, 128, d., 625, b., , 15. Let a tangent be drawn to the ellipse, , x2, + y 2 = 1 at (3 3 cos θ , sinθ), where, 27, π, θ ∈ 0, . Then the value of θ, such that the, 2, sum of intercepts on axes made by this, tangent is minimum is equal to, π, 8, π, c., 6, a., , π, 4, π, d., 3, b., , 16. Define a relation R over a class of n × n real, , 11. Let in a series of 2n observations, half of, them are equal to a and remaining half are, equal to −a. Also, by adding a constant b in, each of these observations, the mean and, standard deviation of new set become 5 and, 20, respectively. Then, the value of a 2 + b2 is, equal to, a. 425, c. 250, , b. 650, d. 925, , 12. Let S1 ⇒ x 2 + y 2 = 9 and S 2 ⇒ ( x − 2) 2 + y 2 = 1., Then the locus of center of a variable circle S, which touches S1 internally and S 2 externally, always passes through the points, a. (0, ±, , JEE Main 2021 ~ Solved Papers, , 3), , 3, c. 2, ± , , 2, , 1, 5, b. , ±, , 2, 2, , , d. (1, ± 2), , matrices A and B as “ARB, if there exists a, non-singular matrix P such that PAP −1 = B”., Then which of the following is true ?, a. R is symmetric, transitive but not reflexive, b. R is reflexive, symmetric but not transitive, c. R is an equivalence relation, d. R is reflexive, transitive but not symmetric, , 17. A pole stands vertically inside a triangular, park ABC. Let the angle of elevation of the, top of the pole from each corner of the park, π, be . If the radius of the circumcircle of ∆ABC, 3, is 2, then the height of the pole is equal to, 2 3, 3, c. 3, , a., , b. 2 3, d., , 1, 3
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65, , MARCH ATTEMPT ~ 18 March 2021, Shift II, 18. If 15sin4 α + 10cos 4 α = 6, for some α ∈R, then, the value of 27sec 6α + 8cos ec 6α is equal to, a. 350, , b. 500, , c. 400, , d. 250, , b., , 3π, 8, , c., , 3π, 2, , d., , π, 16, , 20. Let f : R → R be a function defined as, sin(a + 1) x + sin2x, , if x < 0, , 2x, , f (x ) = , b, ,if x < 0, , x + bx 3 − x, , ,, if x > 0, , bx5 / 2, , If f is continuous at x = 0, then the value of, a + b is equal to, 5, 2, c. −3, , a. −, , b. −2, d. −, , 1, , −1, , 4 y 2 = x 2 (4 − x ) (x − 2) is equal to, π, 8, , which vanishes at x = − 3. Let P( x) have local, minima at x = 1, local maxima at x = − 1and, , ∫ P(x) dx = 18, then the sum of all the, , 19. The area bounded by the curve, a., , 25. Let P( x) be a real polynomial of degree 3, , 3, 2, , coefficients of the polynomial P( x) is equal to, …………… ., , 26. Let the mirror image of the point (1, 3, a) with, respect to the plane r ⋅ (2$i − $j + k$ ) − b = 0 be, (− 3, 5, 2). Then the value of|a + b| is equal to, …………… ., , 27. Let f : R → R satisfy the equation, f ( x + y ) = f ( x) ⋅ f ( y ) for all x , y ∈ R and f ( x) ≠ 0, for any x ∈ R . If the function f is, differentiable at x = 0 and f ′ (0) = 3, then, 1, lim ( f ( h) − 1) is equal to………… ., h→ 0 h, , 28. Let nC r denote the binomial coefficient of x r, , Section B : Numerical Type Questions, 21. If f ( x) and g( x) are two polynomials such that, the polynomial P( x) = f ( x 3) + xg( x 3) is divisible, by x 2 + x + 1, then P(1) is equal to …………… ., , 22. Let I be an identity matrix of order 2 × 2 and, 2 −1, P=, . Then the value of n ∈ N for which, 5 −3, P n = 5I − 8P is equal to …………., 10, , 23. If ∑ r ! ( r 3 + 6r 2 + 2r + 5) = α(11!), then the, r=1, , value of α is equal to ………… ., , 24. The term independent of x in the expansion, 10, , , x+1, x −1 , of 2/ 3, −, , x ≠ 1, is equal, 1/ 3, 1, − x 1/ 2 , x, −, x, +, x, , to …………. ., , in the expansion of (1 + x) n., 10, , If, , ∑ (22 + 3k) nC k = α ⋅ 310 + β ⋅ 210, α , β ∈R,, , k=0, , then α + β is equal to ………… ., , 29. Let P be a plane containing the line, x −1, 3, x −3, , =, , y+6, , 4, y −2, , =, , z+5, , 2, z+5, , and parallel to the line, , . If the point (1, − 1, α ) lies, =, =, −3, 4, 7, on the plane P, then the value of|5α| is equal, to ………… ., , 30. Let y = y ( x) be the solution of the differential, equation, x dy − y dx = ( x 2 − y 2) dx , x ≥ 1, with y(1) = 0. If, the area bounded by the line x = 1, x = e π ,, y = 0 and y = y ( x) is αe 2π + β, then the value, of 10(α + β) is equal to ………… .
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66, , ONLINE, , JEE Main 2021 ~ Solved Papers, , Answers, For solutions scan, the QR code, , Physics, 1. (a), 11. (b), 21. 5, , 2. (a), 12. (c), 22. 6, , 3. (a), 13. (d), 23. 200, , 4. (d), 14. (d), 24. 3, , 5. (c), 15. (c), 25. 50, , 3. (a), 13. (c), 23. 2, , 4. (b), 14. (c), 24. 19, , 5. (b), 15. (b), 25. 1.66, , 3. (a), 13. (b), 23. 160, , 4. (c), 14. (a), 24. 210, , 6. (c), 16. (c), 26. 34, , 7. (c), 17. (a), 27. 12, , 8. (d), 18. (d), 28. 48, , 9. (b), 19. (c), 29. 4, , 10. (d), 20. (a), 30. 6, , 7. (d), 17. (d), 27. 64, , 8. (c), 18. (c), 28. 100, , 9. (b), 19. (c), 29. 50, , 10. (b), 20. (d), 30. 78, , 7. (b), 17. (b), 27. 3, , 8. (c), 18. (d), 28. 19, , 9. (d), 19. (c), 29. 38, , 10. (b), 20. (d), 30. 4, , Chemistry, 1. (a), 11. (d), 21. 10, , 2. (d), 12. (d), 22. 288, , 6. (a), 16. (a), 26. 2, , Mathematics, 1. (a), 11. (a), 21. 0, , 2. (b), 12. (c), 22. 6, , 5. (a), 15. (c), 25. 8, , 6. (c), 16. (c), 26. 1
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JEE Main 2021, 20 JULY SHIFT I, , PHYSICS, Section A : Objective Type Questions, 1. The value of current in the 6 Ω resistance is, 20Ω, , 140V, , a. 4 A, c. 10 A, , 5Ω, , 6Ω, , 1, , b. 8 A, d. 6 A, , mass, negotiating a turn on a 30° banked, road at maximum possible speed without, skidding is …… × 103 kg-m/s2., [Take, µ s = 02, . ], b. 7.2, d. 6.96, , 3. A radioactive material decays by, simultaneous emission of two particles with, half-lives of 1400 yr and 700 yr, respectively., What will be the time after the which, one-third of the material remains ?, [Take, In 3 = 1.1], a. 1110 yr, c. 340 yr, , b. 700 yr, d. 740 yr, , a. 716, , b. 686, , 50 Hz is applied to a parallel plate capacitor., The separation between the plates is 2 mm, and the area is 1 m2. The amplitude of the, oscillating displacement current for the, applied AC voltage is …… ., (Take, ε0 = 885, . × 10−12 F/m), a. 21.14 µA, b. 83.37 µA, c. 27.79 µA, , d. 55.58 µA, , 6. Region I and II are separated by a spherical, surface of radius 25 cm. An object is kept in, region I at a distance of 40 cm from the, surface. The distance of the image from the, surface is, II, , I, 25cm, O, , floor as shown. When three iron cylinders, are placed on it as shown, the block and, cylinders go down with an acceleration, 0.2 m/s2., , a. 55.44 cm, c. 18.23 cm, , The normal reaction R by the floor, if mass of, the iron cylinders are equal and of 20 kg, each, is …… N., , a = 0.2 m/s2, c. 714, d. 684, , 5. AC voltage V (t) = 20 sinωt volt of frequency, , 4. A steel block of 10 kg rests on a horizontal, , [Take, g = 10 m / s 2 and µ s = 02, . ], , 2, , 90V, , 2. The normal reaction N for a vehicle of 800 kg, , a. 10.2, c. 12.4, , 3, , C, , µI=1.25 µII=1.4, , b. 9.52 cm, d. 37.58 cm, , 7. A person whose mass is 100 kg travels from, Earth to Mars in a spaceship. Neglect all other, objects in sky and take acceleration due to, gravity on the surface of the Earth and Mars, as 10 m/s2 and 4 m/s2, respectively.
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4, , ONLINE, Identify from the below figures, the curve that, fits best for the weight of the passenger as a, function of time., , q, 2, c. Q = 4q, , a. Q =, , b. Q = 2q, d. Q = 3q, , 13. A current of 5 A is passing through a, , 1000N A, , non-linear magnesium wire of cross-section, 0.04 m2. At every point, the direction of, current density is at an angle of 60° with the, unit vector of area of cross-section. The, magnitude of electric field at every point of, the conductor is, , I, II, , Weight, , B, , 400N, III, IV, , a. III, , JEE Main 2021 ~ Solved Papers, , b. I, , Time, , c. IV, , d. II, , 8. The amount of heat needed to raise the, , (Take, resistivity of magnesium, ρ = 44 × 10−8 Ω -m), a. 11 × 10−2 V/m, c. 11 × 10−5 V/m, , b. 11 × 10−7 V/m, d. 11 × 10−3 V/m, , 14. Consider a mixture of gas molecule of types, , temperature of 4 moles of a rigid diatomic, gas from 0°C to 50°C when no work is done, is ……… . (R is the universal gas constant), , A, B and C having masses m A < m B < mC . The, ratio of their root mean square speeds at, normal temperature and pressure is, , a. 250 R, c. 175 R, , a. v A = v B = vC = 0, , b., , 1, 1 1, >, >, v A v B vC, , c. v A = v B ≠ vC, , d., , 1, 1 1, <, <, v A v B vC, , b. 750 R, d. 500 R, , 9. If A and B are two vectors satisfying the, , relation A ⋅ B = |A × B|. Then, the value of, |A − B| will be, a. A 2 + B 2, , b. A 2 + B 2 + 2AB, , c. A 2 + B 2 + 2AB, , d. A 2 + B 2 − 2AB, , 10. A deuteron and an α-particle having equal, kinetic energy enter perpendicular into a, magnetic field. Let rd and rα be their, respective radii of circular path. The value of, rd, is equal to, rα, 1, 2, c. 1, , a., , b. 2, , 15. A butterfly is flying with a velocity 4 2 m/s in, North-East direction. Wind is slowly blowing, at 1 m/s from North to South. The resultant, displacement of the butterfly in 3 s is, a. 3 m, c. 12 2 m, , b. 20 m, d. 15 m, , 16. The value of tension in a long thin metal wire, has been changed from T1 to T2. The lengths, of the metal wire at two different values of, tension T1 and T2 are l1 and l 2, respectively., The actual length of the metal wire is, T1l 2 − T2 l1, T1 − T2, l1 + l 2, c., 2, , b., , a., d. 2, , 11. A nucleus of mass M emits γ- ray photon of, frequency ν. The loss of internal energy by, the nucleus is, [Take, c is the speed of electromagnetic wave.], a. hν, b. zero, hν , hν , , c. hν 1 −, d. hν 1 +, 2Mc 2 , , 2Mc 2 , , T1l1 − T2 l 2, T1 − T2, , d. TT, 1 2 l1l 2, , 17. For the circuit shown below, calculate the, value of Iz ., Rs=1000Ω, R, , Iz Iz, , Vi 100V, , 12. A certain charge Q is divided into two parts q, and (Q − q). How should the charges Q and q, be divided, so that q and (Q − q) placed at a, certain distance apart experience maximum, electrostatic repulsion ?, , R = 2000Ω, Vz=50V, , a. 25 mA, c. 0.1 A, , b. 0.15 A, d. 0.05 A
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5, , JULY ATTEMPT ~ 20 July 2021, Shift I, 18. The arm PQ of a rectangular conductor is, moving from x = 0 to x = 2b outwards and, then inwards from x = 2b to x = 0 as shown in, the figure. A uniform magnetic field, perpendicular to the plane is acting from, x = 0 to x = b. Identify the graph showing the, variation of different quantities with distance., , a. 1.36 eV, c. 0.16 eV, , b. 1.88 eV, d. 0.82 eV, , Section B : Numerical Type Questions, 21. In a spring gun having spring constant, , P, , Q, , x=0, , of 5 × 10−4 T. Assume that the radius of the, largest circular path followed by these, electrons is 7 mm, the work-function of, the metal is (Take, mass of electron, = 91, . × 10−31 kg), , x=2b, , x=b, , A, , 100 N/m a small ball B of mass 100 g is put, in its barrel (as shown in figure) by, compressing the spring through 0.05 m., There should be a box placed at a distance d, on the ground, so that the ball falls in it. If, the ball leaves the gun horizontally at a, height of 2 m above the ground. The value, of d is ……… m., (Take, g =10m / s 2 ), Gun, , B, Ball, , C, , x=0, b, , 2b, , b, , a. A - flux, B - power dissipated, C - emf, b. A - power dissipated, B - flux, C - emf, c. A - flux, B - emf , C - power dissipated, d. A - emf , B - power dissipated, C - flux, , 19. The entropy of any system is given by, µkR, , S = α 2β ln 2 + 3, β, J, , , where, α and β are the constants; µ, J , k and R are, number of moles, mechanical equivalent of heat,, Boltzmann constant and gas constant, respectively., Take, S = dQ , , T , Choose the incorrect option., a. α and J have the same dimensions., b. S , β , k and µR have the same dimensions., c. S and α have different dimensions., d. α and k have the same dimensions., , 20. The radiation corresponding to 3 → 2, transition of a hydrogen atom falls on a gold, surface to generate photoelectrons. These, electrons are passed through a magnetic field, , 2m, , 22. In an L-C-R series circuit, an inductor 30 mH, and a resistor 1Ω are connected to an AC, source of angular frequency 300 rad/s. The, value of capacitance for which, the current, 1, leads the voltage by 45° is × 10−3 F. Then,, x, the value of x is …… ., , 23. The amplitude of wave disturbance, propagating in the positive x-direction is, 1, given by y =, at time t = 0 and, (1 + x) 2, 1, at t = 1s, where x and y are in, y=, 1 + ( x − 2) 2, metre. The shape of wave does not change, during the propagation. The velocity of the, wave will be …… m/s., , 24. A body having specific charge 8 µC/g is resting, on a frictionless plane at a distance 10 cm, from the wall (as shown in the figure). It starts, moving towards the wall when a uniform
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6, , ONLINE, electric field of 100 V/m is applied horizontally, towards the wall. If the collision of the body, with the wall is perfectly elastic, then the time, period of the motion will be …… s., , Body, , 100 V/m, , JEE Main 2021 ~ Solved Papers, , 27. A rod of mass M and length L is lying on a, horizontal frictionless surface. A particle of, mass m travelling along the surface hits at, one end of the rod with a velocity u in a, direction perpendicular to the rod. The, collision is completely elastic. After collision,, particle comes to rest. The ratio of masses, m is 1. The value of x will be …… ., M x, , 28. An object viewed from a near point distance, , 25. In the reported figure, heat energy absorbed, by a system in going through a cyclic process, is …… πJ., p(kPa), 40, , of 25 cm, using a microscopic lens with, magnification 6, gives an unresolved image., A resolved image is observed at infinite, distance with a total magnification double, the earlier using an eyepiece along with, the given lens and a tube of length 0.6 m, if, the focal length of the eyepiece is equal to, ……… cm., , 29. The frequency of a car horn encountered a, 20, , 20, , 40, , change from 400 Hz to 500 Hz, when the car, approaches a vertical wall. If the speed of, sound is 330 m/s, then the speed of car is, …… km/h., , L, , 26. A circular disc reaches from top to bottom of, an inclined plane of length L. When it slips, down the plane, it takes time t1. When it rolls, down the plane, it takes time t 2. The value of, t2, 3, is, . The value of x will be …… ., t1, x, , 30. A carrier wave VC (t) = 160sin(2π × 106t) V is, made to vary between Vmax = 200 V and, Vmin = 120 V by a message signal, Vm (t) = Am sin(2π × 103t) V. The peak voltage, Am of the modulating signal is …… ., , CHEMISTRY, Section A : Objective Type Questions, 1. According to the valence bond theory the, hybridisation of central metal atom is dsp2 for, which one of the following compounds?, a. NiCl2 ⋅6H2O, c. [Ni(CO) 4 ], , O–, a., , b. K 2 [Ni(CN) 4 ], d. Na2 [NiCl4 ], , 2. The correct structure of Rhumann's Purple,, the compound formed in the reaction of, ninhydrin with proteins is, , O–, N, , O–, b., , O–, N
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7, , JULY ATTEMPT ~ 20 July 2021, Shift I, O–, c., , O, , N N, , 8. Orlon fibres are made up of, a. polyacrylonitrile, c. polyamide, , +, , N, , b. polyester, d. cellulose, , 9. Given below are two statements : One is, labelled as Assertion A and other is labelled, as Reason R., , O, d., , Assertion A The dihedral angles in H2O 2 in, gaseous phase is 90.2° and in solid phase is 111.5°., Reason R The change in dihedral angle in solid, and gaseous phase is due to the difference in the, intermolecular forces., Choose the most appropriate answer from the, options given below for A and R., a. A is correct but R is not correct., b. Both A and R are correct but R is not the, correct explanation of A., c. Both A and R are correct and R is the correct, explanation of A., d. A is not correct but R is correct., , N, , 3. Green chemistry in day–to–day life is in the, use of, a. chlorine for bleaching of paper., b. large amount of water alone for washing, clothes., c. Tetrachloroethene for laundry., d. Liquified CO 2 for dry cleaning of clothes., , 4. The correct order of intensity of colors of the, compound is, , 10. Chemical nature of the nitrogen oxide, compound obtained from a reaction of, concentrated nitric acid and P4O10 (in 4 : 1, ratio) is, , a. [Ni(CN) 4 ] 2− > [NiCl4 ] 2− > [Ni(H2O) 6 ] 2 +, b. [Ni(H2O) 6 ] 2 + > [NiCl4 ] 2− > [Ni(CN) 4 ] 2−, c. [NiCl4 ] 2− > [Ni(H2O) 6 ] 2 + > [Ni(CN) 4 ] 2−, d. [NiCl4 ] 2− > [Ni(CN) 4 ] 2− > [Ni(H2O) 6 ] 2 +, , 5. The set in which compounds have different, nature is, , a. acidic, c. amphoteric, , 11. An inorganic compound 'X' on treatment, with concentrated H 2SO 4 produces brown, fumes and gives dark brown ring with FeSO 4, in presence of concentrated H 2SO 4 . Also, compound 'X' gives precipitate 'Y', when its, solution in dilute HCl is treated with H 2S gas., The precipitate 'Y' on treatment with, concentrated HNO 3 followed by excess of, NH 4OH further gives deep blue coloured, solution, compound 'X' is, , a. B(OH) 3 and H3PO 3, b. B(OH) 3 and Al(OH) 3, c. NaOH and Ca(OH) 2, d. Be(OH) 2 and Al(OH) 3, , 6. The species given below that does not show, disproportionation reaction is, a. BrO −4, c. BrO −2, , b. BrO −, d. BrO −3, , a. Co(NO 3 ) 2, c. Cu(NO 3 ) 2, , 7. Given below are two statements. One is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) Sharp glass edge becomes smooth, on heating it upto its melting point., Reason (R) The viscosity of glass decreases on, melting., Choose the most appropriate answer from the, options given below., a. A is true but R is false, b. Both A and R are true but R is not the correct, explanation of A., c. A is false but R is true., d. Both A and R are true and R is the correct, explanation of A., , b. basic, d. neutral, , b. P(NO 2 ) 2, d. Pb(NO 3 ) 2, , 12., CH2, , CH2, CH2, , H, (A), , H, (B), , (C), , CH2, (D), , Among the given species the resonance, stabilised carbocations are, a. (C) and (D) only, b. (A), (B) and (D) only, c. (A) and (B) only, d. (A), (B) and (C) only
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8, , ONLINE, , 13. A s-block element (M) reacts with oxygen to, , 18. Identify the incorrect statement from the, following., , form an oxide of the formula MO 2. The oxide, is pale yellow in colour and paramagnetic., The element (M) is, a. Mg, c. Ca, , a. Amylose is a branched chain polymer of, glucose., b. Starch is a polymer of α-D-glucose ., c. β-glycosidic linkage makes cellulose polymer., d. Glycogen is called as animal starch., , b. Na, d. K, , 14. In the given reaction, 3-bromo-2, 2-dimethyl, C 2H5 OH, , butane →, , A, , JEE Main 2021 ~ Solved Papers, , 19., , OH, , ., , O, , Major product, , OH, , CHO, , Product A is, , (I), , a. 2-ethoxy-3, 3-dimethyl butane, b. 1-ethoxy-3, 3-dimethyl butane, c. 2-ethoxy-2, 3-dimethyl butane, d. 2-hydroxy-3, 3-dimethyl butane, , OH, (II), , (III), , (IV), , Which among the above compound/s does/do, not form silver mirror when treated with Tollen's, reagent?, a. (I), (III) and (IV) only b. Only (IV), c. Only (II), d. (III) and (IV) only, , 15. The metal that can be purified economically, by fractional distillation method is, a. Fe, c. Cu, , b. Zn, d. Ni, , 20., KMnO4, H2SO4, ∆, , ' A', (Major product), , KMnO4, H2O, 273K, , 'B', (Major product), , 16. Compound A is converted to B on reaction, with CHCl 3 and KOH. The compound B is, toxic and can be decomposed by C. A, B and, C respectively are, a. primary amine, nitrile compound, conc. HCl, b. secondary amine, isonitrile compound,, conc. NaOH, c. primary amine, isonitrile compound, conc. HCl, d. secondary amine, nitrile compound,, conc. NaOH, , 17. The conditions given below are in the, context of observing Tyndall effect in, colloidal solutions, (A) The diameter of the colloidal particles is, comparable to the wavelength of light used., (B) The diameter of the colloidal particles is, much smaller than the wavelength of light, used., (C) The diameter of the colloidal particles is, much larger than the wavelength of light, used., (D) The refractive indices of the dispersed phase, and the dispersion medium are comparable., (E) The dispersed phase has a very different, refractive index from the dispersion medium., Choose the most appropriate conditions from, the options given below., a. (A) and (E) only, b. (C) and (D) only, c. (A) and (D) only, d. (B) and (E) only, , For above chemical reactions, identify the correct, statement from the following, a. Both compound 'A' and compound 'B' are, dicarboxylic acids., b. Both compound 'A' and compound 'B' are, diols., c. Compound 'A' is diol and compound 'B' is, dicarboxylic acid., d. Compound 'A' is dicarboxylic acid and, compound 'B' is diol., , Section B : Numerical Type Questions, 21. The number of lone pairs of electron on the, central I atom in I−3 is …… ., , 22. 250 mL of 0.5 M NaOH was added to 500 mL, of 1 M HCl. The number of unreacted HCl, molecules in the solution after complete, reaction is ……… × 1021. (Nearest integer), (NA = 6.022 × 1023), , 23. The azimuthal quantum number for the, valence electrons of Ga + ion is ……… ., (Atomic number of Ga = 31), , 24. The spin only magnetic moment value for, the complex [Co(CN) 6 ]4− is …… BM., [Atomic number of Co = 27]
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9, , JULY ATTEMPT ~ 20 July 2021, Shift I, 25. 2SO2( g) + O2( g), , - 2SO ( g), 3, , In an equilibrium mixture, the partial, pressures are, pSO3 = 45kPa; pO2 = 530 Pa and pSO2 = 45kPa., The equilibrium constant K p = ……… × 10−2., (Nearest integer), , 26. The number of nitrogen atoms in a, semicarbazone molecule of acetone is …… ., , 27. To synthesis 1.0 mole of 2-methylpropan -2-ol, from ethylethanoate …… equivalents of, CH 3MgBr reagent will be required. (Integer, value), , 28. The inactivation rate of a viral preparation is, proportional to the amount of virus. In the, first minute after preparation, 10% of the, virus is inactivated. The rate constant for, , viral inactivation is …… × 10−3 min−1. (Nearest, integer), [Use: In 10 = 2303, ; log 10 3 = 0.477; property of, ., logarithm : log x y = y log x ], , 29. An average person needs about 10000 kJ, energy per day. The amount of glucose, (molar mass = 1800, . g mol −1) needed to meet, this energy requirement is ……… g., [Use ∆ cH(glucose) = 2700kJ mol−1], , 30. At 20°C, the vapour pressure of benzene is, 70 torr and that of methyl benzene is 20 torr., The mole fraction of benzene in the vapour, phase at 20°C above an equimolar mixture, of benzene and methyl benzene is…… × 10−2., (Nearest integer), , MATHEMATICS, Section A : Objective Type Questions, 1. The Boolean expression ( p ∧ ~ q) ⇒ (q ∨ ~ p) is, equivalent to, a. q ⇒ p, c. ~q ⇒ p, , b. p ⇒ q, d. p ⇒~ q, , 2. Let a be a positive real number such that, a x − [x ], , ∫0 e, , dx = 10e − 9, where [ x ] is the greatest, , integer less than or equal to x. Then, a is, equal to, a. 10 − log e (1 + e ), c. 10 + log e 3, , b. 10 + log e 2, d. 10 + log e (1 + e ), , 3. The mean of 6 distinct observations is 6.5, , 5. If α and β are the distinct roots of the, equation x 2 + (3)1/ 4 x + 31/ 2 = 0, then the value, of α 96(α 12 − 1) + β 96(β12 − 1) is equal to, a. 56 × 325, , b. 56 × 324, , c. 52 × 324 d. 28 × 325, , 2 3, , a ∈ R be written as P + Q ,, a 0, where P is a symmetric matrix and Q is skew, symmetric matrix. If det (Q) =`9, then the, modulus of the sum of all possible values of, determinant of P is equal to, , 6. Let A = , , a. 36, , b. 24, , c. 45, , d. 18, , 7. If z and ω are two complex numbers such, that|zω| = 1and arg ( z) − arg (ω) =, , 3π, , then, 2, , and their variance is 10.25. If 4 out of 6, observations are 2, 4, 5 and 7, then the, remaining two observations are, , 1 − 2zω , arg , is, 1 + 3zω , , a. 10, 11, c. 8, 13, , (Here, arg (z) denotes the principal argument of, complex number z), 3π, π, π, 3π, c. −, d., a., b. −, 4, 4, 4, 4, , b. 3, 18, d. 1, 20, , 4. The value of the integral, 1, , ∫ log e (, , −1, , 1 − x + 1 + x )dx is equal to, , π 3, 1, a. log e 2 + −, 2, 4 2, π, c. log e 2 + − 1, 2, , π, −1, 4, π 1, d. 2log e 2 + −, 2 2, , b. 2log e 2 +, , 3, 8. If in a triangle ABC , AB = 5 units, ∠B = cos −1 , 5, , and radius of circumcircle of ∆ABC is 5 units,, then the area (in square units) of ∆ABC is, a. 10 + 6 2, c. 6 + 8 3, , b. 8 + 2 2, d. 4 + 2 3
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10, , ONLINE, , 9. Let [ x ] denote the greatest integer ≤ x, where, x ∈ R . If the domain of the real valued function, |[ x ]| − 2, , f ( x) =, , |[ x ]| − 3, , is ( −∞ , a) ∪ [ b, c) ∪ [u, ∞) ,, , c. −2, , b. 1, , y, y, , , equation x tan dy = y tan − x dx ,, x, x, , , π, 1, , −1 ≤ x ≤ 1, y = . Then, the area of the, 2 6, 1, 2, , 1, ( π − 3), 12, 1, d. ( π − 1), 6, , (1 − x)101( x 2 + x + 1)100 is, b. 100 C15, , c. −, , d. −100 C15, , 100, , C16, , ,, if i = j, 1, , a ij = − x, , if|i − j| = 1, 2x + 1 , otherwise, , , b., , 88, 27, , c., , 20, 27, , d. −, , 88, 27, , such that a ⋅ c = |c|,|c − a| = 2 2 and the angle, π, between ( a × b) and c is , then the value of, 6, |( a × b) × c| is, 2, 3, , b. 4, , c. 3, , d. 3/2, , 14. The number of real roots of the equation, tan −1 x (x + 1) + sin −1 x 2 + x + 1 =, a. 1, c. 3, , b. 3, , c. 2, , d. 5, , 18. Words with or without meaning are to be, , 13. Let a = 2$i + $j − 2k$ and b = $i + $j. If c is a vector, , a., , sin x − e x , if, x≤0, , f (x ) = a + [ − x ], if 0 < x < 1, 2x − b ,, if, x≥1, , , a. 4, , Let a function f : R → R be defined as, f ( x) = det (A). Then, the sum of maximum and, minimum values of f on R is equal to, 20, 27, , 3, 4, 3, b. local minimum at x = −, 4, 3, c. local maximum at x =, 4, 3, d. local minimum at x =, 4, , where, [ x ] is the greatest integer less than or, equal to x. If f is continuous on R, then (a + b), is equal to, , 12. Let A = [a ij ] be a 3 × 3 matrix, where, , a. −, , f ( x) = ax 2 + 6x − 15, x ∈ R is increasing in, 3, , 3 , −∞ , and decreasing in , ∞ . Then, the, , 4 , 4, , 17. Let a function f : R → R be defined as, , in the expansion of, , a. 100 C16, , d. 1 + 4e 6, , a. local maximum at x = −, , b., , 11. The coefficient of x, , c. 1 + 4e 3, , function g( x) = ax 2 − 6x + 15 , x ∈ R has a, , and y = y ( x) in the upper half plane is, , 256, , b. 1 − 4e 6, , 16. Let a be a real number such that the function, , 10. Let y = y ( x) be the solution of the differential, , 1, a. ( π − 1), 8, 1, c. ( π − 2), 4, , y, equation e x 1 − y 2dx + dy = 0, y(1) = − 1., x, a. 1 − 4e 3, , d. −3, , region bounded by the curves x = 0, x =, , 15. Let y = y ( x) be the solution of the differential, Then, the value of [ y (3)]2 is equal to, , a < b < c, then the value of a + b + c is, a. 8, , JEE Main 2021 ~ Solved Papers, , b. 4, d. 0, , π, is, 4, , formed using all the letters of the word, EXAMINATION. The probability that the letter, M appears at the fourth position in any such, word is, a. 1/66, , b. 1/11, , c. 1/9, , d. 2/11, , 19. The probability of selecting integers, a ∈ [ −5, 30] such that, x 2 + 2(a + 4) x − 5a + 64 > 0, for all x ∈ R , is, a., , 7, 36, , b., , 2, 9, , c., , 1, 6, , d., , 1, 4, , 20. Let the tangent to the parabola S: y 2 = 2x at, the point P(2, 2) meet the X-axis at Q and, normal at it meet the parabola S at the point, R. Then, the area (in square units) of ∆PQR is, equal to, a., , 25, 2, , b., , 35, 2, , c., , 15, 2, , d. 25
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11, , JULY ATTEMPT ~ 20 July 2021, Shift I, Section B : Numerical Type Questions, , of the region bounded by the tangent T ,, ellipse E, lines x = 1and x = 5 is, 1, α 5 + β + γ cos −1 , then|α + β + γ| is, 5, equal to …… ., , 21. Let a, b , c be three mutually perpendicular, vectors of the same magnitude and equally, inclined at an angle θ, with the vector, a + b + c. Then, 36cos 2 2θ is equal to ……… ., , 27. Let a , b, c , d be in arithmetic progression with, , 1 −1 0 , , , 22. Let A = 0 1 −1 and B = 7A 20 − 20A 7 + 21,, 0 0 1 , , , , common difference λ., x + a −c x + b x + a, If, x −1, x + c x + b = 2,, , where I is an identity matrix of order 3 × 3 . If, B = [ bij ], then b13 is equal to ……… ., , 23. Let P be a plane passing through the points, , (1, 0, 1), (1, −2, 1) and (0, 1, −2). Let a vector, a = α $i + β$j + γk$ be such that a is parallel to, the plane P, perpendicular to ( $i + 2$j + 3k$ ), and a. ( $i + $j + 2k$ ) = 2, then (α − β + γ) 2 equals, …… ., , x −b+d, , x+c, , then value of λ is equal to …… ., 2, , 28. There are 15 players in a cricket team, out of, which 6 are bowlers, 7 are batsmen and 2, are wicketkeepers. The number of ways, a, team of 11 players be selected from them so, as to include atleast 4 bowlers, 5 batsman, and 1 wicketkeeper, is ……… ., , 24. The number of rational terms in the, , binomial expansion of ( 41/ 4 + 51/ 6)120is …… ., , 29. Let y = mx + c, m > 0 be the focal chord of, y 2 = −64 x , which is tangent to, ( x + 10) 2 + y 2 = 4. Then, the value of, 4 2 ( m + c) is equal to ……… ., , 25. If the shortest distance between the lines, , r1 = α i$ + 2$j + 2k$ + λ ( i$ − 2$j + 2k$ ), λ ∈R, α > 0, and r2 = − 4 i$ − k$ + µ(3$i − 2$j − 2k$ ), µ ∈R is 9,, then α is equal to ……… ., , x+ 2, 2 , x , , 30. If the value of lim(2 − cos x cos 2x ) , , 26. Let T be the tangent to the ellipse, , x→ 0, , ) If the area, E : x + 4 y = 5 at the point P(1, 1., 2, , x+d, , 2, , is, , a, , equal to e , then a is equal to ……… ., , Answers, For solutions scan, the QR code, , Physics, 1. (c), 11. (d), 21. 0.003, , 2. (a), 12. (b), 22. 3, , 3. (d), 13. (c), 23. 2, , 4. (b), 14. (d), 24. 1, , 5. (c), 15. (d), 25. 100, , 6. (d), 16. (a), 26. 2, , 7. (a), 17. (a), 27. 4, , 8. (d), 18. (c), 28. 25, , 9. (d), 19. (d), 29. 132, , 10. (b), 20. (d), 30. 40, , 6. (a), 16. (c), 26. 3, , 7. (b), 17. (a), 27. 2, , 8. (a), 18. (a), 28. 106, , 9. (d), 19. (c), 29. 667, , 10. (a), 20. (d), 30. 78, , 6. (a), 16. (a), 26. 1.25, , 7. (b), 17. (b), 27. 1, , 8. (c), 18. (b), 28. 777, , 9. (c), 19. (b), 29. 34, , 10. (a), 20. (a), 30. 3, , Chemistry, 1. (b), 11. (c), 21. 3, , 2. (d), 12. (c), 22. 226, , 3. (d), 13. (d), 23. 0, , 4. (c), 14. (c), 24. 2, , 3. (a), 13. (d), 23. 81, , 4. (c), 14. (d), 24. 21, , 5. (b), 15. (b), 25. 172, , Mathematics, 1. (b), 11. (b), 21. 4, , 2. (b), 12. (d), 22. 910, , 5. (c), 15. (b), 25. 6
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JEE Main 2021, 20 JULY SHIFT II, , PHYSICS, Section A : Objective Type Questions, 1. If the kinetic energy of a moving body, becomes four times of its initial kinetic, energy, then the percentage change in its, momentum will be, a. 100%, c. 300%, , b. 200%, d. 400%, , 2. A boy reaches the airport and finds that the, escalator is not working. He walks up the, stationary escalator in time t1. If he remains, stationary on a moving escalator, then the, escalator takes him up in time t 2. The time, taken by him to walk up on the moving, escalator will be, t1t 2, t 2 − t1, tt, c. 1 2, t 2 + t1, a., , b., , t1 + t 2, 2, , d. t 2 − t1, , 3. A satellite is launched into a circular orbit of, radius R around Earth, while a second, satellite is launched into a circular orbit of, radius 1.02 R. The percentage difference in, the time periods of the two satellites is, a. 1.5, c. 0.7, , b. 2.0, d. 3.0, , l1T2 − l 2T1, T2 − T1, l1 + l 2, d., 2, , a. l1 l 2, c., , b., , l1T2 + l 2T1, T2 + T1, , 6. In an electromagnetic wave, the electric field, vector and magnetic field vector are given as, E = E 0$i and B = B 0k$ , respectively. The, direction of propagation of electromagnetic, wave is along, a. k$, , b. $j, , c. (−k$ ), , d. (− $j ), , 7. For a series L-C-R circuit with R = 100 Ω,, , L = 05, . mH and C = 01, . pF connected across, 220 V-50 Hz AC supply, the phase angle, between current and supplied voltage and, the nature of the circuit is, a. 0°, resistive circuit, b. ≈ 90°, predominantly inductive circuit, c. 0° resonance circuit, d. ≈ 90°, predominantly capacitive circuit, , 8. Which of the following graphs represent the, behaviour of an ideal gas ? (Symbols have, their usual meanings.), pV, , pV, , a., , b., , 4. With what speed should a galaxy move, outward with respect to Earth, so that the, sodium-D line at wavelength 5890 Å is, observed at 5896 Å ?, a. 306 km/s, c. 296 km/s, , T, , T, , pV, , pV, , b. 322 km/s, d. 336 km/s, , 5. The length of a metal wire is l1, when the, tension in it is T1 and is l 2 when the tension is, T2. The natural length of the wire is, , c., , d., T, , T
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13, , JULY ATTEMPT ~ 20 July 2021, Shift II, 9. A particle is making simple harmonic motion, , a. T = 2 π, , x 22 + x12, , b. T = 2 π, , x 22 + x12, , c. T = 2 π, d. T = 2 π, , v12, v12, , +, , x 22, v12, , − x12, , R = Decay rate, , 6, 4, 2, , v 22, 10 20 30 40 50 60, Time, t(s), , + v 22, , a. 9.15 s, c. 2.62 s, , x 22 − x12, v12 − v 22, , a. Zero, 2mcλ 2, h, , b. 6.93 s, d. 4.62 s, , 15. Consider a binary star system of star A and, , is incident on a target in a X-ray tube., Cut-off wavelength of emitted X-ray is, b., d., , 2m 2c 2 λ 2, h2, hc, mc, , 11. A body rolls down an inclined plane without, slipping. The kinetic energy of rotation is, 50% of its translational kinetic energy. The, body is, a. solid sphere, b. solid cylinder, c. hollow cylinder, d. ring, , 12. If time (t), velocity (v ) and angular, momentum ( l) are taken as the fundamental, units, then the dimension of mass ( m) in, terms of t ,v and l is, a. [ t −1v1l −2 ], , b. [ t 1v 2 l −1], , c. [ t −2v −1l1], , d. [ t −1v −2 l1], , 13. The correct relation between the degrees, , of freedom f and the ratio of specific heat γ, is, 2, a. f =, γ −1, γ+1, c. f =, 2, , 8, , − v 22, , 10. An electron having de-Broglie wavelength λ, , c., , the unknown radioactive material is, approximately, , In R, , along the X-axis. If at a distances x1 and x 2, from the mean position, the velocities of the, particle are v1 and v 2 respectively, then the, time period of its oscillation is given as, , 2, b. f =, γ+1, 1, d. f =, γ+1, , 14. For a certain radioactive process, the graph, between InR and t (sec) is obtained as shown, in the figure. Then, the value of half-life for, , star B with masses m A and m B revolving in a, circular orbit of radii rA and rB , respectively. If, TA and TB are the time period of star A and, star B respectively, then, 3, , r 2, T, a. A = A , TB rB , b. TA = TB, c. TA > TB (if m A > m B ), d. TA > TB (if rA > rB ), , 16. At an angle of 30° to the magnetic meridian,, the apparent dip is 45°. Find the true dip., a. tan −1( 3 ), , 1 , b. tan −1, , 3, , 2 , c. tan −1, , 3, , 3, d. tan −1, , 2 , , 17. A body at rest is moved along a horizontal, straight line by a machine delivering a, constant power. The distance moved by the, body in time t is proportional to, 3, , 1, , 1, , 3, , a. t 2, , b. t 2, , c. t 4, , d. t 4, , 18. Two vectors P and Q have equal magnitudes., If the magnitude of P + Q is n times the, magnitude of P − Q, then angle between P, and Q is, n − 1, a. sin −1, , n + 1, , n − 1, b. cos −1, , n + 1, , n 2 − 1, c. sin −1 2, , n + 1, , n 2 − 1, d. cos −1 2, , n + 1
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14, , JEE Main 2021 ~ Solved Papers, , ONLINE, , coalesce to form a single large drop. The, ratio of total surface energy before and after, the change is, 1, , 1, , a. 2 3 : 1, , b. 1: 2 3, , c. 2 : 1, , d. 1 : 2, , 20. The magnetic susceptibility of a material of a, rod is 499. Permeability in vacuum is, 4 π × 10−7 H/m. Absolute permeability of the, material of the rod is, a. 4 π × 10−4 H/m, c. 3 π × 10−4 H/m, , b. 2 π × 10−4 H/m, d. π × 10−4 H/m, , Section B : Numerical Type Questions, 21. A Zener diode having Zener voltage 8 V and, power dissipation rating of 0.5 W is, connected across a potential divider, arranged with maximum potential drop, across Zener diode is as shown in the, diagram. The value of protective resistance, R p is ...........Ω., Rp, , shown in the figure, the dynamic resistance, at ID = 3 mA will be ……… Ω., , 8, 7, 6, 5, 4, 3, 2, 1, , C = 05, . µF is connected across an AC supply of, 250 V, having variable frequency. The power, dissipated at resonance condition is ……, × 102 W ., , +, , 27. One mole of an ideal gas at 27°C is taken, , 23. In the given figure, switches S1 and S 2 are in, open condition. The resistance across, ab when the switches S1 and S 2 are closed, is …… Ω., 4Ω, S1, , from A to B as shown in the given, p-V indicator diagram. The work done by the, system will be …… × 10−1 J ., [Take, R = 8.3 J/ mol-K, In 2 = 06931, ], ., (Round off to the nearest integer), A(p1V1), , 200, , p(N/m2), , inclined plane making an angle of 30° with, the horizontal. The coefficient of friction, x, . if the, between the body and plane is, 5, time of ascent is half of the time of descent., The value of x is …… ., , B(p2V2), , 100, , 6Ω, S2, , b, , 2, 6Ω, , VD(V), , 26. A series L-C-R circuit of R = 5 Ω, L = 20 mH and, , 22. A body of mass m is launched up on a rough, , a, , 25. For the forward biased diode characteristics, , 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9, , 20 V, , 12 Ω, , same material are rolling down without, slipping an inclined plane. The radii of the, bodies are same. The ratio of velocity of the, centre of mass at the bottom of the inclined, plane of the ring to that of the cylinder is x ., 2, Then, the value of x is …… ., , n, p, Vz = 8V, , –, , 24. Two bodies, a ring and a solid cylinder of, , ID(mA), , 19. Two small drops of mercury each of radius R, , 4Ω, , 12 Ω, , 4, V(m 3)
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15, , JULY ATTEMPT ~ 20 July 2021, Shift II, , 28. A certain metallic surface is illuminated by, , monochromatic radiation of wavelength λ., The stopping potential for photoelectric, current for this radiation is 3V0., If the same surface is illuminated with a, radiation of wavelength 2λ, the stopping, potential is V0. The threshold wavelength of, this surface for photoelectric effect is …… λ., , 29. A body rotating with an angular speed of, 600 rpm is uniformly accelerated to 1800, rpm in 10 s. The number of rotations made, in the process is …… ., , 30. A radioactive substance decays to (1/16)th of, its initial activity in 80 days. The half-life of, the radioactive substance expressed in days, is …… ., , CHEMISTRY, Section A : Objective Type Questions, 1. Which one of the following pairs of isomers, , NH2, a., , NH2, ,, , is an example of metamerism ?, Br, , CH, a., , CH3CH2CH2CH2CH3, , and, , H3C—C—CH3, , NH2, b., , NH2, ,, , CH3, Br, , b., , NH2, , H, , C6H5 and H5C6, , c., , OH, c., , H5C6, , NH2, d., , OH and H5C6, , NH2, ,, NH2, ,, , Br, , and, , d., , Br, , 3. The major product P in the following reaction, is, CHO, , NH2 KOBr, , 2., , (i) KOH (alc.), (ii) H+, ∆, , A, (Major product), , Br, , OHC, , NH2 LiAIH+4, H 3O, , B, , a., , b., , (Major product), , CHO, , Br, , In the above reactions, products A and B, respectively are, , c., , d., , P, (Major product)
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16, , ONLINE, , 4. The single largest industrial application of, , JEE Main 2021 ~ Solved Papers, , 11. Which one of the following statements is not, , dihydrogen is, , true about enzymes ?, , a. manufacture of metal hydrides, b. rocket fuel in space research, c. in the synthesis of ammonia, d. In the synthesis of nitric acid, , a. Enzymes are non-specific for a reaction and, substrate., b. Almost all enzymes are proteins., c. Enzymes work as catalysts by lowering the, activation energy of a biochemical reaction., d. The action of enzymes is temperature and pH, specific., , 5. Consider two chemical reactions (A) and (B), that take place during metallurgical process :, ∆, , (A) ZnCO 3 (s) → ZnO (s) + CO 2 ( g ), ∆, , (B) 2ZnS (s) + 3O 2 ( g ) → 2ZnO (s) + 2SO 2 ( g ), The correct option of names given to them, respectively is, a. (A) is calcination and (B) is roasting, b. Both (A) and (B) are producing same product, so both are roasting, c. Both (A) and (B) are producing same product, so both are calcination, d. (A) is roasting and (B) is calcination, , 12. The hybridisations of the atomic orbitals of, nitrogen in NO−2 , NO+2 and NH+4 respectively are, a. sp 3 , sp 2 and sp, b. sp , sp 2 and sp 3, c. sp 3 , sp and sp 2, d. sp 2 , sp and sp 3, , 13. Bakelite is a cross-linked polymer of, formaldehyde and, a. PHBV, b. buna-S, c. novolac, d. dacron, , −, , 6. A solution is 0.1 M in Cl and 0.001 M in, , CrO2−, 4 . Solid AgNO3 is gradually added to it., Assuming that the addition does not change, in volume and K sp(AgCl) = 1.7 × 10−10 M 2 and, K sp(Ag 2CrO4) = 1.9 × 10−12M 3, , 14. Benzene on nitration gives nitrobenzene in, presence of HNO3 and H 2SO4 mixutre, where, a. both H2SO 4 and HNO 3 act as a bases, b. HNO 3 acts as an acid and H2SO 4 acts as a base, c. both H2SO 4 and NHO 3 act as an acids, d. HNO 3 acts as a base and H2SO 4 acts as an acid, , Select correct statement from the following, a. AgCl precipitates first because its K sp is high., b. Ag 2CrO 4 precipitates first as its K sp is low., c. Ag 2CrO 4 precipitates first because the amount, of Ag + needed is low., d. AgCl will precipitate first as the amount of, Ag + needed to precipitate is low., , 7. Outermost electronic configuration of a, , group-13 element E is 4 s 2 4 p1. The electronic, configuration of an element of p-block, period-five placed diagonally to element, E is, a. [Kr]3d10 4 s 2 4 p 2, c. [Xe]5d10 6s 2 6p 2, , b. [Ar]3d10 4 s 2 4 p 2, d. [Kr] 4 d10 5s 2 5p 2, , 8. Metallic sodium does not react normally with, a. gaseous ammonia, c. ethyne, , NH2, NaNO2, HCl, A, 273-278 K, (Major, , 15., , (Major, product), , product), , SO3H, , Consider the above reaction, compound B is, CH3, N, CH3, —N==N—, a. HO3S—, , b., , —N==N —, , —N, , complex of Fe in the presence of a strong, field ligand in BM is, c. 0, , d. 3.46, , 10. Which one of the following species doesn't, , c. HO3S—, , —N==N —, , d. HO3S—, , —, , have a magnetic moment of 1.73 BM (spin, only value) ?, a. O 2+, c. [Cu(NH3 ) 4 ]Cl2, , B, , 273 K, , 2+, , b. 2.82, , CH3, , b. but-2-yne, d. tert-butyl alcohol, , 9. Spin only magnetic moment of an octahedral, a. 4.89, , CH3, , N, , b. CuI, d. O −2, , —N, , CH3, CH3, , —N, , CH3, CH3, , CH3, CH3
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17, , JULY ATTEMPT ~ 20 July 2021, Shift II, , 23. The vapour pressures of A and B at 25°C are, , (i) (C6H5CO)2O2, HBr, P, (ii) CoF2, (Major, , 16., , 90 mm Hg and 15 mm Hg respectively. If A, and B are mixed such that the mole-fraction, of A in the mixture is 0.6, then the mole, fraction of B in the vapour phase is x × 10−1., The value of x is ……… . (Nearest integer), , product), , Br, , Major product P of above reaction is, F, a., , F, , b., Br, , Br, , c., , F, , Br, , contains x g of NaOH and y g of Na 2CO3. The, value of x is …… g. (Nearest integer), F, , d., Br, , give, b. Cu 2I3, , c. CuI, , [Atomic mass : Silver = 108, bromine = 80], , d. Cu(I3 ) 2, , 26. 100 mL of 0.0018% (w/v) solution of Cl− ion, , 18. In Carius method, halogen containing, , was the minimum concentration of Cl−, required to precipitate a negative sol in, one h. The coagulating value of Cl− ion is, ……… (Nearest integer), , organic compound is heated with fuming, nitric acid in the presence of, a. HNO 3, , b. AgNO 3, , c. CuSO 4, , d. BaSO 4, , 19. Which one of the following gases is reported, to retard photosynthesis ?, a. CO, , 20., , (A), , (C), , b. CFCs, , R, , Cl, , R, , O, , c. CO 2, , (B), , R, , (D), , O, , R, , N, , R, , H, , 28. Diamond has a three dimensional structure, of C atoms formed by covalent bonds. The, structure of diamond has face centred cubic, lattice, where 50% of the tetrahedral voids, are also occupied by carbon atoms. The, number of carbon atoms present per unit, cell of diamond is …… ., , H, The correct order of their reactivity towards, hydrolysis at room temperature is, a. (A) > (B) > (C) > (D), b. (D) > (A) > (B) > (C), c. (D) > (B) > (A) > (C), d. (A) > (C) > (B) > (D), , Section B : Numerical Type Questions, 21. For a given chemical reaction, A → B at, , 29. An aqueous solution of NiCl2 was heated, −1, , 300 K the free energy change is −49.4 kJ mol, and the enthalpy of reaction is 51.4 kJ mol−1 ., The entropy change of the reaction is ……, JK −1mol−1., , 22. The wavelength of electrons accelerated, from rest through a potential difference of, 40 kV is x × 10−12 m. The value of x is ……, (Nearest integer), Given : Mass of electron = 91, . × 10−31 kg, Charge on an electron = 16, . × 10−19 C, Planck’s constant = 663, . × 10−34 Js, , 27. PCl5( g) → PCl3( g) + Cl2( g), In the above first order reaction, the, concentration of PCl5 reduces from initial, concentration 50 mol L−1 to 10 mol L−1 in, 120 minutes at 300 K. The rate constant for the, reaction at 300 K is x × 10−2 min −1. The value of x, is …… ., [Given, log 5 = 06989, ], ., , d. NO 2, , R, , 25. When 0.15 g of an organic compound was, analysed using Carius method for estimation, of bromine, 0.2397 g of AgBr was obtained., The percentage of bromine in the organic, compound is …… . (Nearest integer), , 17. Cu 2+ salt reacts with potassium iodide to, a. Cu 2I2, , 24. 4g equimolar mixture of NaOH and Na 2CO3, , with excess sodium cyanide in presence of, strong oxidising agent to form [Ni(CN) 6 ]2− ., The total change in number of unpaired, electrons on metal centre is …… ., , 30. Potassium chlorate is prepared by, electrolysis of KCl in basic solution as shown, by following equation, , 6OH− + Cl− → CIO 3− + 3H2O + 6e −, A current of xA has to be passed for 10th to, produce 10.0 g of potassium chlorate. The value, of x is …… . (Nearest integer), (Molar mass of KClO 3 = 122.6 g mol−1, F = 96500 C )
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18, , JEE Main 2021 ~ Solved Papers, , ONLINE, , MATHEMATICS, Section A : Objective Type Questions, 1. For the natural numbers m , n, if (1 − y ) (1 + y ), m, , 7. If the real part of the complex number, n, , = 1 + a1y + a 2 y 2 + ...... + a m + n y m + n and, a1 = a 2 = 10, then the value of ( m + n) is equal, to, a. 88, c. 100, , b. 64, d. 80, , −181, 69, −291, c., 76, , a., , , , 5, , 13 , , 220, 21, 151, d., 63, , b., , 3. Let r1 and r2 be the radii of the largest and, smallest circles, respectively, which pass, through the point (−4, 1) and having their, centres on the circumference of the circle, r, x 2 + y 2 + 2x + 4 y − 4 = 0. If 1 = a + b 2,, r, 2, then a + b is equal to, a. 3, c. 5, , b. 11, d. 7, , 4. Consider the following three statements,, (A) If 3 + 3 = 7, then 4 + 3 = 8, (B) If 5 + 3 = 8, then earth is flat, (C) If both (A) and (B) are true, then 5 + 6 = 17, Then, which of the following statements is, correct, a. (A) is false, but (B) and (C) are true, b. (A) and (C) are true while (B) is false, c. (A) is true while (B) and (C) are false, d. (A) and (B) are false while (C) is true, , 5. The lines x = ay − 1 = z − 2 and, x = 3 y − 2 = bz − 2, (ab ≠ 0) are coplanar, if, a. b = 1, a ∈ R − {0}, b. a = 1, b ∈ R − {0}, c. a = 2, b = 2, d. a = 2, b = 3, , 6. If [x] denotes the greatest integer less than, or equal to x then the value of the integral, , ∫, , π, 2, π, −, 2, , [[ x ] − sin x ]dx is equal to, , a. −π, c. 0, , b. π, d. 1, , 1, for θ ∈ (0, π ), then the, 5, , θ, , value of the integral ∫ sinx dx is equal to, 0, , a. 1, , 3, 5 , , 2. The value of tan 2 tan−1 + sin−1 is, , , equal to, , (1 − cos θ + 2i sinθ) −1 is, , c. −1, , b. 2, , d. 0, , α, 8. Let f : R − → R be defined by, 6 , 5x + 3, ., f ( x) =, 6x − α, , Then the value of α for which (fof) ( x) = x , for all, α, x ∈ R − is, 6 , a. No such α exists, c. 8, , b. 5, d. 6, , 9. If f : R → R is given by f ( x) = x + 1, then the, value of, lim, , n→∞, , 5(n − 1) , 1, 5, 10 , f (0) + f + f + ....+ f , , n, n, n , n , , is, a. 3/2, , b. 5/2, , c. 1/2, , d. 7/2, , 10. Let A , B and C be three events such that the, probability that exactly one of A and B occurs, is (1 − k), the probability that exactly one of B, and C occurs is (1 − 2k), the probability that, exactly one of C and A occurs is (1 − k) and, the probability of all A , B and C occur, simultaneously is k 2, where 0 < k < 1. Then, the probability that at least one of A , B and C, occur is, a. greater than 1/8 but less than 1/4, b. greater than 1/2, c. greater than 1/4 but less than 2/2, d. exactly equal to 1/2, , 11. The sum of all the local minimum values of, the twice diffrentiable function f :R → R, defined by, f (x ) = x 3 − 3x 2 −, a. −22, c. −27, , 3 f ′ ′ (2), x + f ′ ′ (1) is, 2, b. 5, d. 0
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19, , JULY ATTEMPT ~ 20 July 2021, Shift II, 12. Let in a right angled triangle, the smallest, , angle be θ. If a triangle formed by taking the, reciprocal of its sides is also a right angled, triangle, then sinθ is equal to, 5+1, 4, , a., , b., , 5−1, 2, , 2−1, 2, , c., , 5−1, 4, , d., , dy, −|A|= 0,, dx, , , y sin x 1, , , for all x > 0, where A = 0, −1 1 . If, 1, 2, 0, , x , π, , y( π ) = π + 2, then the value of y is, 2, , 13. Let y = y ( x) satisfies the equation, , a., , π 4, +, 2, π, , b., , π 1, −, 2 π, , c., , 3π 1, −, 2, π, , d., , π 4, −, 2 π, , 14. Consider the line L given by the equation, x −3, 2, , y −1, , =, , 1, , =, , z −2, 1, , ., , system of liner equations, 3x − y + 4 z = 3, x + 2 y − 3z = − 2, 6x + 5 y + kz = − 3, has infinitely many solutions, is, , b. (1, 1, 1), d. (1, 2, 2), , 15. If the mean and variance of six observations, 20, , respectively,, 3, then the value of|a − b| is equal to, , 7, 10, 11, 15, a , b are 10 and, , b. −5, d. −3, , a. 3, c. 5, , 19. If sum of the first 21 terms of the series, log, , 91/ 2, , x + log, , 91/ 3, , x + log, , 91/ 4, , x + ...., where x > 0, , is 504, then x is equal to, a. 243, c. 7, , b. 9, d. 81, , 20. In ∆ ABC , if|BC| = 3,|CA| = 5 and|BA| = 7, then, the projection of the vector BA on BC is, equal to, a., , Let Q be the mirror image of the point (2, 3, −1), with respect to L. Let a plane P be such that, it passes through Q, and the line L is, perpendicular to P. Then which of the, following points is on the plane P?, a. (−1, 1, 2), c. (1, 1, 2), , 18. The value of k ∈ R, for which the following, , 19, 2, , b., , 13, 2, , c., , 11, 2, , d., , 15, 2, , Section B : Numerical Type Questions, 21. Let A = { a ij } be a 3 × 3 matrix, where, ( −1) j − i if, , a ij = 2, if, ( −1) i + j if, , , i< j, i= j, i> j, , −1, , then det [3Adj (2A )] is equal to, , 22. The number of solutions of the equation, , d. 1, , log ( x + 1) (2x 2 + 7x + 5) + log ( 2x + 5) ( x + 1) 2− 4 = 0, x > 0, is, , 16. Let g(t) = ∫ 2π cos t + f ( x) dx , where, , 23. Let a curve y = y ( x) be given by the solution, , a. 9, , b. 11, π, , −, , 2, , f ( x) = log e ( x +, , c. 7, , π, 4, , x 2 + 1,, ) x ∈ R . Then, which, , one of the following is correct ?, a. g (1) = g (0), c. g (1) = 2 g (0), , b. 2 g (1) = g (0), d. g (1) + g (0) = 0, , 17. Let P be a variable point on the parabola, y = 4 x 2 + 1. Then, the locus of the mid point of, the point P and the foot of the perpendicular, drawn from the point P to the line y = x is, a. (3x − y ) 2 + (x − 3 y ) + 2 = 0, b. 2(3x − y ) 2 + (x − 3 y ) + 2 = 0, c. (3x − y ) 2 + 2(x − 3 y ) + 2 = 0, d. 2(x − 3 y ) 2 + (3x − y ) + 2 = 0, , of the differential equation, 1, , cos cos −1(e − x ) dx = e 2x − 1dy, 2, , If it intersects Y-axis at y = − 1and the, intersection point of the curve with X-axis is, (α , 0), then e α is equal to, , 24. For p > 0, a vector V2 = 2i$ + ( p + 1) $j is, obtained by rotating the vector v 1 = 3p $i + $j, by an angle θ about origin in counter, (α 3 − 2), , then, clockwise direction. If tanθ =, ( 4 3 + 3), the value of α is equal to
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20, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 25. Consider a triangle having vertices A( −2, 3), B(1, 9), , 28. For k ∈ N, let, , 26. If the point on the curve y 2 = 6x , nearest to the, 3, point 3, is (α ,β) , then 2 (α + β) is equal to, 2, , where α > 0. Then the value of, 2, A + A15 , 100 14, is equal to …… ., A13, , , , 29. Let { a n } ∞n = 1 be a sequence such that, a1 = 1 , a 2 = 1 and a n +, , = 2a n + 1 + a n for, ∞, an, all n ≥ 1. Then the value of 47, is, n = 1 2 3n, equal to … ., , 27. Let a function g :[0, 4 ] → R be defined as, max (t 3 − 6t 2 + 9t − 3), 0 ≤ x ≤ 3, g (x ) = 0 ≤t ≤x, 4−x, , 3< x ≤ 4, , , 20, , Σ, , 1, Ak, ,, =, α (α + 1)(α + 2) .... (α + 20) k = 0 α + k, , and C(3, 8). If a line L passing through the, circumcentre of ∆ ABC , bisects line BC , and, α, intersects Y-axis at point 0, , then the value of, 2, real number α is, , 2, , Σ, , α xe x − β log e (1 + x) + γx 2e − x, , = 10,, x sin2 x, α, β, γ ∈R, then the value of α + β + γ, is … ., , 30. If lim, , x→ 0, , then the number of points in the interval (0, 4), where g( x) is not differentiable,, is … ., , Answers, For solutions scan, the QR code, , Physics, 1. (a), 11. (b), 21. 192, , 2. (c), 12. (d), 22. 3, , 3. (d), 13. (a), 23. 10, , 4. (a), 14. (d), 24. 3, , 5. (b), 15. (b), 25. 25, , 6. (d), 16. (d), 26. 125, , 7. (d), 17. (a), 27. 17258, , 8. (c), 18. (d), 28. 4, , 9. (d), 19. (a), 29. 32, , 10. (c), 20. (b), 30. 20, , Chemistry, 1. (d), 11. (a), 21. 360, , 2. (d), 12. (d), 22. 6, , 3. (b), 13. (c), 23. 1, , 4. (c), 14. (d), 24. 1, , 5. (a), 15. (c), 25. 68, , 6. (d), 16. (d), 26. 1, , 7. (d), 17. (a), 27. 1, , 8. (b), 18. (b), 28. 8, , 9. (c), 19. (d), 29. 2, , 10. (b), 20. (a), 30. 1, , 3. (c), 13. (a), 23. 2, , 4. (b), 14. (d), 24. 6, , 5. (a), 15. (d), 25. 9, , 6. (a), 16. (b), 26. 9, , 7. (a), 17. (b), 27. 1, , 8. (b), 18. (b), 28. 9, , 9. (d), 19. (d), 29. 7, , 10. (b), 20. (c), 30. 3, , Mathematics, 1. (d), 11. (c), 21. 108, , 2. (b), 12. (b), 22. 1
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JULY ATTEMPT ~ 22 July 2021, Shift II, , JEE Main 2021, 22 JULY SHIFT II, , PHYSICS, Section A : Objective Type Questions, 1. In a circuit consisting of a capacitance and a, , generator with alternating emf E g = E g 0 sinωt,, VC and IC are the voltage and current. Correct, phasor diagram for such circuit is, , VC, ωt, , d., , IC, , Eg, , C V, C, , IC, , VC, , cross-sectional area 3 mm2 is joined with a, similar aluminium (Al) rod as shown in, figure. Find the resistance of the, combination between the ends A and B., (Take, resistivity of copper = 1.7 × 10−8 Ω-m,, resistivity of aluminium = 2.6 × 10−8 Ω-m), Cu, , ωt, , a., , 2. A copper (Cu) rod of length 25 cm and, , A, , B, Al, , IC, , VC, , IC, b., , a. 2.170 m Ω, c. 0.0858 m Ω, , 3. What will be the projection of vector, A = $i + $j + k$ on vector B = $i + $j ?, a. 2 ($i + $j + k$ ), c. 2(i$ + $j ), , ωt, , b. 1.420 m Ω, d. 0.858 m Ω, , b. 2($i + $j + k$ ), d. (i$ + $j ), , 4. A porter lifts a heavy suitcase of mass 80 kg, IC, , c., , VC, ωt, , and at the destination lowers it down by a, distance of 80 cm with a constant velocity., Calculate the work done by the porter in, lowering the suitcase., [Take, g = 9.8 ms −2 ], a. − 627200, . J, b. − 6272, . J, c. + 6272, . J, d. 784.0 J
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22, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 5. T0 is the time period of a simple pendulum at, a place. If the length of the pendulum is, 1, reduced to, times of its initial value, then, 16, the modified time period is, a. T0, c. 4T0, , b. 8 πT0, 1, d. T0, 4, , 6. A ray of light passes from a denser medium, to a rarer medium at an angle of incidence i., The reflected and refracted rays make an, angle of 90° with each other. The angle of, reflection and refraction are respectively r, and r'. The critical angle is given by, , i r, r′, , a. sin −1(cot r ), c. sin −1(tan r ′ ), , b. tan −1(sin i ), d. sin −1(tan r ), , 7. Statement I The ferromagnetic property, depends on temperature. At high, temperature, ferromagnet becomes, paramagnet., Statement II At high temperature, the, domain wall area of a ferromagnetic, substance increases., In the light of the above statements, choose, the most appropriate answer from the options, given below., a. Statement I is true but Statement II is false, b. Both Statement I and Statement II are true, c. Both Statement I and Statement II are false, d. Statement I is false but Statement II is true, , 8. A bullet of 4 g mass is fired from a gun of, mass 4 kg. If the bullet moves with the muzzle, speed of 50 ms −1, the impulse imparted to the, gun and velocity of recoil of gun are, a. 0.4 kg-ms −1, 0.1 ms −1, b. 0.2 kg-ms −1, 0.05 ms −1, c. 0.2 kg-ms −1, 0.1 ms −1, d. 0.4 kg-ms −1 , 0.05 ms −1, , 9. Choose the correct option., a. True dip is not mathematically related to, apparent dip., b. True dip is less than apparent dip., c. True dip is always greater than the apparent, dip., d. True dip is always equal to apparent dip., , 10. Consider a situation in which a ring, a solid, cylinder and a solid sphere roll down on the, same inclined plane without slipping., Assume that they start rolling from rest and, having identical diameter., The correct statement for this situation., a. The sphere has the greatest and the ring has, the least velocity of the centre of mass at the, bottom of the inclined plane., b. The ring has the greatest and the cylinder has, the least velocity of the centre of mass at the, bottom of the inclined plane., c. All of them will have same velocity., d. The cylinder has the greatest and the sphere, has the least velocity of the centre of mass at, the bottom of the inclined plane., , 11. Consider a situation in which reverse biased, current of a particular p-n junction increases, when it is exposed to a light of wavelength, ≤ 621 nm. During this process, enhancement, in carrier concentration takes place due to, generation of hole-electron pairs. The value, of band gap is nearly, a. 2 eV, c. 1 eV, , b. 4 eV, d. 0.5 eV, , 12. A nucleus with mass number 184 initially at, , rest emits an α-particle. If the Q-value of the, reaction is 5.5 MeV, calculate the kinetic, energy of the α-particle., a. 5.0 MeV, c. 0.12 MeV, , b. 5.5 MeV, d. 5.38 MeV, , 13. An electron of mass m e and a proton of, mass m p are accelerated through the same, potential difference. The ratio of the, de-Broglie wavelength associated with the, electron to that with the proton is, a., c., , mp, me, mp, me, , b. 1, d., , me, mp
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23, , JULY ATTEMPT ~ 22 July 2021, Shift II, 14. Match List I with List II., , 18. The motion of a mass on a spring, with, , List I, A. ωL > 1, ωC, , List II, (i), , Current is in phase, with EMF, , B. ωL = 1, ωC, , (ii), , Current lags behind, the applied EMF, , C. ωL < 1, ωC, , (iii), , Maximum current, occurs, , D. Resonant, frequency, , (iv), , Current leads the EMF, , spring constant k is as shown in figure., , x, , The equation of motion is given by, k, m, , Choose the correct answer from the options, given below., , x(t) = A sinωt + B cos ωt with ω =, , Codes, , Suppose that at time t = 0, the position of, mass is x(0) and velocity v(0), then its, displacement can also be represented as, x(t) = C cos(ωt − φ), where C and φ are, , a., b., c., d., , A B C D, (ii) (i) (iv) (iii), (ii) (i) (iii) (iv), (iii) (i) (iv) (ii), (iv) (iii) (ii) (i), , a. C =, , 15. What should be the height of transmitting, antenna and the population covered, if the, television telecast is to cover a radius of, 150 km ? The average population density, around the tower is 2000/km2 and the value, of R e = 65, . × 106 m., a. Height = 1731m, Population covered = 1413 × 105, b. Height = 1241m, Population covered = 7 × 105, c. Height = 1600 m, Population covered = 2 × 105, d. Height = 1800 m, Population covered = 1413 × 108, , 16. What will be the average value of energy for, a monoatomic gas in thermal equilibrium at, temperature T ?, 2, a. K BT, 3, 3, c. K BT, 2, , b. K BT, 1, d. K BT, 2, , 17. Intensity of sunlight is observed as, , 0.092 Wm−2 at a point in free space. What, will be the peak value of magnetic field at, that point?, (ε 0 = 8.85 × 10−12C –2N–1m–2), a. 2.77 × 10−8 T, c. 8.31 T, , b. 1.96 × 10−8 T, d. 5.88 T, , b. C =, c. C =, d. C =, , v (0) , + x (0) 2 , φ = tan −1, , x (0)ω , , 2v (0) 2, ω2, 2v (0) 2, ω2, v (0) 2, ω2, v (0) 2, ω2, , x (0)ω , + x (0) 2 , φ = tan −1, , 2v (0) , , x (0)ω , + x (0) 2 , φ = tan −1, , v (0) , v (0) , + x (0) 2 , φ = tan −1, , x (0)ω , , 19. An electric dipole is placed on X-axis in, proximity to a line charge of linear charge, density 30, . × 10−6 C/m. Line charge is placed, on Z-axis and positive and negative charge of, dipole is at a distance of 10 mm and 12 mm, from the origin, respectively. If total force of, 4 N is exerted on the dipole, find out the, amount of positive or negative charge of the, dipole., a. 815.1 nC, c. 0.485 nC, , b. 8.8 µC, d. 4.44 µC, , 20. A body is projected vertically upwards from, the surface of Earth with a velocity sufficient, enough to carry it to infinity. The time taken, by it to reach height h is ……… s., a., , Re, 2g, , b., , 2R e, g, , 3/ 2, , , h, − 1, 1+, , Re , , , 3/ 2, , , h, − 1, 1+, , Re , ,
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24, , ONLINE, 3/ 2, , 1 Re , h, − 1, 1+, , 3 2g , Re , , , 3/ 2, , , 1 2R e , h, d., − 1, 1+, , 3 g , Re , , , , vectors A and C. The angle between the, 1, direction of motion of P and Q is cos −1, ., x, Then, the value of x is ……… ., , c., , 26. The centre of a wheel rolling on a plane, surface moves with a speed v 0. A particle on, the rim of the wheel at the same level as the, centre will be moving at a speed x v 0. Then,, the value of x is ……… ., , Section B : Numerical Type Questions, 21. In a given circuit diagram, a 5 V Zener diode, along with a series resistance is connected, across a 50 V power supply. The minimum, value of the resistance required, if the, maximum Zener current is 90 mA will be, ……… Ω., , 27. A ray of light passing through a prism, , (µ = 3) suffers minimum deviation. It is, found that the angle of incidence is double, the angle of refraction within the prism., Then, the angle of prism is ……… (in degrees)., , I2, , I, R, , I1, , 28. The area of cross-section of a railway track is, RL, , V =50V, , 0.01 m2. The temperature variation is 10°C., Coefficient of linear expansion of material of, track is 10−5/°C. The energy stored per metre, in the track is …… J/m., , Vz, , Z, , (Take, Young’s modulus of material of track, is 1011Nm−2), , 22. The position of the centre of mass of, a uniform semi-circular wire of radius R, placed in XY-plane with its centre at the, origin and the line joining its ends as X-axis, xR , is given by 0, . Then, the value of|x| is, π, , 29. Three students S1, S 2 and S 3 perform an, experiment for determining the acceleration, due to gravity (g) using a simple pendulum., They use different lengths of pendulum and, record time for different number of, oscillations. The observations are as shown, in the table., , ……… ., , 23. In an electric circuit, a cell of certain EMF, provides a potential difference of 1.25 V, across a load resistance of 5 Ω. However, it, provides a potential difference of 1 V across, a load resistance of 2 Ω. The emf of the cell, x, is given by, V. Then, the value of x is ……… ., 10, , 24. The total charge enclosed in an incremental, −9, , JEE Main 2021 ~ Solved Papers, , volume of 2 × 10 m located at the origin is, …… nC, if electric flux density of its field is, found as D = e − x sin y $i − e − x cos y$j + 2zk$ C/m2., 3, , 25. Three particles P, Q and R are moving along, the vectors A = $i + $j, B = $j + k$ and C = − i$ + $j,, respectively. They strike on a point and start, to move in different directions. Now, particle, P is moving normal to the plane which, contain vectors A and B. Similarly, particle Q, is moving normal to the plane which contain, , Time, No. of, Total time, Student Length of, period, for n, No., pendulum oscillations, (s), oscillations, (cm), (n), , 1., , 64.0, , 8, , 128.0, , 16.0, , 2., , 64.0, , 4, , 64.0, , 16.0, , 3., , 20.0, , 4, , 36.0, , 9.0, , (Least count of length = 01, . m, least count for, time = 01, . s), If E 1 ,E 2 and E 3 are the percentage errors in, g for students 1, 2 and 3 respectively, then, the minimum percentage error is obtained, by student number ……… ., , 30. In 5 min, a body cools from 75°C to 65°C at, room temperature of 25°C. The temperature, of body at the end of next 5 min is ……… °C.
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CHEMISTRY, Section A : Objective Type Questions, , 5. Which of the following compounds does not, exhibit resonance ?, a. CH3CH2OCH == CH2, , 1. The water having more dissolved O 2 is, a. boiling water, b. water at 80°C, c. polluted water, d. water at 4° C, , CH2OH, b., , c. CH3CH2CH2CONH2, d. CH3CH2CH == CHCH2NH2, , 2. Which one of the following statements for, D. Mendeleef, is incorrect ?, a. He authored the textbook - principles of, chemistry., b. At the time, he proposed periodic table of, elements structure of atom was known., c. Element with atomic number 101 is named, after him., d. He invented accurate barometer., , 6. Match List I with List II., List-I, (Elements), A., , Ba, , (i), , B., , Ca, , (ii) Outer electronic, configuration 6s 2, , C., , Li, , (iii) Oxalate insoluble in, water, , D., , Na, , (iv) Formation of very, strong monoacidic, base, , 3. Which purification technique is used for high, boiling organic liquid compound, (decomposes near its boiling point)?, a. Simple distillation, b. Steam distillation, c. Fractional distillation, d. Reduced pressure distillation, , provide a tertiary alcohol on reaction with, excess of CH 3MgBr followed by hydrolysis ?, , a., b., c., d., , CH3, , a., OCH2CH3, , b., , A B C D, (ii) (iii) (i) (iv), (iv) (i) (ii) (iii), (iii) (ii) (iv) (i), (i) (iv) (ii) (iii), , 7., +, , N2 Cl, , –, , NC, C, , + A + H2O, , CH, , OH, , d., , B. Anhyd., AlCl3, , CH2CH3, , (Major product), , CH3, , c., , Organic solvent soluble, compounds, , Choose the correct answer from the options, given below, , 4. Which of the following compounds will, , O, , List-II, (Properties), , In the chemical reactions given above A and, B respectively are, a. H3PO 2 and CH3CH2Cl b. CH3CH2OH and H3PO 2, c. H3PO 2 and CH3CH2OH d. CH3CH2Cl and H3PO 2, , 8. Isotope(s) of hydrogen which emits low, , energy β − particles with t1/ 2 value > 12 years, is/are, a. protium, c. deuterium, , b. tritium, d. deuterium and tritium
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26, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 9. Match List I and List II., List I, (Species), , 14. Match List I with List II., , (A) SF4, , (i), , sp 3d 2, , (B) IF5, , (ii), , d 2 sp 3, , (C) NO 2+, , (iii), , sp 3d, , (iv), , sp 3, , (v), , sp, , +, , (D) NH4, , a., b., c., d., , List I, , List II, (Hybrid orbitals), , List II, , (A) Chloroprene, , (i), , (B) Neoprene, , (ii), , (C) Acryonitrile, , (iii), , Cl, (, , A B C D, (i) (ii) (v) (iii), (ii) (i) (iv) (v), (iii) (i) (v) (iv), (iv) (iii) (ii) (v), , potassium iodide solution then the sol, produced is, a. AgI / I−, b. AgI / Ag +, c. Kl/NO −3, d. AgNO 3 /NO 3−, , ), n, , (iv) CH2 == CH CN, , (D) Isoprene, , 10. When silver nitrate solution is added to, , Choose the correct answer from the options, given below., A B C D, A B C D, a. (iii) (iv) (ii) (i), b. (ii) (iii) (iv) (i), c. (ii) (i) (iv) (iii), d. (iii) (i) (iv) (ii), , 15. The set having ions which are coloured and, paramagnetic both is, a. Cu 2 + , Cr 3 + , Sc +, c. Sc, , 11. Which of the following molecules does not, show stereoisomerism ?, a. 3, 4 - dimethyl hex-3ene, b. 3- methyl hex-1-ene, c. 3 - ethyl hex-3-ene, d. 4- methyl hex-1-ene, , 12. Given below are the statements about, diborane., (A) Diborane is prepared by the oxidation of, NaBH4 and I2 ., (B) Each boron atom is in sp 2 -hybridised, state., (C) Diborane has one bridged 3 centre, -2 - electron bond., (D) Diborane is a planar molecule., The option with correct statement(s) is, a. (C) and (D) only, b. (A) only, c. (C) only, d. (A) and (B) only, , 3+, , ,V, , 5+, , , Ti, , d. Ni2 + , Mn 7 + , Hg 2 +, , 16. Thiamine and pyridoxine are also known, respectively as, a. vitamin B 2 and vitamin E, b. vitamin E and vitamin B 2, c. vitamin B 6 and vitamin B 2, d. vitamin B1 and vitamin B 6, , 17. Sulphide ion is soft base and its ores are, common for metals, (A) Pb, (B) Al, (C) Ag, (D) Mg, Choose the correct answer from the options, given below, a. (A) and (C) only, c. (A) and (B) only, , b. (A) and (D) only, d. (C) and (D) only, , 18. An organic compound A (C 6H6O) gives dark, green colouration with ferric chloride. On, treatment with CHCl 3 and KOH, followed by, acidification gives compound B. Compound B, can also be obtained from compound C on, reaction with pyridinium chlorochromate, (PCC). Identify A, B and C., OH, , is the strongest reducing agent ?, b. BiH3, d. SbH3, , b. Cu 2 + , Zn 2 + , Mn 4 +, , 4+, , 13. Which one of the following group-15 hydride, a. AsH3, c. PH3, , Cl, , OH, , a. A=, , OH, CHO, , B=, , CH2OH, C=
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27, , JULY ATTEMPT ~ 22 July 2021, Shift II, CH2OH, , OH, , OH, , OH, , b. A=, , B=, , C=, OH, , CH2OH, OH, , c. A=, , OH, CHO, , B=, OH, , CH2OH, , OH, , OH, C=, , Cu(s) + 2Ag+ (1 × 10−3 M) →, , NH2, , NHCOCH3, , N2O4 ( g ), , - 2NO (g ) at 288 K is 47.9., 2, , The KC for this reaction at same temperature, is …… (Nearest integer), (R = 0083, L bar K −1mol−1), ., , 26. If the standard molar enthalpy change for, , + (CH3CO)2O/Pyridine, NH2, , E cell for the above reaction is ……… V., (Nearest integer), [Given : log 25, , T = 298 K], . = 03979, ., , 25. Value of K p for the equilibrium reaction, , occur?, , combustion of graphite powder is, −2.48 × 102kJ mol−1, the amount of heat, generated on combustion of 1 g of graphite, powder is …… kJ. (Nearest integer), , NH2, + H2SO4, , b., , 24. Assume a cell with the following reaction, s, Cu2+ (0.250M) + 2Ag(s), E cell, = 2.97 V, , 19. Which one of the following reactions does not, , a., , (including geometrical isomers) for pentene, are ……… ., , C=, , CHO, B=, , d. A=, , 23. The number of acyclic structural isomers, CHO, , 27. A copper complex crystallising in a ccp, SO3H, NH2, , NH3, + AlCl3 + CH3Cl, , c., , CH3, NH2, , NH2, , lattice with a cell edge of 0.4518 nm has, been revealed by employing X-ray, diffraction studies. The density of a copper, complex is found to be 7.62 g cm−3., The molar mass of copper complex is ……, g mol−1. (Nearest integer), [Given : NA = 6022, ., × 1023 mol−1], , 28. Number of electrons that vanadium, , ( Z = 23) has in p-orbitals is equal to ……… ., , d., , + HNO3/H2SO4, , 1, 2, In the above first order reaction the initial, concentration of N2O5 is 2.40 × 10−2 mol L−1, at 318 K. The concentration of N2O5 after 1, hour was 1.60 × 10−2 mol L−1. The rate, constant of the reaction at 318 K is …… ×, 10−3min−1. (Nearest integer) [Given :, ], log 3 = 0.477, log 5 = 0699, ., , 29. N2O5( g) → 2NO2( g) + O2( g), NO2, , 20. Which one of the following 0.06 M aqueous, solutions has lowest freezing point?, a. Al2 (SO 4 ) 3, c. Kl, , b. C 6H12O 6, d. K 2SO 4, , Section B : Numerical Type Questions, 21. The total number of unpaired electrons present, in [Co(NH 3) 6 ]Cl2 and [Co(NH 3) 6 ]Cl3 is …… ., , 22. Methylation of 10 g of benzene gave 9.2 g of, toluene. Calculate the percentage yield of, toluene ……… . (Nearest integer), , 30. If the concentration of glucose (C 6H12O6) in, blood is 0.72 gL−1, the molarity of glucose, in blood is …… ×10−3 M. (Nearest integer), [Given : Atomic mass of C = 12, H = 1,, O = 16 u]
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28, , JEE Main 2021 ~ Solved Papers, , ONLINE, , MATHEMATICS, Section A : Objective Type Questions, 1. Let L be the line of intersection of planes, r ⋅ (i$ − $j + 2k$ ) = 2 and r ⋅ (2$i + $j − k$ ) = 2. If P(α, β, γ), is the foot of perpendicular on L from the point, (1, 2, 0), then the value of 35(α + β + γ) is equal, to, a. 101, , b. 119, , c. 143, , d. 134, , 2. Let S n denote the sum of first n terms of an, arithmetic progression. If S10 = 530, S5 = 140,, then S 20 − S 6 is equal to, a. 1862, c. 1852, , b. 1842, d. 1872, , 3. Let f : R → R be defined as, 4 3, 2, − x + 2 x + 3 x, f ( x) = 3, 3xe x, , , , x >0, , x ≤0, , . Then, f is, , b. (0, 2), , equation cosec 2xdy + 2dx = (1+ y cos 2x), π, cosec 2xdx, with y = 0. Then, the value of, 4, ( y (0) + 1) 2 is equal to, b. e, d. e, , −1/ 2, , numbers shown on these dice are recorded, in 2 × 2 matrices. The probability that such, formed matrices have all different entries, and are non singular, is, 45, 162, , b., , 23, 81, , c., , 22, 81, , d., , 43, 162, , 6. Let a vector a be coplanar with vectors, $ If a is, b = 2$i + $j + k$ and c = $i − $j + k., $, $, perpendicular to d = 3i + 2 j + 6k$ and|a| = 10., Then a possible value of, [a b c ] + [a b d ] + [a c d ] is equal to, a. −42, c. −29, , b. −40, d. −38, , dx =, , απ 3, , α ∈R, where [ x ] is, 1+ 4π2, , the greatest integer less than or equal to x,, then the value of α is, a. 200(1 − e −1), c. 50(e − 1), , b. 100(1 − e ), d. 150 (e −1 − 1), , 8. Let three vectors a, b and c be such that, a × b = c,b × c =`a and|a| = 2. Then, which one, of the following is not true ?, a. a × ((b + c ) × (b − c )) = 0, b. Projection of a on (b × c ) is 2, c. [a b c ] + [c a b] = 8, d.|3a + b − 2c|2 = 51, , 9. The values of λ and µ such that the system of, equations x + y + z = 6, 3x + 5 y + 5z = 26,, x + 2 y + λz = µ has no solution, are, b. λ = 3, µ ≠ 10, d. λ = 2, µ ≠ 10, , 4( x − 2) = 2( y − λ ) = ( z −`3), λ ∈R is, , 1, 38, , , then, , the integral value of λ is equal to, a. 3, , b. 2, , c. 5, , d. −1, , 11. Which of the following Boolean expression is, not a tautology ?, a. (p ⇒ q ) ∨ (~ q ⇒ p ), c. (p ⇒~ q ) ∨ (~ q ⇒ p ), , 5. Four dice are thrown simultaneously and the, , a., , x x , − , e π π , , lines 3( x − 1) = 6( y − 2) = 2( z − 1) and, , 4. Let y = y ( x) be the solution of the differential, , a. e, c. e −1, , 0, , sin2 x, , 10. If the shortest distance between the straight, , d. (−3, − 1), , 1/ 2, , ∫, , a. λ = 3, µ = 5, c. λ ≠ 2, µ = 10, , increasing function in the interval, 1, a. − , 2, 2 , 3, c. −1, , , 2, , 100 π, , 7. If, , b. (q ⇒ p ) ∨ (~ q ⇒ p ), d. (~ p ⇒ q ) ∨ (~ q ⇒ p ), , 12. Let A = [a ij ] be a real matrix of order 3 × 3,, such that a i1 + a i 2 + a i 3 = 1, for i = 1, 2, 3. Then,, the sum of all the entries of the matrix A 3 is, equal to, a. 2, c. 3, , b. 1, d. 9, , 13. Let [ x ] denote the greatest integer less than, or equal to x. Then, the values of x ∈ R, satisfying the equation [e x ]2 + [e x + 1] − 3 = 0, lie in the interval, 1, a. 0, , e , , b. [log e 2, log e 3), , c. [ 1, e ), , d. [ 0, log e 2)
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29, , JULY ATTEMPT ~ 22 July 2021, Shift II, 14. Let the circle S : 36x 2 + 36 y 2 − 108x + 120 y + C, = 0 be such that it neither intersects nor, touches the coordinate axes. If the point of, intersection of the lines x − 2 y = 4 and, 2x − y = 5 lies inside the circle S, then, 25, 13, <C<, 9, 3, b. 100 < C < 165, c. 81 < C < 156, d. 100 < C < 156, , a., , equation z 2 + 3z = 0, where z is a complex, ∞, 1, number. Then, the value of ∑ k is equal to, k=0n, a. 1, , b., , 3, 2, , 4, 3, , x ∈ [0, 4 π ] is equal to, a. 11, c. 5, , − 1, , 2 , , sin , , , is the interval (α, β) ,, , then α + β is equal to, 3, 2, 1, c., 2, , b. 2, , a., , Section B : Numerical Type Questions, 21. Let A = {0, 1, 2, 3, 4, 5, 6, 7}. Then, the, , 22. If the digits are not allowed to repeat in any, , 23. Let A = 1 0 0. Then, the number of 3 × 3, , , , 0 0 1, matrices B with entries from the set {1, 2, 3,, 4, 5} and satisfying AB = BA is ……… ., , distribution, , d. 1, , Class, Frequency, , 1 + 2xe −2 x , , x, , log e , , −x 2 , f (x ) = (1 − cos 2x ) 2, (1 − xe ) , , α, , 3, , , x≠0, , x=0, , If f is continuous at x = 0, then α is equal to, b. 3, , c. 0, , d. 2, , 19. Let a line L : 2x + y = k, k > 0 be a tangent to, the hyperbola x 2 −`y 2 = 3. If L is also a, tangent to the parabola y 2 = αx , then α is, equal to, a. 12, , 6, , 24. Consider the following frequency, , 18. Let f :R → R be defined as, , a. 1, , 3, , 0 1 0, , 17. If the domain of the function, −1 2 x, , 8, , number formed by using the digits 0, 2, 4, 6,, 8, then the number of all numbers greater, than 10000 is equal to ……… ., , b. 7, d. 9, , cos −1 x 2 − x + 1, , 5, , number of bijective functions F : A → A such, that f (1) + f (2) = 3 − f (3) is equal to ……… ., , d. 2, , 16. The number of solutions of sin7 x + cos 7 x = 1,, , f ( x) =, , −1 +, 2, −1 +, b., 2, −1 +, c., 2, −1 +, d., 2, , a., , 15. Let n denote the number of solutions of the, , c., , x2, y2, +, = 1, a > b. Let E 2 be another, a2, b2, ellipse such that it touches the end points of, major axis of E 1 and the foci of E 2 are the end, points of minor axis of E 1. If E 1 and E 2 have, same eccentricities, then its value is, , 20. Let E 1 :, , b. −12, , c. 24, , d. −24, , 0-6 6-12 12-18 18-24 24-30, a, , b, , 12, , 9, , 5, , 309, and median = 14, then the value, 22, (a − b) 2 is equal to ……… ., , If mean =, , 25. The sum of all the elements in the set, , { n ∈ { 1, 2, ....100} : HCF of n and 2040 is 1} is, equal to ……… ., , 26. The area (in square units) of the region, , bounded by the curves x 2 +`2 y − 1 = 0,, y 2 + 4 x − 4 = 0 and y 2 − 4 x − 4 = 0, in the, upper half plane is ……… .
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30, , ONLINE, , 27. Let f : R → R be a function defined as, , 29. Let y = y ( x) be the solution of the, , 3 1 − |x| , if |x|≤ 2, , , f (x ) = , 2, , , if |x| > 2, 0, , differential equation, y + 1, , , , , x + 2, (, x, ), e, +, +`( y +, 2, , , , , Let g :R → R be given by g (x ) = f (x + 2) − f (x − 2),, If n and m denote the number of points in R,, where g is not continuous and not differentiable, respectively, then n + m is equal to ……… ., , 28. If the constant term, in Binomial expansion of, 1, r, 2x + 2 , , x , , JEE Main 2021 ~ Solved Papers, , 10, , , , 1) dx, , , , = (x + 2)dy, y(1) = 1. If the domain of y = y (x ) is, an open interval α, β, then|α + β| is equal to, ……… ., , 30. The number of elements in the set, { n ∈ { 1, 2, 3, ....,100} : (11) n > (10) n + (9) n } is, ……… ., , is 180, then r is equal to ……… ., , Answers, For solutions scan, the QR code, , Physics, 1. (c), 11. (a), 21. 500, , 2. (d), 12. (d), 22. 2, , 3. (d), 13. (c), 23. 15, , 4. (b), 14. (a), 24. 4, , 5. (d), 15. (a), 25. 9, , 6. (d), 16. (c), 26. 4, , 7. (a), 17. (a), 27. 60, , 8. (b), 18. (d), 28. 5, , 9. (b), 19. (d), 29. 1, , 10. (a), 20. (d), 30. 57, , 7. (a), 17. (a), 27. 106, , 8. (b), 18. (a), 28. 12, , 9. (c), 19. (c), 29. 7, , 10. (a), 20. (a), 30. 4, , Chemistry, 1. (d), 11. (c), 21. 1, , 2. (b), 12. (b), 22. 78, , 3. (d), 13. (b), 23. 6, , 4. (a), 14. (b), 24. 3, , 5. (d), 15. (a), 25. 2, , 6. (a), 16. (d), 26. 21, , Mathematics, 1. (b), 11. (d), 21. 720, , 2. (a), 12. (c), 22. 96, , 3. (c), 13. (d), 23. 3125, , 4. (c), 14. (d), 24. 4, , 5. (d), 15. (b), 25. 1251, , 6. (a), 16. (c), 26. 2, , 7. (a), 17. (a), 27. 4, , 8. (d), 18. (a), 28. 8, , 9. (d), 19. (d), 29. 4, , 10. (a), 20. (a), 30. 96
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JEE Main 2021, 25 JULY SHIFT I, , PHYSICS, Section A : Objective Type Questions, 1. For a gas C p − C V = R in a state P and, , 4. Identify the logic operation carried out., A, , C P − C V = 1.10 R in a state Q. TP and TQ are, the temperatures in two different states P, and Q, respectively. Then,, a. TP = TQ, b. TP < TQ, c. TP = 09, . TQ, d. TP > TQ, , a. OR, c. NOR, , b. AND, d. NAND, , 5. A particle of mass 4M at rest disintegrates, , 2. Assertion A Moment of inertia of a circular, disc of mass M and radius R about X , Y -axes, (passing through its plane) and Z-axis which, is perpendicular to its plane were found to, be Ix , I y and Iz , respectively. The respective, radii of gyration about all the three axes will, be the same., Reason R A rigid body making rotational, motion has fixed mass and shape., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Both A and R are correct and R is the correct, explanation of A., b. Both A and R are correct but R is not the, correct explanation of A., c. A is correct but R is not correct., d. A is not correct but R is correct., , 3. What should be the order of arrangement of, de-Broglie wavelength of electron (λ e ), an, α-particle (λ α ) and proton (λ p) given that all, have the same kinetic energy ?, a. λ e = λ p = λ α, c. λ e > λ p > λ α, , Y, B, , b. λ e < λ p < λ α, d. λ e = λ p > λ α, , into two particles of masses M and 3M, respectively having non-zero velocities. The, ratio of de-Broglie wavelength of particle of, mass M to that of mass 3M will be, a. 1 : 3, c. 1 : 3, , b. 3 : 1, d. 1 : 1, , 6. Some nuclei of a radioactive material are, undergoing radioactive decay. The time gap, between the instances when a quarter of the, nuclei have decayed and when half of the, nuclei have decayed is given as, (where, λ is the decay constant), a., , 1 ln 2, 2 λ, , c., , 2ln 2, λ, , ln2, λ, 3, ln, 2, d., λ, b., , 7. Match List I with List II., List I, , List II, C, , (A) C − A − B = 0, , (i), , A, B
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32, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 10. A ray of laser of a wavelength 630 nm is, , C, , (B) A − C − B = 0, , B, , (ii), A, , C, , (C) B − A − C = 0, , (iii) A, B, , A, , (D) A + B = − C, , Choose the correct answer from the options, given below., a. (A) → (iv), (B) → (i) , (C) → (iii), (D) → (ii), b. (A) → (iv), (B) → (iii) , (C) → (i), (D) → (ii), c. (A) → (iii), (B) → (ii) , (C) → (iv), (D) → (i), d. (A) → (i), (B) → (iv) , (C) → (ii), (D) → (iii), , 8. A parallel plate capacitor with plate area A, and distance of separation d is filled with a, dielectric. What is the capacity of the, capacitor when permittivity of the dielectric, varies as, d, ε(x ) = ε0 + kx, for 0 < x ≤ , , 2, , b., , kA, 2ε0 + kd , 2 ln , , 2ε0 , , kA 2ε0 , d., ln , , 2 2ε0 − kd , , c. zero, , joined end-to-end and loaded. The Young's, moduli of the materials of the two wires are, Y1 and Y2. The combination behaves as a, single wire, then its Young's modulus is, a. Y =, , 2YY, 12, 3(Y1 + Y2 ), , b. Y =, , 2YY, 12, Y1 + Y2, , c. Y =, , YY, 12, 2(Y1 + Y2 ), , d. Y =, , YY, 12, Y1 + Y2, , 12. The half-life of 198 Au is 3 days. If atomic, weight of 198 Au is 198 g/mol, then the activity, of 2 mg of 198 Au is [in disintegration/s], a. 267, . × 1012, c. 32.36 × 1012, , b. 606, . × 1018, d. 1618, . × 1012, , 13. Two billiard balls of equal mass 30 g strike a, , d, ε(x ) = ε0 + k (d − x ), for ≤ x ≤ d , 2, , 2 / kA, , a. Angle of refraction is 24.41°, b. Angle of refraction is 30°, c. Refraction is not possible, d. Angle of refraction is 53.4°, , 11. Two wires of same length and radius are, , (iv) C, B, , kd , a. ε0 +, , , 2, , incident at an angle of 30° at the, diamond-air interface. It is going from, diamond to air. The refractive index of, diamond is 2.42 and that of air is 1. Choose, the correct option., , rigid wall with same speed of 108 km/h (as, shown) but at different angles. If the balls, get reflected with the same speed, then the, ratio of the magnitude of impulses imparted, to ball a and ball b by the wall along, x., direction is, y, u, x′, , x, , y, 45º, x′, , x, , 9. A monoatomic ideal gas, initially at, temperature T1 is enclosed in a cylinder fitted, with a frictionless piston. The gas is allowed, to expand adiabatically to a temperature T2, by releasing the piston suddenly. If l1 and l 2, are the lengths of the gas column, before, and after the expansion respectively, then, T, the value of 1 will be, T2, 2, , l 3, a. 1 , l2 , l2, c., l1, , 2, , l 3, b. 2 , l1 , l, d. 1, l2, , Ball (a), , a. 1 : 1, , y′, , b. 2 : 1, , Ball (b), , c. 2 : 1, , y′, , d. 1 : 2, , 14. In the Young’s double slit experiment, the, distance between the slits varies in time as, d(t) = d 0 + a 0 sinωt, where d 0, ω and a 0 are, constants. The difference between the, largest fringe width and the smallest fringe, width obtained over time is given as, a., , 2λD (d 0 ), , (d 02 − a 02 ), λD, c. 2 a 0, d0, , b., , 2λDa 0, , (d 02 − a 02 ), λD, d., d0 + a 0
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33, , JULY ATTEMPT ~ 25 July 2021, Shift I, 15. Two different metal bodies A and B of equal, mass are heated at a uniform rate under, similar conditions. The variation of, temperature of the bodies is graphically, represented as shown in the figure. The ratio, of specific heat capacities is, , Temperature T(°C), , 150, A, , 120, , B, , 90, 60, , 18. In amplitude modulation, the message signal, Vm (t ) = 10sin(2 π × 105 t ) volts, and carrier signal, V c (t ) = 20sin(2 π × 107 t ) volts, The modulated signal now contains the message, signal with lower side band and upper side band, frequency., Therefore, the bandwidth of modulated signal is, α kHz. The value of α is, a. 200 kHz, b. 50 kHz, c. 100 kHz, d. zero, , 19. Water droplets are coming from an open tap, , 30, 1, , a., , 2, , 8, 3, , 3, , b., , 4, , 5, , 3, 8, , c., , 6, , 7, , 3, 4, , d., , 8, Time t(s), , 4, 3, , 16. A linearly polarised electromagnetic wave in, , vacuum is E = 31, . cos[(1.8) z − (5.4 × 106) t ] $i N/C, is incident normally on a perfectly reflecting, wall at z = a ., Choose the correct option., a. The wavelength is 5.4 m, b. The frequency of electromagnetic wave is, 54 × 104 Hz., c. The transmitted wave will be, 31, . cos[(18, . ) z − (5.4 × 106 )t ] $i N/C, d. The reflected wave will be, 31, . cos[(18, . ) z + (5.4 × 106 )t ] $i N/C, , 17. In the given figure, there is a circuit of, , potentiometer of length AB = 10 m. The, resistance per unit length is 0.1 Ω per cm., Across AB, a battery of EMF E and internal, resistance r is connected. The maximum, value of emf measured by this, potentiometer is, +, , E, , r, , –, , G, , A, 550 cm, , +, , 450cm, , –, 6V, , a. 5 V, , B, , J, , K, , 20W, , b. 2.25 V, , c. 6 V, , d. 2.75 V, , at a particular rate. The spacing between a, droplet observed at 4th second after its fall, to the next droplet is 34.3 m. At what rate,, the droplets are coming from the tap ?, (Take, g = 9.8 m/s2), a. 3 drops / 2 s, b. 2 drops / s, c. 1 drop / s, d. 1 drop / 7 s, , 20. The minimum and maximum distances of a, planet revolving around the Sun are x1 and, x 2. If the minimum speed of the planet on its, trajectory is v 0, then its maximum speed will, be, a., c., , v 0 x12, x 22, v 0 x1, x2, , b., , v 0 x 22, , x12, v x, d. 0 2, x1, , Section B : Numerical Type Questions, 21. A body of mass 2 kg moving with a speed of, 4 m/s makes an elastic collision with another, body at rest and continues to move in the, original direction but with one-fourth of its, initial speed. The speed of the two body, x, centre of mass is, m/s. Then, the value of x, 10, is ……… ., , 22. Student A and student B used two screw, gauges of equal pitch and 100 equal circular, divisions to measure the radius of a given, wire. The actual value of the radius of the, wire is 0.322 cm. The absolute value of the, difference between the final circular scale, readings observed by the students A and B, is ……… .
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34, , ONLINE, [Figure shows position of reference O when, jaws of screw gauge are closed], Given, pitch = 0.1 cm., O, , JEE Main 2021 ~ Solved Papers, , surface is assumed to be frictionless. The, angular frequency will be ……… rad/s when, k = 20 N/m., , O, A, , k, , 4k, , S1, , S2, , B, , 26. The value of aluminium susceptibility is, 0, 5, Screw gauge, (A), , 10, , 95, 90 92, Screw gauge, (B), , 2.2 × 10−5. The percentage increase in the, magnetic field, if space within a current, carrying toroid is filled with aluminium is, x, , then the value of x is ……… ., 104, , 27. A particle of mass 1 mg and charge q is lying, 23. An inductor of 10 mH is connected to a 20 V, battery through a resistor of 10 kΩ and a, switch. After a long time, when maximum, current is set up in the circuit, the current is, switched off. The current in the circuit after, x, 1 µs is, mA. Then, x is equal to …… . (Take,, 100, e −1 = 037, . ), , 24. A circular conducting coil of radius 1 m is, , at the mid-point of two stationary particles, kept at a distance 2 m when each is carrying, same charge q. If the free charged particle is, displaced from its equilibrium position, through distance x (x << 1 m), the particle, executes SHM. Its angular frequency of, oscillation will be …… × 105 rad/s, if q 2 =10C 2., , 28. An electric bulb rated as 200 W at 100 V is, used in a circuit having 200 V supply. The, resistance R that must be put in series with, the bulb, so that the bulb delivers the same, power is …… Ω., , being heated by the change of magnetic field, B passing perpendicular to the plane in, which the coil is laid. The resistance of the, coil is 2 µΩ. The magnetic field is slowly, switched off such that its magnitude, changes in time as, t , 4, T, B = × 10−3 1 −, 100, π, , 29. A pendulum bob has a speed of 3 m/s at its, , The energy dissipated by the coil before the, magnetic field is switched off completely is, E = …… mJ., , 30. A particle of mass m is moving in time t on a, , 25. In the reported figure, two bodies A and B of, masses 200 g and 800 g are attached with, the system of springs. Springs are kept in a, stretched position with some extension, when the system is released. The horizontal, , lowest position. The pendulum is 50 cm long., The speed of bob when the length makes an, angle of 60° to the vertical will be ……. m/s., ( Take, g = 10 m / s 2), trajectory given by, r = 10α t 2$i + 5β(t − 5) $j, where, α and β are dimensional constants., The angular momentum of the particle, becomes the same as it was for t = 0 at time t, is …… s.
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CHEMISTRY, Section A : Objective Type Questions, OH, , 1., , —CH2, , 6. At 298.2 K the relationship between enthalpy, of bond dissociation (in kJ mol −1) for, hydrogen (E H) and its isotope, deuterium (E D),, is best described by, , OH, CH2, , is a repeating unit for, a. novolac, c. acrilan, , CH2—, , 1, a. EH = E D, 2, c. EH ~, − E D − 7.5, , b. buna-N, d. neoprene, , NaOH, , (i) I2/NaOH, filter, , ‘P’, (Major product), , (ii) Filtrate + HCl, , ‘X’, , Consider the given reaction, the product X is, , to an external magnetic field, a.[Fe(H 2O)6] 3 +, c.[Co(CN)6] 3−, , d. EH = 2E D, , CH3CHO, , 7., , 2. Which one of the following species responds, , b. EH = E D, , OH, , b.[Ni(CN)4 ] 2−, d.[Ni(CO)4 ], a., , b., , (i) C2H5MgBr, dry ether, (ii) H2O, HCl, , P, (Major product), , 3., , OH, , Consider the above reaction, the major product P, is, OH, , OH, a., , b., , CHO, , c., , OH, , OH, , 8., Br, (Major product), , d. Cl, Cl, −, , 4. Sodium stearate CH3(CH2 )16COO Na, , +, , is an, anionic surfactant which forms micelles in oil., Choose the correct statement for it from the, following., −, a. It forms spherical micelles with CH3 (CH2 )16, group pointing towards the centre of sphere., b. It forms non-spherical micelles with COO −, group pointing outwards on the surface., −, c. It forms spherical micelles with CH3 (CH2 )16, group pointing outwards on the surface of, sphere, d. It forms non–spherical micelles with, −, group pointing towards the centre., CH3 (CH2 )16, , 5. The water soluble protein is, a. fibrin, b. albumin, c. myosin, d. collagen, , OH, , OH, , OH, c., , d., , The given reaction can occur in the presence of, (A) bromine water, (B) Br2 in CS2 , 273 K, (C) Br2 / FeBr3, (D) Br2 in CHCl 3, 273 K, Choose the correct answer from the options, given below, a. (B) and (D) only, b. (A) and (C) only, c. (B), (C) and (D) only, d. (A), (B) and (D) only, , 9. Given below are two statements, one is, labelled as :, Assertion (A) and other is labelled as Reason (R)., Assertion (A) Gabriel phthalimide synthesis cannot, be used to prepare aromatic primary amines., Reason (R) Aryl halides do not undergo, nucleophilic substitution reaction., In the light of the above statements, choose the, correct answer from the options given below, a. Both (A) and (R) true but (R) is not the correct, explanation of (A)., b. (A) is false but (R) is true., c. Both (A) and (R) true and (R) is correct, explanation of (A)., d. (A) is true but (R) is false.
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36, , ONLINE, , JEE Main 2021 ~ Solved Papers, , 12. The ionic radii of K+, Na+, Al3 + and Mg 2+ are in, , 10. For the following graphs, , (B), , Time, , (D), , Time, , Concentration, , Initial, concentration, , Concentration, , (C), , a. Na+ < K + < Mg 2+ < Al3 +, b. Al3+ < Mg 2+ < K + < Na+, c. Al3+ < Mg 2+ < Na+ < K +, d. K + < Al3+ < Mg 2+ < Na+, , t 1/2, , (A), , Rate, , the order, , 13. Which one of the following compounds of, group-14 elements is not known?, , 14. Which one among the following resonating, structures is not correct ?, Time, , Rate, , a., , (E), , b. [Sn(OH) 6 ] 2 −, d. [SiF6 ] 2−, , a. [GeCl6 ] 2−, c. [SiCl6 ] 2−, , O, N, O, , b., Concentration, , O, , Choose from the options given below, the correct, one regarding order of reaction is, a. (B) zero order (C) and (E) first order, b. (A) and (B) zero order (E) first order, c. (B) and (D) zero order (E) first order, d. (A) and (B) zero order (C) and (E) first order, , 11. Which one of the products of the following, reactions does not react with Hinsberg, reagent to form sulphonamide?, CN, a., , + Na/Hg, , C2H5OH, , NO2, CN, b., , + SnCl2 + HCl, CN, , c., , + LiAIH4, , O, N, , H3O+, , O, c., , N, O, O, , d., , N, O, , 15. Given below are two statements., Statement I None of the alkaline earth metal, hydroxides dissolve in alkali., Statement II Solubility of alkaline earth metal, hydroxides in water increases down the group., According the above statements, choose the most, appropriate answer from the options given below, a. Statement I is correct but statement II is, incorrect., b. Statement I is incorrect but statement II is, correct., c. Statement I and statement II both are incorrect., d. Statement I and statement II both are correct., , 16. The correct order of following 3d-metal oxides,, according to their oxidation numbers is, , CHO, CN, d., , + H2/Ni, CH3, , (B) Fe2O 3, (A) CrO 3, (C) MnO 2, (D) V2O 5, (E) Cu 2O, a. (D) > (A) > (B) > (C) > (E), b. (A) > (C) > (D) > (B) > (E), c. (A) > (D) > (C) > (B) > (E), d. (C) > (A) > (D) > (E) > (B)
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37, , JULY ATTEMPT ~ 25 July 2021, Shift I, 17. Which one of the following chemical agent is, not being used for dry cleaning of clothes ?, b. CCl4, d. Cl2C == CCl2, , a. H2O 2, c. Liquid CO2, , 18. Which one of the following compounds will, liberate CO 2, when treated with NaHCO3?, r s, a. (CH3 ) 3 NHCl, O, , rs, b. (CH3 ) 3 NOH, , c. CH3 C NH2, , d. CH3NH2, , , , 19. In the leaching of alumina from bauxite, the, ore expected to leach out in the process by, reacting with NaOH is, a. TiO 2, , b. Fe2O 3, , c. ZnO, , with KMnO4 / H+ yield’s compound ‘B’ C 3H 6O., Compound ‘A’ also yields compound ‘B’ an, ozonolysis. Compound ‘A’ is, a. 2-methylpropene, b. 1-methylcyclopropane, c. but-2-ene, c. cyclobutane, , Section B : Numerical Type Questions, 21. The number of sigma bonds in, H 3C C == CH C ≡≡ C — H is …… ., , , H, , 22. Three moles of AgCl get precipitated when, one mole of an octahedral co-ordination, compound with empirical formula, CrCl3 ⋅ 3NH 3 ⋅ 3H 2O reacts with excess of silver, nitrate. The number of chloride ions, satisfying the secondary valency of the metal, ion is ……… ., , 23. A source of monochromatic radiation of, wavelength 400 nm provides 1000 J of, energy in 10 seconds. When this radiation, falls on the surface of sodium, x × 1020, electrons are ejected per second. Assume, that wavelength 400 nm is sufficient for, ejection of electron from the surface of, sodium metal. The value of x is …… ., (h = 6626, ., × 10, , −34, , Js), , drink manufacturing process at 298 K. If CO2, exerts a partial pressure of 0.835 bar then x m, mol of CO2 would dissolve in 0.9 L of water. The, value of x is ……… . (Nearest integer), (Henry’s law constant for CO2 at 298 K is, 167, . × 103 bar), , 25. For the reaction, A + B, , - 2C, , The value of equilibrium constant is 100 at, 298 K. If the initial concentration of all the, three species is 1 M each, then the, equilibrium concentration of C is x × 10−1 M., The value of x is …… . (Nearest integer), , d. SiO 2, , 20. An organic compound ‘A’ C 4H8 on treatment, , (Nearest integer), , 24. CO2 gas is bubbled through water during a soft, , 26. Consider the cell at 25° C, Zn|Zn2 +(aq), (1M)||Fe 3 +(aq), Fe 2 +(aq)| Pt(s), The fraction of total iron present as Fe 3+ ion, at the cell potential of 1.500 V is x × 10−2 . The, value of x is ……… . (Nearest integer), (Given, E ° 3 + 2 + = 077, . V, E ° 2 +, = − 076, . V), Fe, , /Fe, , Zn, , / Zn, , 27. At 298 K, the enthalpy of fusion of a solid ( X ) is, 2.8 kJ mol −1 and the enthalpy of vaporisation, of the liquid ( X ) is 98.2 kJ mol −1. The enthalpy, of sublimation of the substance ( X ) in kJ mol −1, is …… . (Nearest integer), , 28. A home owner uses 4.00 × 103m3 of methane, (CH 4) gas, (assume CH 4 is an ideal gas) in a Year, to heat his home. Under the pressure of 1.0, atm and 300 K, mass of gas used is x × 105 g., The value of x is …… . (Nearest integer), (Given, R = 0083, L atm K −1mol−1), ., , 29. When 10 mL of an aqueous solution of Fe 2+, ions was titrated in the presence of, dil. H 2SO4 using diphenylamine indicator,, 15 mL of 0.02 M solution of K 2Cr2O7 was, required to get the end point. The molarity of, the solution containing Fe 2+ ions is x × 10−2 M., The value of x is …… . (Nearest integer), , 30. Consider the complete combustion of butane,, the amount of butane utilised to produce, 72.0 g of water is …… ×10−1 g. (Nearest integer)
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38, , ONLINE, , JEE Main 2021 ~ Solved Papers, , MATHEMATICS, Section A : Objective Type Questions, 1. A spherical gas balloon of radius 16 m, subtends an angle 60° at the eye of the, observer A while the angle of elevation of its, center from the eye of A is 75°. Then the, height (in metre) of the top most point of the, balloon from the level of the observer's eye, is, a. 8(2 + 2 3 + 2 ), c. 8( 2 + 2 + 3 ), , b. 8( 6 + 2 + 2), d. 8( 6 − 2 + 2), , 2. Let f ( x) = 3sin4 x + 10sin3 x + 6sin2 x − 3, π π, x ∈ − , . Then, f is, 6 2 , π π, a. increasing in − , , 6 2, π, b. decreasing in 0, , 2, π, c. increasing in − , 0, 6 , π, d. decreasing in − , 0, 6 , , where, [ x ] is the greatest integer less than or, equal to x. If f is continuous at x = 2, then, λ + µ is equal to, a. e (−e + 1), c. 1, 5π, 24, , b. e (e − 2), d. 2e − 1, , dx, , ∫ 1 + 3 tan2x is, , π, 24, , π, 3, π, c., 12, , a., , arithmetic progression, If S 3n = 3S 2n, then the, S, value of 4n is, S 2n, b. 4, d. 8, , 4. The locus of the centroid of the triangle, formed by any point P on the hyperbola, 16x 2 − 9 y 2 + 32x + 36 y − 164 = 0, and its foci, is, a. 16x 2 − 9 y 2 + 32x − 36 y − 36 = 0, b. 9x 2 − 16 y 2 + 36x − 32 y − 144 = 0, c. 16x 2 − 9 y 2 + 32x − 36 y − 144 = 0, d. 9x 2 − 16 y 2 + 36x − 32 y − 36 = 0, , 5. Let the vectors, $, (2 + a + b) i$ + (a + 2b + c) $j −( b + c)k,, $, (1 + b) $i + 2b$j − bk$ and (2 + b) $i + 2b$j + (1 − b) k,, a , b, c ∈ R be co-planar., Then, which of the following is true?, a. 2b = a + c, b. 3c = a + b, c. a = b + 2c, d. 2a = b + c, , λ|x 2 − 5x + 6|, , x<2, , µ ( x − x2 − ), 5 tan( x − 2 ) 6, , f (x ) = e x − [ x], , x>2, , µ, , x =2, , , , , 7. The value of the definite integral, , 3. Let S n be the sum of the first n terms of an, , a. 6, c. 2, , 6. Let f : R → R be defined as, , π, 6, π, d., 18, , b., , 8. If b is very small as compared to the value of, a, so that the cube and other higher powers, b, of can be neglected in the identity, a, 1, 1, 1, 1, +, +, + K+, a − b a − 2b a − 3b, a − nb, = αn + βn 2 + γn 3 , then the value of γ is, a2 + b, a+ b, a., b., 3, 3a 2, 3a, a + b2, b2, c. 3, d., 3a, 3a 3, , 9. Let y = y ( x) be the solution of the differential, dy, = 1 + xe y − x , − 2 < x < 2,, dx, y(0) = 0, then the minimum value of, y ( x), x ∈ ( − 2 , 2) is equal to, , equation, , a. (2 − 3 ) − log e 2, b. (2 + 3 ) − log e 2, c. (1 + 3 ) − log e ( 3 − 1), d. (1 − 3 ) − log e ( 3 − 1), , 10. The Boolean expression, (p ⇒ q ) ∧ (q ⇒ ~ p ) is equivalent to, a. ~q, b. q, c. p, , d. ~ p
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39, , JULY ATTEMPT ~ 25 July 2021, Shift I, 11. The area (in sq. units) of the region, given by, , the set {( x , y ) ∈ R × R|x ≥ 0, 2x 2 ≤ y ≤ 4 − 2x } is, a., , 8, 3, , b., , 17, 3, , c., , 13, 3, , d., , 7, 3, , 12. The sum of all values of x in [0, 2π], for which, sin x + sin2x + sin3x + sin 4 x = 0, is equal to, a. 8π, , b. 11π, , c. 12π, , d. 9π, , 13. Let g : N → N be defined as, g(3n + 1) = 3n + 2,, g(3n + 2) = 3n + 3,, g(3n + 3) = 3n + 1, for all n ≥ 0., Then which of the following statements is, true ?, a. There exists an onto function f : N → N such, that fog = f, b. There exists a one-one function f : N → N such, that fog = f, c. gogog = g, d. There exists a function f : N → N such that, gof = f, , 14. Let f : [0, ∞) → [0, ∞) be defined as, x, , f (x ) = ∫ [ y ] dy, , 17. Let a parabola P be such that its vertex and, focus lie on the positive x-axis at a distance, 2 and 4 units from the origin, respectively. If, tangents are drawn from O(0, 0) to the, parabola P which meet P at S and R, then the, area (in sq. units) of ∆SOR is equal to, b. 16, d. 8 2, , a. 16 2, c. 32, , 18. The number of real roots of the equation, e 6 x − e 4 x − 2e 3 x − 12e 2 x + e x + 1 = 0 is, a. 2, b. 4, c. 6, d. 1, , x2, y2, +, = 1, a 2 > b2, passes, a2, b2, 3 , 1, . If a, through , , 1 and has eccentricity, 2, , , 3, , 19. Let an ellipse E ⇒, , circle, centered at focus F (α , 0), α > 0, of E and, 2, radius, , intersects E at two points P andQ,, 3, then PQ 2 is equal to, 8, 3, 16, c., 3, , 4, 3, d. 3, , a., , b., , 0, , where, [ x ] is the greatest integer less than or, equal to x. Which of the following is true ?, a. f is continuous at every point in [ 0, ∞ ) and, differentiable except at the integer points, b. f is both continuous and differentiable except, at the integer points in [ 0, ∞ ), c. f is continuous everywhere except at the, integer points in [ 0, ∞ ), d. f is differentiable at every point in [ 0, ∞ ), , 15. The values of a and b, for which the system, of equations, 2x + 3 y + 6z = 8, x + 2 y + az = 5, 3x + 5 y + 9z = b, has no solution, are, a. a = 3, b ≠ 13, c. a ≠ 3, b = 3, , b. a ≠ 3, b ≠ 13, d. a = 3, b = 13, , 20. Let the foot of perpendicular from a point, , x y, z, = =, 1 0 −1, be N. Let a line be drawn from P parallel to, the plane x + y + 2z = 0 which meets L at, point Q. If α is the acute angle between the, lines PN and PQ, then cosα is equal to, , P(1, 2, − 1) to the straight line L ⇒, , a., , 1, 5, , b., , 3, 2, , c., , 1, 3, , d., , 1, 2 3, , Section B : Numerical Type Questions, 21. Let y = y ( x) be solution of the following, differential equation, dy, π, ey, − 2e y sin x + sin x cos 2 x = 0, y = 0., 2, dx, If y (0) = log e (α + βe −2 ), then 4(α + β ) is equal to, …… ., , 16. Let 9 distinct balls be distributed among 4, boxes, B1, B 2 , B 3 and B 4. If the probability that, 9, 3, B 3 contains exactly 3 balls is k , then k, 4, lies in the set, a. { x ∈ R :|x − 3|< 1}, c. { x ∈ R :|x − 13|< 1}, , b. { x ∈ R :|x − 2|≤ 1}, d. { x ∈ R :|x − 5|≤ 1}, , 22. If the value of, 2, 6, 10 , , 1 + + 2 + 3 , 3 3, 3 , , + .... upto ∞, , , 1, 1, , 1, + ...... upto ∞ , log ( 0. 25 ) +, +, , 3 32 33, , is l, then l 2 is equal to …… .
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40, , ONLINE, , 23. Consider the following frequency, , 27. There are 5 students in class 10, 6 students, , distribution, Class, , in class 11 and 8 students in class 12. If the, number of ways in which 10 students can be, selected from them so as to include at least, 2 students from each class and at most 5, students from the total 11 students of class, 10 and 11 is 100 k, then k is equal to ………, , 10-20 20-30 30-40 40-50 50-60, , Frequency α, , 110, , 54, , 30, , β, , If the sum of all frequencies is 584 and median, is 45, then|α − β| is equal to …… ., , 24. Let p = 2$i + 3$j + k$ and q = i$ + 2$j + k$ be two, , 28. If α, β are roots of the equation., x 2 + 5( 2) x + 10 = 0, α > β and Pn = α n − β n for, each positive integer n, then the value of, P17P20 + 5 2P17P19 , , , P P + 5 2P 2 is equal to …… ., 18 19, 18 , , vectors. If a vector r = (α$j + β$j + γk$ ) is, perpendicular to each of the vectors (p + q), and (p − q), and|r| = 3, then |α | + | β | + | γ | is, equal to …… ., , 29. The term independent of x in the expansion, 10, , x +1, x −1 , of 23, , where x ≠ 0, 1, −, 1/ 3, 1/ 2, x − x + 1 x − x , , 25. The ratio of the coefficient of the middle, , term in the expansion of (1 + x) 20 and the, sum of the coefficients of two middle terms, in expansion of (1 + x)19 is …… ., , , JEE Main 2021 ~ Solved Papers, , , a b, : a , b, c , d ∈ { ±3, ± 2, ± 1, 0} , c, d, , , , , 26. Let M = A = , , , Define f : M → Z, as f (A ) = det(A ), for all A ∈ M,, where Z is set of all integers. Then the number, of A ∈ M such that f (A ) = 15 is equal to ……, , is equal to …… ., n, , 0 i a b a b , =, , , , , 30. Let S = n ∈ N 1 0 c d c d ,, , , ∀a , b , c , d ∈ R, , , where i = −1. Then the number of 2-digit, numbers in the set S is ……… ., , Answers, For solutions scan, the QR code, , Physics, 1. (d), 11. (b), 21. 25, , 2. (d), 12. (d), 22. 13, , 3. (c), 13. (b), 23. 74, , 4. (b), 14. (b), 24. 80, , 5. (d), 15. (b), 25. 10, , 6. (d), 16. (d), 26. 22, , 7. (b), 17. (a), 27. 6000, , 8. (b), 18. (a), 28. 50, , 9. (b), 19. (c), 29. 2, , 10. (c), 20. (d), 30. 10, , Chemistry, 1. (a), 11. (b), 21. 10, , 2. (a), 12. (c), 22. 0, , 3. (c), 13. (c), 23. 2, , 4. (a), 14. (a), 24. 25, , 5. (b), 15. (b), 25. 25, , 6. (c), 16. (c), 26. 24, , 7. (d), 17. (b), 27. 101, , 8. (c), 18. (a), 28. 26, , 9. (c), 19. (d), 29. 18, , 10. (b), 20. (a), 30. 464, , 3. (a), 13. (a), 23. 164, , 4. (a), 14. (a), 24. 3, , 5. (a), 15. (a), 25. 1, , 6. (a), 16. (a), 26. 16, , 7. (c), 17. (b), 27. 238, , 8. (c), 18. (a), 28. 1, , 9. (d), 19. (c), 29. 210, , 10. (d), 20. (c), 30. 11, , Mathematics, 1. (b), 11. (d), 21. 4, , 2. (d), 12. (d), 22. 3
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JEE Main 2021, 25 JULY SHIFT II, , PHYSICS, Section A : Objective Type Questions, 1. The relation between time t and distance x, , for a moving body is given as t = mx 2 + nx ,, where m and n are constants. The, retardation of the motion is (when v stands, for velocity), a. 2 mv 3, c. 2 nv 3, , b. 2 mnv 3, d. 2n 2v 3, , 2. In a simple harmonic oscillation, what, fraction of total mechanical energy is in the, form of kinetic energy, when the particle is, midway between mean and extreme, position., 1, 2, 1, c., 3, a., , its efficiency get doubled. The temperature, of the source is, a. 124°C, c. 62°C, , 6. In the given potentiometer circuit, arrangement, the balancing length AC is, measured to be 250 cm. When the, galvanometer connection is shifted from, point (1) to point (2) in the given diagram,, the balancing length becomes 400 cm. The, ε, ratio of the EMF of two cells, 1 is, ε2, K, , 3, 4, 1, d., 4, b., , 4. A prism of refractive index µ and angle of, prism A is placed in the position of minimum, angle of deviation. If minimum angle of, deviation is also A, then in terms of refractive, index,, µ, a. 2cos −1 , 2, , µ, b. sin −1 , 2, , µ − 1, c. sin −1, , 2 , , , µ, d. cos −1 , 2, , 1, 6, the temperature of sink is reduced by 62°C,, , 5. A heat engine has an efficiency of . When, , C, , B, , G, 1, , mass 5 kg. If the body starts from rest its, position vector r at time t = 10 s, will be, b. (100$i + 100$j ) m, d. (400$i + 400$j ) m, , V, , A, , 3. A force F = ( 40$i + 10$j) N acts on a body of, a. (100$i + 400$j ) m, c. (400$i + 100$j ) m, , b. 37°C, d. 99°C, , E1, , 5, a., 3, , 8, b., 5, , 2, E2, , c., , 4, 3, , d., , 3, 2, , 7. Two ions having same mass have charges in, the ratio 1 : 2. They are projected normally in, a uniform magnetic field with their speeds in, the ratio 2 : 3. The ratio of the radii of their, circular trajectories is, a. 1 : 4, c. 3 : 1, , b. 4 : 3, d. 2 : 3, , 8. A 10 Ω resistance is connected across, 220 V - 50Hz AC supply. The time taken by, the current to change from its maximum, value to the rms value is, a. 2.5 ms, c. 3.0 ms, , b. 1.5 ms, d. 4.5 ms
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42, , ONLINE, , 9. A balloon was moving upwards with a, uniform velocity of 10 m/s. An object of finite, mass is dropped from the balloon when it, was at a height of 75 m from the ground, level. The height of the balloon from the, ground when object strikes the ground was, around, is, (Take, the value of g = 10 m/s 2), a. 300 m, b. 200 m, c. 125 m, d. 250 m, , JEE Main 2021 ~ Solved Papers, , 13. Two spherical soap bubbles of radii r1 and r2, in vacuum combine under isothermal, conditions. The resulting bubble has a radius, equal to, a., , r1r2, r1 + r2, , b. r1r2, , c. r12 + r22, , d., , r1 + r2, 2, , 14. The force is given in terms of time t and, displacement x by the equation, , 10. If q f is the free charge on the capacitor, plates and q b is the bound charge on the, dielectric slab of dielectric constant K placed, between the capacitor plates, then bound, charge q b can be expressed as, a. q b = q f 1 −, , , c. q b = q f 1 +, , , 1, K, 1, K, , , , , , , , , 1, b. q b = q f 1 − , , K, 1, d. q b = q f 1 + , , K, , F = A cos Bx + C sin Dt, AD, The dimensional formula of, is, B, b. [ML2T −3 ], a. [M 0LT −1 ], c. [M1L1T −2 ], , d. [M 2L2T −3 ], , 15. The given potentiometer has its wire of, , resistance 10 Ω. When the sliding contact is, in the middle of the potentiometer wire, the, potential drop across 2 Ω resistor is, 20 V, , 11. Consider a planet in some solar system, which has a mass double the mass of Earth, and density equal to the average density of, Earth. If the weight of an object on Earth is w,, the weight of the same object on that planet, will be, a. 2 w, , 1, c. 2 3, , b. w, , w, , d. 2 w, , their dipole moment p1 and p2 respectively,, are placed on a plane with their centres at O, as shown in the figure. At point C on the axis, of dipole A, the resultant electric field is, making an angle of 37° with the axis. The, p, ratio of the dipole moment of A and B, 1 is, p2, 3, (Take, sin 37° = ), 5, –, , a., , 3, 8, , O, +, 3, b., 2, , B, +, , C, , c., , 2, 3, , 2Ω, , a. 10 V, 40, V, c., 9, , b. 5 V, 40, d., V, 11, , 16. An electron moving with speed v and a, , 12. Two ideal electric dipoles A and B, having, , A–, , B, , A, , d., , photon moving with speed c, have same, de-Broglie wavelength. The ratio of kinetic, energy of electron to that of photon is, 3c, v, v, c., 2c, a., , 17. The instantaneous velocity of a particle, moving in a straight line is given as, v = αt + βt 2, where α and β are constants. The, distance travelled by the particle between 1s, and 2s is, a. 3α + 7β, , 4, 3, , v, 3c, 2c, d., v, b., , c., , α β, +, 2 3, , 3, 7, b. α + β, 2, 3, 3, 7, d. α + β, 2, 2
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43, , JULY ATTEMPT ~ 25 July 2021, Shift II, 18. A ray of light entering from air into a denser, 4, medium of refractive index , as shown in, 3, figure. The light ray suffers total internal, reflection at the adjacent surface as shown., The maximum value of angle θ should be, equal to, , θ′, , θ′′, , c. sin, , −1, , µ=4/3, , 7, 3, 7, 4, , b. sin −1, d. sin, , −1, , 5, 4, 5, 3, , 19. When radiation of wavelength λ is incident, on a metallic surface, the stopping potential, of ejected photoelectrons is 4.8 V. If the, same surface is illuminated by radiation of, double the previous wavelength, then the, stopping potential becomes 1.6 V. The, threshold wavelength of the metal is, a. 2 λ, c. 8 λ, , 22. A light beam of wavelength 500 nm is, incident on a metal having work-function of, 1.25 eV, placed in a magnetic field of, intensity B. The electrons emitted, perpendicular to the magnetic field B, with, maximum kinetic energy are bent into, circular arc of radius 30 cm. The value of B is, …… ×10−7 T., (Take, hc = 20 × 10−26 J-m, mass of electron, = 9 × 10−31 kg), , θ, , a. sin −1, , are 10 Å and 5 Å, respectively. They suffer, collision at room temperature. The ratio of, average distance covered by the molecule A, to that of B between two successive, collisions is …… ×10−2., , b. 4 λ, d. 6 λ, , 23. A message signal of frequency 20 kHz and, peak voltage of 20 V is used to modulate a, carrier wave of frequency 1 MHz and peak, voltage of 20 V. The modulation index will, be …… ., , 24. A 16 Ω wire is bend to form a square loop. A, 9 V supply having internal resistance of 1 Ω, is connected across one of its sides. The, potential drop across the diagonals of the, square loop is …… ×10−1 V., , 25. Two circuits are shown in the figures (a) and, (b). At a frequency of ……… rad/s, the average, power dissipated in one cycle will be same in, both the circuits., 5Ω, , 40µF, , 5Ω, , 0.1 H, , R, , C, , R, , L, , 20. Two vectors x and y have equal magnitude., The magnitude of ( x − y ) is n times the, magnitude of ( x + y ). The angle between, x and y is, − n 2 − 1, a. cos −1 2, , n −1 , n2 + 1 , c. cos −1 , , 2, − n − 1, , n2 − 1 , b. cos −1 , , 2, − n − 1, n 2 + 1, d. cos −1 2, , n − 1, , Section B : Numerical Type Questions, 21. A system consists of two types of gas, molecules A and B having same number, density 2 × 1025 /m3. The diameter of A and B, , 220 V, Fig. (a), , 220 V, Fig. (b), , 26. From the given data, the amount of energy, required to break the nucleus of aluminium, 27, −3, J., 13 Al is x × 10, Mass of neutron = 100866, u, ., Mass of proton = 100726, u, ., Mass of aluminium nucleus = 2718846, u, ., (Assume 1 u corresponds to x joule of energy), (Round off to the nearest integer)
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44, , ONLINE, , 27. A force of F = (5 y + 20) $j N acts on a particle., The work done by this force when the particle, is moved from y = 0 m to y10 m is 450., , 28. A solid disc of radius 20 cm and mass 10 kg, is rotating with an angular velocity of, 600 rpm, about an axis normal to its circular, plane and passing through its centre of, mass. The retarding torque required to bring, the disc at rest in 10 s is π × 10−1 N-m., , JEE Main 2021 ~ Solved Papers, , 29. In a semiconductor, the number density of, intrinsic charge carriers at 27°C is, 1.5 × 1016/ m3. If the semiconductor is doped, with impurity atom, the hole density, increases to 4.5 × 1022 / m3. The electron, density in the doped semiconductor is ……, ×109 /m3., , 30. The nuclear activity of a radioactive element, becomes (1/ 8) th of its initial value in 30 yr., The half-life of radioactive element is yr., , CHEMISTRY, Section A : Objective Type Questions, 1. In the following the correct bond order, sequence is, , a. O 22 − > O 2+ > O 2− > O 2, b. O +2 > O −2 > O 22 − > O 2, c. O +2 > O 2 > O 2− > O 22 −, d. O 2 > O 2– > O 22 − > O +2, , is most stable?, a. [Co(en)(NH 3) 4 ]Cl2, c. [Co(en) 2(NH 3) 2 ]Cl2, , b. [Co(en) 3 ]Cl2, d. [Co(NH 3) 6 ]Cl2, , 5. Match List I with List II : (Both having, metallurgical terms), , 2. A biodegradable polyamide can be made, from, a. glycine and isoprene, b. hexamethylene diamine and adipic acid, c. glycine and aminocaproic acid, d. styrene and caproic acid, , 3. Match List I with List II., List I, (Elements), , 4. Which one of the following metal complexes, , List II, (Properties), , (A) Li, , I., , Poor water, solubility of I − salt, , (B) Na, , II. Most abundant element in, cell fluid, , (C) K, , III. Bicarbonate salt used in, fire extinguisher, , (D) Cs, , IV. Carbonate salt decomposes, easily on heating, , Choose the correct answer from the options, given below., A, B, C, D, a. IV, III II, I, b. I, III, II, IV, c. IV, II, III, I, d., I, II, III IV, , List I, , List II, , (A) Concentration I., of Ag ore, , Reverberatory furnace, , (B) Blast furnace, , II., , Pig iron, , (c) Blister copper, , III., , Leaching with, dilute NaCN solution, , (d) Froth floatation IV., method, , Sulphide ores, , Choose the correct answer from the options, given below., A, B, C, D, a. III, II, I, IV, b. III IV, I, II, c. IV, I, III, II, d. IV III, II, I, , 6. The ionic radii of F− and O2− respectively are, 1.33 Å and 1.4 Å while the covalent radius of, N is 0.74Å, The correct statement for the ionic radius of N 3−, from the following is, a. it is smaller than F− and N, b. it is bigger than O2− and F−, c. it is bigger thanF− and N, but smaller than of O2−, d. it is smaller than O2− and F− , but bigger than, of N
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45, , JULY ATTEMPT ~ 25 July 2021, Shift II, 7. The correct decreasing order of densities of, , 11. Which one of the following is correct, , the following compounds is, Cl, , structure for cytosine?, Br, , Cl, , N, , a., , (A), , (B), , Cl, , (C), , Cl, , (D), , H3C, , a. (D) > (C) > (B) > (A), b. (C) > (D) > (A) > (B), c. (C) > (B) > (A) > (D), d. (A) > (B) > (C) > (D), , 8. C 6H5NO2 → A →, +, H, , N, |, H, , N, |, H, H 2N, , N, , d., , N, |, H, , P, , (Yellow coloured, compound), , N, |, H, , 12. Identify the species having one π - bond and, maximum number of canonical forms from, the following, , N==N—, NH2, N== N—, , N, , c., , Consider the above reaction, the product P is, , a., , N—H, , NH2, , +, C 6H5N2 Cl –, , Sn +HCl, , H 3C, b., , a. SO3, —NH2, , b. O2, , c. SO2, , d. CO2−, 3, , 13. Which one of the following metals forms, , b., , interstitial hydride easily ?, a. Cr, , N, , b. Fe, , c. Mn, , d. Co, , N—, c., H, , 14., , O, , N== N—N—, d., , 9. A reaction of benzonitrile with one, equivalent CH3MgBr followed by hydrolysis, produces a yellow liquid P. The compound P, will give positive, a. iodoform test, b. Schiff’s test, c. ninhydrin’s test, d. Tollen’s test, , 10. The spin only magnetic moments (in BM) for, free Ti3+ , V 2+ , and Sc 3+ ions respectively are, (Atomic number: Sc = 21, Ti = 22, V = 23), a. 3.87, 1.73, 0, b. 1.73, 3.87, 0, c. 1.73, 0, 3.87, d. 0, 3.87, 1.73, , (Maleic anhydride), , Maleic anhydride can be prepared by, a. heating trans-but-2-enedioic acid, b. heating cis-but-2-enedioic acid, c. treating cis-but-2-enedioic acid with alcohol, and acid, d. treating trans-but-2-enedioic acid with alcohol, and acid, , 15. Given below are two statements :, Statement I Chlorofluoro carbons break, down by radiation in the visible energy, region and release chlorine gas in the, atmosphere which then reacts with, stratospheric ozone., Statement II Atmospheric ozone reacts with, nitric oxide to give nitrogen and oxygen, gases, which add to the atmosphere.
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46, , ONLINE, For the above statements choose the correct, answer from the options given below :, , 18. What is the major product P of the following, reaction ?, , a. Statement I is incorrect but statement II is true, b. Both statement I and II are false, c. Statement I is correct but statement II is false, d. Both statement I and II are correct, , 16., , Br, , EtOH (excess), Dry HCl gas, , CHO, , A, , CH3, , (i) NaNO2, HCl, 278K, , NH2, , (ii) H2O, , P, (Major, product), , CH3, , BuO–K+, , (Major, product), , JEE Main 2021 ~ Solved Papers, , CH3, , a., , B, , b., CH3, , (Major, product), , Cl, , OH, , [where, Et = C 2H5, Bu = (CH 3) 3C —], , OEt, ,, , OEt, , oxidation state is five, a. Cr2O72− → 2Cr 3 +, c. CrO24− → Cr 3 +, , CHO, , EtO, , acid ?, , EtO, , ,, , OEt, EtO, , c., , OEt, , BuO, OEt, , List II, , (A), , Cheese, , I., , Dispersion of liquid in, liquid, , (B), , Pumice stone II., , Dispersion of liquid in, gas, , (C), , Hair cream, , III. Dispersion of gas in, solid, , (D) Cloud, , a., b., c., d., , B, III, I, IV, III, , C, II, III, I, I, , D, I, II, II, II, , d., , 21. A system does 200 J of work and at the same, time absorbs 150 J of heat. The magnitude of, the change in internal energy is ……… J., (Nearest integer), , 22. An accelerated electron has a speed of, , 5 × 106ms −1 with an uncertainty of 0.02%. The, uncertainty in finding its location while in, motion is x × 10−9m. The value of x is ……… ., (Nearest integer), [Use mass of electron = 91, . × 10−31 kg,, −34, Js, π = 314, . ], h = 663, . × 10, , 23. Number of electrons present in 4 f orbital of, Ho 3+ ion is …… . (Given, atomic number of, Ho = 67), , IV. Dispersion of liquid in, solid, , Choose the most appropriate answer from the, options given below., A, IV, IV, III, IV, , c., , Section B : Numerical Type Questions, , 17. Match List I with List II., List I, , b., , OEt, t, , ,, , OEt, , OEt, , H 2C, , OEt, Br, , d., , a. CH3CH2CH2CH3, OEt, , ,, , OEt, , b. MnO−4 → Mn2 +, d. C2O42− → 2CO2, , 20. Which among the following is the strongest, , OEt, OtBu, , b., , OH, , 19. Identify the process in which change in the, , OEt, , H2C, , Br, , d., N2 Cl, , Consider the above reaction sequence,, product A and product B formed respectively, are, a., , CH3, , c., , t, , H3C, , H, , 24., , + Br2, H3C, , CCl4, , Product (P), , H, , Consider the above chemical reaction. The, total number of stereoisomers possible for, product P is ……
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47, , JULY ATTEMPT ~ 25 July 2021, Shift II, 25. For a chemical reaction A → B, it was found, that concentration of B is increased by, 0.2 mol L−1 in 30 min. The average rate of the, reaction is ……×10−1 mol L−1 h −1. (Nearest, integer), , 26. The number of significant figures in 0.00340, is …… ., , 27. Assuming that Ba(OH) 2 is completely ionised, in aqueous solution under the given, conditions the concentration of H3 O+ ions in, 0.005 M aqueous solution of Ba(OH) 2 at 298 K, is …… ×10−12mol L−1. (Nearest integer), , 28. 0.8 g of an organic compound was analysed, by Kjeldahl's method for the estimation of, nitrogen. If the percentage of nitrogen in the, , compound was found to be 42%, then ………, mL of 1 M H2SO4 would have been, neutralised by the ammonia evolved during, the analysis., , 29. When 3.00 g of a substance 'X' is dissolved in, 100 g of CCl4, it raises the boiling point by, 0.60 K. The molar mass of the substance 'X', is ……… g mol−1. (Nearest integer), [Given, K b for CCl4 is 5.0 K kg mol−1], , 30. An LPG cylinder contains gas at a pressure of, 300 kPa at 27°C. The cylinder can withstand, the pressure of 12 × 106 Pa. The room in, which the cylinder is kept catches fire. The, minimum temperature at which the bursting, of cylinder will take place is ……… °C., (Nearest integer), , MATHEMATICS, Section A : Objective Type Questions, 1. The sum of all those terms which are, rational numbers in the expansion of, (21/ 3 + 31/ 4)12 is, a. 89, , b. 27, , c. 35, , d. 43, , 2. The first of the two samples in a group has, 100 items with mean 15 and standard, deviation 3. If the whole group has 250 items, with mean 15.6 and standard deviation, 13.44 , then the standard deviation of the, second sample is, a. 8, , b. 6, , c. 4, , d. 5, , , (5 + |1 − t|)dt , x > 2, If f ( x) = ∫, , then, 0, , x, x, ,, +, ≤, 5, 1, 2, , x, , 3., , a. f (x ) is not continuous at x = 2, b. f (x ) is everywhere differentiable, c. f (x ) is continuous but not differentiable at x = 2, d. f (x ) is not differentiable at x = 1, , 4. If the greatest value of the term independent, cos α 10, is, of x in the expansion of x sinα + a, , x , 10!, , then the value of a is equal to, (5!) 2, a. −1, , b. 1, , c. −2, , d. 2, , 5. Consider the statement "The match will be, played only if the weather is good and, ground is not wet"., Select the correct negation from the following, a. The match will not be played and weather is, not good and ground is wet., b. If the match will not be played, then either, weather is not good or ground is wet., c. The match will be played and weather is not, good or ground is wet., d. The match will not be played or weather is, good and ground is not wet., , 6. The value of cot, , π, is, 24, , a. 2 + 3 + 2 − 6, c. 2 − 3 − 2 + 6, , b. 2 + 3 + 2 + 6, d. 3 2 − 3 − 6, , 7. The lowest integer, which is greater than, 100, 1 , , 1 + 100 , , 10 , , 10, , is, , a. 3, c. 2, , b. 4, d. 1, 1, , 8. The value of the integral ∫ log( x + x 2 + 1)dx, −1, , is, a. 2, , b. 0, , c. −1, , d. 1
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48, , ONLINE, , 9. Let a , b and c be distinct positive numbers. If, the vectors a $i + a$j + ck$ , $i + k$ and c $i + c$j + bk$, are coplanar, then c is equal to, a., , 2, 1 1, +, a b, , b., , a+ b, 2, , c., , 1 1, +, a b, , d. ab, , 10. If [ x ] be the greatest integer less than or, 100, , equal to x , then, a. 0, , ( −1) n n , is equal to, 2 , , Σ, n=8, , b. 4, , c. −2, , d. 2, , 11. The number of distinct real roots of, sin x, , cos x cos x, , cos x sin x cos x = 0 in the interval, cos x cos x sin x, π, π, − ≤ x ≤ is, 4, 4, a. 4, , b. 1, , c. 2, , d. 3, , 12. If|a| = 2,|b| = 5 and|a × b| = 8, then|a. b| is, b. 4, , c. 3, , d. 5, , 13. The number of real solutions of the equation, x 2 − |x| − 12 = 0 is, a. 2, , b. 3, , c. 1, , d. 4, , 14. Consider function f : A → B and, g : B → C ( A , B , C ⊆ R ) such that ( gof ) −1, exists, then, a. f and g both are one-one, b. f and g both are onto, c. f is one-one and g is 0 into, d. f is onto and g is one-one, , 1, , 0, , 50, 15. If P = , , then P is, 1, /, 2, 1, , , , 1 0, 25 1, , , 1 25, c., 0 1 , , , , a., , 3, 1, and, 8, 8, 3, 1, c. and, 4, 9, , a., , 3, 1, and, 4, 8, 3, 1, d. and, 4, 16, b., , 17. If a tangent to the ellipse x 2 + 4 y 2 = 4 meets, the tangents at the extremities of its major, axis at B and C , then the circle with BC as, diameter passes through the point, a. ( 3 , 0), c. (1, 1), , b. ( 2 , 0), d. (−1, 1), , 18. Let the equation of the pair of lines, y = px and, y = qx can be written as ( y − px)( y − qx) = 0, Then, the equation of the pair of the angle, bisectors of the line x 2 − 4 xy − 5 y 2 = 0 is, a. x 2 − 3xy + y 2 = 0, b. x 2 + 4 xy − y 2 = 0, c. x 2 + 3xy − y 2 = 0, d. x 2 − 3xy − y 2 = 0, , 19. If nPr = nPr + 1 and nC r = nC r − 1, then the value, of r is equal to, , equal to, a. 6, , JEE Main 2021 ~ Solved Papers, , 1 50, 0 1 , , , 1 0, d., 50 1, , , , b., , 16. Let x be a random variable such that the, probability function of a distribution is given, 1, 1, by P( X = 0) = , P( X =`j) = j ( j = 1, 2, 3, .... ∞)., 2, 3, Then, the mean of the distribution and P, (X is positive and even ) respectively are, , a. 1, c. 2, , b. 4, d. 3, , 20. Let y = y ( x) be the solution of the differential, equation xdy = ( y + x 3 cos x)dx with y( π ) = 0,, π, then y is equal to, 2, π2, π, +, 4, 2, π2 π, c., −, 2, 4, a., , π2, π, +, 2, 4, π2 π, d., −, 4, 2, b., , Section B : Numerical Type Questions, 21. Let n ∈ N and [ x ] denote the greatest integer, less than or equal to x. If the sum of ( n + 1), terms nC 0 , 3.n C 1, 5.n C 2 , 7.n C 3 …… is equal to, n − 1, 2100. 101, then 2, is equal to ……… ., 2 , , 22. Consider the function, P( x), , f ( x) = sin( x − 2), , 7, , , x ≠2, , x =2, , where, P( x) is a polynomial such that P′′( x) is, always a constant and P(3) = 9. If f ( x) is, continuous at x = 2, then P(5) is equal to …… .
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49, , JULY ATTEMPT ~ 25 July 2021, Shift II, 23. The equation of a circle is, , Re( z 2) + 2[Im( z)]2 + 2Re( z) = 0. where, z = x + iy . A, line which passes through the center of the, given circle and the vertex of the parabola,, x 2 − 6x − y + 13 = 0, has y-intercept equal to …… ., , 24. If a rectangle is inscribed in an equilateral, triangle of side length 2 2 as shown in the, figure, then the square of the largest area of, such a rectangle is ……… ., , real value of x. Then the value of f (e) is, equal to …… ., , 27. If a + b + c = 1, ab + bc + ca = 2 and, abc = 3,, then the value of a 4 + b4 + c 4 is equal to, …… ., , 28. A fair coin is tossed n times such that the, probability of getting at least one head is, at least 0.9. Then the minimum value of n, is …… ., , 29. If the co-efficient of x 7 and x 8 in the, , x n, expansion of 2 + are equal, then, , 3, the value of n is equal to ……… ., , 25. If ( a + 3b) is perpendicular to (7a − 5b) and, ( a − 4 b) is perpendicular to (7a − 2b), then the, angle between a and b (in degrees) is …… ., , 26. Let a curve y = f ( x) pass through the point, [2, (log e 2) 2 ] and have slope, , 2y, for all positive, x log e x, , 30. If the lines, , x −k, , x+1, , 1, , =, , y −2, 2, , =, , z −3, 3, , and, , y + 2 z +3, are co-planar, then, =, =, 3, 2, 1, the value of k is ……… ., , Answers, For solutions scan, the QR code, , Physics, 1. (a), 11. (c), 21. 25, , 2. (b), 12. (c), 22. 125, , 3. (c), 13. (c), 23. 1, , 4. (a), 14. (b), 24. 45, , 5. (d), 15. (c), 25. 500, , 6. (a), 16. (c), 26. 27.16, , 7. (b), 17. (b), 27. 450, , 8. (a), 18. (a), 28. 4, , 9. (c), 19. (b), 29. 5, , 10. (b), 20. (b), 30. 10, , Chemistry, 1. (c), 11. (c), 21. 50, , 2. (c), 12. (d), 22. 58, , 3. (a), 13. (a), 23. 10, , 4. (b), 14. (b), 24. 2, , 5. (a), 15. (b), 25. 4, , 6. (b), 16. (a), 26. 3, , 7. (a), 17. (d), 27. 1, , 8. (b), 18. (d), 28. 12, , 9. (a), 19. (b), 29. 250, , 10. (b), 20. (d), 30. 927, , 3. (c), 13. (a), 23. 1, , 4. (d), 14. (c), 24. 3, , 5. (c), 15. (a), 25. 60, , 6. (b), 16. (b), 26. 1, , 7. (a), 17. (a), 27. 13, , 8. (b), 18. (c), 28. 4, , 9. (d), 19. (c), 29. 55, , 10. (b), 20. (a), 30. 1, , Mathematics, 1. (d), 11. (b), 21. 98, , 2. (c), 12. (a), 22. 39
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JEE Main 2021, 27 JULY SHIFT I, , PHYSICS, Section A : Objective Type Questions, List I, , 1. In the given figure, a battery of emf E is, connected across a conductor PQ of length l, and different area of cross-sections having, radii r1 and r2( r2 < r1)., P, , r1, , r2 Q, , List II, 2, , B. Moment of inertia of the rod II. ML, (length L, mass 2M, about an, 3, axis perpendicular to the, rod passing through one of, its end), , 2, C. Moment of inertia of the rod III. ML, (length 2L, mass M, about an, 12, axis perpendicular to the, rod passing through its, midpoint), , –, +, + –, E, , K, , Choose the correct option as one moves, from P to Q., a. Drift velocity of electron increases, b. Electric field decreases, c. Electron current decreases, d. All of the above, , 2. The number of molecules in 1 L of an ideal, gas at 300 K and 2 atm pressure with mean, kinetic energy 2 × 10−9 J per molecules is, a. 0.75 × 1011, c. 15, . × 1011, , b. 3 × 1011, d. 6 × 1011, , 3. The relative permittivity of distilled water is, 81. The velocity of light in it will be, (Take, µ r = 1), a. 4.33 × 107 m/s, c. 3.33 × 107 m/s, , b. 2.33 × 107 m/s, d. 5.33 × 107 m/s, , 4., List I, A. Moment of inertia of the rod I., (length L, mass M, about an, axis perpendicular to the, rod passing through the, mid-point), , List II, 8 ML2, 3, , 2, D. Moment of inertia of the rod IV. 2 ML, (length 2L, mass 2M, about, 3, an axis perpendicular to the, rod passing through one of, its end), , Choose the correct answer from the options, given below., A, B, C, D, a. (II) (III) (I) (IV), b. (II) (I) (III) (IV), c. (III) (IV) (II) (I), d. (III) (IV) (I) (II), , 5. Three objects A , B and C are kept in a straight, line on a frictionless horizontal surface. The, masses of A, B and C are m , 2m and 2m,, respectively. A moves towards B with a speed, of 9 m/s and makes an elastic collision, with it. There after B makes a completely, inelastic collision with C . All motions occur, along same straight line. The final speed of, C is, , a. 6 m/s, , A, , B, , C, , m, , 2m, , 2m, , b. 9 m/s, , c. 4 m/s, , d. 3 m/s
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51, , JULY ATTEMPT ~ 27 July 2021, Shift I, 6. A capacitor of capacitance C = 1µF is, suddenly connected to a battery of 100 V, through a resistance R = 100 Ω. The time, taken for the capacitor to be charged to get, 50 V is, R=100Ω, C=1µF, , 100 V, , 9. In Young’s double slit experiment, if the, source of light changes from orange to blue,, then, a. the central bright fringe will become a dark, fringe, b. the distance between consecutive fringes will, decrease, c. the distance between consecutive fringes will, increase, d. the intensity of the minima will increase, , 10. In the reported figure, there is a cyclic, , [Take, In 2 = 069, . ], −4, , −4, , a. 144, . × 10 s, c. 069, . × 10−4 s, , b. 3.33 × 10 s, d. 0.30 × 10−4 s, , 7. In the reported figure, a capacitor is formed, by placing a compound dielectric between, the plates of parallel plate capacitor. The, expression for the capacity of the said, capacitor will be (Take, area of plate = A), C1, , C2, , C3, , K, , 3K, , 5K, , d, , 2d, , 3d, , 15 K ε0 A, a., 34 d, 25 K ε0 A, c., 6 d, , process ABCDA on a sample of 1 mol of a, diatomic gas. The temperature of the gas, during the process A → B and C → D are T1, and T2 (T1 > T2) , respectively., p, 5p0, , A, B, , p0, , 15 K ε0 A, 6 d, 9 K ε0 A, d., 6 d, , O, , 8. The figure shows two solid discs with radius R, and r, respectively. If mass per unit area is, same for both, what is the ratio of MI of bigger, disc around axis AB (which is perpendicular to, the plane of the disc and passing through its, centre) of MI of smaller disc around one of its, diameters lying on its plane?, Given, M is the mass of the larger disc. (MI, stands for moment of inertia), A, , V0, , 1.5V0, , C, , b. 2r 4 : R 4, , V, , 11. Assertion A If A , B , C , D are four points on a, semi-circular arc with centre at O such that, |AB| =|BC| =|CD|, then, AB + AC + AD = 4 AO + OB + OC, Reason R Polygon law of vector addition, yields, AB + BC + CD + AD = 2AO, O, , B, , B, , a. R 2 : r 2, , 5.5V0, , D, , D, R, , M, , 3.5V0, , Choose the correct option out of the following for, work done, if processes BC and DA are adiabatic., a. WAB = WDC, b. WAD = WBC, d. WAB < WCD, c. WBC + WDA > 0, , A, r, , C, , D, , b., , c. 2R 2 : r 2, , d. 2R 4 : r 4, , C, , In the light of the above statements, choose, the most appropriate answer from the, options given below.
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52, , JEE Main 2021 ~ Solved Papers, , ONLINE, a. Both A and R are correct and R is the correct, explanation of A., b. Both A and R are correct but R is not the, correct explanation of A., c. A is correct but R is not correct., d. A is not correct but R is correct., , 12. A light cylindrical vessel is kept on a, horizontal surface. Area of base is A. A hole, of cross-sectional area a is made just at its, bottom side. The minimum coefficient of, friction necessary to prevent sliding the, vessel due to the impact force of the, emerging liquid is (a << A) ., A, , a, , a., , V, K+2, , b., , V, K, , c., , 3V, K+2, , d., , 3V, K, , 16. A ball is thrown up with a certain velocity, so, that it reaches a height h. Find the ratio of, the two different times of the ball reaching, , h, 3, , in both the directions., a., , 2−1, 2+1, , b., , 1, 3, , c., , 3− 2, 3+ 2, , d., , 3−1, 3+1, , 17. A 0.07 H inductor and a 12 Ω resistor are, connected in series to a 220 V, 50 Hz AC, source. The approximate current in the circuit, and the phase angle between current and, source voltage are, respectively. [Take, π as, 22, ], 7, 11, 11, a. 8.8 A and tan −1 b. 88 A and tan −1 , 6, 6, 11, 6, c. 0.88 A and tan −1 d. 8.8 A and tan −1 , 6, 11, , 18. Two identical tennis balls each having mass, A, a., 2a, 2a, c., A, , b. None of these, d., , a, A, , m and charge q are suspended from a fixed, point by threads of length l. What is the, equilibrium separation when each thread, makes a small angle θ with the vertical ?, 1, , 13. A particle starts executing simple harmonic, motion (SHM) of amplitude a and total energy, 3E, , then, 4, its displacement y is given by, , E. At any instant, its kinetic energy is, , a. y = a, , b. y =, , a, 2, , c. y =, , a 3, a, d. y =, 2, 2, , 14. If f denotes the ratio of the number of nuclei, , decayed (Nd ) to the number of nuclei at t = 0, (N0), then for a collection of radioactive, nuclei, the rate of change of f with respect to, time is given as, [λ is the radioactive decay constant], b. λ (1− e − λt ), a. − λ (1 − e − λt ), − λt, c. λe, d. − λe − λt, , 15. Two capacitors of capacities 2C and C are, joined in parallel and charged upto potential, V. The battery is removed and the capacitor, of capacity C is filled completely with a, medium of dielectric constant K. The, potential difference across the capacitors, will now be, , 1, , q2l 2, a. d = , , 2πε0 mg , , q2l 3, b. d = , , 2πε0 mg , 1, , q2l 2 3, c. d = , , 2, 2πε0 m g , , 1, , , 3, q2l 2, d. d = , , 2 2, m, g, 2πε, , , 0, , 19. Assertion A If in five complete rotations of, the circular scale, the distance travelled on, main scale of the screw gauge is 5 mm and, there are 50 total divisions on circular scale,, then least count is 0.001 cm., Reason R Least count, Pitch, =, Total divisions on circular scale, In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Both A and R are correct and R is the correct, explanation of A., b. Both A and R are correct and R is not the, correct explanation of A., c. A is correct but R is not correct., d. A is not correct but R is correct.
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53, , JULY ATTEMPT ~ 27 July 2021, Shift I, 20. A body takes 4 min to cool from 61° C to, 59°C. If the temperature of the surroundings, is 30°C, then the time taken by the body to, cool from 51°C to 49° C is, a. 4 min, b. 3 min, c. 8 min, d. 6 min, , Section B : Numerical Type Questions, 21. Consider an electrical circuit containing a, two way switch S. Initially S is open and then, T1 is connected to T2. As the current in R = 6 Ω, attains a maximum value of steady state, level, T1 is disconnected from T2 and, immediately connected to T3. Potential drop, across r = 3 Ω resistor immediately after T1 is, connected to T3 is ……… V., (Round off to the nearest integer), R = 6Ω, , T 2 T3, S T1, L, r = 3Ω, , 6V, , 22, . × 166 m/s, then the current associated, with the electron will be …………… × 10−2 mA., 22, [Take, π as ], 7, 24. A radioactive sample has an average life of, 30 ms and is decaying. A capacitor of, capacitance 200 µF is first charged and later, connected with resistor R. If the ratio of, charge on capacitor to the activity of, radioactive sample is fixed with respect to, time, then the value of R should be ……… Ω., , 25. A particle of mass 91, . × 10–31 kg travels in a, , medium with a speed of 106 m/s and a, photon of a radiation of linear momentum, 10–27 kg-m/s travels in vacuum. The, wavelength of photon is ……… times the, wavelength of the particle., , 26. A prism of refractive index n1 and another, prism of refractive index n2 are stuck, together (as shown in the figure). n1 and n2, depend on λ, the wavelength of light,, according to the relation, n1 = 12, . +, , 22. Suppose two planets (spherical in shape) of, radii R and 2R, but mass M and 9M, respectively have a centre to centre, separation 8R as shown in the figure. A, satellite of mass m is projected from the, surface of the planet of mass M directly, towards the centre of the second planet. The, minimum speed v required for the satellite, to reach the surface of the second planet is, a GM, , then the value of a is …………… ., 7 R, [Take, the two planets are fixed in their, position], , 108, . × 10−14, , and n2 = 145, . +, , λ2, 18, . × 10−14, , λ2, The wavelength for which rays incident at, any angle on the interface BC pass through, without bending at that interface will be, …………… nm., D, 90°, C, , 70°, n2, , N, i, , 9M, , M, , 2R, , A, , °, , R, , 20, , n1, 60°, , 40°, B, , 27. A stone of mass 20 g is projected from a, 8R, , 23. In Bohr’s atomic model, the electron is, assumed to revolve in a circular orbit of, radius 0.5 Å. If the speed of electron is, , rubber catapult of length 0.1 m and area of, cross-section 10–6 m2 stretched by an, amount 0.04 m. The velocity of the projected, stone is ………… m/s., (Take, Young’s modulus of rubber = 05, . × 109 N/m2)
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54, , ONLINE, , 28. A transistor is connected in common emitter, circuit configuration, the collector supply, voltage is 10 V and the voltage drop across a, resistor of 1000 Ω in the collector circuit is, 0.6 V. If the current gain factor (β) is 24, then, the base current is …………… µA. (Round off to, the nearest integer), , 29. The amplitude of upper and lower side, bands of AM wave, where a carrier signal, with frequency 11.21 MHz, peak voltage 15 V, , JEE Main 2021 ~ Solved Papers, , is amplitude modulated by a 7.7 kHz sine, a, b, wave of 5 V amplitude are, V and, V,, 10, 10, a, respectively. Then, the value of is ………… ., b, 30. In a uniform magnetic field, the magnetic, needle has a magnetic moment 985, . × 10−2, 2, A/m and moment of inertia 5 × 10−6 kg-m2. If, it performs 10 complete oscillations in, 5 s, then the magnitude of the magnetic field, is ……… mT. [Take, π 2 as 9.85], , CHEMISTRY, Section A : Objective Type Questions, 1. Which one of the following compounds will, give orange precipitate when treated with, 2, 4 dinitrophenyl hydrazine?, , and H 4P2O6, respectively are, a. 7, 5 and 6, c. 5, 3 and 4, , b. 5, 4 and 3, d. 6, 4 and 5, , 5. For a reaction of order n, the unit of the rate, , OH, a., , 4. The oxidation states of ‘P’ in H4P2O7 , H4P2O5, , constant is, , OCH2CH3, , a. mol1− n L1− n s, c. mol1− n L n − 1 s −1, , b. mol1− n L 2n s −1, d. mol1− n L1− n s −1, , 6. Given below are two statements., OCH2CH3, , b., , C—OH, c., , a. Statement I is true but statement II is false., b. Statement I is false but statement II is true., c. Both statement I and statement II are true., d. Both statement I and statement II are false., , OH, , d., , CH3, , 7. The type of hybridisation and magnetic, , 2. The product obtained from the electrolytic, oxidation of acidified sulphate solutions, is, a. HSO −4, c. HO 2SOSO 2H, , b. HO 3SOOSO 3H, d. HO 3SOSO 3H, , 3. The parameters of the unit cell of a, , substance are a = 25, . , b = 30, . , c = 4.0,, α = 90° , β = 120° , γ = 90°. The crystal system, of the substance is, a. hexagonal, c. monoclinic, , Statement I Aniline is less basic than, acetamide., Statement II In aniline, the lone pair of, electrons on nitrogen atom is delocalised, over benzene ring due to resonance and, hence less available to a proton., Choose the most appropriate option :, , b. orthorhombic, d. triclinic, , property of the complex [MnCl6 ]3− ,, respectively, are, a. sp 3d 2 and diamagnetic, b. d 2 sp 3 and diamagnetic, c. d 2 sp 3 and paramagnetic, d. sp 3d 2 and paramagnetic, , 8. The number of geometrical isomers found in, the metal complexes [PtCl2(NH 3) 2 ], [Ni(CO) 4 ],, [Ru(H 2O) 3Cl3 ] and [CoCl2(NH 3) 4 ]+ respectively,, are, a. 1, 1, 1, 1, c. 2, 0, 2, 2, , b. 2, 1, 2, 2, d. 2, 1, 2, 1
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55, , JULY ATTEMPT ~ 27 July 2021, Shift I, 9. Which one of the following statements is not, , 14. The statement that is incorrect about, Ellingham diagram is, , correct ?, , a. provides idea about the reaction rate., b. provides idea about free energy change., c. provides idea about changes in the phases, during the reaction., d. provides idea about reduction of metal oxide., , a. Eutrophication indicates that water body, is polluted., b. The dissolved oxygen concentration below, 6 ppm inhibits fish growth., c. Eutrophication leads to increase in the oxygen, level in water., d. Eutrophication leads to anaerobic conditions., , 10. Given below are two statements :, Statement I Rutherford’s gold foil experiment, cannot explain the line spectrum of hydrogen, atom., Statement II Bohr’s model of hydrogen atom, contradicts Heisenberg’s uncertainty principle., In the light of the above statements, choose the, most appropriate answer from the options given, below :, a. Statement I is false but statement II is true., b. Statement I is true but statement II is false., c. Both statement I and statement II are false., d. Both statement I and statement II are true., , OH, , OH, , hν, , CH3, OH, , OH, c., , d., , H3C, H, , tests is used to distinguish monosaccharide, from disaccharide ?, a. Seliwanoff's test, c. Barfoed test, , b. Iodine test, d. Tollen’s test, , 13. Match List-I with List-II., List-II, (Class of drug), , A. Furacin, , I., , Antibiotic, , B. Arsphenamine, , II., , Tranquilisers, , C. Dimetone, , III. Antiseptic, , D. Valium, , IV. Synthetic, antihistamines, , b., d., , N, H, (A ), , The compound ‘A’ is a complementary base, of …………… in DNA stands., a. uracil, c. adenine, , b. guanine, d. cytosine, , A, III, III, , B, IV, I, , ethane are, a. polymers, c. enantiomers, , b. rotamers, d. mirror images, , 18. Match List-I with List-II., List-I, , Choose the most appropriate match :, D, II, IV, , H, , 17. Staggered and eclipsed conformers of, , List-I, (Drug), , C, IV, III, , N, , 16., , 12. Which one among the following chemical, , B, III, I, , OH, , CH3 I + HI, , a. HOCl, b. dilute HNO 2, c. Liquid NH 3, d. Concentrated HIO 3, , A, I, II, , P, (Major, product), , b., OH, , Reversible, , a., c., , CH3, , a., , reversibility of the following reaction, and, change it to a irreversible reaction :, , =, , (BH3)2, H2O2/OH–, H2O, , A, (Major, product), , Consider the above reaction and identify the, product (P)., , 11. Presence of which reagent will affect the, , CH4 + I2, , H3PO4, 120ºC, , 15., , C, II, IV, , D, I, II, , List-II, , A. NaOH, , I., , Acidic, , B. Be(OH) 2, , II., , Basic, , C. Ca(OH) 2, , III. Amphoteric, , D. B(OH) 3, E. Al(OH) 3
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56, , ONLINE, Choose the most appropriate answer from the, options given below, A B C D E, a. II II III II III, c. II II III I III, , A B C D E, b. II III II I III, d. II I, II III III, , CH2, , 19., , JEE Main 2021 ~ Solved Papers, , 23. The conductivity of a weak acid HA of, , concentration 0.001 mol L −1 is 2.0 × 10−5 S cm −1., If Λ°m(HA) = 190 S cm 2 mol −1, the ionisation, constant (K a) of HA is equal to ………… × 10−6., (Round off to the nearest integer), , 24. 1.46 g of a biopolymer dissolved in a 100 mL, CH2==CH, , CH3—CH2, , (B), , (C), , H2C ≡≡C, (D), , (A ), , The correct order of stability of given, carbocation is, a. A > C > B > D, c. D > B > A > C, , b. D > B > C > A, d. C > A > D > B, , 20. Given below are two statements., One is labelled as Asseriton A and the other, labelled as Reason R., Assertion A Lithium halides are some what, covalent in nature., Reason R Lithium possess high polarisation, capability., According the above statements, choose the, most appropriate answer from the options, given below, a. A is true but R is false, b. A is false but R is true, c. Both A and R are true but R is not the correct, explanation of A, d. Both A and R are true and R is the correct, explanation of A, , Section B : Numerical Type Questions, 21. The density of NaOH solution is 1.2 g cm −3., The molality of this solution is ………… m., (Round off to the nearest integer), [Use : Atomic masses : Na = 23.0 u, O = 16.0 u,, H = 1.0 u, density of H2O : 1.0 g cm −3 ], , 22. CO 2 gas adsorbs on charcoal following, Freundlich adsorption isotherm. For a given, amount of charcoal, the mass of CO 2, adsorbed becomes 64 times when the, pressure of CO 2 is doubled., The value of n in the Freundlich isotherm, equation is ………… × 10−2 . (Round off to the, nearest integer), , water at 300 K exerted an osmotic pressure, of 2.42 × 10−3 bar., The molar mass of the biopolymer is ………, × 104 g mol −1. (Round off to the nearest integer), [Use : R = 0083, L bar mol −1 K −1], ., , 25. An organic compound is subjected to, chlorination to get compound A using 5.0 g, of chlorine. When 0.5 g of compound A is, reacted with AgNO 3 [Carius method], the, percentage of chlorine in compound A is, ………… when it forms 0.3849 g of AgCl., (Round off to the nearest integer), (Atomic masses of Ag and CI are 107.87 and, 35.5 respectively), , 26. The number of geometrical isomers possible, in triamminetrinitrocobalt (III) is X and in, trioxalatochromate (III) is Y. Then, the value, of X + Y is …………… ., , 27. In gaseous triethyl amine the “—C—N—C—”, bond angle is ………… degree., , 28. For water at 100°C and 1 bar,, ∆ vapH − ∆ vap U = …………… × 102 J mol −1., (Round off to the nearest integer), [Use : R = 8.31 J mol −1 K −1], [Assume volume of H2O(l ) is much smaller than, volume of H2O( g ). Assume H2O( g ) treated as an, ideal gas], , 29. PCl5, , = PCl + Cl , K, 3, , 2, , c, , = 1.844, , 3.0 moles of PCl5 is introduced in a 1 L closed, reaction vessel at 380 K. The number of moles, of PCl5 at equilibrium is ………… × 10−3 ., (Round off to the nearest integer), , 30. The difference between bond orders of CO, and NO⊕ is X /2. where, x = ………… ., (Round off to the nearest integer).
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57, , JULY ATTEMPT ~ 27 July 2021, Shift I, , MATHEMATICS, Section A : Objective Type Questions, 1. If the mean and variance of the following, data :, 6, 10, 7, 13, a, 12, b, 12, 37, respectively, then (a − b ) 2 is equal to, are 9 and, 4, a. 24, b. 12, c. 32, d. 16, , 1, n→ ∞ n, , 2. The value of lim, 3, a. 5 + log e , 2, 2, c. 3 + 2log e , 3, , n, , (2 j − 1) + 8n, , ∑ (2 j − 1) + 4 n is equal to, , j =1, , 2, b. 2 − log e , 3, 3, d. 1 + 2log e , 2, , 3. Let a = $i + $j + 2k$ and b = − $i + 2$j + 3k$ . Then, the vector product, ( a + b) × [( a × {( a − b) × b) } × b] is equal to, a. 5(34 $i − 5$j + 3k$ ), c. 7(30$i − 5$j + 7k$ ), , b. 7(34 $i − 5$j + 3k$ ), d. 5(30$i − 5$j + 7k$ ), , 4. The value of the definite integral, π, 4, , ∫, −, , π, 4, , dx, (1 + e x cos x ) (sin 4 x + cos 4 x ), , π, 2, π, c. −, 4, a. −, , is equal to, , π, 2 2, π, d., 2, b., , 5. Let C be the set of all complex numbers. Let, S1 = { z ∈ C|| z − 3 − 2i|2 = 8},, S 2 = { z ∈ C| Re (z) ≥ 5} and, S 3 = { z ∈ C|| z − z| ≥ 8., Then, the number of elements in, S1 ∩ S 2 ∩ S 3 is equal to, a. 1, c. 2, , b. 0, d. Infinite, , 6. If the area of the bounded region, 1, R = (x , y ) : max {0, log e x } ≤ y ≤ 2x , ≤ x ≤ 2, 2, , , is, α (log e 2) −1 + β (log e 2) + γ , then the value of, (α + β − 2γ ) 2 is equal to, a. 8, b. 2, c. 4, d. 1, , 7. A ray of light through (2, 1) is reflected at a, point P on the Y-axis and then passes, through the point (5, 3). If this reflected ray is, 1, the directrix of an ellipse with eccentricity, 3, and the distance of the nearer focus from, 8, this directrix is, , then the equation of the, 53, other directrix can be, a. 11x + 7 y + 8 = 0 or 11x + 7 y − 15 = 0, b. 11x − 7 y − 8 = 0 or 11x + 7 y + 15 = 0, c. 2x − 7 y + 29 = 0 or 2x − 7 y − 7 = 0, d. 2x − 7 y − 39 = 0 or 2x − 7 y − 7 = 0, , 8. If the coefficients of x 7 in x 2 +, , , 1, , bx , , 11, , and x −7, , 11, , 1 , , in x −, , b ≠ 0, are equal, then the value, , bx 2 , of b is equal to, a. 2, , b. − 1, , c. 1, , d. − 2, , 9. The compound statement (P ∨ Q) ∧ (~ P) ⇒ Q, is equivalent to, a. P ∨ Q, c. ~ (P ⇒ Q ), , b. P ∧ ~ Q, d. ~ (P ⇒ Q ) ⇔ P ∧ ~ Q, , 1, 2, 16[sin(2θ) + cos( 4θ) + sin(6θ)] is equal to, , 10. If sinθ + cos θ = , then, a. 23, , b. −27, , c. − 23, , d. 27, , 1 2, −1, . If A = αI + βA , α, β ∈ R , I is a, 1, 4, −, , , 2 × 2 identity matrix, then 4(α − β) is equal to, , 11. Let A = , a. 5, c. 2, , b. 8/3, d. 4, , π π, 12. Let f : − , → R be defined as, 4 4, 3a, , −π, |sin x|, (1 + |sin x|), ,, < x <0, 4, , f ( x) = , b,, x =0, cot 4 x, , π, , e cot 2x ,, 0<x <, 4, , If f is continuous at x = 0, then the value of, 6a + b2 is equal to, , a. 1− e, c. 1+ e, , b. e − 1, d. e
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58, , ONLINE, , 13. Let y = y ( x) be solution of the differential, , JEE Main 2021 ~ Solved Papers, , 19. The probability that a randomly selected, , dy , equation log e = 3x + 4 y , with y(0) = 0., dx , , 2-digit number belongs to the set, {n ∈N : (2n − 2) is a multiple of 3} is equal to, , 2, If y − log e 2 = α log e 2 , then the value of α is, 3, , equal to, 1, 1, b., a. −, 4, 4, 1, c. 2, d. −, 2, , a., , 14. Let the plane passing through the point, , ( −1, 0, − 2) and perpendicular to each of the, planes 2x + y − z = 2 and x − y − z = 3 be, ax + by + cz + 8 = 0. Then the value of, a + b + c is equal to, a. 3, c. 5, , b. 8, d. 4, , 15. Two tangents are drawn from the point, , P( −1, 1) to the circle x 2 + y 2 − 2x − 6 y + 6 = 0., If these tangents touch the circle at points A, and B, and if D is a point on the circle such, that length of the segments AB and AD are, equal, then the area of the ∆ ABD is equal to, a. 2, c. 4, , b. (3 2 + 2), d. 3( 2 − 1), , 16. Let f : R → R be a function such that f (2) = 4, and f ′ (2) = 1. Then, the value of, x 2 f (2) − 4 f ( x), is equal to, lim, x→ 2, x −2, a. 4, c. 16, , b. 8, d. 12, , 17. Let P and Q be two distinct points on a circle, which has center at C(2,3) and which passes, through origin O. If OC is perpendicular to, both the line segments CP and CQ, then the, set { P ,Q } is equal to, a. {(4, 0), (0, 6)}, b. {(2 + 2 2 , 3 − 3 ), (2 − 2 2 , 3 + 5 )}, c. {(2 + 2 2 , 3 + 5 ), (2 − 2 2 , 3 − 5 ), d. {(−1, 5), (5, 1)}, , 18. Let α, β be two roots of the equation, x 2 + (20)1/ 4 x + (5)1/ 2 = 0. Then, α 8 + β 8 is equal, to, a. 10, c. 50, , b. 100, d. 160, , 1, 6, , b., , 2, 3, , c., , 1, 2, , d., , 1, 3, , 20. Let A = {(x , y ) ∈R × R | 2x 2 + 2 y 2 − 2x − 2 y = 1},, B = {x, y) ∈R × R | 4 x 2 + 4 y 2 − 16 y + 7 = 0}, C = {( x , y ) ∈R × R |x 2 + y 2 − 4 x − 2 y + 5 ≤ r 2 }, Then the minimum value of |r| such that, A ∪ B ⊆ C is equal to, 3 + 10, 2, 3+ 2 5, c., 2, , a., , b., , 2 + 10, 2, , d. 1 + 5, , Section B : Numerical Type Questions, 21. For real numbers α and β, consider the, following system of linear equations, x + y − z = 2, x + 2 y + αz = 1,, 2x − y + z = β., If the system has infinite solutions, then, α + β is equal to ……………… ., , 22. Let a = i$ + $j + k$ , b and c = $j − k$ be three, vectors such that a × b = c and a ⋅ b = 1. If the, length of projection vector of the vector b on, the vector a × c is l, then the value of 3I 2 is, equal to …………, 7, 23. If log 3 2, log 3(2x − 5), log 3 2x − are in an, , , 2, arithmetic progression, then the value of x is, equal to ………… ., , 24. Let the domain of the function, f ( x) = log 4[log 5(log 3(18x − x 2 − 77))] be (a , b)., Then the value of the integral, b, sin3 x, ∫ [sin3 x + sin3 (a + b − x)] dx is equal to …………, a, sin2 x, , 25. Let f ( x) = 2 + sin x, 2, , sin2 x, , − 2 + cos 2 x, , cos 2x, , cos 2 x, cos 2 x, , cos 2x ,, 1 + cos 2x, , x ∈[0, π ], Then the maximum value of f ( x) is equal to, ………… .
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59, , JULY ATTEMPT ~ 27 July 2021, Shift I, , π, 29. If y = y ( x), y ∈ 0, is the solution of the, , 26. Let f : [3, 5] → R be a twice differentiable, function on (3, 5) such that, , 2, differential equation, dy, sec y, − sin( x + y ) − sin( x − y ) = 0, with, dx, π, y(0) = 0, then 5 y′ is equal to ………… ., 2, , x, , f ( x) = e − x ∫ [3t 2 + 2t + 4 f ′ (t)] dt., 3, , If f ′ ( 4) =, , αe β − 224, (e β − 4) 2, , , then α + β is equal to ……… ., , 27. Let a plane P pass through the point (3, 7, − 7), , 30. Let f : [0, 3] → R be defined by, , x −2, , y −3 z + 2, . If, =, =, −3, 2, 1, distance of the plane P from the origin is d, then, d 2 is equal to …………… ., and contain the line,, , f (x ) = min{ x − [ x ], 1 + [ x ] − x ], where [ x ] is the greatest integer less than, or equal to x. Let P denote the set, containing all x ∈ (0, 3), where f is, discontinuous and Q denote the set, containing all x ∈ (0, 3), where f is not, differentiable., Then the sum of number of elements in P, and Q is equal to ………… ., , 28. Let {S = 1, 2, 3, 4 , 5, 6, 7}. Then the number of, possible functions f : S → S such that, f ( m ⋅ n) = f ( m) ⋅ f ( n) for every m, n ∈ S and m ⋅ n ∈ S, is equal to ………… ., , Answers, For solutions scan, the QR code, , Physics, 1. (a), 11. (c), 21. 3, , 2. (c), 12. (c), 22. 4, , 3. (c), 13. (d), 23. 112, , 4. (c), 14. (c), 24. 150, , 5. (d), 15. (c), 25. 910, , 6. (c), 16. (c), 26. 600, , 7. (a), 17. (a), 27. 20, , 8. (d), 18. (b), 28. 25, , 3. (c), 13. (d), 23. 12, , 4. (c), 14. (a), 24. 15, , 5. (c), 15. (d), 25. 19, , 6. (b), 16. (c), 26. 2, , 7. (d), 17. (b), 27. 108, , 8. (c), 18. (b), 28. 31, , 3. (b), 13. (a), 23. 3, , 4. (b), 14. (d), 24. 1, , 5. (a), 15. (c), 25. 6, , 6. (b), 16. (d), 26. 16, , 7. (c), 17. (d), 27. 3, , 8. (c), 18. (c), 28. 490, , 9. (b), 19. (d), 29. 1, , 10. (b), 20. (d), 30. 8, , 9. (c), 19. (a), 29. 1400, , 10. (d), 20. (d), 30. 0, , 9. (d), 19. (c), 29. 2, , 10. (c), 20. (c), 30. 5, , Chemistry, 1. (d), 11. (d), 21. 5, , 2. (b), 12. (c), 22. 17, , Mathematics, 1. (d), 11. (d), 21. 5, , 2. (d), 12. (c), 22. 2
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ONLINE, , JEE Main 2021 ~ Solved Papers, , JEE Main 2021, 27 JULY SHIFT II, , PHYSICS, Section A : Objective Type Questions, 1. An electron and proton are separated by a, large distance. The electron starts, approaching the proton with energy 3 eV., The proton captures the electrons and forms, a hydrogen atom in second excited state., The resulting photon is incident on a, photosensitive metal of threshold, wavelength 4000 Å. What is the maximum, kinetic energy of the emitted photoelectron?, a. 7.61 eV, b. 1.41 eV, c. 3.3 eV, d. No photoelectron would be emitted, , (Take, density of water, ρ w =1000 kg m −3 and, density of air, ρ a = 1.2 kg m −3, g = 10 m/s2,, coefficient of viscosity of air, η, = 1.8 × 10–5 N-s m −2), a. 250.6 ms −1, c. 4.94 ms −1, , b. 43.56 ms −1, d. 14.4 ms −1, , 4. One mole of an ideal gas is taken through an, adiabatic process, where the temperature, rises from 27°C to 37°C. If the ideal gas is, composed of polyatomic molecule that has, 4 vibrational modes, which of the following is, true? [Take, R = 8314, J mol −1 K −1], ., a. Work done by the gas is close to 332 J, b. Work done on the gas is close to 582 J, , 2. The expected graphical representation of the, variation of angle of deviation δ with angle of, incidence i in a prism is, Y, , a., , b., , i, , δ, , X, , i, , Y, , d. Work done on the gas is close to 332 J, , 5. An object of mass 0.5 kg is executing simple, , Y, , δ, , c. Work done by the gas is close to 582 J, , X, , Y, , harmonic motion. It amplitude is 5 cm and, time period (T) is 0.2 s. What will be the, potential energy of the object at an instant, T, t = s starting from mean position ? Assume, 4, that, the initial phase of the oscillation is, zero., b. 6.2 × 10−3 J, , a. 0.62 J, , d. 6.2 × 103 J, , c. 1.2 × 10 J, 3, , c., , d., , δ, , δ, , 6. Match List I with List II., i, , X, , i, , X, , 3. A raindrop with radius R = 02, . mm falls from, , a cloud at a height h = 2000 m above the, ground. Assume that, the drop is spherical, throughout its fall and the force of buoyance, may be neglected, then the terminal speed, attained by the raindrop is, , List I, , List II, , A. Capacitance, C, , I. M L T −3 A −1, , B. Permittivity of free, space, ε0, , II. M −1 L−3 T 4 A 2, , C. Permeability of free, space, µ 0, , III. M −1 L−2 T 4 A 2, , D. Electric field, E, , IV. M1 L1 T −2 A −2, , 1 1
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61, , ~ 27 July, 2021, Shift II, Choose the correct answer from the options, given below., A B C D, a. III II IV I, b. III IV II I, c. IV II III I, d. IV III II I, , U(J), , t, , Emech=8J, , q, C1 (V 2 − V1) , a. tan −1, ×, , mg, (, C, 1 + C 2 ) (d − t ) , , q, C 2 (V 2 − V1) , b. tan −1, ×, (, + C 2 ) (d − t ) , mg, C, 1, , , q, C1 (V1 + V 2 ) , d. tan −1, ×, , mg, (, C, 1 + C 2 ) (d − t ) , , , 6, , 10. Two Carnot engines A and B operate in series, , 4, 2, 0, , d, , q, C 2 (V1 + V 2 ) , c. tan −1, ×, , mg (C1 + C 2 ) (d − t ) , , 10, 8, , –V1, , m, +q, Air, , +V2, , 7. Given below is the plot of a potential energy, function U( x) for a system, in which a particle, is in one-dimensional motion, while a, conservative force F ( x) acts on it. Suppose, that Emech = 8 J, the incorrect statement for, this system is, , /, , Medium, (K), , x1, , x2, , x3, , x4, , x, , [where, KE = kinetic energy], a. at x > x 4 , KE is constant throughout the region., b. at x < x1, KE is smallest and the particle is, moving at the slowest speed., c. at x = x 2 , KE is greatest and the particle is, moving at the fastest speed., d. at x = x 3 , KE = 4 J., , such that engine A absorbs heat at T1 and, rejects heat to a sink at temperature T ., engine B absorbs half of the heat rejected by, engine A and rejects heat to the sink at T3., When work done in both the cases is equal,, then the value of T is, 2, a. T1 +, 3, 3, c. T1 +, 2, , 2, T3, 3, 1, T3, 3, , and B represented in the following figure., A, , inductor are connected in series across a, 250 V supply at variable frequency. Calculate, the value of inductance of inductor at which, resonance will occur. Given that the, resonant frequency is 60 Hz., , B, , Y, , a., , A, 0, 0, 1, 1, , B, 0, 1, 0, 1, , Y, 0, 1, 0, 0, , b., , A, 0, 0, 1, 1, , B, 0, 1, 0, 1, , Y, 1, 0, 1, 1, , c., , A, 0, 0, 1, 1, , B, 0, 1, 0, 1, , Y, 0, 0, 0, 1, , d., , A, 0, 0, 1, 1, , B, 0, 1, 0, 1, , Y, 0, 1, 1, 1, , a. 0.70 H, b. 70.3 mH, c. 703, . × 10−5 H, d. 70.3 H, , charge + q suspended in the electric field, produced by two conducting parallel plates, as shown. The value of deflection of, pendulum in equilibrium position will be, , 1, b. T1 +, 3, 2, d. T1 +, 3, , 11. Find the truth table for the function Y of A, , 8. A 100 Ω resistance, a 0.1 µF capacitor and an, , 9. A simple pendulum of mass m, length l and, , 3, T3, 2, 1, T3, 3
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62, , ONLINE, , 12. Figures A and B shown two long straight, , JEE Main 2021 ~ Solved Papers, , 15. What will be the magnitude of electric field at, , wires of circular cross-section (a and b with, a < b), carrying current I which is uniformly, distributed across the cross-section. The, magnitude of magnetic field B varies with, radius r and can be represented as, , point O as shown in figure? Each side of the, figure is l and perpendicular to each other., C, l, (2q), , A(–q), l, , l, (+)q, , B, , a, , Fig. B, , b, , b, r, , O, , r, , O, B, , B, c., , d., , a, , b, , b, , a, , r, , O, , r, , O, , round a circle of radius R, under the action of, their mutual gravitational attraction. The, angular speed of each particle is, G, 2R 3, , (–q), H, , q, 1, (2 2 − 1), 4 πε0 (2l 2 ), 1 2q, d., ( 2), 4 πε0 2l 2, b., , 16. A physical quantity y is represented by the, formula y = m 2r −4 g x l −3/ 2. If the percentage, errors found in y , m , r , l and g are 18, 1, 0.5,, 4 and p respectively, then find the value of x, and p., a. 5 and ± 2, 3, 16, and ±, c., 2, 3, , b. 4 and ± 3, d. 8 and ± 2, , 17. An automobile of mass m accelerates, , 13. Two identical particles of mass 1 kg each go, , a., , (q), F, , E, , a, , b., , a, , l, , 1 q, a., 4 πε0 l 2, q, c., 4 π ε0 (2l ) 2, , B, , B, , l, , l, (2q), , a., , l, , I, , Fig. A, , G(2q), , O, , l, , b, I, , D, (+q), , b., , 1 G, 2 R3, , c., , 1 1, 2R G, , d., , 2G, R3, , 14. Consider the following statements., A. Atoms of each element emit, characteristics spectrum., B. According to Bohr's postulate, an, electron in a hydrogen atom, revolves in, a certain stationary orbit., C. The density of nuclear matter depends, on the size of the nucleus., D. A free neutron is stable but a free proton, decay is possible., E. Radioactivity is an indication of the, instability of nuclei., , Choose the correct answer from the options, given below., a. A, B, C, D and E, c. B and D, , b. A, B and E, d. A, C and E, , starting from origin and initially at rest, while, the engine supplies constant power P. The, position is given as a function of time by, 1, , 3, , 8P 2 3, b. , ⋅t, 9m , , 1, , 3, , 8P 2 2, d. , ⋅t, 9m , , 9P 2 2, a. , ⋅t, 8m , 9m 2 2, c. , ⋅t, 8P , , 1, , 2, , 1, , 3, , 18. The planet Mars has two Moons, if one of, them has a period 7 h, 30 min and an orbital, radius of 90, . × 103 km. Find the mass of Mars., 2, , 4π, 11 −1 −2, 2, Take, G = 6 × 10 N m kg , , , a. 596, . × 1019 kg, , b. 325, . × 1021 kg, , c. 702, . × 10, , d. 600, . × 1023 kg, , 25, , kg, , 19. A particle of mass M originally at rest is, subjected to a force whose direction is, constant but magnitude varies with time, according to the relation, t − T 2, F = F 0 1 − , , T
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63, , ~ 27 July, 2021, Shift II, where, F 0 and T are constants. The force acts, only for the time interval 2T . The velocity v of, the particle after time 2T is, a., , 2F0T, M, , b., , F0T, 2M, , c., , 4 F0T, 3M, , d., , R=2Ω, , F0T, 3M, , 20. The resistance of a conductor at 15°C is 16 Ω, and at 100°C is 20 Ω. What will be the, temperature coefficient of resistance of the, conductor?, a. 0.010°C, c. 0.003°C, , −1, , −1, , b. 0.033°C, d. 0.042°C, , 25. A particle executes simple harmonic motion, represented by displacement function as, x(t) = A sin (ωt + φ), , −1, −1, , Section B : Numerical Type Questions, 21. In the given figure, two wheels P and Q are, connected by a belt B. The radius of P is, three times as that of Q. In case of same, rotational kinetic energy, the ratio of, I , rotational inertias 1 will be x : 1. The value, I2 , of x will be ………… ., , If the position and velocity of the particle at, t = 0 s are 2 cm and 2ω cms −1 respectively,, then its amplitude is x 2 cm, where the, value of x is ………… ., , 26. A swimmer wants to cross a river from point, A to point B. Line AB makes an angle of 30°, with the flow of river. Magnitude of velocity, of the swimmer is same as that of the river., The angle θ with the line AB should be ……°,, so that the swimmer reaches point B., B, , Q, , P, R, , 3R, , θ, , B, , 22. The difference in the number of waves when, yellow light propagates through air and, vacuum columns of the same thickness is, one. The thickness of the air column is, ………… mm., [Take, refractive index of air = 10003, ,, ., wavelength of yellow light in vacuum = 6000, Å], , 27. For the circuit shown, the value of current at, time t = 32, . s will be ………… A., 10, V (t), 5, 0, , 23. The maximum amplitude for an amplitude, , The magnitude of current through R = 2 Ω, resistor at t = 5 s is ………… mA., , 2, , 3, t (s), , 4, , R=1Ω, , V (t), , through the loop increases according to the, relation φ B (t) = 10t 2 + 20t, where φ B is in, milliwebers and t is in seconds., , 1, , Fig. (1), , modulated wave is found to be 12 V, while, the minimum amplitude is found to be 3 V., The modulation index is 06, . x, where x, is ………… ., , 24. In the given figure, the magnetic flux, , 30º, , A, , I, , 5V, , Fig. (2), , [Voltage distribution V (t) is shown by Fig. (1), and the circuit is shown in Fig. (2).]
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64, , ONLINE, , 28. A small block slides down from the top of, hemisphere of radius R = 3 m as shown in, the figure. The height h at which the block, will lose contact with the surface of the, sphere is ………… m., (Assume there is no friction between the, block and the hemisphere), , JEE Main 2021 ~ Solved Papers, , 29. The K α X-ray of molybdenum has wavelength, 0.071 nm. If the energy of a molybdenum, atom with a K electron knocked out is, 27.5 keV, the energy of this atom when an L, electron is knocked out will be ……… keV., (Round off to the nearest integer), [Take, h = 4.14 × 10−15 eV-s, c = 3 × 108 ms −1], , 30. The water is filled upto height of 12 m in a, A, , R, , θ, , tank having vertical sidewalls. A hole is made, in one of the walls at a depth h below the, water level. The value of h for which the, emerging stream of water strikes the ground, at the maximum range is ………… m., , (R–h), h, , O, , CHEMISTRY, Section A : Objective Type Questions, 1. Which one of the following set of elements, can be detected using sodium fusion extract ?, a. Sulphur, nitrogen, phosphorus, halogens, b. Phosphorus, oxygen, nitrogen, halogens, c. Nitrogen, phosphorus, carbon, sulphur, d. Halogens, nitrogen, oxygen, sulphur, OH, , 2., , C—OCH3, , Conc.HBr, , Consider the above reaction, the major, product P formed is, Br, a., , C––OCH3 b., , CH3, , C––OCH3, CH3, Br, , OBr, c., , CH3, , Br, C––OCH3 d., , C––Br, CH3, , 3. The number of neutrons and electrons,, respectively, present in the radioactive, isotope of hydrogen is, a. 1 and 1, b. 3 and 1, c. 2 and 1, d. 2 and 2, , List I, , List II, , A. Li, , I. Photoelectric cell, , B. Na, , II. Absorbent of CO 2, , C. K, , III. Coolant in fast breeder, nuclear reactor, , D. Cs, , IV. Treatment of cancer, V. Bearings for motor engines, , P, (Major product), , H3C, , 4. Match List I with List II., , Choose the correct answer from the options, given below., A B C D, A B C D, a. V I II IV, b. V II IV I, c. IV III I II, d. V III II I, , 5. Given below are two statement : one is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) SO2 ( g) is adsorbed to a large, extent than H2 ( g) on activated charcoal., Reason (R) SO2 ( g) has a higher critical, temperature than H2 ( g)., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Both A and R are correct but R is not the, correct explanation of A, b. Both A and R are correct and R is the correct, explanation of A., c. A is not correct but R is correct., d. A is correct but R is not correct.
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65, , ~ 27 July, 2021, Shift II, 6. The correct order of first ionisation enthalpy, is, , R, , a. Mg < S < Al < P, , S, , N, H, , CH3, CH3, , b. Mg < Al < S < P, N, , c. Al < Mg < S < P, , H, , d. Mg < Al < P < S, , Choose the correct option., , 7. Given below are two statements., , a., b., c., d., , Statement I Hyperconjugation is a, permanent effect., Statement II Hyperconjugation in ethyl, +, , cation (CH 3 C H 2) involves the overlapping, , D-glucose on hydrolysis. The compound A is, a. amylose, c. maltose, , Choose the correct option :, a. Both statement I and statement II are false., b. Statement I is incorrect but statement II is, true., c. Statement I is true but statement II is false., d. Both Statement I and statement II are true., , 8. Given below are two statements., , (i) DIBAL –H, (ii) H2 O, , Consider the above reaction and identify Y., , OH, , [Co(C 2O4) 3 ]3– are d 2sp3 hybridised., , a., b., c., d., , 9. To an aqueous solution containing ions such, as Al3+, Zn2+, Ca 2+, Fe 3+, Ni2+, Ba 2+ and Cu2+, conc. HCl, was added followed by H 2S. The, total number of cations precipitated during, this reaction is/are, a. 1, , b. 3, , c. 4, , d. 2, , Conc. H2SO4, ∆, , 3–, , Statement I is true but statement II is false, Both statement I and statement II are false, Statement I is false but statement II is true, Both statement I and statement II are true, , 10. Given below are two statements., Statement I Penicillin is a bacteriostatic, type antibiotic., Statement II The general structure of, penicillin is, , b. CONH2, d. COOH, , a. — CH2NH2, c. CHO, , 13., , In the light of the above statements, choose, the correct answer from the options given, below, , b. sucrose, d. lactose, , 12. R CN → R Y, , Statement I [Mn(CN) 6 ]3– , [Fe(CN) 6 ]3– and, Statement II [MnCl6 ] and [FeF6 ] are, paramagnetic and have 4 and 5 unpaired, electrons, respectively., , Both statement I and statement II are false, Statement I is false but statement II is true, Both statement I and statement II are true, Statement I is true but statement II is false, , 11. Compound A gives D-galactose and, , of C sp2 H1s bond with empty 2p orbital of, other carbon., , 3–, , COOH, , +, A, , B, , Consider the above reaction, and choose the, correct statement., a., b., c., d., , The reaction is not possible in acidic medium., Both compounds A and B are formed equally., Compound A will be the major product., Compound B will be the major product., , 14. Match List I with List II., List I, (Compound), , List II, (Effect/affected, species), , A. Carbon monoxide, , I. Carcinogenic, , B. Sulphur dioxide, , II. Metabolised by pyrus, plants, , C. Polychlorinated, biphenyls, , III. Haemoglobin, , D. Oxides of nitrogen IV. Stiffness of flower, buds, , Choose the correct answer from the options, given below :, A B C D, A B C D, a. III IV I II, b. IV I III II, c. I II III IV, d. III IV II I
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66, , ONLINE, , 15. If the Thomson model of the atom was, correct, then the result of Rutherford's gold, foil experiment would have been, a. all of the α-particles pass through the gold foil, without decrease in speed., b. α-particles are deflected over a wide range of, angles., c. all α-particles get bounced back by 180°., d. α-particles pass through the gold foil deflected, by small angles and with reduced speed., , 16. Number of Cl== O bonds in chlorous acid,, chloric acid and perchloric acid respectively, are, a. 3, 1 and 1, c. 1, 1 and 3, , b. 4, 1 and 0, d. 1, 2 and 3, , (A) Crystalline solids have long range order., (B) Crystalline solids are isotropic., (C) Amorphous solids are sometimes called, pseudo solids., (D) Amorphous solids soften over a range of, temperatures., (E) Amorphous solids have a definite heat of, fusion., , Choose the most appropriate answer from, the options given below., b. (B), (D) only, d. (A), (C), (D) only, , 18. What is A in the following reaction?, CH2Br (i), (ii) OH/H2O, , N K, , 19. The correct sequence of correct reagents for, the following transformation is, NO2, , OH, , Cl, , a. (i) Fe, HCl, (iii) NaNO 2 , HCl, 0°C, b. (i) Fe, HCl, (iii) H2O / H+, c. (i) Cl2 , FeCl3, (iii) NaNO 2 , HCl , 0°C, d. (i) Cl2 , FeCl3, (iii) Fe, HCl, , (ii) Cl2 , HCl, (iv) H2O / H+, (ii) NaNO 2 , HCl, 0°C, (iv) Cl2 , FeCl3, (ii) Fe, HCl, (iv) H2O / H+, (ii) NaNO 2 , HCl, 0°C, (iv) H2O / H+, , 20. The addition of silica during the extraction of, copper from its sulphide ore, , 17. Select the correct statements., , a. (A), (B), (E) only, c. (C), (D) only, , JEE Main 2021 ~ Solved Papers, , A, (Major, product), , a., b., c., d., , converts copper sulphide into copper silicate, converts iron oxide into iron silicate, reduces copper sulphide into metallic copper, reduces the melting point of the reaction, mixture, , Section B : Numerical type Questions, 21. The equilibrium constant for the reaction, A (s), , = M(s) + 21 O (g ), 2, , is K p = 4. At equilibrium, the partial pressure, of O2 is ……… atm. (Round off to the nearest, integer), , 22. When 400 mL of 0.2 M H2SO4 solution is, mixed with 600 mL of 0.1 M NaOH solution,, the increase in temperature of the final, solution is …………… × 10−2 K. (Round off to, the nearest integer)., [Use : H + (aq) + OH + (aq) → H 2O;, , a., , NHCH2, , ∆ yH = − 571, . kJ mol −1], , Specific heat of H 2O = 0.18 J K −1 g −1,, , CH2OH, , density of H 2O = 1.0 g cm −3., , Assume no change in volume of solution on, mixing., , b., , 23. 2 SO2( g) + O2( g) → 2SO3( g), c., , NH, , CH2NH2, d., , The above reaction is carried out in a vessel, starting with partial pressure pSO 2, = 250 m bar, pO 2 = 750 m bar and p SO 3 = 0., When the reaction is complete, the total, pressure in the reaction vessel is ………… m, bar. (Round off of the nearest integer).
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67, , ~ 27 July, 2021, Shift II, 24. 10.0 mL of 0.05 M KMnO4 solution was, consumed in a titration with 10.0 mL of given, oxalic acid dihydrate solution. The strength, of given oxalic acid solution is …… × 10−2 g/L., (Round off to the nearest integer), , 25. The total number of electrons in all bonding, molecular orbitals of O2−, 2 is ........… ., (Round off to the nearest integer), , 26. 3 moles of metal complex with formula, Co(en)2Cl3 gives 3 moles of silver chloride on, treatment with excess of silver nitrate. The, secondary valency of Co in the complex is, ………… ., , ethane is .........… degree. (Round off to the, nearest integer), , 29. For the first order reaction, A → 2B, 1 mole, of reactant A gives 0.2 moles of B after, 100 minutes. The half-life of the reaction is, …………… min. (Round off to the nearest, integer). [Use : In 2 = 069, . , In 10 = 23, ., properties of logarithms : ln x y = y ln x;, x, ln = In x − ln y], y, , 30. For the cell, Cu( s)|Cu2+ (aq) (0.1) M )|| Ag + (aq) (001, . M)| Ag( s), the cell potential, E 1 = 03095, V, ., , (Round off to the nearest integer), , 27. In a solvent 50% of an acid HA dimerises and, the rest dissociates. The van’t Hoff factor of, the acid is ………… × 10−2., (Round off to the nearest integer), , 28. The dihedral angle in staggered form of, Newman projection of 1, 1, 1-trichloro, , For the cell,, Cu( s)|Cu2+ (aq) (001, . M )|| Ag + (aq) (0001, ., M), | Ag ( s), the cell potential = …………… × 10−2 V., (Round off the nearest integer)., 2303, ., RT, , , ., = 0059, , Use :, F, , , , MATHEMATICS, Section A : Objective Type Questions, 1. The point P(a , b) undergoes the following, three transformations successively, (A) Reflection about the line y = x., (B) Translation through 2 units along the, positive direction of X-axis., π, (C) Rotation through angle about the, 4, origin in the anti-clockwise direction., If the co-ordinates of the final position of, 1 7, the point P are −, ,, , then the, , 2 2, value of 2a + b is equal to, a. 13, c. 5, , b. 9, d. 7, , 2. A possible value of ‘x’, for which the ninth, term in the expansion of, , , 25 x − 1 +, log, 3 3, , to 180, is, a. 0, c. 2, , 7, , +3, , 10, − 1 log (5 x − 1 + 1) , , , 3, , 8, , , , , is equal, , b. −1, d. 1, , 3. For real numbers α and β ≠ 0, if the point of, intersection of the straight lines, x −α y −1 z −1, =, =, 1, 2, 3, x − 4 y −6 z −7, and, =, =, β, 3, 3, lies on the plane x + 2 y − z = 8, then α − β is, equal to, a. 5, c. 3, , b. 9, d. 7
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68, , ONLINE, , 4. Let f : R → R be defined as, 1, f ( x + y ) + f ( x − y ) = 2 f ( x) f ( y ), f = − 1., 2, 20, , Then, the value of, , 1, ∑ sin(k) sin[ k + f (k)] is, k =1, , equal to, , c. cosec 2 (1) cosec (21) sin (20), , 5. Let C be the set of all complex numbers., Let S1 = { z ∈ C :|z − 2| ≤ 1} and, S 2 = { z ∈ C : z (1 + i) + z(1 − i) ≥ 4 }., , 2, , for, , 17, 3, , d., , 16, 3, , 9. The area of the region bounded by y − x = 2, 16, 3, , b., , 2, 3, , c., , 9, 2, , d., , 4, 3, , equation ( x − x 3) dy = ( y + yx 2 − 3x 4) dx , x > 2., If y(3) = 3, then y( 4) is equal to, a. 4, , b. 12, , c. 8, , d. 16, , x, , , , is, 11. The value of lim , x → 0 8 1 − sin x − 8 1 + sin x , , equal to, a. 0, c. − 4, , 5+ 2 2, 2, 5+ 2 2, d., 4, , b., , b. 4, d. − 1, , 12. Two sides of a parallelogram are along the, , 6. A student appeared in an examination, consisting of 8 true-false type questions. The, student guesses the answers with equal, probability. The smallest value of n, so that, the probability of guessing at least ‘n’ correct, 1, answers is less than , is, 2, b. 6, d. 4, , π, 7π, 7. If tan , x , tan are in arithmetic, 18 , , 9, , c., , , , 5, Then, the maximum value of z −, 2, , a. 5, c. 3, , b. 5, , 10. Let y = y ( x) be the solution of the differential, , d. sec 2 (21) sin (20) sin (2), , 3+ 2 2, 4, 3+ 2 2, c., 2, , a. 4, , a., , b. sec 2 (1) sec (21) cos(20), , a., , be 6 and 6.8, respectively. If x 3 is changed, from 8 to 7, then the mean for the new data, will be, , and x 2 = y is equal to, , a. cosec 2 (21) cos(20) cos(2), , z ∈ S1 ∩ S 2 is equal to, , JEE Main 2021 ~ Solved Papers, , π, 5π , progression and tan , y , tan are also, 9, 18 , , lines 4 x + 5 y = 0 and 7x + 2 y = 0. If the, equation of one of the diagonals of the, parallelogram is 11x + 7 y = 9, then other, diagonal passes through the point, a. (1, 2), c. (2, 1), , b. (2, 2), d. (1, 3), , 13. Let α = max { 82 sin 3x ⋅ 4 4 cos 3x } and, x ∈R, , β = max { 82 sin 3x ⋅ 4 4 cos 3 x } . If 8x 2 + bx + c = 0 is, x ∈R, , a quadratic equation whose roots are α 1/5, and β1/5, then the value of c − b is equal to, a. 42, c. 43, , b. 47, d. 50, , 14. Let f : [0, ∞) → [0, 3] be a function defined by, , in arithmetic progression, then|x − 2 y| is, equal to, , max{sint : 0 ≤ t ≤ x } , 0 ≤ x < π, f ( x) = , 2 + cos x ,, x>π, , , a. 4, , b. 3, , Then which of the following is true ?, , c. 0, , d. 1, , a. f is continuous everywhere but not, differentiable exactly at one point in (0, ∞ ), b. f is differentiable everywhere in (0, ∞ ), c. f is not continuous exactly at two points in, (0, ∞ ), d. f is continuous everywhere but not, differentiable exactly at two points in (0, ∞ ), , 8. Let the mean and variance of the frequency, distribution, x, , x1 = 2, , x2 = 6, , x3 = 8, , x4 = 9, , f, , 4, , 4, , α, , β
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69, , ~ 27 July, 2021, Shift II, 15. Let N be the set of natural numbers and a, relation R on N be defined by, R = { ( x , y ) ∈ N × N : x 3 − 3x 2 y − xy 2 + 3 y 3 = 0 }., Then the relation R is, a. symmetric but neither reflexive nor transitive, b. reflexive but neither symmetric nor transitive, c. reflexive and symmetric, but not transitive, d. an equivalence relation, , 16. Which of the following is the negation of the, statement “for all M > 0, there exists x ∈ S, such that x ≥ M” ?, , a. there exists M > 0, such that x < M for all x ∈ S, b. there exists M > 0, there exists x ∈ S such that, x≥ M, c. there exists M > 0, there exists x ∈ S such that, x< M, d. there exists M > 0, such that x ≥ M for all x ∈ S, , 17. Consider a circle C which touches the Y-axis, at (0, 6) and cuts off an intercept 6 5 on the, X-axis. Then the radius of the circle C is equal, to, a. 53, , b. 9, , c. 8, , d. 82, , Section B : Numerical type Questions, 21. Let a = $i − α $j + βk$ , b = 3$i + β$j − αk$ and, c = − α i$ − 2$j + k$ , where α and β are integers., If a ⋅ b = − 1and b ⋅ c = 10, then (a × b) ⋅ c is, equal to ……… ., , 22. The distance of the point P(3, 4 , 4) from the, point of intersection of the line joining the, points. Q(3, − 4 , − 5) and R(2, − 3, 1) and the, plane 2x + y + z = 7, is equal to …………… ., , 23. If the real part of the complex number, z=, , 3 + 2i cos θ, 1 − 3i cos θ, , π, , θ ∈ 0, is zero, then the, 2, , value of sin2 3θ + cos 2 θ is equal to ………… ., , 24. Let E be an ellipse whose axes are parallel to, the co-ordinates axes, having its center at, (3, − 4), one focus at ( 4 , − 4) and one vertex at, (5, − 4). If mx − y = 4 , m > 0 is a tangent to the, ellipse E, then the value of 5m 2 is equal to, …………… ., π, , 18. Let a, b and c be three vectors such that, a = b × (b × c). If magnitudes of the vectors, a, b and c are 2 , 1 and 2, respectively and, π, the angle between b and c is θ 0 < θ < ,, , 2, then the value of (1 + tanθ) is equal to, a. 3 + 1, , b. 2, , c. 1, , d., , 3+1, 3, , 19. Let A and B be two 3 × 3 real matrices such, that ( A 2 − B 2) is invertible matrix. If A5 = B5, and A 3B 2 = A 2 B 3, then the value of the, determinant of the matrix A 3 + B 3 is equal to, a. 2, c. 1, , b. 4, d. 0, , 20. Let f : (a , b) → R be twice differentiable, function such that f ( x) =, , x, , ∫a g (t) dt for a, , differentiable function g( x). If f ( x) = 0 has, exactly five distinct roots in (a , b), then, g( x) g′ ( x) = 0 has at least, a. twelve roots in (a , b ), b. five roots in (a , b ), c. seven roots in (a , b ), d. three roots in (a , b ), , 2, , 25. If ∫ (sin3 x) e − sin xdx = α −, 0, , (α + β) is equal to ………… ., , β 1, t e tdt, then, e ∫0, , 26. The number of real roots of the equation, , e 4x − e 3x − 4e 2x − e x + 1 = 0 is equal to ……… ., , 27. Let y = y ( x) be the solution of the differential, equation dy = e αx + ydx ; α ∈ N. If, 1, y ( log e 2) = log e 2 and y (0) = log e , then the, 2, value of α is equal to ………… ., , 28. Let n be a non-negative integer. Then the, , number of divisors of the form“4 n + 1” of the, number (10)10. (11)11.(13)13 is equal to ………… ., , 29. Let A = { n ∈ N | n2 ≤ n + 10,000} ,, B = { 3k + 1| k ∈ N } and C = { 2k | k ∈ N } , then, the sum of all the elements of the set, A ∩ (B − C ) is equal to ………… ., 1 1 1, , 30. If A = 0 1 1 and M = A + A 2 + A 3 + …… + A 20,, , , 0 0 1, then the sum of all the elements of the, matrix M is equal to …………… .
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70, , ONLINE, , JEE Main 2021 ~ Solved Papers, , Answers, For solutions scan, the QR code, , Physics, 1. (b), 11. (b), 21. 9, , 2. (b), 12. (c), 22. 2, , 3. (c), 13. (b), 23. 1, , 4. (b), 14. (b), 24. 60, , 3. (c), 13. (c), 23. 875, , 4. (d), 14. (a), 24. 1575, , 3. (d), 13. (a), 23. 1, , 4. (c), 14. (b), 24. 3, , 5. (a), 15. (d), 25. 2, , 6. (a), 16. (c), 26. 30, , 7. (b), 17. (d), 27. 1, , 8. (d), 18. (d), 28. 2, , 9. (c), 19. (c), 29. 10, , 10. (d), 20. (c), 30. 6, , 8. (d), 18. (d), 28. 60, , 9. (a), 19. (c), 29. 656, , 10. (b), 20. (b), 30. 28, , Chemistry, 1. (a), 11. (d), 21. 16, , 2. (b), 12. (c), 22. 82, , 5. (b), 15. (d), 25. 10, , 6. (c), 16. (d), 26. 6, , 7. (c), 17. (d), 27. 125, , Mathematics, 1. (b), 11. (c), 21. 9, , 2. (d), 12. (b), 22. 7, , 5. (d), 15. (b), 25. 5, , 6. (a), 16. (a), 26. 2, , 7. (c), 17. (b), 27. 2, , 8. (c), 18. (b), 28. 924, , 9. (c), 19. (d), 29. 832, , 10. (b), 20. (c), 30. 2020
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3, , AUGUST ATTEMPT ~ 26 August 2021, Shift I, , JEE Main 2021, 26 AUGUST SHIFT I, PHYSICS, Section A : Objective Type Questions, 1. The fractional change in the magnetic field, intensity at a distance r from centre on the, axis of current carrying coil of radius a to the, magnetic field intensity at the centre of the, same coil is (Take, r < a ), 3 a2, 2 r2, 2 r2, c., 3 a2, , 2 a2, 3 r2, 3 r2, d., 2 a2, b., , a., , A, 30°, 60°, , X, , c. tan, , (1 − 3 − 2 ), , (1 + 3 + 2 ), −1 ( 3 − 1 + 2 ), (1 − 3 + 2 ), , b. tan −1, d. tan, , ( 3 − 1 + 2), , (1 +, −1 (1 +, , 3 − 2), 3 − 2), , (1 − 3 − 2 ), , 3. Car B overtakes another car A at a relative, , speed of 40 ms −1. How fast will the image of, car B appear to move in the mirror of focal, length 10 cm fitted in car A, when the car B is, 1.9 m away from the car A?, a. 4 ms −1, b. 0.2 ms −1, c. 40 ms −1, d. 0.1 ms −1, , a. I, III and IV, c. I, II and III, , b. Only V, d. II, III and IV, , 5. Two narrow bores of diameter 5.0 mm and, , a. 3.62 mm, c. 5.34 mm, , B, , a. tan −1, , III. the gravitational field is same everywhere., IV. the gravitation potential is same everywhere., , 8.0 mm are joined together to form a, U-shaped tube open at both ends. If this, U-tube contains water, what is the difference, in the level of two limbs of the tube. [Take, surface tension of water T = 73, . × 10−2 Nm−1,, angle of contact = 0, g = 10 ms −2 and density, of water = 10, . × 103 kg m −3], , Y, , O, , II. the gravitational potential is zero., , V. All of the above, , the given figure are equal. The direction of, OA + OB − OC with X-axis will be, , 45°, , I. the gravitational field is zero., , Choose the most appropriate answer from, the options given below ., , 2. The magnitude of vectors OA, OB, and OC in, , C, , 4. Inside a uniform spherical shell, , b. 2.19 mm, d. 4.97 mm, , 6. An electric appliance supplies 6000 J/min, heat to the system. If the system delivers a, power of 90W. How long it would take to, increase the internal energy by 25, . × 103 J?, a. 25, . × 102 s, c. 2.4 × 103 s, , b. 4.1 × 101 s, d. 25, . × 101 s, , 7. An inductor coil stores 64 J of magnetic field, energy and dissipates energy at the rate of, 640 W when a current of 8A is passed, through it. If this coil is joined across an ideal, battery, find the time constant of the circuit, in seconds., a. 0.4, , b. 0.8, , c. 0.125, , d. 0.2
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4, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 8. A series L-C-R circuit driven by 300 V at a, frequency of 50 Hz contains a resistance, R = 3 kΩ, an inductor of inductive reactance, X L = 250 πΩ and an unknown capacitor. The, value of capacitance to maximise the, average power should be (Take, π 2 = 10), a. 4 µF, , b. 25 µF, , c. 400 µF, , 13. A solid metal sphere of radius R having, charge q is enclosed inside the concentric, spherical shell of inner radius a and outer, radius b as shown in figure. The approximate, variation electric field as a function of, distance r from centre O is given by, , d. 40 µF, , 9. Identify the logic operation carried out by, the given circuit., , b, , X, , A, , a, , Z, B, , Y, , a. OR, , b. AND, , c. NOR, , d. NAND, , 10. A particular hydrogen like ion emits, , a., , E, , radiation of frequency 292, . × 1015 Hz when it, makes transition from n = 3 to n = 1. The, frequency in Hz of radiation emitted in, transition from n = 2 to n = 1will be, a. 0.44 × 1015, c. 4.38 × 1015, , b. 657, . × 1015, d. 2.46 × 1015, , 11. In a photoelectric experiment ultraviolet light, of wavelength 280 nm is used with lithium, cathode having work-function φ = 25, . eV. If, the wavelength of incident light is switched, to 400 nm, find out the change in the, stopping potential. (h = 663, . × 10−34 Js, and, , b., , b. 1.1 V, , c. 1.9 V, , a, , R, , R, , a, , b, , R, , a, , b, , R, , a, , b, , r, , E, , c = 3 × 108 ms −1), a. 1.3 V, , R, , r, , d. 0.6 V, , 12. In the given figure, the emf of the cell is 2.2 V, , c., , E, , and if internal resistance is 06, . Ω. Calculate, the power dissipated in the whole circuit, 4W, 4W, , 4W, , A, , B, 2W, , r, , 8W, , d., , E, , 8W, , 2.2 V, r =0.6W, , a. 1.32 W, , b. 0.65 W, , c. 2.2 W, , d. 4.4 W, , r
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5, , AUGUST ATTEMPT ~ 26 August 2021, Shift I, 14. The rms speeds of the molecules of, hydrogen, oxygen and carbondioxide at the, same temperature are vH , v O and VCO 2, respectively, then, a. vH > v O > v CO2, c. vH = v O > v CO2, , b. v CO2 > v O > vH, d. vH = v O = v CO2, , 15. In a screw gauge, 5th division of the circular, scale coincides with the reference line when, the ratchet is closed. There are 50 divisions, on the circular scale, and the main scale, moves by 0.5 mm on a complete rotation., For a particular observation the reading on, the main scale is 5 mm and the 20th division, of the circular scale coincides with reference, line. Calculate the true reading., a. 5.00 mm, c. 5.15 mm, , b. 5.25 mm, d. 5.20 mm, , 16. What equal length of an iron wire and a, copper-nickel alloy wire, each of 2 mm, diameter connected parallel to give an, equivalent resistance of 3Ω?, (Given, resistivities of iron and copper-nickel, alloy wire are 12 µΩ cm and 51 µΩ cm, respectively), a. 82 m, c. 110 m, , b. 97 m, d. 90 m, , 17. The initial mass of a rocket is 1000 kg., Calculate at what rate the fuel should be, burnt, so that the rocket is given an, acceleration of 20 ms −1. The gases come out, at a relative speed of 500 ms −1 with respect, to the rocket [Use, g = 10 m/s 2], a. 60, . × 102 kg s −1, c. 10 kg s −1, , b. 500 kg s −1, d. 60 kg s −1, , 18. If E , L, M and G denote the quantities as, energy, angular momentum, mass and, constant of gravitation respectively, then the, dimension of P in the formula P = EL2M −5G −2, is, a. [M 0L1T 0 ], c. [M1L1T −2 ], , b. [M −1L−1T 2 ], d. [M 0L0 T 0 ], , 19. The material filled between the plates of a, parallel plate capacitor has resistivity, 200 Ωm. The value of capacitance of the, capacitor is 2pF. If a potential difference of, 40 V is applied across the plates of the, , capacitor, then the value of leakage current, flowing out of the capacitor is (Given, the, value of relative permittivity of material is, 50.), a. 9.0 µA, c. 0.9 mA, , b. 9.0 mA, d. 0.9 µA, , 20. Statement I By doping silicon, semiconductor with pentavalent material,, the electrons density increases., Statement II The n-type semiconductor has, net negative charge., In the light of the above statements, choose, the most appropriate answer from the options, given below., a. Statement I is true but statement II is false., b. Statement I is false but statement II is true., c. Both statement I and statement II are true., d. Both statement I and statement II are false., , Section B : Numerical Type Questions, 21. A uniform chain of length 3 m and mass 3 kg, overhangs a smooth table with 2 m laying on, the table. If k is the kinetic energy of the, chain in joule as it completely slips off the, table, then the value of k is ……… ., (Take, g = 10 m/s 2), , 22. The electric field in a plane electromagnetic, wave is given by, E = 200cos, 05, V, . × 103 , rad, x − 15, . × 1011, × t $j, , , , m, s, , , m, If this wave falls normally on a perfectly, reflecting surface having an area of 100 cm 2 ., If the radiation pressure exerted by the EM, wave on the surface during a 10 min exposure, x, is 9 ⋅ Find the value of x., 10, , 23. A source and a detector move away from, each other in absence of wind with a speed, of 20 m/s with respect to the ground. If the, detector detects a frequency of 1800 Hz of, the sound coming from the source, then the, original frequency of source considering, speed of sound in air 340 m/s will be ........, Hz.
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6, , ONLINE, , 24. Two spherical balls having equal masses, with radius of 5 cm each are thrown, upwards along the same vertical direction at, an interval of 3s with the same initial velocity, of 35 m/s, then these balls collide at a height, of .......... m. (Take, g = 10 m/s 2), , 25. A soap bubble of radius 3 cm is formed, inside the another soap bubble of radius, 6 cm. The radius of an equivalent soap, bubble which has the same excess pressure, as inside the smaller bubble with respect to, the atmospheric pressure is ........ cm., , JEE Main 2021 ~ Solved Papers, , y = 10, . mm cos (157, . cm−1 ) x sin(785, . s −1 ) t., The node closest to the origin in the region, x > 0 will be at x is ……… cm., , 29. White light is passed through a double slit, and interference is observed on a screen, 1.5 m away. The separation between the slits, is 0.3 mm. The first violet and red fringes are, formed 2.0 mm and 3.5 mm away from the, central white fringes. The difference in, wavelengths of red and violet light is ........., nm., , 30. Consider a badminton racket with length, scales as shown in the figure., , 26. An amplitude modulated wave is, represented by C m (t) = 10 (1 + 02, . cos 12560t), sin(111 × 104t) V., The modulating frequency in kHz will be …… ., , 27. Two short magnetic dipoles m1 and m 2 each, , P, , A, , 2, , having magnetic moment of 1 Am are, placed at point O and P, respectively. The, distance between OP is 1 m. The torque, experienced by the magnetic dipole m 2 due, to the presence of m1 is …… × 10−7 Nm., m1, , m2, P, , O, , 28. Two travelling waves produces a standing, wave represented by equation., , r, 2, 6r, , 2r, , If the mass of the linear and circular portions, of the badminton racket are same (M ) and the, mass of the threads are negligible, the, moment of inertia of the racket about an axis, perpendicular to the handle and in the plane, r, of the ring at, distance from the end A of the, 2, handle will be ........ Mr 2 ., , CHEMISTRY, Section A : Objective Type Questions, , 3. Which one of the following when dissolved in, , 1. Which one of the following complexes is, , water gives coloured solution in nitrogen, atmosphere?, , violet in colour?, a. [Fe(CN) 6 ] 4−, c. Fe4 [Fe(CN6 )] 3 .H2O, , b. [Fe(SCN) 6 ] 4−, d. [Fe(CN) 5 NOS] 4−, , 2. Which one of the following is correct for the, adsorption of a gas at a given temperature, on a solid surface?, a. ∆H > 0, ∆S > 0, c. ∆H < 0, ∆S < 0, , b. ∆H > 0, ∆S < 0, d. ∆H < 0, ∆S > 0, , b. AgCl, d. Cu 2Cl2, , a. CuCl2, c. ZnCl2, , 4. The major products formed in the following, reaction sequence A and B are, , CH3, , Br2, KOH, , A+B
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7, , AUGUST ATTEMPT ~ 26 August 2021, Shift I, 6. The major product formed in the following, a. A=, , ,, , —C, OK, , reaction is, , B=CHBr3, , HBr, , Major product, , (excess), , b. A=, , —CCH2Br , B=, , —CCH2OH, , Br, a., , b., Br, , Br, , Br, , Br, Br, , c. A=, , —CCBr3 ,, , B=, , —CHO, , Br, , —CCH3 ,, , B=, , Br, Br, , formaldehyde is, —CCH3, , HO, , Br, , reaction is, COOH, SOCl2, CH3OH, , NH2, , CO2CH3, a., , a. bakelite, , b. polyester, , c. melamine, , d. nylon 6,6, , 8. Given below are two statements., , 5. The major product formed in the following, , N, H, , d., , 7. The polymer formed on heating novolac with, HO, , Br, d. A=, , c., , Major, product, , Statement I The limiting molar conductivity, of KCl (strong electrolyte) is higher compared, to that of CH 3COOH (weak electrolyte)., Statement II Molar conductivity decreases, with decrease in concentration of electrolyte., In the light of the above statements, choose, the most appropriate answer from the, options given below, a. Statement I is true but statement II is false., , N, H.HCl, , NH2HCl, , b. Statement I is false but statement II is true., c. Both statement I and statement II are true., CO2M, , Cl, b., N, H, , d. Both statement I and statement II are false., , 9. The correct options for the products A and B, , NH2, , of the following reactions are, OH, , CO2CH3, A, , c., N, H, , Br2 (excess), , Br2, , H2 O, , CS2, <5ºC, , NH2HCl, OH, , COCl, , a., , Br, A=, , OH, Br, , Br, ,, , B=, , d., N, H, , B, , NH2, , Br, , Br
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8, , ONLINE, , b., , ,, , H3C, , B=, , Br, , Br, , OH, , OH, , A=, , ,, , Br, B=, , Br, , Cl, , b. IV, , III, , CH3, , c. I, , IV, , CH2I, , d. III, , 13. Which one of the following methods is most, , b. Clark’s method, OH, ,, , Br, , B=, , c. Calgon’s method, d. Permutit method, , 14. Given below are two statements., Br, , 10. The conversion of hydroxyapatite occurs due, to presence of F − ions in water. The correct, formula of hydroxyapatite is, a. [3Ca3 (PO 4 ) 2 Ca(OH) 2 ], b. [3Ca(OH) 2 CaF2 ], c. [Ca3 (PO 4 ) 2 CaF2 ], d. [3Ca3 (PO 4 ) 2 CaF2 ], , 11. Given below are two statements., Statement I In the titration between strong, acid and weak base methyl orange is suitable, as an indicator., Statement II For titration of acetic acid with, NaOH phenolphthalein is not a suitable, indicator., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Statement I is false but statement II is true., b. Statement I is true but statement II is false., c. Both statement I and statement II are true., d. Both statement I and statement II are false., , 12. Among the following compounds I-IV, which, one forms a yellow precipitate on reacting, (i) NaOH, (ii) dil. HNO 3, (iii) AgNO 3 ?, , CH3, , a. Synthetic resin method, , OH, , sequentially with, , II, , suitable for preparing deionised water?, , Br, , A=, , I, , a. II, , Br, , d., , Br, , Cl, , Br, , Br, c., , Cl, , OH, , OH, Br, A=, , JEE Main 2021 ~ Solved Papers, , Statement I The choice of reducing agent for, metals extraction can be made by using, Ellingham diagram, a plot of ∆G vs, temperature., Statement II The value of ∆S increases from, left to right in Ellingham diagram., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Both statement I and statement II are true., b. Statement I is false but statement II is true., c. Both statement I and statement II are false., d. Statement I is true but statement II is false., , 15. What are the products formed in sequence, when excess of CO2 is passed in slaked lime?, a. Ca(HCO 3 ) 2 ,CaCO 3, c. CaO, Ca(HCO 3 ) 2, , b. CaCO 3 ,Ca(HCO 3 ) 2, d. CaO, CaCO 3, , 16. Given below are two statements., Statement I According to Bohr’s model of an, atom, qualitatively the magnitude of velocity, of electron increases with decrease in positive, charges on the nucleus as there is no strong, hold on the electron by the nucleus., Statement II According to Bohr’s model of an, atom, qualitatively the magnitude of velocity of, electron increases with decrease in principal, quantum number., In the light of the above statements, choose, the most appropriate answer from the options, given below.
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9, , AUGUST ATTEMPT ~ 26 August 2021, Shift I, a. Both statement I and statement II are false., b. Both statement I and statement II are true., c. Statement I is false but statement II is true., d. Statement I is true but statement II is false., , Section B : Numerical Type Questions, 21. AB 3 is an interhalogen T -shaped molecule., The number of lone pairs of electron on A is, ………. . (Integer answer), , 17. The correct sequential addition of reagents, in the preparation of 3-nitrobenzoic acid, from benzene is, , 22. These are physical properties of an element., +, , a. Br2 /AlBr3 , HNO 3 /H2SO 4 , Mg /ether, CO 2 ,H3O, b. Br2 / AlBr3 , NaCN, H3O + , HNO 3 / H2SO 4, c. Br2 /AlBr3 , HNO 3 /H2SO 4 , NaCN, H3O +, d. HNO 3 /H2SO 4 , Br2 / AlBr3 , Mg/ether, CO 2 , H3O +, , 18. Given below are two statements., Statement I Frenkel defects are vacancy as, well as interstitial defects., Statement II Frenkel defect leads to colour in, ionic solids due to presence of F-centres., Choose the most appropriate answer for the, statements from the options given below., a. Statement I is false but Statement II is true., b. Both statement I and statement II are true., c. Statement I is true but statement II is false., d. Both Statement I and statement II are false., , 19. Choose the incorrect statement., a. Cl2 is more reactive than CIF., b. F2 is more reactive than CIF., c. On hydrolysis CIF froms HOCl and HF., d. F2 is a stronger oxidising agent than Cl2 in, aqueous solution., , 20. Excess of isobutane on reaction with Br2 in, presence of light at 125°C gives which one of, the following, as the major product?, Br, , a. CH3 C CH2 Br, , CH3, b. CH3 C H CH2Br, , CH2Br, c. CH3 C H CH2Br, , CH3, CH3, , d. CH3 C Br, , CH3, , A. Sublimation enthalpy, B. Ionisation enthalpy, C. Hydration enthalpy, D. Electron gain enthalpy, , The total number of above properties that, affect the reduction potential is ……… (Integer, answer), , 23. Of the following four aqueous solutions,, total number of those solutions whose, freezing point is lower than that of 0.10 M, C 2H5OH is ………… . (Integer answer), (i) 0.10 M Ba3 (PO 4 ) 2, (iii) 0.10 M KCl, , (ii) 0.10 M Na2SO 4, (iv) 0.10 M Li3PO 4, , 24. The OH− concentration in a mixture of, 5.0 mL of 0.0504 M NH 4Cl and 2 mL of, 0.0210 M NH 3 solution is x × 10−6 M. The, value of x is ……… . (Nearest integer), [Given, K w = 1 × 10−14 and K b = 18, . × 10−5], , 25. The number of 4 f electrons in the ground, state electronic configuration of Gd 2+ is, [Atomic number of Gd is 64.], , 26. The ratio of number of water molecules in, Mohr’s salt and potash alum is …………, × 10−1., (Integer answer), , 27. The following data was obtained for, chemical reaction given below at 975 K., 2NO( g) + 2H 2( g) → N2( g) + 2H 2O( g), [NO] mol L −1 [H2 ] mol L −1 Rate mol L −1, A., , 8 × 10−5, , 8 × 10−5, , 7 × 10−9, , B., , 24 × 10−5, , 8 × 10−5, , 21, . × 10−8, , C., , −5, , 24 × 10, , −5, , 32 × 10, , 8.4 × 10−8, , The order of the reaction with respect to NO, is ………… . [Integer answer]
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10, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 28. The Born-Haber cycle for KCl is evaluated, with the following data :, ∆ f H° for KCl = − 4367, . kJ mol −1, ∆ subH° for K = 892, . kJ mol −1,, ∆ionisationH° for K = 4190, . kJ mol −1;, . kJ mol−1,, ∆ electron gain H ∪ for Cl(g) = − 3486, −1, ∆bondH° for Cl2 = 2430, . kJ mol, The magnitude of lattice enthalpy of KCl in kJ, mol −1 is ……… (Nearest integer), , 29. The total number of negative charge in the, tetrapeptide, Gly-Glu-Asp-Tyr, at pH 12.5 will, be ……… . (Integer answer), , 30. An aqueous KCl solution of density 1.20gmL −1, has a molality of 3.30 mol kg −1. The molarity, of the solution in mol L−1 is ……… ., (Nearest integer), [Molar mass of KCl = 74.5 ], , MATHEMATICS, Section A : Objective Type Questions, 1. The sum of solutions of the equation, , π π, π, π, cos x, = |tan2x|, x∈ − , − , − is, 2 2 4, 4, 1 + sin x, 11 π, a. −, 30, , π, b., 10, , 7π, c. −, 30, , π, d. −, 15, , 2. The mean and standard deviation of 20, observations were calculated as 10 and 2.5, respectively. It was found that by mistake, one data value was taken as 25 instead of, 35. If α and β are the mean and standard, deviation respectively for correct data, then, (α , β) is, a. (11, 26), c. (11, 25), , b. (10.5, 25), d. (10.5, 26), , x2, y2, +, = 1. Let P be a point in, 8, 4, the second quadrant such that the tangent, at P to the ellipse is perpendicular to the, line x + 2 y = 0. Let S and S′ be the foci of the, ellipse and e be its eccentricity. If A is the, area of the ∆SPS' then, the value of (5 − e 2) ⋅ A, is, b. 12, , c. 14, , d. 24, , 4. Lety = y ( x) be a solution curve of the, differential equation ( y + 1) tan2 x dx + tan x, π, dy + y dx = 0, x ∈ 0, . If lim + xy ( x) = 1,, 2, x→ 0, π, , then the value of y is, 4, π, a. −, 4, , π, b. − 1, 4, , π, c. + 1, 4, , P( A) = p and P(B) = 2p. The largest value of p,, 5, for which P (exactly one of A , B occurs) = , is, 9, 1, 3, 4, c., 9, , π, d., 4, , 2, 9, 5, d., 12, , b., , a., , π, 6. Let θ ∈ 0, . If the system of linear, , 2, equations, (1 + cos 2 θ) x + sin2 θy + 4 sin3θz = 0, cos 2 θx + (1 + sin2 θ) y + 4 sin3θz = 0, cos 2 θx + sin2 θ y + (1 + 4 sin3θ) z = 0, has a non-trivial solution, then the value of θ is, a., , 3. On the ellipse, , a. 6, , 5. Let A and B be independent events such that, , 4π, 9, , b., , 7π, 18, , c., , , , , , , , , , π, 18, , d., , 1− x , ,0 < x < 1., x , , 7. Let f ( x) = cos 2 tan−1sin cot −1, Then,, a. (1 − x ) 2 f ′ (x ) − 2( f (x )) 2 = 0, b. (1 + x ) 2 f ′ (x ) + 2( f (x )) 2 = 0, c. (1 − x ) 2 f ′ (x ) + 2( f (x )) 2 = 0, d. (1 + x ) 2 f ′ (x ) − 2 f (x )) 2 = 0, , 8. The sum of the series, , 1, 2, 22, + 2, + 4, + ...., x+1 x +1 x +1, 2100, , +, x, , 2100, , a. 1 +, c. 1 −, , , when x = 2 is, +1, , 2101, 4 −1, 2100, 101, , 4100 − 1, , b. 1 +, d. 1 −, , 5π, 18, , 2100, −1, 2101, , 101, , 4, , 4101 − 1
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11, , AUGUST ATTEMPT ~ 26 August 2021, Shift I, 9. If 20C r is the coefficient of x r in the expansion, of (1 + x) , then the value of, 20, , 20, , Σ, , r= 0, , r, , 15. A plane P contains the line, x + 2 y + 3z + 1 = 0 = x − y − z − 6 and is, , 2 20, , C r is, , perpendicular to the plane –2x + y + z + 8 = 0., Then which of the following points lies on P ?, , equal to, a. 420 × 219, c. 380 × 218, , b. 380 × 219, d. 420 × 218, , a. (− 1, 1, 2), c. (1, 0, 1), , 10. Out of all the patients in a hospital 89% are, found to be suffering from heart ailment and, 98% are suffering from lungs infection. If K%, of them are suffering from both ailments,, then K can not belong to the set, a. {80, 83, 86, 89}, b. {84, 86, 88, 90}, c. {79, 81, 83, 85}, d. {84, 87, 90, 93}, , 16., , b. (0, 1, 1), d. (2, − 1, 1), , 2, 1, , , 5, 5 , B = 1 0 , i = −1 , and, If A = , , , 1, i 1, −2, 5, 5, T, Q = A BA, then the inverse of the matrix, A Q 2021AT is equal to, 1, − 2021, , a. 5, , 1 , 2021, , 5 , 0, 1, c. , , 2021i 1, , z − 1 π, = represents a, z + 1 4, , 11. The equation arg , , 0, 1, b. , , −2021i 1, 1 −2021i , d. , , 1 , 0, , circle with, a. centre at (0, − 1) and radius 2, b. centre at (0, 1) and radius 2, c. centre at (0, 0) and radius 2, d. centre at (0, 1) and radius 2, , 17. If the sum of an infinite GP a , ar , ar 2 , ar 3 , ... is, 15 and the sum of the squares of its each, term is 150, then the sum of ar 2 , ar 4 , ar 6, …, is, a. 5/2, , 12. Let a = $i + $j + k$ and b = $j − k$ . If c is a vector, such that a × c = b and a ⋅ c = 3, then a ⋅ (b × c), is equal to, a. − 2, c. 6, , b. − 6, d. 2, , 4 x 2 + 4 y 2 + 120x + 675 = 0, passes through the, point (− 30, 0) and is tangent to the parabola, y 2 = 30x, then the length of this chord is, b. 7, d. 3 5, , , x + 1 2 x − 1 2, The value of ∫ , +, − 2, , x − 1, x + 1, , −1 2 , 1/ 2, , 14., , is, a. log e 4, b. log e 16, c. 2log e 16, d. 4 log e (3 + 2 2 ), , 1, n→ ∞ n, , 18. The value of lim, 1, a. tan −1(2), 2, c. tan −1(4 ), , 13. If a line along a chord of the circle, , a. 5, c. 5 3, , b. 1/2, , 1/ 2, , dx, , c. 25/2, 2n − 1, , Σ, , r= 0, , d. 9/2, , n2, is, n + 4r2, 2, , 1, b. tan −1(4 ), 2, 1, d. tan −1(4 ), 4, , 19. Let ABC be a triangle with A( − 3, 1) and, , π, . If the equation of the, 2, median through B is 2x + y − 3 = 0 and the, equation of angle bisector of C is, 7x − 4 y − 1 = 0, then tanθ is equal to, ∠ACB = θ, 0 < θ <, , a. 1/2, , b. 3/4, , c. 4/3, , d. 2, , 20. If the truth value of the Boolean expression, , (( p ∨ q) ∧ (q → r) ∧ (~ r) → ( p ∧ q) is false, then, the truth values of the statements, p,q and r, respectively can be, a. T F T, , b. F F T, , c. T F F, , d. F T F
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12, , ONLINE, , Section B : Numerical Type Questions, 21. Let z =, , minimum and the circumference of the circle, 4, , is k (m), then + 1 k is equal to, π, , , 1− i 3, , and i = −1. Then the value of, 2, 3, 3, 1, 1, , , 21 + z + + z 2 + 2 , , , z, z , , 26. The area of the region, S = {(x , y ) : 3x 2 ≤ 4 y ≤ 6 x + 24 } is, , 3, , 3, , 1, 1, + z 3 + 3 + ... + z 21 + 21 is, , , z , z , , 27. The locus of a point, which moves such that, the sum of squares of its distances from the, points (0, 0), (1, 0), (0, 1) (1, 1) is 18 units, is a, circle of diameter d. Then, d 2 is equal to, , 22. The sum of all integral values of k ( k ≠ 0) for, which the equation, , 2, 1, 2, −, = in x has, x −1 x −2 k, , no real roots, is, , 28. If y = y ( x) is an implicit function of x such that, log e ( x + y ) = 4 xy , then, , 23. Let the line L be the projection of the line, , x −1 y − 3 z − 4, in the plane x − 2 y − z = 3., =, =, 2, 1, 2, If d is the distance of the point (0, 0, 6) from L,, then d 2 is equal to, , 24. If 1P1 + 2 ⋅2 p1 + 3 ⋅3 P3 + ... + 15 ⋅15P15 = qPr − s ,, 0 ≤ s ≤ 1 , then, , q+ s, , JEE Main 2021 ~ Solved Papers, , d2y, at x = 0 is equal to, dx 2, , 29. The number of three-digit even numbers,, formed by the digits 0, 1, 3, 4, 6, 7, if the, repetition of digits is not allowed, is, , 30. Let a , b ∈ R, b ≠ 0. Define a function, a sin π (x − 1), for x ≤ 0, , 2, f (x ) = , tan2x − sin2x, , for x > 0, , , bx 3, , C r − s is equals to, , 25. A wire of length 36 m is cut into two pieces,, one of the pieces is bent to form a square, and the other is bent to form a circle. If the, sum of the areas of the two figures is, , If f is continuous at x = 0, then 10 − ab is equal to, , Answers, For solutions scan, the QR code, , Physics, 1. (d), 11. (a), 21. 40, , 2. (a), 12. (c), 22. 354, , 3. (d), 13. (a, b), 23. 2025, , 4. (a), 14. (a), 24. 50, , 5. (b), 15. (c), 25. 2, , 6. (a), 16. (b), 26. 2, , 7. (d), 17. (d), 27. 1, , 8. (a), 18. (d), 28. 1, , 9. (c), 19. (c), 29. 300, , 10. (d), 20. (a), 30. 52, , Chemistry, 1. (d), 11. (b), 21. 2, , 2. (c), 12. (b), 22. 3, , 3. (a), 13. (a), 23. 4, , 4. (a), 14. (d), 24. 3, , 5. (c), 15. (b), 25. 7, , 6. (a), 16. (c), 26. 5, , 7. (a), 17. (d), 27. 1, , 8. (d), 18. (c), 28. 718, , 9. (b), 19. (a), 29. 4, , 10. (a), 20. (d), 30. 3, , 3. (a), 13. (d), 23. 26, , 4. (d), 14. (b), 24. 136, , 5. (d), 15. (b), 25. 36, , 6. (b), 16. (b), 26. 27, , 7. (c), 17. (b), 27. 16, , 8. (d), 18. (b), 28. 40, , 9. (d), 19. (c), 29. 52, , 10. (c), 20. (c), 30. 14, , Mathematics, 1. (a), 11. (b), 21. 13, , 2. (d), 12. (a), 22. 66
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13, , AUGUST ATTEMPT ~ 26 August 2021, Shift II, , JEE Main 2021, 26 AUGUST SHIFT II, PHYSICS, Section A : Objective Type Questions, , 5. The angle between vector A and ( A − B) is, , 1. The temperature of equal masses of three, different liquids x , y and z are 10ºC, 20ºC and, 30ºC, respectively. The temperature of, mixture when x is mixed with y is 16ºC and, that when y is mixed with z is 26°C. The, temperature of mixture when x and z are, mixed will be, a. 28.32ºC, c. 23.84ºC, , b. 25.62ºC, d. 20.28ºC, , B, , A, β, , 120º, , –B, , 2. The de-Broglie wavelength of a particle, , having kinetic energy E is λ. How much extra, energy must be given to this particle, so that, the de-Broglie wavelength reduces to 75% of, the initial value ?, 1, a. E, 9, , b., , 7, E, 9, , c. E, , d., , 16, E, 9, , 3. A particle of mass m is suspended from a, ceiling through a string of length L. The, particle moves in a horizontal circle of radius, L, . The speed of particle will, r such that r =, 2, be, a. rg, , b. 2rg, , c. 2 rg, , d., , 4. A cylindrical container of volume, , rg, 2, , 4.0 × 10− 3 m3 contains one mole of hydrogen, and two moles of carbon dioxide. Assume, the temperature of the mixture is 400 K. The, pressure of the mixture of gases is, [Take, gas constant = 8.3 J mol− 1K − 1], a. 249 × 101 Pa, c. 24.9 × 105 Pa, , b. 24.9 × 103 Pa, d. 24.9 Pa, , , B , , −, 2 , a. tan − 1, 3, , , A −B, , 2 , A , b. tan − 1, , 0.7B , 3B , c. tan − 1, , 2A − B , B cos θ , d. tan − 1, , A − B sin θ , , 6. A light beam is described by, , x, E = 800 sin ωt − . An electron is allowed to, , c, move normal to the propagation of light, beam with a speed 3 × 107 ms − 1. What is the, maximum magnetic force exerted on the, electron?, a. 1.28 × 10− 17 N, b. 1.28 × 10− 18 N, c. 12.8 × 10− 17 N, d. 12.8 × 10− 18 N
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14, , ONLINE, , 7. The two thin co-axial rings, each of radius a, , and having charges + Q and − Q respectively,, are separated by a distance of s. The, potential difference between the centres of, the two rings is, , JEE Main 2021 ~ Solved Papers, , 10. A parallel-plate capacitor with plate area A, has separation d between the plates. Two, dielectric slabs of dielectric constant K1 and, K 2 of same area A / 2 and thickness d / 2 are, inserted in the space between the plates., The capacitance of the capacitor will be given, by, , a., , Q, 2 πε0, , 1, +, a, , , , s + a , , b., , Q, 4 πε0, , 1, +, a, , , , s + a , , Q, 4 πε0, , 1, −, a, , , , 2, 2, s + a , , K1, , c., , Q, 2 πε0, , 1, −, a, , , , s + a , , K2, , d., , 1, , 2, , 2, , 1, , 2, , +Q, , 2, , 1, , d, , 1, , 2, , 2, , –Q, , 8. If you are provided a set of resistances, , 2Ω , 4 Ω , 6Ω and 8Ω. Connect these, resistances, so as to obtain an equivalent, 46, resistance of, Ω., 3, a. 4 Ω and 6 Ω are in parallel with 2 Ω and 8 Ω in, series., b. 6 Ω and 8 Ω are in parallel with 2 Ω and 4 Ω in, series., c. 2 Ω and 6 Ω are in parallel with 4 Ω and 8 Ω in, series., d. 2 Ω and 4 Ω are in parallel with 6 Ω and 8 Ω in, series., , 9. The solid cylinder of length 80 cm and mass, M has a radius of 20 cm. Calculate the, density of the material used, if the moment, of inertia of the cylinder about an axis CD, parallel to AB as shown in figure is 2.7 kg m2 ., C, , A, , a., , ε0 A 1, K 1K 2 , +, , d 2 K1 + K 2 , , b., , ε0 A 1, K 1K 2 , , +, d 2 2 (K 1 + K 2 ) , , c., , ε0 A 1 K 1 + K 2 , , +, d 2, K 1K 2 , , d., , ε0 A 1 2(K 1 + K 2 ) , , +, d 2, K 1K 2 , , 11. A bomb is dropped by fighter plane flying, horizontally. To an observer sitting in the, plane, the trajectory of the bomb is a, a. hyperbola, b. parabola in the direction of motion of plane, c. straight line vertically down the plane, d. parabola in a direction opposite to the motion, of plane, , 12. At time t = 0, a material is composed of two, L M, , L/2, , r, , a. 14.9 kg / m3, c. 75, . × 102 kg / m3, , B, , D, , b. 75, . × 101 kg / m3, d. 149, . × 102 kg / m3, , radioactive atoms A and B, where, NA (0) = 2NB (0). The decay constant of both, kind of radioactive atoms is λ. However, A, disintegrates to B and B disintegrates to C ., Which of the following figures represents the, evolution of NB (t) / NB (0) with respect to time, t?, N A (0) = Number of A atoms at t = 0, N (0) = Number of B atoms at t = 0 , B,
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15, , AUGUST ATTEMPT ~ 26 August 2021, Shift II, 14. A refrigerator consumes an average 35 W, , power to operate between temperature, − 10º C to 25ºC. If there is no loss of energy,, then how much average heat per second, does it transfer ?, , 1, a., , NB(t), NB(0), , a. 263 J/s, b. 298 J/s, c. 350 J/s, d. 35 J/s, , t, , 1/2λ, , 15. An electric bulb of 500 W at 100 V is used in, a circuit having a 200 V supply. Calculate the, resistance R to be connected in series with, the bulb, so that the power delivered by the, bulb is 500 W., , 1, b., , NB(t), NB(0), , a. 20 Ω, b. 30 Ω, c. 5 Ω, d. 10 Ω, , t, , 1/λ, , 16. Four NOR gates are connected as shown in, c., , figure., The truth table for the given figure is, , 1, , A, , NB(t), NB(0), , Y, , t, , 1/2λ, , B, , a., 1, d., , NB(t), NB(0), , 1/2λ, , t, , b., A, , B, , Y, , A, , B, , Y, , 0, , 0, , 1, , 0, , 0, , 0, , 0, , 1, , 0, , 0, , 1, , 1, , 1, , 0, , 1, , 1, , 0, , 1, , 1, , 1, , 0, , 1, , 1, , 0, , c., , d., , 13. A transmitting antenna at top of a tower has, , A, , B, , Y, , A, , B, , Y, , a height of 50 m and the height of receiving, antenna is 80 m. What is range of, communication for line of sight (LOS) mode ?, [Use radius of Earth = 6400 km], , 0, , 0, , 0, , 0, , 0, , 1, , 0, , 1, , 1, , 0, , 1, , 0, , 1, , 0, , 0, , 1, , 0, , 0, , a. 45.5 km, c. 144.1 km, , 1, , 1, , 1, , 1, , 1, , 1, , b. 80.2 km, d. 57.28 km
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16, , ONLINE, , a. 125 cm, c. 12.5 cm, , 17. Match List-I with List-II., List-I, Magnetic induction, , 1., , [ML2 T − 2 A − 1], , B., , Magnetic flux, , 2., , [ML−1A], , C., , Magnetic permeability 3., , [MT − 2 A − 1], , D., , Magnetisation, , [MLT − 2 A − 2 ], , 4., , B, 4, 2, , C, 1, 4, , D, 3, 1, , b., d., , A, 2, 3, , B, 1, 1, , C, 4, 4, , Section B : Numerical Type Questions, 21. Two waves are simultaneously passing, , Choose the most appropriate answer from the, options given below., A, 2, 3, , b. 1250 cm, d. 1.25 cm, , List-II, , A., , a., c., , JEE Main 2021 ~ Solved Papers, , D, 3, 2, , 18. In the given circuit the AC source has, , ω = 100 rad s − 1. Considering the inductor and, capacitor to be ideal, what will be the current, I flowing through the circuit?, 100 µF 100 Ω, , through a string and their equations are, y1 = A1sin k( x − vt), y 2 = a 2 sin k( x − vt + x 0 )., [Given, amplitudes A1 = 12 mm and, A2 = 5 mm, x 0 = 35, . cm and wave number, k = 6.28 cm− 1]. The amplitude of resulting, wave will be .......... mm., , 22. A source of light is placed in front of a, screen. Intensity of light on the screen is I., Two polaroids P1 and P2 are so placed in, between the source of light and screen that, the intensity of light on screen is I / 2. P2, should be rotated by an angle of ..........., (degrees), so that the intensity of light on the, screen becomes 3I / 8., , 23. If the maximum value of accelerating, , I, 0.5 H, , potential provided by a radio frequency, oscillator is 12 kV. The number of revolution, made by a proton in a cyclotron to achieve, one sixth of the speed of light is ........... ., [Given, mp = 1.67 × 10 − 27 kg, e = 1.6 × 10− 19 C,, c = 3 × 108 m/s], , 50 Ω, , 200 V, , a. 5.9 A, , b. 4.24 A, , c. 0.94 A, , 24. The acceleration due to gravity is found upto, d. 6 A, , 19. If the length of the pendulum in pendulum, clock increases by 0.1%, then the error in, time per day is, a. 86.4 s, , b. 4.32 s, , c. 43.2 s, , d. 8.64 s, , 20. Two blocks of masses 3 kg and 5 kg are, connected by a metal wire going over a, smooth pulley. The breaking stress of the, metal is (24 / π ) × 102 Nm− 2 . What is the, minimum radius of the wire?, (Take, g = 10 ms − 2 ), , an accuracy of 4% on a planet. The energy, supplied to a simple pendulum to known, mass m to undertake oscillations of time, period T is being estimated. If time period is, measured to an accuracy of 3%, the accuracy, to which E is known as ..........%., , 25. A circular coil of radius 8.0 cm and 20 turns, is rotated about its vertical diameter with an, angular speed of 50 rad s − 1 in a uniform, horizontal magnetic field of 30, . × 10− 2 T. The, maximum emf induced in the coil will be, .......... × 10− 2 V., (rounded off to the nearest integer.), , 26. Two simple harmonic motions are, , 3kg, 5kg, , represented by the equations, π, x1 = 5sin 2 πt + and, , 4, x2 = 5 2(sin2 πt + cos 2 πt ), The amplitude of second motion is .............., times the amplitude in first motion.
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17, , AUGUST ATTEMPT ~ 26 August 2021, Shift II, 27. A coil in the shape of an equilateral triangle, of side 10 cm lies in a vertical plane, between the pole pieces of permanent, magnet producing a horizontal magnetic, field 20 mT. The torque acting on the coil, when a current of 0.2 A is passed through it, and its plane becomes parallel to the, magnetic field will be x × 10− 5 Nm. The, value of x is.......... ., , 28. For the given circuit, the power across, Zener diode is ............ mW., 1 kΩ, , at 8 cm as shown in the figure. Image of, object coincides with the object., , Image, Image in, the absence, of mirror, , Object, 12 cm, , 8 cm, , When the convex mirror is removed, a real and, inverted image is formed at a position. The, distance of the image from the object will be, ........ cm., , 30. The coefficient of static friction between two, , Iz, R L = 5kΩ, , 24 V, V z = 10 V, , blocks is 0.5 and the table is smooth. The, maximum horizontal force that can be, applied to move the blocks together is .......N., (Take, g = 10 ms − 2 ), Table, , 29. An object is placed at a distance of 12 cm, from a convex lens. A convex mirror of focal, length 15 cm is placed on other side of lens, , 1 kg, , µ=0.5, , 2kg, , F, , CHEMISTRY, Section A : Objective Type Questions, 1. Which one of the following phenols does, not give colour when condensed with, phthalic anhydride in presence of conc., H 2SO4 ?, OH, OH, b., , a., , CH3, OH, , OH, OH, , c., , d., OH, , 2. Given below are two statements. One is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) Photochemical smog causes, cracking of rubber., Reason (R) Presence of ozone, nitric oxide,, acrolein, formaldehyde and peroxyacetyl, nitrate in photochemical smog makes it, oxidising., Choose the most appropriate answer from the, options given below., a. Both (A) and (R) are true but (R) is not the, correct explanation of (A)., b. Both (A) and (R) are true and (R) is the correct, explanation of (A)., c. (A) is false but (R) is true., d. (A) is true but (R) is false.
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18, , JEE Main 2021 ~ Solved Papers, , ONLINE, , Choose the most appropriate option given, below., , 3. The interaction energy of London forces, between two particles is proportional to r x ,, where r is the distance between the, particles. The value of x is, a. 3, , b. − 3, , c. − 6, , a., c., , d. 6, , 4. The number of non-ionisable hydrogen, b. 2, , c. 1, , 5. The bond order and magnetic behaviour of, O−2 ion are, respectively, a. 1.5 and paramagnetic, b. 1.5 and diamagnetic, c. 2 and diamagnetic, d. 1 and paramagnetic, , 7. Match List-I with List-II., , A. CH3COOC 2H5 →, C 2H5OH, , List-II, (Reagent used), 1., , CH3MgBr / H3O +, (1.equivalent), , B. CH3COOCH3 →, 2., CH3CHO, , H2SO 4 / H2O, , C. CH3C ≡≡ N → CH3CHO 3., , DIBAL - H / H2O, , D. CH3C ≡≡ N →, , SnCl2 , HCl / H2O, , 4., O, , CH3, , CH3, , 9., , A, 4, 3, , b., d., , B, 2, 2, , C, 3, 1, , D, 1, 4, , NH2, (CH3CO)2O, , NH2, , P, (Major product), , The major product in the above reaction is, NH2, , NHCOCH3, a., , NHCOCH3, , b., , +, , NH3CH3COO –, c., , List-I, (Chemical reaction), , D, 1, 1, , a. Both (A) and (R) are true and (R) is the correct, explanation of (A)., b. (A) is true but (R) is false., c. Both (A) and (R) are true and (R) is not the true, explanation of (A)., d. (A) is false but (R) is true., , 6. Given below are two statements : One is, , a. Both (A) and (R) are true but (R) is not the, correct explanation of (A)., b. (A) is false but (R) is true., c. (A) is true but (R) is false., d. Both (A) and (R) are true and (R) is the correct, explanation of (A)., , C, 3, 4, , labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) Barium carbonate is insoluble, in water and is highly stable., Reason (R) The thermal stability of the, carbonates increases with increasing cationic, size., , d. 3, , labelled as, Assertion (A) and other is labelled as Reason, (R)., Assertion (A) Sucrose is a disaccharide and a, non-reducing sugar., Reason (R) Sucrose involves glycosidic, linkage between C 1 of β-glucose and C 2 of, α-fructose., Choose the most appropriate answer from, the options given below., , B, 4, 3, , 8. Given below are two statements : One is, , atoms present in the final product obtained, from the hydrolysis of PCl5 is, a. 0, , A, 2, 2, , NHCOCH3, , NHCOCH3, , NHCOCH3, d., , NH2, , 10. Indicate the complex/complex ion which did, not show any geometrical isomerism., a. [CoCl2 (en) 2 ], c. [Co(NH3 ) 3 (NO 2 ) 3 ], , b. [Co(CN) 5 (NC)] 3−, d. [Co(NH3 ) 4Cl2 ] +, , 11. The sol given below with negatively charged, colloidal particles is, a. FeCl3 added to hot water, b. KI added to AgNO 3 solution, c. AgNO 3 added to KI solution, d. Al2O 3 ⋅ xH2O in water
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19, , AUGUST ATTEMPT ~ 26 August 2021, Shift II, , The class of drug to which chlordiazepoxide, with above structure belongs is, , 12. Given below are two statements., Statement I Sphalerite is a sulphide ore of, zinc and copper glance is a sulphide ore of, copper., Statement II It is possible to separate two, sulphide ores by adjusting proportion of oil to, water or by using ‘depressants’ in a froth, flotation method., Choose the most appropriate answer from, the options given below., , a. antacid, c. tranquilizer, , b. analgesic, d. antibiotic, , 16. Chalcogen group elements are, a. Se, Tb and Pu, c. S, Te and Pm, , b. Se, Te and Po, d. O, Ti and Po, , 17. Which one of the following compounds is, not aromatic ?, , a. Statement I is true but statement II is false., b. Both statement I and statement II are true., c. Statement I is false but statement II is true., d. Both statement I and statement II are false., , b., , a., +, , O, , 13. Given below are two statements., One is labelled as Assertion (A) and the other, is labelled as Reason (R)., Assertion (A) Heavy water is used for the, study of reaction mechanism., Reason (R) The rate of reaction for the, cleavage of O H bond is slower than that of, O D bond., Choose the most appropriate answer from, the options given below., , c., , d., , 18. The number of stereoisomers possible for, 1,2- dimethylcyclopropane is, a. one, , b. four, , c. two, , d. three, , 19., , OH, X, HCN,H2O, , H, , a. Both (A) and (R) are true but (R) is not the, correnct explanation of (A)., b. Both (A) and (R) are true and (R) is the correct, explanation of (A)., c. (A) is false but (R) is true., d. (A) is true but (R) is false., , CN, H, , Y, , LiAIH4, H3O+, , (Major product), , Consider the given reaction, identify X and Y., OH, , 14. Arrange the following cobalt complexes in, the order of increasing crystal field, stabilisation energy (CFSE) value., Complexes [CoF6 ]3 − , [Co(H2O) 6 ]3 + ,, (A ), , H, , NH, H, , a. X = NaOH, Y =, , OH, , (B), , b. X = HNO3, Y =, , [Co(NH3 ) 6 ]3 + and [Co(en) 3 ]3 +, , H NH2, , ( D), , (C ), , OH, , Choose the correct option., a. A < B < C < D, c. B < C < D < A, , b. B < A < C < D, d. C < D < B < A, , c. X = NaOH, Y =, , H, , NH2, , OH, , 15., , H, N, , Cl, , N, , C, , C, , N+, , C, O–, , Chlordiazepoxide, , CH3, H, , d. X = HNO3, Y =, , NH2, H, , 20., , H, Br2, AIBr3/(C2H5)2O, , ' A', (Major product), , Consider the given reaction, the product A is
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20, , ONLINE, Br, , JEE Main 2021 ~ Solved Papers, , 25. For the galvanic cell,, Zn( s) + Cu2 + (002, . M) → Zn2 + (004, . M) + Cu( s),, E Cell = ……… × 10− 2 V. (Nearest integer), º, º, [Use E Cu, = − 0.34 V, E Zn, = + 0.76 V,, / Cu 2 +, / Zn 2 +, , a., , 2.303 RT, = 0.059 V], F, , b., Br, , 26. 100 mL of Na 3PO4 solution contains 3.45 g of, sodium. The molarity of the solution is ……, × 10− 2 mol L− 1. (Nearest integer), [Atomic masses - Na = 23.0 u, O = 16.0 u,, P = 31.0 u], , c., Br, , 27. The overall stability constant of the complex, , d., , Br, , Section B : Numerical Type Questions, 21. In the sulphur estimation, 0.471 g of an, organic compound gave 1.44 g of barium, sulphate. The percentage of sulphur in the, compound is _____%., (Nearest integer), (Atomic mass of Ba = 137 u), , 22. The equilibrium constant KC at 298 K for the, reaction A + B, C + D is 100. Starting with, an equimolar solution with concentrations of, A , B , C and D all equal to 1M, the equilibrium, concentration of D is ……… × 10− 2 M. (Nearest, integer), , -, , 23. For water ∆ vapH = 41kJ mol− 1 at 373 K and, 1 bar pressure. Assuming that water vapour, is an ideal gas that occupies a much larger, volume than liquid water, the internal, energy change during evaporation of water, is ……… kJ mol −1., [Use R = 8.3 J mol− 1 K − 1], , 24. A metal surface is exposed to 500 nm, radiation. The threshold frequency of the, metal for photoelectric current is, 4.3 × 1014 Hz. The velocity of ejected electron, is ……… × 105 ms − 1. (Nearest integer), [Use h = 663, . × 10− 34 Js, me = 90, . × 10− 31 kg], , ion [Cu(NH 3 ) 4 ]2 + is 21, . × 1013 . The overall, dissociations constant is y × 10− 14 . Then, y is, ……… . (Nearest integer), , 28. 83 g of ethylene glycol dissolved in 625 g of, water. The freezing point of the solution is, ………K. (Nearest integer), [Use, molal freezing point depression constant, of water = 1.86 K kg mol− 1,, Freezing point of water = 273 K and, Atomic masses : C = 12.0 u, O = 16.0 u,, H = 1.0 u], , 29. The reaction rate for the reaction, [PtCl4 ]2 − + H2O, , [Pt(H2O)Cl3 ]− + Cl−, , -, , was measured as a function of concentrations, of different species. It was observed that, − d[(PtCl4 ) 2 − ], = 4.8 × 10− 5 [ (PtCl4 ) 2 − ], dt, = 2.4 × 10−3 [{Pt(H2O)Cl3 }− ][Cl− ], where, square brackets are used to denote, molar concentrations. The equilibrium, constant, KC = .……… . (Nearest integer), , 30. A chloro compound A,, (i) Forms aldehydes on ozonolysis followed by, the hydrolysis., (ii) When vaporised completely, 1.53 g of A gives, 448 mL of vapour at STP., , The number of carbon atoms in a molecule of, compound A is ……… .
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21, , AUGUST ATTEMPT ~ 26 August 2021, Shift II, , MATHEMATICS, Section A : Objective Type Questions, 1. Let [t] denote the greatest integer less than, or equal to t. Let f ( x) = x − [ x ] ,, g( x) = 1 − x + [ x ] , and, h( x) = min{ f ( x), g( x)}, x ∈ [ − 2 , 2]. Then h is, , a. continuous in [− 2, 2] but not differentiable at, more than four points in (− 2, 2), b. not continuous at exactly three points in, [− 2, 2], c. continuous in [− 2, 2] but not differentiable at, exactly three points in (− 2, 2), d. not continuous at exactly four points in [− 2, 2], , 1 0 0, , , , 2. Let A = 0 1 1 . Then A 2025 − A 2020 is equal to, 1 0 0, , , , a. A 6 − A, c. A 5 − A, , b. A 5, d. A 6, , 3. The local maximum value of the function, 2, f ( x) = , x, 1, , a. (2 e ) e, , x2, , ,x >0, e, , 4 4, b. , , e), , 2, , c. (e ) e, , d. 1, , 4. If the value of the integral, 5, , x + [x], , ∫0 e x − [ x], α, β ∈ R , 5α + 6β = 0 and [x] denotes the, greatest integer less than or equal to x, then, the value of (α + β)2 is equal to :, a. 100, c. 16, , dx = αe − 1 + β, where, , b. 25, d. 36, , 5. The point P ( − 2 6 , 3) lies on the hyperbola, x2, y2, 5, . If the, − 2 = 1 having eccentricity, 2, a, b, 2, tangent and normal at P to the hyperbola, intersect its conjugate axis at the point Q and, R respectively, then QR is equal to, a. 4 3, c. 6 3, , b. 6, d. 3 6, , 6. Let y ( x) be the solution of the differential, equation 2x 2dy + (e y − 2x) dx = 0, x > 0 . If, y (e) = 1, then y (1) is equal to, a. 0, c. log e 2, , b. 2, d. log e (2e ), , 7. Consider the two statements :, (S1) : ( p → q) ∨ (~ q → p) is a tautology, (S 2 ) : ( p ∧ ~ q) ∧ (~ p ∨ q) is a fallacy, Then,, a. only (S1) is true, b. both (S1) and (S 2 ) are false, c. both (S1) and (S 2 ) are true, d. only (S 2 ) is true, , 1+ x, is, x , , 8. The domain of the function cosec − 1, 1, a. − 1, − ∪ (0, ∞ ), , 2 , 1, b. − , 0 ∪ [ 1, ∞ ), 2 , , 1, c. − , ∞ − {0}, 2 , 1, d. − , ∞ − {0}, 2 , , 9. A fair die is tossed until six is obtained on it., Let X be the number of required tosses, then, the conditional probability P ( X ≥ 5|X > 2) is, 125, 216, 5, c., 6, a., , 50, , 10. If ∑ tan− 1, r =1, , a., , 101, 102, , c. 100, , 11, 36, 25, d., 36, b., , 1, = p, then the value of tan p is, 2r 2, 50, 51, 51, d., 50, , b., , 11. Two fair dice are thrown. The numbers on, , them are taken as λ and µ, and a system of, linear equations, x + y + z = 5, x + 2 y + 3 z = µ and, x + 3y + λ z = 1
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22, , JEE Main 2021 ~ Solved Papers, , ONLINE, is constructed. If p is the probability that the, system has a unique solution and q is the, probability that the system has no solution,, then, 1, 1, and q =, 6, 36, 5, 1, c. p = and q =, 6, 36, , 5, and q =, 6, 1, d. p = and q =, 6, , a. p =, , b. p =, , 5, 36, 5, 36, , 12. The locus of the mid-points of the chords of, the hyperbola x 2 − y 2 = 4, which touch the, parabola y 2 = 8x , is, a. y (x − 2) = x, c. y 2 (x − 2) = x 3, 3, , b. x (x − 2) = y, d. x 2 (x − 2) = y 3, , 2, , 3, , 2, , 13. The value of, , π, 2π, 3π, 6π, 5π , 7π , 2sin sin sin sin sin sin , 8, 8, 8, 8, 8, 8, is, 1, 4 2, 1, c., 8, , a. (3, 3, 2), b. (6, − 6, 2), c. (4, 2, 2), d. (− 8, 8, 6), , 17. A 10 inches long pencil AB with mid-point C, and a small eraser P are placed on the, horizontal top of a table such that PC = 5, inches and ∠PCB = tan−1(2). The acute angle, through which the pencil must be rotated, about C so that the perpendicular distance, between eraser and pencil becomes exactly, 1 inch is, , b., , √5, , 3 − 1) x − 3 = 0, 3 + 1) x + 3 = 0, 3 − 1) x − 3 = 0, 3 + 1) x + 3 = 0, , 10m × 10m (see the figure) and vertical walls., If the ∠ GPH between the diagonals AG and, 1, BH is cos − 1 , then the height of the hall (in m), 5, is, , b. tan −1(1), 1, d. tan − 1 , 2, , ∫, −, , π, 2, 3π, c., 4, , π, 2, , 1 + sin2 x , dx is, , sin x , , 1+ π, 5π, 4, 3π, d., 2, , a., , b., , (2,1) and intersects the circle, C 1 : x 2 + y 2 + 2 y − 5 = 0 at two points P and Q, such that PQ is a diameter of C 1. Then the, diameter of C is, b. 15, d. 4 15, , a. 7 5, c. 285, , P, B, , A, , c. 5 3, , , , 9, , , , x, , , is equal, 20. xlim, → 2 ∑ n( n + 1) x 2 + 2(2 n + 1) x + 4 , n =1, , to, , C, , b. 2 10, , 18. The value of, , 5 in, , 19. A circle C touches the line x = 2 y at the point, , F, , G, , D, , C, , 3, a. tan − 1 , 4, 4, c. tan − 1 , 3, π, 2, , 15. A hall has a square floor of dimension, , H, , P, B, , 5 in, , roots of the equation, , E, , in, , A, , 14. If ( 3 + i)100 = 299 ( p + iq), then p and q are, , a. 5, , (1,2,3) and the line of intersection of the, planes r ⋅ ( i$ + $j + 4k$ ) = 16 and r ⋅ ( − $i + $j + k$ ) = 6., Then which of the following points does not, lie on P ?, , 1, 4, 1, d., 8 2, , a., , a. x 2 − (, b. x 2 + (, c. x 2 + (, d. x 2 − (, , 16. Let P be the plane passing through the point, , 9, 44, 1, c., 5, a., , d. 5 2, , 5, b., 24, 7, d., 36
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23, , AUGUST ATTEMPT ~ 26 August 2021, Shift II, n, , Section B : Numerical Type Questions, , 26. Let denotes n C k and, k, , 21. The sum of all three-digit numbers less than, or equal to 500, that are formed without using, the digit 1 and they all are multiple of 11, is, , 22. Let a be the points of local maximum and local, minimum of the function f ( x) = 2x 3 − 3x 2 − 12x, . If A is the total area of the region bounded by, y = f ( x), the X-axis and the lines x = a and, x = b, then 4A is equal to, , 23. If the projection of the vector $i + 2$j + k$ on the, sum of the two vectors 2$i + 4 $j − 5k$ and, − λ $i + 2$j + 3k$ is 1, then λ is equal to, , 24. Let a1, a 2 …… , a10 be an AP with common, difference −3 and b1, b2 ,…… , b10 be a GP with, common ratio 2., Let c k = ak + bk , k = 1, 2 , …… , 10. If c 2 = 12 and, c 3 = 13, then, , 10, , ∑c, , k, , is equal to, , n, n , if 0 ≤ k ≤ n, =, k k , 0,, otherwise, , 9, 9, 12, , , If Ak = ∑ , +, i = 0 i 12 − k + i , , 8 , , 8, , 13, , , , ∑ i 13 − k + i , , i=0, , and A4 − A3 = 190 p, then p is equal to, , 27. Let λ ≠ 0 be in R. If α and β are the roots of, the equation x 2 − x + 2λ = 0 and α and γ, are the roots of equation, βγ, is equal to, 3x 2 − 10x + 27λ = 0, then, λ, , 28. Let the mean and variance of four, , numbers 3, 7, x and y ( x > y ) be 5 and 10, respectively. Then, the mean of four, numbers 3 + 2x , 7 + 2 y , x + y and x − y is, , 29. Let A be a 3 × 3 real matrix., , k =1, , 25. Let Q be the foot of the perpendicular from the, point P (7, − 2 ,13) on the plane containing the, x + 1 y −1 z −3, lines, and, =, =, 6, 7, 8, x + 1 y −2 z −3, =, =, ⋅ Then ( PQ) 2 is equal to, 3, 5, 7, , If det(2Adj(2 Adj(Adj(2A)))) = 241, then the, value of det(A 2 ) equal, , 30. The least positive integer n such that, (2i) n, , i = − 1, is a positive integer, is, (1 − i) n − 2, , Answers, For solutions scan, the QR code, , Physics, 1. (c), 11. (c), 21. 7, , 2. (b), 12. (c), 22. 30, , 3. (a), 13. (d), 23. 543, , 4. (c), 14. (a), 24. 14, , 5. (c), 15. (a), 25. 60, , 6. (a,d), 16. (d), 26. 2, , 7. (d), 17. (*), 27. 3, , 8. (d), 18. (*), 28. 120, , 9. (d), 19. (c), 29. 50, , 10. (a), 20. (c), 30. 15, , 8. (a), 18. (d), 28. 269, , 9. (d), 19. (c), 29. 50, , 10. (b), 20. (c), 30. 3, , 8. (d), 18. (c), 28. 12, , 9. (d), 19. (a), 29. 4, , 10. (b), 20. (a), 30. 6, , Chemistry, 1. (b), 11. (c), 21. 42, , 2. (b), 12. (b), 22. 182, , 3. (c), 13. (d), 23. 38, , 4. (a), 14. (a), 24. 5, , 5. (a), 15. (c), 25. 109, , 6. (c), 16. (b), 26. 50, , 7. (c), 17. (c), 27. 5, , Mathematics, 1. (a), 11. (b), 21. 7744, , 2. (a), 12. (c), 22. 114, , 3. (c), 13. (c), 23. 5, , 4. (b), 14. (a), 24. 2021, , Note (*) None of the option is correct., , 5. (c), 15. (d), 25. 96, , 6. (c), 16. (c), 26. 49, , 7. (c), 17. (a), 27. 18
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24, , ONLINE, , JEE Main 2021 ~ Solved Papers, , JEE Main 2021, 27 AUGUST SHIFT I, PHYSICS, Section A : Objective Type Questions, 1. A uniformly charged disc of radius R having, , surface charge density σ is placed in the, xy-plane with its centre at the origin. Find the, electric field intensity along the Z-axis at a, distance Z from origin, , c. E =, , 2ε0, σ, , , , Z, , 1−, 2, 2 , , (Z + R ) , , , , Z, , 1+, , (Z 2 + R 2 ) , , , , 1, , + Z, , (Z 2 + R 2 ), , , , d. E =, , σ, 2ε0, , , 1, 1, , + 2, (Z 2 + R 2 ) Z , , , , a. E =, b. E =, , σ, 2ε0, σ, 2ε0, , 2. There are 1010 radioactive nuclei in a given, radioactive element. Its half-life time is 1min., How many nuclei will remain after 30 s?, ( 2 = 1414, ), ., a. 2 × 1010, c. 105, , b. 7 × 109, d. 4 × 1010, , 3. Which of the following is not a dimensionless, quantity ?, a. Relative magnetic permeability (µ r ), b. Power factor, c. Permeability of free space (µ 0 ), d. Quality factor, , 4. If E and H represent the intensity of electric, field and magnetising field respectively, then, the unit of E / H will be, a. ohm, c. joule, , b. mho, d. newton, , 5. The resultant of these forces OP, OQ, OR, OS, and OT is approximately ...... N., [Take, 3 = 1. 7, 2 = 1. 4 and given $i and $j unit, vectors along X , Y axis], P, T, , 15N, , 20N, , Y, , Q, , 60° 30°, , 10N, 30°, , X', , 45°, , O, , X, , 45°, , 15N, S, , a. 9.25i$ + 5$j, c. 2.5$i − 14 .5$j, , 20N, , Y', , R, , b. 3i$ + 15$j, d. − 1.5$i − 155, . $j, , 6. A balloon carries a total load of 185 kg at, normal pressure and temperature of 27ºC., What load will the balloon carry on rising to, a height at which the barometric pressure is, 45 cm of Hg and the temperature is − 7ºC?, [Assuming, the volume constant.], a. 181.46 kg, c. 219.07 kg, , b. 214.15 kg, d. 123.54 kg, , 7. An object is placed beyond the centre of, curvature C of the given concave mirror. If, the distance of the object is d1 from C and, the distance of the image formed is d 2 from, C , the radius of curvature of this mirror is, 2d1d 2, d1 − d 2, dd, c. 1 2, d1 + d 2, , a., , 2d1d 2, d1 + d 2, dd, d. 1 2, d1 − d 2, b.
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25, , AUGUST ATTEMPT ~ 27 August 2021, Shift I, 8. A huge circular arc of length 4.4 ly subtends, an angle 4s at the centre of the circle. How, long it would take for a body to complete, 4 rev if its speed is 8 AU per sec ?, [Given, 1 ly = 9.46 × 1015 m,1 AU = 1.5 × 1011 m], a. 4.1 × 108 s, c. 3.5 × 106 s, , b. 4 .5 × 1010 s, d. 7.2 × 108 s, , 14. A bar magnet is passing through a, conducting loop of radius R with velocity v., The radius of the bar magnet is such that it, just passes through the loop. The induced, emf in the loop can be represented by the, approximate curve, l, R, , 9. Calculate the amount of charge on capacitor, of 4 µF. The internal resistance of battery is, 1 Ω., 4µF, , S, , N, loop, , 2µF, , v, , 6Ω, , 5V, , 2µF, , A, , emf, , B, , a., , t, I/v, , 4Ω, , a. 8 µC, , b. zero, , c. 16 µC, , d. 4 µC, , 10. Moment of inertia of a square plate of side l, about the axis passing through one of the, corner and perpendicular to the plane of, square plate is given by, Ml 2, a., 6, , b. Ml, , 2, , Ml 2, c., 12, , 2, d. Ml 2, 3, , emf, , b., , t, , I/v, , 11. For a transistor in CE mode to be used as an, amplifier, it must be operated in, a. both cut-off and saturation, b. saturation region only, c. cut-off region only, d. the active region only, , emf, , 12. An ideal gas is expanding such that, , I/v, , c., , t, , pT 3 = constant. The coefficient of volume, expansion of the gas is, a. 1/ T, , b. 2 / T, , c. 4 / T, , d. 3 / T, , 13. In a photoelectric experiment, increasing the, intensity of incident light, a. increases the number of photons incident and, also increases the KE of the ejected electrons., b. increases the frequency of photons incident, and increases the KE of the ejected electrons., c. increases the frequency of photons incident, and the KE of the ejected electrons remains, unchanged., d. increases the number of photons incident and, the KE of the ejected electrons remains, unchanged., , emf, d., , I/v, , t
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26, , ONLINE, , 15. Two ions of masses 4 amu and 16 amu have, , charges +2e and +3e, respectively. These ions, pass through the region of constant, perpendicular magnetic field. The kinetic, energy of both ions is same. Then,, a. lighter ion will be deflected less than heavier, ion, b. lighter ion will be deflected more than heavier, ion, c. both ions will be deflected equally, d. no ion will be deflected, , 20. The variation of displacement with time of a, particle executing free simple harmonic, motion is shown in the figure., x, , f =+10cm, , A, , O, , B, C, , t, , The potential energy U( x) versus time (t) plot of, the particle is correctly shown in figure :, , 16. Find the distance of the image from object O,, formed by the combination of lenses in the, figure., , JEE Main 2021 ~ Solved Papers, , U(x), a., , O, , A, , B, , A, , B, , C, , t, , f =–10cm f =+30cm, , U(x), b., , O, , C, , O, , t, , U(x), , 30cm, , a. 75 cm, , 5cm, , b. 10 cm, , c., , 10cm, , c. 20 cm, , viscous force acting on an uncharged drop of, radius 2.0 × 10− 5 m and density, 12, . × 103kgm− 3? Take viscosity of liquid, = 18, . × 10− 5Nsm− 2. (Neglect buoyancy due to, air)., b. 39, . × 10− 10 N, d. 58, . × 10− 10 N, , is given by E = 50sin(500x − 10 × 10 t) V/m., The velocity of electromagnetic wave in this, medium is, (Given, c = speed of light in vacuum), b. c, , 2, c. c, 3, , d., , U(x), d., , A, , B, t, , O, , C, , 21. A body of mass 2M splits into four masses, , 10, , 3, c, 2, , c, 2, , {m, M − m , m , M − m}, which are rearranged, to form a square as shown in the figure. The, M, ratio of, for which, the gravitational, m, potential energy of the system becomes, maximum is x : 1. The value of x is……… ., m, , M–m, , 19. Five identical cells each of internal resistance, 1 Ω and emf 5V are connected in series and, in parallel with an external resistance R ., For what value of R , current in series and, parallel combination will remain the same ?, a. 1Ω, , b. 25 Ω, , c. 5 Ω, , t, , Section B : Numerical Type Questions, , 18. Electric field in a plane electromagnetic wave, , a., , C, , d. infinity, , 17. In Millikan’s oil drop experiment, what is, , a. 38, . × 10− 11N, c. 18, . × 10− 10 N, , B, , A, , O, , d. 10 Ω, , d, , M–m, , d, , m
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27, , AUGUST ATTEMPT ~ 27 August 2021, Shift I, 22. The alternating current is given by, , sound as emitted by a passenger in car X,, heard by the passenger in car Y is 1320 Hz. If, the velocity of sound in air is 340 m/s, the, actual frequency of the whistle sound, produced is ........ Hz., , 2π, i = 42 sin t + 10 A, , T , , , , The rms value of this current is ........ A., , 23. A uniform conducting wire of length is 24 a,, and resistance R is wound up as a current, carrying coil in the shape of an equilateral, triangle of side a and then in the form of a, square of side a . The coil is connected to a, voltage source V0. The ratio of magnetic, moment of the coils in case of equilateral, triangle to that for square is 1: y . The value, of where y is ……… ., , 24. A circuit is arranged as shown in figure. The, output voltage V0 is equal to ....... V., V0, , 27. If the velocity of a body related to, , displacement x is given by v = 5000 + 24 x, m/ s , then the acceleration of the body is, ...... m / s 2., , 28. A rod CD of thermal resistance 10.0 kW − 1 is, joined at the middle of an identical rod AB as, shown in figure. The end A , B and D are, maintained at 200ºC, 100ºC and 125ºC, respectively. The heat current in CD is P watt., The value of P is ....... ., A, , B, , D1, R, , R, , 200°C, , C, , 100°C, , 5V, D2, , R, , 125°C, , D, , 5V, , 29. Two persons A and B perform same amount, 25. First, a set of n equal resistors of 10 Ω each, are connected in series to a battery of emf, 20 V and internal resistance 10 Ω. A current l, is observed to flow. Then, the n resistors are, connected in parallel to the same battery. It, is observed that the current is increased, 20 times, then the value of n is ......... ., , 26. Two cars X and Y are approaching each other, with velocities 36 km/h and 72 km/h, respectively. The frequency of a whistle, , of work in moving a body through a certain, distance d with application of forces acting at, angle 45º and 60º with the direction of, displacement respectively. The ratio of force, applied by person A to the force applied by, 1, person B is, . The value of x is ....... ., x, , 30. A transmitting antenna has a height of, 320 m and that of receiving antenna is, 2000 m. The maximum distance between, them for satisfactory communication in line, of sight mode is d. The value of d is ........ km.
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28, , JEE Main 2021 ~ Solved Papers, , ONLINE, , CHEMISTRY, Section A : Objective Type Questions, , Choose the most appropriate answer from the, options given below :, , 1. In the following sequence of reactions, the, a., b., c., d., , final product D is, OH, , CH3 C==C H+NaNH2, , A, , Br, , CH3, H2/Pd–C, , A, 4, 3, 3, 4, , B, 1, 4, 2, 2, , C, 2, 2, 4, 1, , D, 3, 1, 1, 3, , B, C, , CrO3, , 4. In which one of the following molecules, D, , O, , a. H3C CH2 CH2 CH2 CH2 C H, , strongest back donation of an electron pair, from halide to boron is expected?, a. BCl3, c. BBr3, , b. CH3 CH == CH CH2 CH2 CH2 COOH, c. H3C CH == CH CH(OH) CH2 CH2 CH3, O, , d. CH3 CH2 CH2 CH2 CH2 C CH3, , 2. The structure of the starting compound P, , b. BF3, d. BI3, , 5. Deuterium resembles hydrogen in, properties but, a. reacts slower than hydrogen, b. reacts vigorously than hydrogen, c. reacts just as hydrogen, d. emits β + particles, , used in the reaction given below is, , 6. Which refining process is generally used in, , OH, P, , (i) NaOCl, (ii) H3O+, , b., , a., , H, , the purification of low melting metals ?, a. Chromatographic method, b. Liquation, c. Electrolysis, d. Zone refining, , 7. Match List-I with List-II., O, , c., , List-I, (Property), , d., , 3. Match List-I with List-II., List-I, (Species), , List-II, (Number of lone pair, of electrons on the, central atom), , A., , XeF2, , 1., , 0, , B., , XeO 2F2, , 2., , 1, , C., , XeO 3F2, , 3., , 2, , D., , XeF4, , 4., , 3, , List-II, (Example), , A., , Diamagnetism, , 1., , MnO, , B., , Ferrimagnetism, , 2., , O2, , C., , Paramagnetism, , 3., , NaCl, , D., , Antiferromagnetism, , 4., , Fe3O 4, , Choose the most appropriate answer from the, options given below., a., b., c., d., , A, 2, 1, 3, 4, , B, 1, 3, 4, 2, , C, 3, 4, 2, 1, , D, 4, 2, 1, 3
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29, , AUGUST ATTEMPT ~ 27 August 2021, Shift I, 8. Consider the following structures :, CH3, , c. CH3 C H CH2 CH2OH, , CH3, , N, , A., HO, , O, , OH, , CH3, , HO, , C., , HO, , d. CH3 C H CH2 CH2 Cl, , CH3, , 10. Which of the following is not a correct, statement for primary aliphatic amines?, , N, B., , b. CH3 C H CH2 CH2 CH2OH, , CH3, , N, , CH2CH2NH2, , a. The intermolecular association in primary, amines is less than the intermolecular, association in secondary amines., b. Primary amines on treating with nitrous acid, solution form corresponding alcohols except, methyl amine., c. Primary amines are less basic than the, secondary amines., d. Primary amines can be prepared by the, gabriel phthalimide synthesis., , 11. Acidic ferric chloride solution on treatment, , N, H, , with excess of potassium ferrocyanide gives, a prussian blue coloured colloidal species. It, is, , CH3, N, , a. Fe4 [Fe(CN) 6 ] 3, c. HFe[Fe(CN) 6 ], , D., , b. K 5Fe[Fe(CN) 6 ] 2, d. KFe[Fe(CN) 6 ], , 12. The gas ‘A’ is having very low reactivity, H3CO, , O, , OH, , The correct statement about (A), (B), (C) and (D), is, a. (A), (B) and (C) are narcotic analgesics, b. (B), (C) and (D) are tranquillizers, c. (A) and (D) are tranquillizers, d. (B) and (C) are tranquillizers, , 9. The major product of the following reaction is, CH3, O, , , CH3 CH CH2 CH2 C Cl, (i) Alcoholic NH3, (ii) NaOH, Br, , 2, , → Major product, , (iii) NaNO2 ,HCl, (iv) H2O, , Br, , a. CH3 C H C H CH2OH, , CH3, , reaches to stratosphere. It is non-toxic and, non-flammable but dissociated by, UV-radiations in stratosphere. The, intermediates formed initially from the gas, ‘A’ are, •, , •, , •, , •, , a. ClO + C F2Cl, , b. ClO + C H3, , c. C H3 + C F2 Cl, , d. C l + C F2 Cl, , •, , •, , •, , •, , 13. The number of water molecules in gypsum,, dead burnt plaster and plaster of Paris,, respectively are, a. 2, 0 and 1, c. 5, 0 and 0.5, , b. 0.5, 0 and 2, d. 2, 0 and 0.5, , 14. The nature of oxides V2O3 and CrO is indexed, as ‘X’ and ‘Y ’ type respectively. The correct set, of X and Y is, a. X = basic, Y = amphoteric, b. X = amphoteric, Y = basic, c. X = acidic, Y = acidic, d. X = basic, Y = basic
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30, , ONLINE, , 15. Out of the following isomeric forms of uracil,, which one is present in RNA ?, OH, , OH, , N, , a., HO, , N, , b., O, , N, , N, H, O, , O, c., , HN, , HN, HO, , d., O, , N, , N, H, , 16. Given below are two statements : one is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) Synthesis of ethyl phenyl ether, may be achieved by Williamson synthesis., Reason (R) Reaction of bromobenzene with, sodium ethoxide yields ethyl phenyl ether., In the light of the above statements, choose, the most appropriate answer from the options, given below, a. Both (A) and (R) are correct and (R) is the, correct explanation of (A), b. (A) is correct but (R) is incorrect, c. (A) is incorrect but (R) is correct, d. Both (A) and (R) are correct but (R) is not the, correct explanation of (A), , 17. In the following sequence of reactions the P, is, Cl, + Mg, , Dry, ether, , (A), , O—CH2CH3, , CH2CH3, c., , d., , (P), Major product, , 18. The unit of the van der Waals’ gas equation, , an2 , parameter ‘a ’in p + 2 (V − nb) = nRT is, , V , a. kg ms − 2, c. kg ms − 1, , b. dm3 mol− 1, d. atm dm6mol− 2, , 19. In polythionic acid, H2S xO6( x = 3 to 5) the, oxidation state(s) of sulphur is/are, a. only + 5, b. only + 6, c. + 3 and + 5, d. 0 and + 5, , 20. Tyndall effect is more effectively shown by, a. true solution, b. lyophilic colloid, c. lyophobic colloid, d. suspension, , Section B : Numerical Type Questions, 21. In carius method for estimation of halogens,, 0.2 g of an organic compound gave 0.188 g, of AgBr. The percentage of bromine in the, compound is ……… (Nearest integer), [Atomic mass; Ag = 108, Br = 80], , 22. The reaction that occurs in a breath, analyser, a device used to determine the, alcohol level in a person’s blood stream is, 2K 2Cr2O7 + 8H2SO4 + 3C 2H6O → 2Cr2 (SO4 ) 3, + 3C 2H4O2 + 2K 2SO4 + 11H2O, If the rate of appearance of Cr2 (SO4 ) 3 is, 2.67 mol min − 1 at a particular time, the rate of, disappearance of C 2H6O at the same time is, ……… mol min − 1. (Nearest integer), , 23. The kinetic energy of an electron in the, second Bohr orbit of a hydrogen atom is, h2, equal to, . The value of 10x is ……… ., xma 02, , a., , b., , Ethanol, , JEE Main 2021 ~ Solved Papers, , (a 0 is radius of Bohr’s orbit) (Nearest integer), [Given, π = 3.14], , 24. 1 kg of 0.75 molal aqueous solution of, , sucrose can be cooled up to − 4ºC before, freezing. The amount of ice (in g) that will be, separated out is ……… . (Nearest integer), [Given, Kf (H2O) = 1.86 K kg mol − 1]
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31, , AUGUST ATTEMPT ~ 27 August 2021, Shift I, 25. 1 mol of an octahedral metal complex with, formula MCl3 ⋅2L on reaction with excess of, AgNO3 gives 1 mol of AgCl. The denticity of, ligand L is ……… . (Integer answer), , 26. The number of moles of CuO, that will be, utilised in Dumas method for estimation, nitrogen in a sample of 57.5 g of, N, N-dimethylaminopentane is ……… × 10− 2., (Nearest integer), , 27. The number of f -electrons in the ground, state electronic configuration of Np (Z = 93), is ……… ., (Nearest integer), , 28. 200 mL of 0.2 M HCl is mixed with 300 mL of, 0.1 M NaOH. The molar heat of, neutralisation of this reaction is − 571, . kJ. The, increase in temperature in ºC of the system, on mixing is x × 10− 2., The value of x is ……… (Nearest integer), , [Given, specific heat of water = 4.18 J g − 1 K − 1, Density of water = 1.00 g cm− 3 ], (Assume no volume change on mixing), , 29. The number of moles of NH3, that must be, added to 2 L of 0.80 M AgNO3 in order to, reduce the concentration of Ag + ions to, 50, . × 10− 8 M (Kformation for, [Ag(NH 3) 2 ]+ = 10, . × 108) is ……… (Nearest, integer), [Assume no volume change on adding NH3 ], , 30. When 10 mL of an aqueous solution of, KMnO4 was titrated in acidic medium, equal, volume of 0.1 M of an aqueous solution of, ferrous sulphate was required for complete, discharge of colour., The strength of KMnO4 in g/L is, ……… × 10− 2. (Nearest integer), [Atomic mass of K = 39, Mn = 55, O = 16], , MATHEMATICS, Section A : Objective Type Questions, 3, 2, , 5, 3, , 1. If 0 < x < 1, then x 2 + x 3 +, , 7 4, x + ……, is, 4, , equal to, 1+ x, a. x , + log e (1 − x ), 1− x, , moving point (2t, 0). Let M be the mid-point, of AB and the perpendicular bisector of AB, meets the Y-axis at C., The locus of the mid-point P of MC is, a. 3x 2 − 2 y − 6 = 0, c. 2x 2 + 3 y − 9 = 0, , 1− x, b. x , + log e (1 − x ), 1+ x, 1− x, c., + log e (1 − x ), 1+ x, 1+ x, d., + log e (1 − x ), 1− x, , b. 3x 2 + 2 y − 6 = 0, d. 2x 2 − 3 y + 9 = 0, , 4. If (sin− 1 x) 2 − (cos − 1 x) 2 = a, 0 < x < 1, a ≠ 0, then, the value of 2x 2 − 1 is, 4a , 2a , a. cos , b. sin , π, π, , 2a, 4a , c. cos d. sin, , π, π , , 0 2 , satisfies, K − 1, , 5. If the matrix A = , , 2. If x , y ∈ R , x > 0, , A ( A 3 + 3I ) = 2 I, then the value of K is, , y = log 10 x + log 10 x 1/ 3 + log 10 x 1/ 9 + … upto ∞, 2 + 4 + 6 +… + 2 y, 4, , then, terms and, =, 3 + 6 + 9 +… + 3 y log 10 x, the ordered pair (x , y ) is equal to, a. (106 , 6), c. (102 , 3), , 3. Let A be a fixed point (0, 6) and B be a, , b. (104 , 6), d. (106 , 9), , a., , 1, 2, , b. −, , 1, 2, , c. − 1, , d. 1, , 6. The distance of the point (1, −2, 3) from the, plane x − y + z = 5 measured parallel to a, line, whose direction ratios are 2, 3, −6 is, a. 3, , b. 5, , c. 2, , d. 1
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32, , ONLINE, , , z−i, , , , z + 2i, , 7. If S = z ∈ C :, , , ∈ R , then, , , 15. Let, , a. b 2 − a 2 = a 2 + c 2, b. b 2 , c 2 and a 2 are in AP, c. c 2 , a 2 and b 2 are in AP, d. a 2 , b 2 and c 2 are in AP, , 8. Let y = y ( x) be the solution of the differential, equation, a. 2e, , π2, , +5, , b. e, , 2, , π2, , 16. If α , β are the distinct roots of x 2 + bx + c = 0,, , +5, , then, 2, e2( x, lim, , 2, , c. 3e π + 5, , sin A sin( A − C ), , where A, B and C are, =, sinB sin(C − B), , angles of a ∆ABC . If the lengths of the sides, opposite these angles are a , b and c, respectively, then, , a. S contains exactly two elements., b. S contains only one element., c. S is a circle in the complex plane., d. S is a straight line in the complex plane., , dy, = 2( y + 2 sin x − 5) x − 2 cos x, dx, such that, y(0) = 7. Then y( π ) is equal to, , JEE Main 2021 ~ Solved Papers, , d. 7e π + 5, , + bx + c ), , (x − β ) 2, , x→ β, , 9. Equation of a plane at a distance 2 /21 from, the origin, which contains the line of, intersection of the planes x − y − z − 1 = 0, and 2x + y − 3z + 4 = 0, is, a. 3x − y − 5z + 2 = 0, c. − x + 2 y + 2 z − 3 = 0, , 10. If U n = 1 +, , , a. b 2 + 4c, c. 2 (b 2 − 4c ), , 1, −x, 6, and its opposite face occurs with probability, 1, + x. All other faces occur with probability, 6, 1/6. Note that opposite faces sum to 7 in any, 1, die. If 0 < x < , and the probability of, 6, obtaining total sum = 7, when such a die is, rolled twice is 13/96, then the value of x is, , n, , , 1 , 22 , n2 , 1, 1, …, +, +, , then, , , , , , n2 , n2 , n2 , , −4, 2, , n→ ∞, , b. 4 /e, , c. 16/e 2, , d. 4 /e 2, , 11. The statement ( p ∧ ( p → q) ∧ (q → r)) → r is, b. equivalent to p → ~ r, d. equivalent to q →~ r, , a. a tautology, c. a fallacy, , a. 1/16, , ∑ ( 20C k) 2 is equal to, , 1 1, 1 1, 1 1, a. − , and − , b. − , and [1, 3], 3 3 , 3 3 , 3 3 , 1 1, c. [1, 3] and [1, 3], d. [1, 3] and − , , 3 3 , , 19., , 16, , ∫6, , log e x 2, dx is equal, log e x + log e ( x 2 − 44 x + 484), , a. 6, , k=0, , a., , d. 1/12, , 2, , to, , 20, , 13., , c. 1/9, , respectively lie in the intervals, , through the point (− 2, 2) and the slope of the, tangent to the curve at any point ( x , f ( x)) is, given by f ( x) + xf ′ ( x) = x 2 Then, b. x 3 + 2x f (x ) + 12 = 0, d. x 2 + 2x f (x ) + 4 = 0, , b. 1/8, , 18. If x 2 + 9 y 2 − 4 x + 3 = 0, x , y ∈ R , then x and y, , 12. Let us consider a curve, y = f ( x) passing, , a. x 2 + 2x f (x ) − 12 = 0, c. x 3 − 3x f (x ) − 4 = 0, , b. 2 (b 2 + 4c ), d.b 2 − 4c, , particular face occurs with probability, , lim (U n) n is equal to, , a. e 2 / 16, , is equal to, , 17. When a certain biased die is rolled, a, , b. 3x − 4 z + 3 = 0, d. 4 x − y − 5z + 2 = 0, 2, , − 1 − 2 (x 2 + bx + c ), , 40, , C 21, , b., , 40, , C19, , c., , 40, , C 20, , d., , 41, , C 20, , 14. A tangent and a normal are drawn at the, , point P(2, − 4) on the parabola y 2 = 8x , which, meet the directrix of the parabola at the, points A and B respectively. If Q (a , b ) is a, point such that AQBP is a square, then 2a + b, is equal to, a. − 16, , b. − 18, , b. 8, , c. 5, , d. 10, , 20. A wire of length 20 m is to be cut into two, , c. − 12, , d. − 20, , pieces. One of the pieces is to be made into, a square and the other into a regular, hexagon. Then, the length of the side (in m), of the hexagon, so that the combined area of, the square and the hexagon is minimum, is, 5, 2+ 3, 5, c., 3+ 3, , a., , 10, 2+ 3 3, 10, d., 3+ 2 3, b.
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33, , AUGUST ATTEMPT ~ 27 August 2021, Shift I, Section B : Numerical Type Questions, , constant of integration, then the value of, 9( 3 a + b) is equal to, , 21. Let a = $i + 5$j + αk$ , b = i$ + 3$j + βk$ and, , 26. If the system of linear equations, , c = − i$ + 2$j − 3k$ be three vectors such that,, | b × c | = 5 3 and a is perpendicular to b., Then, the greatest amongst the values of, | a|2 is, , 2x + y − z = 3, x− y − z =α, 3x + 3 y + βz = 3, has infinitely many solution, then α + β − αβ is, equal to, , 22. The number of distinct real roots of the, equation 3x 4 + 4 x 3 − 12x 2 + 4 = 0 is, , 27. Let n be an odd natural number such that, the variance of 1, 2, 3, 4, ..., n is 14. Then n is, equal to, , 23. Let the equation x + y + px + (1 − p) y + 5 = 0, 2, , 2, , represent circles of varying radius r ∈(0, 5]., Then, the number of elements in the set, S = { q : q = p2 and q is an integer} is, , 28. If the minimum area of the triangle formed, , x2, y2, +, = 1 and, 2, b, 4a 2, the coordinate axis is kab, then k is equal to, , by a tangent to the ellipse, , 24. If A = { x ∈ R: | x − 2| > 1} ,, B = { x ∈ R : x 2 − 3 > 1} and, , 29. A number is called a palindrome if it reads, , C = { x ∈ R :|x − 4 | ≥ 2} and Z is the set of all, integers, then the number of subsets of the, set ( A ∩ B ∩ C )C ∩ Z is, dx, 2 x + 1, = a tan− 1, , , ( x 2 + x + 1) 2, 3 , 2x + 1 , + C , x > 0 where C is the, + b 2, x + x + 1, , 25. If ∫, , the same backward as well as forward. For, example 285582 is a six digit palindrome., The number of six digit palindromes, which, are divisible by 55, is, , 30. If y 1/ 4 + y − 1/ 4 = 2x , and ( x 2 − 1), + αx, , d2y, dx 2, , dy, + βy = 0 then| α − β | is equal to, dx, , Answers, For solutions scan, the QR code, , Physics, 1. (a), 11. (d), 21. 2, , 2. (b), 12. (c), 22. 11, , 3. (c), 13. (d), 23. 3, , 4. (a), 14. (c), 24. 5, , 5. (a), 15. (b), 25. 20, , 6. (d), 16. (a), 26. 1210, , 7. (a), 17. (b), 27. 12, , 8. (b), 18. (c), 28. 2, , 9. (a), 19. (a), 29. 2, , 10. (d), 20. (d), 30. 224, , 8. (d), 18. (d), 28. 82, , 9. (c), 19. (d), 29. 4, , 10. (a), 20. (c), 30. 316, , 9. (d), 19. (c), 29. 100, , 10. (a), 20. (d), 30. 17, , Chemistry, 1. (d), 11. (a), 21. 40, , 2. (a), 12. (d), 22. 4, , 3. (d), 13. (d), 23. 3155, , 4. (b), 14. (d), 24. 518, , 5. (a), 15. (d), 25. 2, , 6. (b), 16. (b), 26. 1125, , 3. (c), 13. (c), 23. 61, , 4. (b), 14. (a), 24. 256, , 5. (a), 15. (b), 25. 15, , 6. (d), 16. (c), 26. 5, , 7. (c), 17. (a), 27. 18, , Mathematics, 1. (a), 11. (a), 21. 90, , 2. (d), 12. (c), 22. 4, , 7. (d), 17. (b), 27. 13, , 8. (a), 18. (c), 28. 2
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34, , JEE Main 2021 ~ Solved Papers, , ONLINE, , JEE Main 2021, 27 AUGUST SHIFT II, PHYSICS, Section A : Objective Type Questions, 1. Curved surfaces of a plano-convex lens of, , refractive index µ1 and a plano-concave lens, of refractive index µ 2 have equal radius of, curvature as shown in figure. Find the ratio, of radius of curvature to the focal length of, the combined lenses., , 3. For a transistor α and β are given as α =, and β =, , IC, . Then, the correct relation, IB, , between α and β will be, a. α =, , 1− β, β, , c. αβ = 1, , 1, µ 2 − µ1, , b. µ 1 − µ 2, , c., , 1, µ1 − µ 2, , d. µ 2 − µ 1, , 2. The boxes of masses 2 kg and 8 kg are, connected by a massless string passing over, smooth pulleys. Calculate the time taken by, box of mass 8 kg to strike the ground, starting from rest., (Use, g = 10 m/s 2 ), , shower onto the floor, from a height of, 9.8 m. The drops fall at a regular interval of, time. When the first drop strikes the floor, at, that instant, the third drop begins to fall., Locate the position of second drop from the, floor when the first drop strikes the floor., a. 4.18 m, b. 2.94 m, c. 2.45 m, d. 7.35 m, , 5. Two discs have moments of inertia I1 and I2, about their respective axes perpendicular to, the plane and passing through the centre., They are rotating with angular speeds, ω1, and ω 2 respectively and are brought into, contact face to face with their axes of, rotation co-axial. The loss in kinetic energy of, the system in the process is given by, I1I 2, (ω1 − ω 2 ) 2, (I1 + I 2 ), (I − I ) 2 ω1ω 2, b. 1 2, 2(I1 + I 2 ), II, c. 1 2 (ω1 − ω 2 ) 2, 2(I1 + I 2 ), (ω − ω 2 ) 2, d. 1, 2(I1 + I 2 ), a., , 8kg, 20cm, , a. 0.34 s, , b. 0.2 s, , α, 1− α, β, d. α =, 1− β, , b. β =, , 4. Water drops are falling from a nozzle of a, , µ1 µ2, , a., , IC, IE, , 2kg, , c. 0.25 s, , d. 0.4 s
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35, , AUGUST ATTEMPT ~ 27 August 2021, Shift II, 6. Three capacitors C 1 = 2µF, C 2 = 6µF and, C 3 = 12µF are connected as shown in figure., Find the ratio of the charges on capacitors, C 1, C 2 and C 3, respectively., , O, , D, A, , x=0, , C2, , C3, , B, , C1, , b. 2 : 3 : 3, d. 3 : 4 : 4, , 7. The colour coding on a carbon resistor is, shown in the given figure. The resistance, value of the given resistor is, , Gold, Red, Green, Violet, , a. (5700 ± 285) Ω, b. (7500 ± 750) Ω, c. (5700 ± 375) Ω, d. (7500 ± 375) Ω, , 8. An antenna is mounted on a 400 m tall, building. What will be the wavelength of, signal that can be radiated effectively by the, transmission tower upto a range of 44 km?, a. 37.8 m, c. 75.6 m, , a. 1 V, c. 2 V, , b. 2π V, d. 0, , b. 605 m, d. 302 m, , uniform spherical shell of mass 100 kg and, radius 50 m. If the gravitational potential at a, point, 25 m from the centre is, V kg/m. The value of V is, a. − 60 G, c. − 20 G, , is 160 m/s, find the rms speed of hydrogen, molecules at 0°C., b. 40 m/s, d. 332 m/s, , 10. A constant magnetic field of 1 T is applied in, , the x > 0 region. A metallic circular ring of, radius 1 m is moving with a constant velocity, of 1 m/s along the X-axis. At t = 0 s, the, centre of O of the ring is at x = − 1m. What, will be the value of the induced emf in the, ring at t = 1s?, (Assume the velocity of the ring does not, change.), , b. + 2 G, d. − 4 G, , 12. For full scale deflection of total 50 divisions,, 50 mV voltage is required in galvanometer., The resistance of galvanometer if its current, sensitivity is 2 div/mA will be, a. 1 Ω, c. 4 Ω, , b. 5 Ω, d. 2 Ω, , 13. A monochromatic neon lamp with, wavelength of 670.5 nm illuminates a, photo-sensitive material which has a, stopping voltage of 0.48 V. What will be the, stopping voltage if the source light is, changed with another source of wavelength, of 474.6 nm?, a. 0.96 V, c. 0.24 V, , b. 1.25 V, d. 1.5 V, , 14. Match List-I with List-II., List-I, , List-II, , A., , R H (Rydberg constant) 1., , kg m − 1s − 1, , B., , h (Planck’s constant), , 2., , kg m 2 s − 1, , C., , µ B (Magnetic field, energy density), , 3., , m−1, , D., , η (Coefficient of, viscosity), , 4., , kg m − 1s − 2, , 9. If the rms speed of oxygen molecules at 0°C, a. 640 m/s, c. 80 m/s, , x, , 11. A mass of 50 kg is placed at the centre of a, , V, , a. 2 : 1 : 1, c. 1 : 2 : 2, , v, , Choose the most appropriate answer from the, options given below., a., b., c., d., , A, 2, 3, 4, 3, , B, 3, 2, 2, 2, , C, 4, 4, 1, 1, , D, 1, 1, 3, 4
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36, , ONLINE, , 15. If force (F ), length (L) and time (T ) are taken as, , JEE Main 2021 ~ Solved Papers, , y, A, , the fundamental quantities. Then what will, be the dimension of density :, a. [FL−4 T 2 ], c. [FL−5 T 2 ], , b. [FL−3 T 2 ], d. [FL−3 T 3 ], , 16. A co-axial cable consists of an inner wire of, radius a surrounded by an outer shell of, inner and outer radii b and c, respectively., The inner wire carries an electric current i 0,, which is distributed uniformly across, cross-sectional area. The outer shell carries, an equal current in opposite direction and, distributed uniformly. What will be the ratio, of the magnetic field at a distance x from the, axis when (i) x < a and (ii) a < x < b?, a., c., , x2, , a2, , b., x2, , d., , b2 − a2, , a2, , x2, b2 − a2, , b. 14.76º C, d. 0.014º C, , −1, , of 25 ms at an angle of 45º from the, ground. What are the maximum height and, the time taken by the football to reach at the, highest point during motion ?, (Take, g = 10 ms − 2), a. hmax = 10 m, T = 2.5 s, b. hmax = 15.625 m, T = 3.54 s, c. hmax = 15.625 m, T = 1.77 s, d. hmax = 3.54 m, T = 0.125 s, , B, , a., c., , 3 3Q $, (i ), , 8 πε0R 2, 3 3Q, , 16 π 2 ε0R 2, , b., ($i ), , d., , 3 3Q, 8 π 2ε0R 2, 3 3Q, 8 π 2 ε0R 2, , ($i ), (−i$ ), , reservoir at temperature T2 = 400 K and a hot, reservoir at temperature T1. It takes 300 J of, heat from the hot reservoir and delivers, 240 J of heat to the cold reservoir in a cycle., The minimum temperature of the hot, reservoir has to be ............ K., , represented by the equations y1 = 10, π, , sin 3πt + and y 2 = 5 (sin 3πt + 3 cos 3πt), , 3, Ratio of amplitude of y1 to y 2 = x : 1. The value, of x is ............ ., , 23. x different wavelengths may be observed in, the spectrum from a hydrogen sample if the, atoms are exited to states with principal, quantum number n = 6? The value of x is, ........ ., , 19. The light waves from two coherent sources, , have same intensity I1 = I2 = I0. In, interference pattern the intensity of light at, minima is zero. What will be the intensity of, light at maxima ?, c. 5 I 0, , R, , 22. Two simple harmonic motion, are, , 18. A player kicks a football with an initial speed, , b. 2 I 0, , x, , 21. A heat engine operates between a cold, , the difference in temperature of water at the, top and at the bottom of fall ?, [Given, 1 cal = 4.2 J and specific heat of water, = 1 cal g − 1ºC − 1], , a. I 0, , 120º, , 60º, 60º, , Section B : Numerical Type Questions, , x2, , 17. The height of victoria falls is 63 m. What is, , a. 0.147º C, c. 1.476º C, , O, , d. 4 I 0, , 20. Figure shows a rod AB, which is bent in a, 120º circular arc of radius R. A charge (− Q) is, uniformly distributed over rod AB. What is, the electric field E at the centre of curvature, O?, , 24. A Zener diode of power rating 2W is to be, used as a voltage regulator. If the Zener, diode has a breakdown of 10 V and it has to, regulate voltage fluctuated between 6 V and, 14 V, the value of R S for safe operation, should be ........ Ω, Rs, Unregulated, voltage, , Regulated, voltage
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37, , AUGUST ATTEMPT ~ 27 August 2021, Shift II, 25. Wires W1 and W2 are made of same material, having the breaking stress of 125, . × 109 N/m 2., W1 and W2 have cross-sectional area of, 8 × 10− 7 m 2 and 4 × 10 − 7m 2, respectively., Masses of 20 kg and 10 kg hang from them, as shown in the figure. The maximum mass, that can be placed in the pan without, breaking the wires is .......... kg., (Use, g = 10 m/s 2 ), W1, , 27. An AC circuit has an inductor and a resistor, of resistance R in series, such that X L = 3R ., Now, a capacitor is added in series such that, X C =2R . The ratio of new power factor with, the old power factor of the circuit is 5: x, The value of x is., , 28. The ratio of the equivalent resistance of the, network (shown in figure) between the, points a and b when switch is open and, switch is closed is x : 8. The value of x is, , 20 kg, , 2R, , R, , W2, 10 kg, , a, , S, , b, , Pan, , 26. A bullet of 10 g, moving with velocity v,, collides head-on with the stationary bob of a, pendulum and recoils with velocity 100 m/s., The length of the pendulum is 0.5 m and, mass of the bob is 1 kg. The minimum value, of v .......... m/s, so that the pendulum, describes a circle. (Assume, the string to be, inextensible and g = 10 m/s 2), , 2R, , R, , 29. A plane electromagnetic wave with, frequency of 30 MHz travels in free space. At, particular point in space and time, electric, field is 6 V/m. The magnetic field at this, point will be x × 10− 8 T. The value of x is., , 30. A tuning fork is vibrating at 250 Hz. The, length of the shortest closed organ pipe that, will resonate with the tuning fork will be, ......... cm., , 0.5 m, v, 10 g, , (Take, speed of sound in air as 340 ms − 1), , 1 kg, , CHEMISTRY, Section A : Objective Type Questions, 1. Choose the correct statement from the, following., a. The standard enthalpy of formation for alkali, metal bromide becomes less negative on, descending the group., b. The low solubility of CsI in water is due to its, high lattice enthalpy., c. Among the alkali metal halides, LiF is least, soluble in water., d. LiF has least negative standard enthalpy of, formation among alkali metal fluorides., , 2. The addition of dilute NaOH to Cr 3 + salt, solution will give, , a. a solution of [Cr(OH) 4 ] −, b. precipitate of Cr2O 3 (H2O) n, c. precipitate of [ Cr(OH) 6 ] 3 −, d. precipitate of Cr(OH) 3, , 3. Given below are two statements., Statement I Ethyl pent–4–yn–oate on reaction, with CH3MgBr gives a 3° alcohol., Statement II In this reaction, one mole of, ethyl pent–4–yn–oate utilizes two moles of, CH3MgBr .
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38, , ONLINE, In the light of the above statements, choose, the most appropriate answer from the options, given below., a. Both statement I and statement II are false., b. Statement I is false but statement II is true., c. Statement I is true but statement II is false., d. Both statement I and statement II are true., , JEE Main 2021 ~ Solved Papers, , c. CH3CH2CCl3 + OH− / H3O +, d. CH3CH2CH2Br + Mg, CO 2 , dry ether/H3O +, , 9. The correct order of ionic radii for the ions,, P3 − , S 2 − , Ca 2 + , K + , Cl− is, , a. P 3 − > S2 − > Cl − > K + > Ca 2 +, b. Cl − > S 2 − > P 3 − > Ca 2 + > K +, c. P 3 − > S 2 − > Cl − > Ca 2 + > K +, d. K + > Ca 2 + > P 3 − > S 2 − > Cl −, , 4. In stratosphere most of the ozone formation, , 10. Which one of the following is the major, , is assisted by, a. cosmic rays, b. γ–rays, c. ultraviolet radiations d. visible radiations, , product of the given reaction?, CH3, , 5. The compound/s which will show significant, , NC, , intermolecular H–bonding is/are, NO2, , HO, , (A ), , CH3, , H, N, , OH, , CH3, , (i) 2CH3MgBr, Major product, (ii) H3O+, (iii) H2SO4, heat, , CH3, HO, , (B), , CH3, , a. CH3, , CH3, , (C), , a. (B) only, c. (A) and (B), , b. (C) only, d. (A), (B) and (C), , 6. Which one of the following chemicals is, , CH3, NC, , CH3, , b., , responsible for the production of HCl in the, stomach leading to irritation and pain?, , CH3, , CO, a., , CH3, , NH, , NC, , SO2, , CH3, , c., CH3, , HN, b., N, , NH2, , CH3, NH2, , HO, c., , CH3, , d. CH3, , CH3, , N, H, , 11. The major product ( A) formed in the reaction, , H, NNH2, , given below is, , d., , CH3—CH2—CH—CH2Br, , 7. The oxide that gives H2O2 most readily on, treatment with H 2O is, a. PbO 2, , b. Na2O 2, , c. SnO 2 d. BaO 2 ⋅ 8H2O, , + CH3O, , a. CH3—CH2—CH—CH2Br, , 8. Which one of the following reactions will not, yield propionic acid?, , a. CH3CH2COCH3 + OI− / H3O +, b. CH3CH2CH3 + KMnO 4 (Heat), OH– / H3O +, , OCH3, , CH3OH, , A, Major, product
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39, , AUGUST ATTEMPT ~ 27 August 2021, Shift II, , 16. Which one of the following tests used for the, , b. CH3—CH2—C==CH2, , identification of functional groups in organic, compounds does not use copper reagent ?, a. Barfoed’s test, b. Seliwanoff’s test, c. Benedict’s test, d. Biuret test for peptide bond, , c. CH3—CH2—CH—CH2—OH, , 17. Hydrolysis of sucrose gives, a. α -D-(−)-glucose and β -D-(−)-fructose, b. α -D-(+ )-glucose and β -D-(+)-fructose, c. α -D-(−)-glucose and β-D-(+ )-fructose, d. α -D-(+ )-glucose and β-D-(−)-fructose, , d. CH3—CH2—CH—CH2—OCH3, , 18. Match List-I with List-II., 12. Which one of the following is used to remove, most of plutonium from spent nuclear fuel?, b. O 2F2, d. BrO 3, , a. ClF3, c. I2O 5, , 13. Lyophilic sols are more stable than lyophobic, sols because, a. there is a strong electrostatic repulsion, between the negatively charged colloidal, particles., b. the colloidal particles have positive charge., c. the colloidal particles have no charge., d. the colloidal particles are solvated., , 14. The major product of the following reaction,, if it occurs by SN2 mechanism is, , , O, a., , O, , (Name of, ore/mineral), , (Chemical formula), , A., , Calamine, , 1., , ZnS, , B., , Malachite, , 2., , FeCO 3, , C., , Siderite, , 3., , ZnCO 3, , D., , Sphalerite, , 4., , CuCO 3 ⋅ Cu(OH) 2, , Choose the most appropriate answer from the, options given below, a., c., , A, 3, 4, , B, 4, 3, , C, 2, 1, , D, 1, 2, , b., d., , A, 3, 3, , B, 4, 2, , C, 1, 4, , D, 2, 1, , (mainly) when red phosphorus is heated in a, sealed tube at 803 K ?, , K2CO3, Acetone, , Br, , List-I, , 19. Which one of the following is formed, , OH, +, , List-I, , a. White phosphorus b. Yellow phosphorus, c. β-black phosphorus d. α-black phosphorus, O, , 20. The correct structures of A and B formed in, the following reactions are, , b., , OH, , c., , O, , H2/Pd, C2H5OH, , O, d., , a. paramagnetic and colourless, b. diamagnetic and green, c. diamagnetic and colourless, d. paramagnetic and green, , 1 eq., , B, (Major product), , NO2, OH, , 15. Potassium permanganate on heating at, 513 K gives a product which is, , O, , A, , a., , A=, , OH, ,, , NH2, , CH3, , B=, NH2
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40, , ONLINE, , JEE Main 2021 ~ Solved Papers, , 24. 100 g of propane is completely reacted with, O, b., , O, , CH3, , A=, , ,, , CH3, , B=, , NH2, , CH3, , NH, , OH, , O, , CH3, , 1000 g of oxygen. The mole fraction of, carbon dioxide in the resulting mixture is, x × 10− 2. The value of x is ........ . (Nearest, integer), [Atomic weight : H = 1.008, C = 12.00, O =16.00], , 25. 40 g of glucose (Molar mass = 180) is mixed, with 200 mL of water. The freezing point of, solution is ............ K. (Nearest integer), [Given, K f = 1.86 K kg mol − 1, density of water =, 1.00 g cm − 3 , freezing point of water = 273.15 K], , 26. The resistance of a conductivity cell with cell, c., , d., , A=, , ,, NH2, , NH2, , OH, , OH, , A=, , ,, NH2, , constant 1.14 cm − 1, containing 0.001 M KCl at, 298 K is 1500 Ω. The molar conductivity of, 0.001 M KCl solution at 298 K in S cm 2mol − 1, is .......... . (Integer answer), , B=, , 27. The number of photons emitted by a, , B=, NH, , CH3, , monochromatic (single frequency) infrared, range finder of power 1 mW and wavelength, of 1000 nm, in 0.1 second is x × 1013. The, value of x is ......... . (Nearest integer), (h = 6.63 × 10 − 34 Js, c = 3.00 × 10 8 ms − 1), , Section B : Numerical Type Questions, 21. The first order rate constant for the, decomposition of CaCO3 at 700 K is, 6.36 × 10− 3 s − 1 and activation energy is, 209 kJ mol − 1. Its rate constant (in s − 1) at, 600 K is x × 10− 6. The value of x is .......... ., (Nearest integer), [Given, R = 8.31 JK − 1mol − 1, log 6.36 × 10− 3, = – 2.19, 10− 4.79 = 1.62 × 10− 5], , 22. The number of optical isomers possible for, [Cr(C 2O4) 3 ]3 − is ..., , 23. Two flasks I and II shown below are, connected by a valve of negligible volume., 2.8 g N2, 300 K, 1L, , 0.2 g N2, 60 K, 2L, , When the valve is opened, the final pressure of, the system in bar is x × 10− 2 . The value of x is, .............. . (Integer answer), [Assume, Ideal gas, 1 bar = 105 Pa, molar mass, of N2 = 28.0 g mol − 1; R = 8.31 J mol − 1 K − 1], , 28. When 5.1 g of solid NH4HS is introduced into, a two litre evacuated flask at 27°C, 20% of, the solid decomposes into gaseous, ammonia and hydrogen sulphide. The K p for, the reaction at 27°C is x × 10− 2. The value of, x is ........... . (Integer answer), [Given, R = 0.082 L atm K − 1 mol − 1], , 29. The number of species having, non–pyramidal shape among the following is, (i) SO 3, , (ii) NO −3, , (iii) PCl3, , (iv) CO 23 −, , 30. Data given for the following reaction is as, follows., FeO(s) + C (graphite) → Fe(s) + CO( g ), Substance, , ∆H ° (kJ mol − 1) ∆S ° (J mol − 1 K − 1), , FeO(s), , − 266.3, , 57.49, , C (graphite), , 0, , 5.74, , Fe(s), , 0, , 27.28, , CO( g ), , − 110.5, , 197.6, , The minimum temperature in K at which the, reaction becomes spontaneous is ..........., (Integer answer)
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41, , AUGUST ATTEMPT ~ 27 August 2021, Shift II, , MATHEMATICS, Section A : Objective Type Questions, 1. The angle between the straight lines, whose, direction cosines are given by the equations, 2l + 2m − n = 0 and mn + nl + lm = 0, is, a., , π, 2, , 4, b. π − cos − 1 , 9, π, d., 3, , 8, c. cos − 1 , 9, , [ x + 1] [ x + 2] [ x + 3], , , [ x + 3] [ x + 3] , where [t ], [x], [ x + 2] [ x + 4 ], , , 2. Let A = [ x ], , denotes the greatest integer less than or, equal to t. If det(A) = 192, then the set of, values of x is the interval, a. [68, 69) b. [62, 63), , c. [65, 66) d. [60, 61), , 3. Let M and m respectively be the maximum, and minimum values of the function, π, f ( x) = tan− 1(sin x + cos x) in 0, , then the, 2 , value of tan(M − m) is equal to, a. 2 + 3, c. 3 + 2 2, , b. 2 − 3, d. 3 − 2 2, , tosses three fair coins. The probability that, both of them get the same number of heads, is, 1, 8, , b., , 5, 8, , c., , 5, 16, , d. 1, , 5. A differential equation representing the, family of parabolas with axis parallel to, Y-axis and whose length of latus rectum is, the distance of the point (2, – 3) from the line, 3x + 4 y = 5, is given by, a. 10, c. 10, , d2 y, , dx 2, d2x, dy 2, , = 11, = 11, , the line of intersection of the planes, r ⋅( i$ + $j + k$ ) = 1and r ⋅(2$i + 3$j − k$ ) + 4 = 0 and, parallel to the X-axis is, a. r ⋅ ( $j − 3k$ ) + 6 = 0, b. r ⋅ ( $i + 3k$ ) + 6 = 0, c. r ⋅ ( $i − 3k$ ) + 6 = 0, d. r ⋅ ( $j − 3k$ ) − 6 = 0, , 8. If the solution curve of the differential, , equation (2x − 10 y 3)dy + ydx = 0, passes, through the points (0, 1) and (2, β), then β is a, root of the equation, a. y 5 − 2 y − 2 = 0, c. 2 y 5 − y 2 − 2 = 0, , b. 2 y 5 − 2 y − 1 = 0, d. y 5 − y 2 − 1 = 0, , 9. Let A(a , 0), B ( b, 2b + 1) and C (0, b), b ≠ 0,|b|≠ 1,, be points such that the area of ∆ABC is, 1 sq. unit, then the sum of all possible values, of a is, a., , − 2b, b+1, , b., , 2b, b+1, , c., , 2b 2, b+1, , d., , − 2b 2, b+1, , 10. Let λ be the greatest integer less than or, , 4. Each of the persons A and B independently, , a., , 7. The equation of the plane passing through, , d2x, b. 11 2 + 10, dy, d2 y, d. 11 2 = 10, dx, , equal to λ. The set of all values of λ for which, the system of linear equations x + y + z = 4,, 3x + 2 y + 5z = 3, 9x + 4 y + (28 + λ ) z = λ, has a solution is, a. R, c. [ − 9, − 8), , b. (− ∞ ,− 9) ∪ (− 9, ∞), d. (− ∞ , − 9) ∪ [ − 8, ∞ ), , 11. The set of all values of k > − 1, for which the, equation (3x 2 + 4 x + 3) 2− ( k + 1) (3x 2 + 4 x + 3), (3x 2 + 4 x + 2) + k(3x 2 + 4 x + 2) 2 = 0 has real, roots, is, 5, a. 1,, 2 , , b. [ 2, 3), , 1 , c. − , 1, 2 , , 1 3, d. ,, − {1}, 2 2 , , 12. A box open from top is made from a, 6. If two tangents drawn from a point P to the, parabola y 2 = 16( x − 3) are at right angles,, then the locus of point P is, a. x + 3 = 0, c. x + 2 = 0, , b. x + 1 = 0, d. x + 4 = 0, , rectangular sheet of dimension a × b by, cutting squares each of side x from each of, the four corners and folding up the flaps. If, the volume of the box is maximum, then x is, equal to
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42, , ONLINE, a., b., c., d., , 1, a. e 2, 2, , a + b − a 2 + b 2 − ab, 12, a + b − a 2 + b 2 + ab, , is, , 6, , is equivalent to, b. (q ∧ r ) ⇒ ( p ∧ q ), d. ( p ∧ r ) ⇒ ( p ∧ q ), , 14. Let Z be the set of all integers,, A = {(x , y ) ∈ Z × Z :(x − 2) + y ≤ 4 },, B = {(x , y ) ∈ Z × Z : x 2 + y 2 ≤ 4 } and, C = {(x , y ) ∈ Z × Z :(x − 2) 2 + ( y − 2) 2 ≤ 4 }, If the total number of relation from A ∩ B to, A ∩ B is 2p , then the value of p is, 2, , 2, , c. 49, , d. 9, , 15. The area of the region bounded by the, , parabola ( y − 2) 2 = ( x − 1) , the tangent to it at, the point whose ordinate is 3 and the X-axis, is, b. 10, , c. 4, , d. 6, , 1 + sin x + 1 − sin x , ,, , 1 + sin x − 1 − sin x , dy, 5π, , then, at x =, is, dx, 6, , 16. If y ( x) = cot − 1, π , ⋅ x ∈ , π, 2 , 1, a. −, 2, , 1, c., 2, , b. − 1, , d. 0, , 17. Two poles, AB of length a m and CD of length, , a + b ( b ≠ a) metres are erected at the same, horizontal level with bases at B and D. If BD =, 1, x and tan ∠ ACB ! = , then, 2, , 2, 3, 1, at x = is, 2, , 18. If 0 < x < 1 and y = x 2 + x 3 +, the value of e1 +, , y, , d. 2e 2, , x dx, , π, 8, , 3, , 2 , 3, , 6 , , , 1 −, , π, d. 1 −, 4, b., , π, 4, , 3, , 6 , 3, , 2 , , 20. If lim ( x 2 − x + 1 − ax) = b, then the ordered, x→ ∞, , pair (a , b) is, 1, a. 1, , 2, 1, , c. − 1, , , 2, , 1, , b. 1, − , , 2, 1, , d. − 1, − , , 2, , Section B : Numerical Type Questions, 21. Let S be the sum of all solutions (in radians), , of the equation sin4 θ + cos 4 θ − sinθ cos θ = 0, 8S, is equal to, in [0, 4 π ]. Then,, π, , 22. Let S be the mirror image of the point Q, (1, 3, 4) with respect to the plane, 2x − y + z + 3 = 0 and let R(3, 5, γ) be a point, of this plane. Then the square of the length, of the line segment SR is, , 23. The probability distribution of random, variable X is given by, X, , 1, , 2, , 3, , 4, , 5, , P (X ), , K, , 2K, , 2K, , 3K, , K, , Let p = P (1 < X < 4| X < 3). If 5p = λK then, λ equal, to, , 24. Let Z1 and Z 2 be two complex numbers such, π, and Z1, Z 2 satisfy the, 4, equation Z − 3 = Re( Z ). Then, the imaginary, part of Z1 + Z 2 is equal to, , a. x 2 + 2(a + 2b ) x − b (a + b ) = 0, b. x 2 + 2(a + 2b ) x + a (a + b ) = 0, c. x 2 − 2ax + b (a + b ) = 0, d. x 2 − 2ax + a (a + b ) = 0, , 1, 2, , , 1 −, , π, c. 1 −, 8, a., , 13. The Boolean expression ( p ∧ q) ⇒ (( r ∧ q) ∧ p), , a. 9, , 1, e, 2, , (1+ x) (1 + 3x)(3 + x), 0, , 6, a + b + a 2 + b 2 − ab, , b. 25, , c., , 1, , a + b − a 2 + b 2 − ab, , a. 16, , b. 2e, , 19. The value of the integral ∫, , 6, , a. ( p ∧ q ) ⇒ ( r ∧ q ), c. ( p ∧ q ) ⇒ (tr ∨ q ), , JEE Main 2021 ~ Solved Papers, , that arg ( Z1 − Z 2) =, , 3 4 + ..., then, x, 4, , 25. Let S = {1, 2, 3, 4, 5, 6, 9}. Then, the number, of elements in the set T = {A ⊆ S: A ≠ φ and, the sum of all the elements of A is not a, multiple of 3} is
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43, , AUGUST ATTEMPT ~ 27 August 2021, Shift II, 26. Let A (sec θ , 2 tan θ) and B (sec φ , 2 tan φ) ,, , 29. An online exam is attempted by 50, , where θ + φ = π / 2, be two points on the, hyperbola 2x 2 − y 2 = 2 . If (α, β) is the point of, the intersection of the normals to the, hyperbola at A and B, then (2β)2 is equal to, , candidates out of which 20 are boys. The, average marks obtained by boys is 12 with a, variance 2. The variance of marks obtained, by 30 girls is also 2. The average marks of all, 50 candidates is 15. If µ is the average marks, of girls and σ 2 is the variance of marks of, 50 candidates, then µ + σ 2 is equal to, , 27. Two circles each of radius 5 units touch each, other at the point (1, 2). If the equation of, their common tangent is 4 x + 3 y = 10 and, C 1(α, β) and C 2(γ, δ), C 1 ≠ C 2 are their centres,, then|(α + β) (γ + δ)| is equal to, , 30. If ∫, , 2e x + 3e − x, 4e x + 7e − x, , dx =, , 1, (ux + v log e, 14, , ( 4e x + 7e − x )) + C , where C is a constant of, integration, then u + v is equal to, , 28. 3 × 722 + 2 × 1022 − 44 when divided by 18, leaves the remainder, , Answers, For solutions scan, the QR code, , Physics, 1. (b), 11. (d), 21. 500, , 2. (d), 12. (d), 22. 1, , 3. (b), 13. (b), 23. 15, , 4. (d), 14. (b), 24. 20, , 5. (c), 15. (a), 25. 40, , 6. (c), 16. (a), 26. 400, , 7. (d), 17. (a), 27. 1, , 8. (b), 18. (c), 28. 9, , 9. (a), 19. (d), 29. 2, , 10. (c), 20. (d), 30. 34, , Chemistry, 1. (c), 11. (b), 21. 16, , 2. (b), 12. (b), 22. 2, , 3. (c), 13. (d), 23. 84, , 4. (c), 14. (d), 24. 19, , 5. (a), 15. (d), 25. 271, , 6. (b), 16. (b), 26. 760, , 7. (b), 17. (d), 27. 50, , 8. (d), 18. (a), 28. 6, , 9. (a), 19. (d), 29. 3, , 10. (a), 20. (d), 30. 964, , 3. (d), 13. (a), 23. 30, , 4. (c), 14. (b), 24. 6, , 5. (d), 15. (a), 25. 80, , 6. (b), 16. (a), 26. (*), , 7. (a), 17. (c), 27. 40, , 8. (d), 18. (a), 28. 15, , 9. (d), 19. (a), 29. 25, , 10. (a), 20. (b), 30. 7, , Mathematics, 1. (a), 11. (a), 21. 56, , 2. (b), 12. (c), 22. 72, , Note (*) None of the option is correct.
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44, , JEE Main 2021 ~ Solved Papers, , ONLINE, , JEE Main 2021, 31 AUGUST SHIFT I, PHYSICS, Section A : Objective Type Questions, 1. A helicopter is flying horizontally with a, speed v at an altitude h has to drop a food, packet for a man on the ground. What is the, distance of helicopter from the man when, the food packet is dropped?, , 2v 2 h, + h2, g, , d., , 2 gh, v2, , lens having focal length f . What is the, magnification and distance of the image, from the optical centre of the lens?, , + h2, , 2. In the following logic circuit, the sequence of, the inputs A, B are (0, 0), (0,1),, (1, 0) and (1, 1). The output Y for this, sequence will be, A, B, P, , Y, , Q, , a. 1, 0, 1, 0, c. 1, 1, 1, 0, , b. 0, 1, 0, 1, d. 0, 0, 1, 1, , a. 1, ∞, , b. Very high, ∞, , 1 f, c. ,, 2 2, , 1 f, d. ,, 4 4, , 6. A sample of a radioactive nucleus A, disintegrates to another radioactive nucleus, B, which in turn disintegrates to some other, stable nucleus C . Plot of a graph showing the, variation of number of atoms of nucleus B, versus time is, (Assume that at t = 0, there are no B atoms in, the sample), , 3. Two particles A and B having charges 20 µC, and − 5 µC respectively are held fixed with a, separation of 5 cm. At what position a third, charged particle should be placed, so that it, does not experience a net electric force?, 20µC, A, , a., , Time, , –5µC, 5 cm, , c. 180.4°C d. 382°C, , 5. An object is placed at the focus of concave, , b. 2 ghv 2 + h 2, , h2, , b. 280°C, , No. of atoms, , c., , 2 ghv 2 + 1, , a. 174°C, , B, , a. At 5 cm from 20 µC on the left side of system, b. At 5 cm from – 5 µC on the right side, c. At 1.25 cm from – 5 µC between two charges, d. At mid-point between two charges, , b., , No. of atoms, , a., , 1, 4, the temperature of the sink is reduced by, 58°C, its efficiency becomes double., Calculate the temperature of the sink., , 4. A reversible engine has an efficiency of . If, , Time
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45, , AUGUST ATTEMPT ~ 31 August 2021, Shift I, , No. of atoms, , b, then the coefficient of mutual inductance, between the two loops is, , c., , µ0, a2, 8 2, 4π, b, µ, b2, c. 0 8 2, 4π, a, , a., , µ0, 4π, µ, d. 0, 4π, b., , 8 2, a, 8 2, b, , Time, , 11. Choose the correct wave form that can, No. of atoms, , represent the voltage across R of the, following circuit, assuming the diode is ideal, one., , d., , D, Time, , 7. A coil having N turns is wound tightly in the, form of a spiral with inner and outer radii a, and b, respectively. Find the magnetic field at, centre, when a current I passes through coil, a., , µ 0IN, b, ln , 2(b − a ) a , , b., , µ 0I a + b , ln , , 8, a − b , , c., , µ 0I, 1 1, ln − , 4 (a − b ) a b , , d., , µ 0I a − b , ln , , 8, a + b, , R, V i =10 sinωt ~, , +, –, , 3V, , V, , a., , +3, , t, , –3, , 8. A body of mass M moving at speed v 0 collides, elastically with a mass m at rest. After the, collision, the two masses move at angles θ1, and θ 2 with respect to the initial direction of, motion of the body of mass M. The largest, possible value of the ratio M/m, for which the, angles θ1 and θ 2 will be equal, is, a. 4, c. 3, , V, , b., , +3, t, –3, , b. 1, d. 2, , 9. The masses and radii of the Earth and Moon, are (m1, R1) and (m 2, R 2), respectively. Their, centres are at a distance r apart. Find the, minimum escape velocity for a particle of, mass m to be projected from the middle of, these two masses., 1 4G (m1 + m 2 ), r, 2, 1 2G (m1 + m 2 ), c. v =, r, 2, , a. v =, , V, , c., , +3, , t, , –3, , 4G (m1 + m 2 ), r, 2G (m1 + m 2 ), d. v =, r, b. v =, , V, , 10. A small square loop of side a and one turn is, placed inside a larger square loop of side b, and one turn (b >> a). The two loops are, coplanar with their centres coinciding. If a, current l is passed in the square loop of side, , d., , +3, –3, , t
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46, , ONLINE, , 12. A uniform heavy rod of weight 10 kg ms −2,, 2, , cross-sectional area 100 cm and length 20 cm, is hanging from a fixed support. Young’s, modulus of the material of the rod is, 2 × 1011 Nm − 2. Neglecting the lateral, contraction, find the elongation of rod due to, its own weight., a. 2 × 10− 9 m, c. 4 × 10− 8 m, , b. 5 × 10− 8 m, d. 5 × 10− 10 m, , 13. Two plane mirrors M1 and M 2 are at right, angle to each other shown. A point source P, is placed at a and 2a meter away from M1, and M 2, respectively. The shortest distance, between the images thus formed is, (Take 5 = 2.3), a, , JEE Main 2021 ~ Solved Papers, , p0, aeR, c. infinity, , ap 0, cR, d. 0ºC, , a., , b., , 16. Which of the following equations is, dimensionally incorrect ?, Where, t = time, h = height, s = surface, tension, θ = angle, ρ = density, a, r = radius, g =, acceleration due to gravity, V = volume , p =, pressure, W = work done, τ = torque, ε =, permittivity, E = electric field, J = current, density, L = length., πpa 4, 8ηL, ∂E, c. J = ε, ∂t, , a. V =, , b. h =, , 2s cos θ, ρrg, , d. W = τθ, , 17. Angular momentum of a single particle, , P, , moving with constant speed along circular, path, M1, , a. changes in magnitude but remains same in the, direction, b. remains same in magnitude and direction, c. remains same in magnitude but changes in the, direction, d. is zero, , 2a, , M2, , 18. In an AC-circuit, an inductor, a capacitor and, , b. 4.6 a, d. 2 10 a, , a. 3a, c. 2.3 a, , a resistor are connected in series with, X L = R = X C . Impedance of this circuit is, , 14. Match List-I with List-II., , a. 2R 2, , List-I, , List-I, , A., , Torque, , 1., , MLT − 1, , B., , Impulse, , 2., , MT − 2, , C., , Tension, , 3., , ML2 T − 2, , D., , Surface tension, , 4., , MLT − 2, , a., c., , B, 1, 3, , C, 4, 4, , D, 2, 2, , b., d., , A, 2, 3, , B, 1, 4, , c. R, , d. R 2, , 19. A moving proton and electron have the same, de-Broglie wavelength. If k and p denote the, KE and momentum, respectively. Then,, choose the correct option., a. K p < K e and p p = p e, c. K p < K e and p p < p e, , Choose the most appropriate answer from, the options given below., A, 3, 1, , b. Zero, , C, 4, 1, , D, 3, 2, , 15. For an ideal gas the instantaneous change in, pressure p with volume V is given by the, dp, equation, = − ap. If p = p0 at V = 0 is the, dV, given boundary condition, then the, maximum temperature one mole of gas can, attain is, (Here R is the gas constant), , b. K p = K e and p p = p e, d. K p > K e and p p = p e, , 20. Consider a galvanometer shunted with 5 Ω, resistance and 2% of current passes through, it. What is the resistance of the given, galvanometer ?, a. 300 Ω, c. 245 Ω, , b. 344 Ω, d. 226 Ω, , Section B : Numerical Type Questions, 21. When a rubber ball is taken to a depth of ......, m in deep sea, its volume decreases by 0.5%., (The bulk modulus of rubber = 9.8 × 108 Nm − 2., Density of sea water = 103 kg m − 3,, g = 9.8 m/s 2)
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47, , AUGUST ATTEMPT ~ 31 August 2021, Shift I, 22. A particle of mass 1 kg is hanging from a spring, of force constant 100 Nm − 1. The mass is pulled, slightly downward and released, so that it, executes free simple harmonic motion with, time period T . The time when the kinetic, energy and potential energy of the system will, become equal, is T / x . The value of x is., , 23. If the sum of the heights of transmitting and, receiving antennas in the line of sight of, communication is fixed at 160 m, then the, maximum range of LOS communication is, .......... km., (Take, radius of Earth = 6400 km), , 27. A block moving horizontally on a smooth, , surface with a speed of 40 ms − 1 splits into, two equal parts. If one of the parts moves, at 60 ms − 1 in the same direction, then the, fractional change in the kinetic energy will, be x : 4, where x is, , 28. The electric field in an electromagnetic, wave, x, is given by E = (50 NC − 1) sin ω t − ., , c, , 24. A square shaped wire with resistance of each, side 3Ω is bent to form a complete circle. The, resistance between two diametrically opposite, points of the circle in unit of Ω will be, , 25. A wire having a linear mass density, , 9.0 × 10− 4 kg/m is stretched between two rigid, supports with a tension of 900 N. The wire, resonates at a frequency of 500 Hz. The next, higher frequency at which the same wire, resonates is 550 Hz. The length of the wire is, ......... m., , 26. The voltage drop across 15Ω resistance in the, , The energy contained in a cylinder of, volume V is 55, . × 10− 12 J. The value of V is, .......... cm 3 ., (Given ε0 = 8.85 × 10− 12 C 2 N − 1 m − 2 )., , 29. A capacitor of 50 µF is connected in a, circuit as shown in figure. The charge on, the upper plate of the capacitor is .............., µC., 2 kΩ, 6V, 2 kΩ, , 2 kΩ, , C=50 µF, , given figure will be ......... V., 4Ω, , 15Ω, 2Ω, , 4Ω, a, , 10Ω, , 8Ω, , 12Ω, , 8Ω, , 12Ω, , 12 V, , 1Ω, , 30. A car is moving on a plane inclined at 30º, b, , to the horizontal with an acceleration of, 10 ms −2 parallel to the plane upward. A, bob is suspended by a string from the, roof of the car. The angle in degrees which, the string makes with the vertical is ........., (Take, g = 10 ms − 2 )
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48, , ONLINE, , JEE Main 2021 ~ Solved Papers, , CHEMISTRY, Section A : Objective Type Questions, 1. The correct order of reactivity of the given chlorides with acetate in acetic acid is, CH3, Cl, >, , a., , Cl Cl, >, , CH3, >, , CH2Cl, , Cl, , CH3, , CH3, CH3, CH2Cl, >, , b., , Cl, >, , Cl, >, CH3, , CH3, Cl, >, , c., , CH2Cl Cl, >, , Cl, , CH, >, , CH3, CH3, Cl, >, , d., , CH2Cl CI, >, , Cl, >, , CH3, , CH3, , 2. Select the graph that correctly describes the adsorption isotherms at two temperatures T1 and T2, (T1 > T2) for a gas., (x = mass of the gas adsorbed ; m = mass of adsorbent ; p = pressure), x, m, , x, m, , T2, , a., , T1, , b., , p, , x, m, , T1, , x, m, , T1, , c., , T2, , T2, , d., , T1, , T2, p, , p, , p, , 3. The major component/ingredient of Portland cement is, a. tricalcium aluminate, , b. tricalcium silicate, , c. dicalcium aluminate, , d. dicalcium silicate, , 4. In the structure of the dichromate ion, there is a, a. linear symmetrical Cr O Cr bond., c. linear unsymmetrical Cr O Cr bond., , b. non-linear symmetrical Cr O Cr bond., d. non-linear unsymmetrical Cr O Cr bond., , 5. Which one of the following compounds contain β-C 1 C 4 glycosidic linkage ?, a. Lactose, , b. Sucrose, , c. Maltose, , d. Amylose
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49, , AUGUST ATTEMPT ~ 31 August 2021, Shift I, 6. The major products A and B in the following, , 9. The major product formed in the following, reaction is, , set of reactions are, , CH3, , OH, A, , H3O+, H2SO4, , LiAIH4, H3O+, , B, , CH3—C—CH—CH3, , a. A =, , OH, ,, , a., , CH3—C, , CHO, , OH, , OH, , CH3, , ,, , H 3C, CO2H, , ,, , B=, , ——COOH, d., , d. A =, , OH, ,, , B=, , —NH2, , CHO, , 7. Which one of the following lanthanides, , exhibits + 2 oxidation state with diamagnetic, nature ?, (Given, Z for Nd = 60, Yb = 70, La= 57, Ce = 58), a. Nd, c. La, , b. Yb, d. Ce, , 8. Given below are two statements., One is labelled as Assertion (A) and the other, is labelled as Reason (R)., Assertion (A) Aluminium is extracted from, bauxite by the electrolysis of molten mixture, of Al2O3 with cryolite., Reason (R) The oxidation state of Al in cryolite, is + 3 ., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. (A) is true but (R) is false, b. (A) is false but (R) is true., c. Both (A) and (R) are true and (R) is the correct, explanation of (A)., d. Both (A) and (R) are true but (R) is not the, correct explanation of (A)., , CH3, , C, , CH—CH3, , CH3, , —NH2, OH, , CH3, , CH3, c., , OH, c. A =, , CH3, , b., , B=, , —CHO, , CH—CH2CH3, , CH3, , B=, , —OH, , b. A =, , Major product, , CH3 OH, , CN, , OH, , Conc.H2SO4, a few drops, , CH3—C—CH, , CH2, , CH3, , 10. Monomer of novolac is, a. 3-hydroxybutanoic acid, b. phenol and melamine, c. o-hydroxymethylphenol, d. 1,3-butadiene and styrene, , 11. Given below are two statements., Statement I The process of producing, syn-gas is called gasification of coal., Statement II The composition of syn-gas is, CO + CO2 + H 2 (1 : 1 : 1), In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Statement I is false but statement II is true., b. Statement I is true but statement II is false., c. Both statement-I and statement II are false., d. Both statement-I and statement II are true., , 12. Given below are two statements., One is labelled as Assertion (A) and the other, is labelled as Reason (R)., Assertion (A) Treatment of bromine water, with propene yields 1-bromopropan-2-ol., Reason (R) Attack of water on bromonium, ion follows Markownikoff rule and results in, 1-bromopropan-2-ol.
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50, , JEE Main 2021 ~ Solved Papers, , ONLINE, In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Both (A) and (R) are true but (R) is not the, correct explanation of (A)., b. (A) is false but (R) is true., c. Both (A) and (R) are true and (R) is the correct, explanation of (A)., d. (A) is true but (R) is false, , 13. The denticity of an organic ligand, biuret is, a. 2, , b. 4, , c. 3, , d. 6, , 14. Given below are two statements : one is, labelled as Assertion (A) and the other is, labelled as Reason (R)., Assertion (A) Metallic character decreases, and non-metallic character increases on, moving from left to right in a period., Reason (R) It is due to increase in ionisation, enthalpy and decrease in electron gain, enthalpy, when one moves from left to right, in a period., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. (A) is false but (R) is true., b. (A) is true but (R) is false, c. Both (A) and (R) are correct and (R) is the, correct explanation of (A)., d. Both (A) and (R) are correct but (R) is not the, correct explanation of (A)., , 15. Choose the correct name for compound, given below, , c., , pV, , d., , pV, , p, , p, , 17. Given below are two statements., One is labelled as Assertion (A) and the other, is labelled as Reason (R)., Assertion (A) A simple distillation can be, used to separate a mixture of propanol and, propanone., Reason (R) Two liquids with a difference of, more than 20°C in their boiling points can be, separated by simple distillations., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. (A) is false but (R) is true., b. Both (A) and (R) are correct but (R) is not the, correct explanation of (A)., c. (A) is true but (R) is false, d. Both (A) and (R) are correct and (R) is the, correct explanation of (A)., , 18. Which one of the following 0.10 M aqueous, solutions will exhibit the largest freezing, point depression ?, a. Hydrazine, c. Glycine, , b. Glucose, d. KHSO 4, , 19. BOD values (in ppm) for clean water ( A) and, polluted water (B) are expected respectively, a. A > 50, B < 27, b. A > 25, B < 17, c. A < 5, B > 17, d. A > 15, B > 47, , Br, , a. (4E)-5-bromohex-4-en-2-yne, b. (2E)-2-bromohex-4-yn-2-ene, c. (2E)-2-bromohex-2-en-4-yne, d. (4E)-5-bromohex-2-en-4-yne, , 20. The structure of product C , formed by the, , 16. Which one of the following is the correct pV, vs p plot at constant temperature for an, ideal gas ? (p and V stand for pressure and, volume of the gas respectively), , following sequence of reactions is, CH3COOH + SOCl2 → A Benzene, → B KCN, , → C, − OH, , AlCl 3, , NC, , OH, CH3, , a., , b., , CH3, CN, , a., , pV, , pV, , H, , b., , c., p, , COOH, , CH2—CH2CN, , C, p, , CH3, , d.
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51, , AUGUST ATTEMPT ~ 31 August 2021, Shift I, Section B : Numerical Type Questions, 21. Consider the following cell reaction,, Cd( s) + Hg 2SO4( s) +, , 9, H O(I), 5 2, , -, , CdSO4, , 9, ⋅ H 2O( s) + 2Hg ( l), 5, °, is 4.315 V at 25°C. If, The value of E cell, ∆H° = − 825.2 kJ mol − 1, the standard entropy, change ∆S° in J K − 1 is ....... (Nearest integer), [Given, Faraday constant = 96487 C mol − 1], , time for 50% completion is ........... (Integer, answer), , 27. The number of hydrogen bonded water, molecule(s) associated with stoichiometry, CuSO4 ⋅5H 2O is/are., , 28. According to the following figure, the, magnitude of the enthalpy change of the, reaction A + B → M + N in kJ mol − 1 is equal to, .......... (Integer answer), , 22. The molarity of the solution prepared by, , x, , A+B, , x=20 kJ mol –1, y=45 kJ mol –1, z=15 kJ mol–1, , y, , Energy, , dissolving 6.3 g of oxalic acid (H 2C 2O4 ⋅ 2H 2O), in 250 mL of water in mol L − 1 is x × 10− 2., The value of x is ......... (Nearest integer), [Atomic mass H = 1.0, C = 12.0, O = 16.0], , M+N, , 23. Consider the sulphides HgS, PbS, CuS, Sb2S 3,, z, , As 2S 3 and CdS. Number of these sulphides, soluble in 50% HNO3 is, , Reaction coordinate, , 24. The total number of reagents from those, given below, that can convert nitrobenzene, into aniline is ........ (Integer answer), I. Sn - HCl, III. Fe- HCl, V. H2 - Pd, , II. Sn - NH4OH, IV. Zn - HCl, VI. H2-Raney nickel, , 25. The number of halogen (s) forming halic (V), acid is, , 26. For a first order reaction, the ratio of the, time for 75% completion of a reaction to the, , 29. Ge(Z = 32) in its ground state electronic, configuration has x completely filled orbitals, with m l = 0. The value of x is, , 30. A3B 2 is a sparingly soluble salt of molar mass, M (g mol − 1 ) and solubility x g L− 1. The, x 5, solubility product satisfies K sp = a . The, M, value of a is .......... (Integer answer), , MATHEMATICS, Section A : Objective Type Questions, , 3. The sum of 10 terms of the series, 3, , 1. Let *, , ∈ { ∧ , ∨ } be such that the Boolean, expression ( p * ~ q) ⇒ (p, , q) is a tautology., , Then, a. * = ∨,, c. * = ∧,, , =∨, =∨, , b. * = ∧,, , =∧, , d. * = ∨,, , =∧, , 2. The number of real roots of the equation, e 4 x + 2e 3 x − e x − 6 = 0 is, a. 2, , b. 4, , c. 1, , d. 0, , 12 × 22, a. 1, , +, , 5, 22 × 32, , +, , 7, 32 × 4 2, , + ... is, , b. 120/121 c. 99/100, , d. 143/144, , 4. Let the equation of the plane, that passes, through the point (1, 4, –3) and contains the, line of intersection of the planes, 3x − 2 y + 4 z − 7 = 0 and x + 5 y − 2 z + 9 = 0, be α x + βy + γ z + 3 = 0, then α + β + γ is, equal to, a. − 23, , b. − 15, , c. 23, , d. 15
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52, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 5. Let f be a non–negative function in [0, 1] and, twice differentiable in (0, 1). If, x, , ∫0, , x, , ∫0 f (t) dt, 0 ≤ x ≤ 1and, 1 x, f (0) = 0, then lim 2 ∫ f (t) dt, 0, x → 0x, 1 − ( f ′ (t)) 2 dt =, , a. equals 0, c. does not exist, , b. equals 1, d. equals 1/2, , | 2a + 3b | = | 3a + b | and the angle between a, 1, and b is 60°. If a is a unit vector, then| b | is, 8, equal to, b. 6, , c. 5, , d. 8, | 9 x 2 − 12 x + 4 |, , 7. The function f ( x) = | x − 2x − 3| ⋅ e, 2, , is not differentiable at exactly, a. four points, c. two points, , b. three points, d. one point, , geometric progression with common ratio r., If the middle number is doubled, then the, new numbers are in an arithmetic, progression with common difference d. If the, fourth term of GP is 3 r 2, then r 2 − d is equal, to, b. 7 +, , c. 7 − 3, , d. 7 + 3 3, , 3, , 9. Which of the following is not correct for, relation R on the set of real numbers ?, a. (x , y ) ∈ R ⇔ 0 <| x| −| y|≤ 1is neither transitive, nor symmetric., b. (x , y ) ∈ R ⇔ 0 <| x − y|≤ 1is symmetric and, transitive., c. (x , y ) ∈ R ⇔| x| −| y|≤ 1is reflexive but not, symmetric., d. (x , y ) ∈ R ⇔ | x − y|≤ 1is reflexive and, symmetric., , 10. The integral ∫, , 1, 4 (x, , − 1) ( x + 2), 3, , 5, , dx is equal to, , (where C is a constant of integration), a., , 3 x + 2, , , 4 x − 1, , 4 x − 1, c. , , 3 x + 2, , 1/ 4, , +C, , 1/ 4, , +C, , 3 x + 2, , , 4 x − 1, , 5/ 4, , 4 x − 1, d. , , 3 x + 2, , 5/ 4, , b., , a. 4 p 2 + q 2 b. 2p 2 + q 2 c. p 2 + 2q 2 d. p 2 + 4q 2, , a. x 2 + 2x − 4 = 0, c. x 2 − 2x + 4 = 0, , b. 4 x 2 + 2x − 1 = 0, d. x 2 − 2x − 4 = 0, , 13. If the following system of linear equations, 2x + y + z = 5, x − y + z = 3 and x + y + az = b, has no solution, then, 1, 7, and b ≠, 3, 3, 1, 7, c. a ≠ − and b =, 3, 3, , 1, and b =, 3, 1, d. a = and b ≠, 3, , a. a = −, , b. a ≠, , 7, 3, 7, 3, , 14. The length of the latus rectum of a parabola,, , 8. Three numbers are in an increasing, , a. 7 − 7 3, , perpendiculars from the origin on the lines,, x cosec α − y sec α = k cot 2α and, x sin α + y cos α = k sin 2α, respectively, then k 2 is equal to, , 12. cosec 18° is a root of the equation, , 6. Let a and b be two vectors such that, , a. 4, , 11. If p and q are the lengths of the, , whose vertex and focus are on the positive, X-axis at a distance R and S( > R) respectively, from the origin, is, a. 4(S + R ), , c. 4(S − R ) d. 2(S + R ), , 15. If the function, , , 1+ x , , 1, a, ,x <0, x log e , x, 1− , , , b, , k, ,x =0, f ( x) = , cos 2 x − sin2 x − 1, ,x >0, , x2 + 1 − 1, , , , 1 1 4, is continuous at x = 0, then + + is equal, a b k, to, a. − 5, , 16. If, , dy 2, =, dx, , c. − 4, , b. 5, x+ y, , 2, , −2, y, , 17. lim, , , y(0) = 1, then y(1) is equal to, b. log 2 ( 1+ e ), d. log 2 (1+ e 2 ), , sin2( π cos 4 x), , x→ 0, , a. π 2, , d. 4, , x, , a. log 2 (2 + e ), c. log 2 (2e ), , +C, +C, , b. 2(S − R ), , x4, b. 2 π 2, , is equal to, c. 4 π 2, , d. 4 π
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53, , AUGUST ATTEMPT ~ 31 August 2021, Shift I, 18. A vertical pole fixed to the horizontal ground, is divided in the ratio 3 : 7 by a mark on it, with lower part shorter than the upper part., If the two parts subtend equal angles at a, point on the ground 18 m away from the, base of the pole, then the height of the pole, (in m) is, a. 12 15, , b. 12 10, , c. 8 10, , d. 6 10, , 2 rπ, 2 rπ, ,r = 1, 2, 3, ...., + i sin, 9, 9, a1 a 2 a 3, i = − 1, then the determinant a 4 a5 a 6 is, a7 a8 a9, , 19. If a r = cos, , equal to, a. a 2a 6 − a 4a 8, c. a1a 9 − a 3a 7, , b. a 9, d. a 5, , 20. The line 12x cos θ + 5 y sin θ = 60 is tangent to, which of the following curves?, a. x 2 + y 2 = 169, c. 25x 2 + 12 y 2 = 3600, , b. 144 x 2 + 25 y 2 = 3600, d. x 2 + y 2 = 60, , Section B : Numerical Type Questions, 21. Let [t ] denote the greatest integer ≤ t. Then, 1, , the value of 8., , ∫ ([2x ] + | x |) dx is, −, , 1, 2, , 22. A point z moves in the complex plane such, z − 2 π, that arg , = , then the minimum, z + 2 4, , value of| z − 9 2 − 2i |2equal to, , 23. The square of the distance of the point of, , y −2 z + 1, =, =, 2, 3, 6, and the plane 2x − y + z = 6 from the point, ( − 1, − 1, 2) is, intersection of the line, , x−1, , 24. If R is the least value of a such that the, , function f ( x) = x 2 + ax + 1is increasing on, [1, 2] and S is the greatest value of a such, that the function f ( x) = x 2 + ax + 1is, decreasing on [1, 2], then the value of|R − S|, is, , 25. The mean of 10 numbers, 7 × 8 , 10 × 10, 13 × 12, 16 × 14, .... is, , 26. If the variable line 3x + 4 y = α lies between, the two circles ( x − 1) 2 + ( y − 1) 2 = 1 and, ( x − 9) 2 + ( y − 1) 2 = 4, without intercepting a, chord on either circle, then the sum of all the, integral values of α is, , 27. The number of six letter words (with or, without meaning), formed using all the, letters of the word ‘VOWELS’, so that all the, consonants never come together, is, x, , 28. If x φ ( x)= ∫ (3t 2 − 2φ′ (t) dt, x > − 2, and φ(0) = 4,, 5, , then φ(2) is, 36 , k is the term, independent of x, in the, 44, , 29. If , , 12, , x 12 , binomial expansion of − 2 , then k is, 4 x , equal to, , 30. An electric instrument consists of two units., Each unit must function independently for, the instrument to operate. The probability, that the first unit functions is 0.9 and that of, the second unit is 0.8. The instrument is, switched on and it fails to operate. If the, probability that only the first unit failed and, second unit is functioning is P, then 98 P is, equal to
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54, , ONLINE, , JEE Main 2021 ~ Solved Papers, , Answers, For solutions scan, the QR code, , Physics, 1. (c), 11. (*), 21. 500, , 2. (c), 12. (d), 22. 8, , 3. (b), 13. (b), 23. 64, , 4. (a), 14. (a), 24. 3, , 5. (c), 15. (a), 25. 10, , 6. (b), 16. (a), 26. 6, , 7. (a), 17. (b), 27. 5, , 8. (c), 18. (c), 28. 500, , 9. (b), 19. (a), 29. 100, , 10. (a), 20. (c), 30. 30, , Chemistry, 1. (a), 11. (b), 21. 25, , 2. (d), 12. (c), 22. 20, , 3. (b), 13. (a), 23. 4, , 4. (b), 14. (b), 24. 5, , 5. (a), 15. (c), 25. 3, , 6. (c), 16. (a), 26. 2, , 7. (b), 17. (d), 27. 1, , 8. (d), 18. (d), 28. 45, , 9. (b), 19. (c), 29. 7, , 10. (c), 20. (a), 30. 108, , 3. (b), 13. (d), 23. 61, , 4. (a), 14. (c), 24. 2, , 5. (d), 15. (a), 25. 398, , 6. (c), 16. (b), 26. 105, , 7. (c), 17. (c), 27. 576, , 8. (b), 18. (b), 28. 4, , 9. (b), 19. (c), 29. 55, , 10. (c), 20. (b), 30. 28, , Mathematics, 1. (c), 11. (a), 21. 5, , 2. (c), 12. (d), 22. 98, , Note (*) None of the option is correct.
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55, , AUGUST ATTEMPT ~ 31 August 2021, Shift II, , JEE Main 2021, 31 AUGUST SHIFT II, PHYSICS, Section A : Objective Type Questions, 1. Four identical hollow cylindrical columns of, mild steel support a big structure of mass, 50 ´ 103 kg. The inner and outer radii of, each column are 50 cm and 100 cm,, respectively. Assuming, uniform local, distribution, calculate the compression, strain of each column., [Use, Y = 2.0 × 1011 Pa, g = 9.8 m/s 2]., a. 3.60 ´ 10-8, c. 1.87 ´ 10-3, , b. 2.60 ´ 10-7, d. 7.07 ´ 10-4, , 2. A current of 1.5 A is flowing through a, triangle, of side 9 cm each. The magnetic, field at the centroid of the triangle is, (Assume that, the current is flowing in the, clockwise direction.), a. 3 ´ 10- 7 T, outside the plane of triangle, b. 2 3 ´ 10- 7 T, outside the plane of triangle, c. 2 3 ´ 10- 5 T, inside the plane of triangle, d. 3 ´ 10- 5 T, inside the plane of triangle, , 3. A system consists of two identical spheres, each of mass 1.5 kg and radius 50 cm at the, end of light rod. The distance between the, centres of the two spheres is 5 m. What will, be the moment of inertia of the system, about an axis perpendicular to the rod, passing through its mid-point ?, a. 18.75 kgm 2, c. 19.05 kgm 2, , b. 1.905 ´ 105 kgm 2, d. 1.875 ´ 105 kgm 2, , 4. Statement I Two forces (P + Q) and (P - Q), where P ^ Q, when act at an angle q1 to each, other, the magnitude of their resultant is, 3(P 2 + Q 2) , when they act at an angle q2, the, magnitude of their resultant becomes, , 2(P 2 + Q 2) . This is possible only when, q1 < q2., Statement II In the situation given above., q1 = 60° and q2 = 90°., In the light of the above statements, choose, the most appropriate answer from the options, given below., a. Statement I is false but statement II is true., b. Both statement I and statement II are true., c. Statement I is true but statement II is false., d. Both statement I and statement II are false., , 5. A free electron of 2.6 eV energy collides with, a H + ion. This results in the formation of a, hydrogen atom in the first excited state and, a photon is released. Find the frequency of, the emitted photon., (h = 6.6 ´ 10- 34 Js), a. 1.45 ´ 1016 MHz, c. 1.45 ´ 109 MHz, , b. 0.19 ´ 1015 MHz, d. 9.0 ´ 1027 MHz, , 6. Two thin metallic spherical shells of radii r1, and r2 (r1 < r2) are placed with their centres, coinciding. A material of thermal, conductivity K is filled in the space between, the shells. The inner shell is maintained at, temperature q1 and the outer shell at, temperature q2( q1 < q2). The rate at which, heat flows radially through the material is, 4 pKr1r2 (q 2 - q1), r2 - r1, pr1r2 (q 2 - q1), b., r2 - r1, K (q 2 - q1), c., r2 - r1, K (q 2 - q1) (r2 - r1), d., 4 p r1r2, , a.
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56, , ONLINE, , 7. If VA and VB are the input voltages (either 5V or, 0V) and V0 is the output voltage then the two, gates represented in the following circuit ( A), and (B) are, V=5V, D1, , RC=1 kΩ, V0, , VA, , β=150, , V0 VB, RB=100 kΩ, R=1kΩ, , VB, , n-p -n, , D2, (B), , (A ), , a. AND and OR gate, b. OR and NOT gate, c. NAND and NOR gate d. AND and NOT gate, , 8. Consider two separate ideal gases of, electrons and protons having same number, of particles. The temperature of both the, gases are same. The ratio of the uncertainty, in determining the position of an electron to, that of a proton is proportional to, 3, æ mp ö 2, , a. ç, ÷, è me ø, , b., , me, mp, , c., , mp, me, , d., , 11. If velocity [v ], time [T ] and force [F ] are, choosen as the base quantities, the, dimensions of the mass will be, a. [ FT - 1v - 1] b. [ FTv - 1], , c., , 3, T, 4, , d., , d. [ FvT - 1], , electromagnetic wave is given by, $i + $j, B = B0, cos( kz - wt) T where $i, $j, 2, represents unit vector along X and Y-axis, respectively. At t = 0, two electric charges q1, p, of 4 p C and q 2 of 2p C located at æç 0,0, ö÷, è, kø, 3p ö, æ, and ç 0,0, ÷ respectively, have the same, è, k ø, velocity of 0.5 c $i. (where, c is the velocity of, light). The ratio of the force acting on, charge q1 to q 2 is, a. 2 2 : 1, , b. 1: 2, , c. 2 : 1, , d. 2 : 1, , 13. The equivalent resistance of the given, circuit between the terminals A and B is, 2Ω, , mp, , 2Ω, A, , me, , length l undergoes simple harmonic, oscillations with time period T . If the bob is, immersed in a liquid that has density 1/4, times that of the bob and the length of the, thread is increased by 1/3rd of the original, length, then the time period of the simple, harmonic oscillations will be, 3, b. T, 2, , c. [ FT 2v ], , 12. The magnetic field vector of an, , 5Ω, , 9. A bob of mass m suspended by a thread of, , a. T, , JEE Main 2021 ~ Solved Papers, , 4, T, 3, , 10. Statement I If three forces F1 × F2 and F3 are, represented by three sides of a triangle and, F1 + F2 = - F3, then these three forces are, concurrent forces and satisfy the condition, for equilibrium., Statement II A triangle made up of three forces, F1, F2 and F3 as its sides taken in the same order,, satisfy the condition for translatory equilibrium., In the light of the above statements, choose the, most appropriate answer from the options, given below., a. Statement I is false but statement II is true., b. Statement I is true but statement II is false., c. Both statement I and statement II are false., d. Both statement I and statement II are true., , 2Ω, , 3Ω, , 3Ω, B, , a. 0, , b. 3 W, , c. 9 / 2 W, , d. 1 W, , 14. Choose the incorrect statement., A. The electric lines of force entering into a, Gaussian surface provide negative flux., B. A charge q is placed at the centre of a cube., The flux through all the faces will be the, same., C. In a uniform electric field net flux through a, closed Gaussian surface containing no net, charge is zero., D. When electric field is parallel to a Gaussian, surface, it provides a finite non-zero flux., , Choose the most appropriate answer from, the options given below., a. (C) and (D), c. Only (D), , b. (B) and (D), d. (A) and (C), , 15. A mixture of hydrogen and oxygen has, , volume 500 cm 3, temperature 300 K,, pressure 400 kPa and mass 0.76 g. The, ratio of masses of oxygen to hydrogen will, be, a. 3 : 8, c. 16 : 3, , b. 3 : 16, d. 8 : 3
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57, , AUGUST ATTEMPT ~ 31 August 2021, Shift II, , surface with a speed of 40 m/s splits into two, parts with masses in the ratio of 1: 2. If the, smaller part moves at 60 m/s in the same, direction, then the fractional change in, kinetic energy is, a. 1/3, , b. 2/3, , c. 1/8, , below., Induced, current, B, , A current is induced in the coil because B is, a. outward and decreasing with time, b. parallel to the plane of coil and decreasing, with time, c. outward and increasing with time, d. parallel to the plane of coil and increasing with, time, , 18. For a body executing SHM, A. potential energy is always equal to its kinetic, energy., B. average potential and kinetic energy over any, given time interval are always equal., C. sum of the kinetic and potential energy at any, point of time is constant., D. average kinetic energy in one time period is, equal to average potential energy in one time, period., , Choose the most appropriate option from the, options given below., a. (C) and (D), c. (B) and (C), , between the acceleration due to gravity at a, depth r below and a height r above the Earth, surface is (Given, r < R E ), a. 1 -, , r, r2 r3, - 2 - 3, RE RE RE, , b. 1 +, , r, r2 r3, + 2 + 3, RE RE RE, , c. 1 +, , r, r2 r3, - 2 + 3, RE RE RE, , d. 1 +, , r, r2 r3, - 2 - 3, RE RE RE, , d. 1/4, , 17. A coil is placed in a magnetic field B as shown, Coil, , 20. If R E be the radius of Earth, then the ratio, , b. Only (C), d. Only (B), , 19. Statement I To get a steady DC output from, the pulsating voltage received from a full, wave rectifier we can connect a capacitor, across the output parallel to the load R L., Statement II To get a steady DC output from, the pulsating voltage received from a full wave, rectifier we can connect an inductor in series, with RL., In the light of the above statements, choose, the most appropriate answer from the options, given below., a. Statement I is true but statement II is false., b. Statement I is false but statement II is true., c. Both statement I and statement II are false., d. Both statement I and statement II are true., , Section B : Numerical Type Questions, 21. A bandwidth of 6 MHz is available for AM, transmission. If the maximum audio signal, frequency used for modulating the carrier, wave is not to exceed 6 kHz. The number of, stations that can be broadcasted within this, band simultaneously without interfering with, each other will be ............ ., , 22. A parallel plate capacitor of capacitance, 200 µF is connected to a battery of 200 V. A, dielectric slab of dielectric constant 2 is now, inserted into the space between plates of, capacitor while the battery remain, connected. The change in the electrostatic, energy in the capacitor will be ......... J., , 23. A long solenoid with 1000 turns/m has a core, material with relative permeability 500 and, volume 10 3cm 3. If the core material is, replaced by another material having relative, permeability of 750 with same volume, maintaining same current of 0.75 A in the, solenoid, the fractional change in the, magnetic moment of the core would be, c ö, ÷. Find the value of c., approximately æç, è 499 ø, , 24. A particle is moving with constant, , acceleration a. Following graph shows v 2, versus x (displacement) plot. The acceleration, of the particle is ........ m/s 2, , C, , 80, v2 (m/s)2, , 16. A block moving horizontally on a smooth, , 60, , B, , 40, , A, , 20, 0, , 10, , 20 30, x (m)
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58, , ONLINE, , 25. In a Young’s double slit experiment, the, , JEE Main 2021 ~ Solved Papers, 2Ω 0.5F, , 1Ω 0.5F, , slits are separated by 0.3 mm and the, screen is 1.5 m away from the plane of, slits. Distance between fourth bright, fringes on both sides of central bright is, 2.4 cm. The frequency of light used is, ........ ´ 1014 Hz., , 1Ω, , 0.5F, 2Ω 0.5F, , 20H, , 220V, , 26. The diameter of a spherical bob is, measured using a Vernier callipers. 9, divisions of the main scale, in the vernier, calipers, are equal to 10 divisions of, vernier scale. One main scale division is, 1 mm. The main scale reading is 10 mm, and 8th division of vernier scale was, found to coincide exactly with one of the, main scale division. If the given vernier, callipers has positive zero error of 0.04, cm, then the radius of the bob is .........., ´ 10- 2 cm., , 29. Cross–section view of a prism is the equilateral, triangle ABC in the figure. The minimum, deviation is observed using this prism when the, angle of incidence is equal to the prism angle., The time taken by light to travel from P, (mid-point of BC ) to A is ..... ´ 10- 10 s., (Given, speed of light in vacuum = 3 ´ 108 m/s and, 3, ), cos 30° =, 2, A, , 27. A sample of gas with g = 1.5 is taken, through an adiabatic process in which the, volume is compressed from 1200 cm 3 to, 300 cm 3. If the initial pressure is 200 kPa., The absolute value of the work done by, the gas in the process is ......... J., , 10 cm, , 10 cm, , B, , C, , P, , 30. A resistor dissipates 192 J of energy in 1 s when, a current of 4 A is passed through it. Now, when, the current is doubled, the amount of thermal, energy dissipated in 5 s is ........ J., , 28. At very high frequencies, the effective, impedance of the given circuit will be, .........W., , CHEMISTRY, Section A : Objective Type Questions, , CH3, , 1. Arrange the following conformational, isomers of n-butane in order of their, increasing potential energy, CH3, H, , CH3, , CH3, , II., H, , H, CH3, , H, , H, H, , H, , CH3, , H, , H, , III., , H, , I., , H, , H, , IV., , H, a. II < III < IV < I, b. I < IV < III < II, c. II < IV < III < I, d. I < III < IV < II, , H, H 3C, , H, , H, CH3
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59, , AUGUST ATTEMPT ~ 31 August 2021, Shift II, 2. The Eu2 + ion is a strong reducing agent in, spite of its ground state electronic, configuration (outermost) : [Atomic number, of Eu = 63], a. 4 f 7 6s 2, c. 4 f, , b. 4 f 6, , 7, , d. 4 f 6 6s 2, , Choose the most appropriate answer from, the options given below, A, 3, 1, , a., c., , B, 1, 4, , C, 4, 3, , following reaction are : [Ph = ¾C 6H5 ], , AlCl3(2eq), , Zn/Hg, , A, , b. A =, , Ph, OH ,, Ph, , B=, , B=, , ,, , Ph, OH ,, , A, , Ph, , a. A =, , Ph, , Br2, CH3COOH, , ,, , B, , NH, , CH3, ,, , CH3, , B=, Br, , OH, Ph, , NH, b. A =, , NH, , CH3, ,, , CH3, , B=, Br, , OH, , B = Ph, , B=, , D, 4, 4, , Room temperature, , NH2, , NH2, d. A =, , C, 2, 3, , B, , HCl, , OH, , c. A =, , B, 1, 1, , NH2, , NH, , a. A =, , A, 3, 2, , following reaction sequence are, , O, , O, , b., d., , 6. The major products A and B formed in the, , 3. The structures of A and B formed in the, , +, , D, 2, 2, , Br, , Ph, , c., , A=, , ,, , B=, COCH3, , COCH3, , 4. In which one of the following sets all species, 2a. ClO -2 , F2 , MnO 24 and Cr2O 7, , NH2, , NH2, , show disproportionation reaction, d. A =, , ,, , Br, B=, , Br, , b. Cr2O 27 - , MnO -4 , ClO -2 and Cl2, c. ClO -2 , Cl2 and Mn 3 +, d. ClO -4 , MnO 24 , ClO 2 and F2, , COCH3, , 7. Which of the following is not an example of, , 5. Match List-I with List-II., List-I, (Parameter), , COCH3, , fibrous protein ?, List-II, (Unit), , a. Keratin, , b. Albumin c. Collagen d. Myosin, , 8. The depositions of X and Y on ground, , A., , Cell constant, , 1. S cm 2 mol - 1, , B., , Molar conductivity, , 2. Dimensionless, , surfaces is referred to as wet and dry, depositions, respectively. X and Y are, , C., , Conductivity, , 3. m - 1, , a. X = Ammonium salts, Y = CO 2, , D., , Degree of dissociation, of electrolyte, , -1, , 4. W m, , -1, , b. X = SO 2 , Y = Ammonium salts, c. X = Ammonium salts, Y = SO 2, d. X = CO 2 , Y = SO 2
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60, , JEE Main 2021 ~ Solved Papers, , ONLINE, , 13. Which one of the following statements is, , 9. For the reaction given below., , incorrect ?, , CHO, 1. NaOH, ∆, 2. H3O+, , a. Atomic hydrogen is produced when H2, molecules at a high temperature are, irradiated with UV radiation., b. At around 2000 K, the dissociation of, dihydrogen into its atoms is nearly 8.1%., , Product, , CH2OH, , c. Bond dissociation enthalpy of H2 is highest, among diatomic gaseous molecules which, contain a single bond ., d. Dihydrogen is produced on reacting zinc with, , The compound which is not formed as a, product in the reaction is a, a. compound with both alcohol and acid, functional groups, b. monocarboxylic acid, c. dicarboxylic acid, d. diol, , HCl as well as NaOH(aq )., , 14. Which among the following is not a, polyester ?, , 10. Spin only magnetic moment in BM of, , a. Novolac, c. Dacron, , [Fe(CO) 4 (C 2O4 ) ]+ is, a. 5.92, c. 1, , b. 0, d. 1.73, , b. PHBV, d. Glyptal, , 15. Which one of the following correctly, represents the order of stability of oxides,, , 11. Given below are two statements : One is, , X 2O (X = halogen) ?, , labelled as Assertion (A) and the other is, , a. Br > Cl > I, b. Br > I > Cl, c. Cl > I > Br, d. I > Cl > Br, , labelled as Reason (R)., Assertion (A) Lithium salts are hydrated., Reason (R) Lithium has higher polarising, power than other alkali metal group members., In the light of the above statements, choose, the most appropriate answer from the options, given below, a. Both (A) and (R) are true but (R) is not the, correct explanation of (A)., , 16. Match List-I with List-II., List-I, (Metal ion), A., , Mn 2 +, , 1., , Group - III, , 3+, , 2., , Group - IIA, , 3., , Group - IV, , 4., , Group - IIB, , b. (A) is true but (R) is not true, , B., , As, , c. (A) is false but (R) is ture., , C., , Cu 2 +, , D., , d. Both (A) and (R) are true (R) is the correct, explanation of (A)., , following is, DGSystem, DS Total, , b. ln k =, c. k = e, , -, , a., c., , = - T (at constant p), , A, 1, 1, , B, 2, 4, , C, 3, 2, , D, 4, 3, , b., d., , A, 3, 4, , B, 4, 2, , C, 2, 3, , D, 1, 1, , 17. The major product of the following reaction, , DH° - TDS °, RT, , is, , DG °, RT, , d. For isothermal process, Wreversible = - nRT ln, , 3+, , Choose the most appropriate answer from the, options given below., , 12. The incorrect expression among the, a., , Al, , List-II, (Group in qualitative, analysis), , CH3, , Vf, Vi, , Cl, , NaOH, C2H5OH, , Major product
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61, , AUGUST ATTEMPT ~ 31 August 2021, Shift II, CH3, , NO2, CH3, , b., , a., , c. A =, , NO2, B=, Cl, , ,, , OH, , HO, , NH2, CH3, CH3, , OH, d., , c., , C=, ,, Cl, NO2, d. A =, , 18. For the following, 1. Br2/Fe/∆, 2. Mg/dry ether, , Cl, NH2, ,, , OCH3, + HMgBr, , H, b., , + Mg, CH3, , c., , ,, , Product, , 3. CH3OH, , a., , NO2, B=, , + Mg, , C=, OH, , 20. The number of S == O bonds present in, , OCH3, Br, , sulphurous acid, peroxodisulphuric acid and, pyrosulphuric acid, respectively are, , OH, , a. 2, 3 and 4, c. 2, 4 and 3, , Br, , b. 1, 4 and 3, d. 1, 4 and 4, , Section B : Numerical Type Questions, Br, d., , + Mg, , 21. CH4 is adsorbed on 1 g charcoal at 0°C, , OH, , following the Freundlich adsorption, isotherm. 10.0 mL of CH 4 is adsorbed at, 100 mm of Hg, whereas 15.0 mL is adsorbed, at 200 mm of Hg. The volume of CH 4, adsorbed at 300 mm of Hg is 10x mL. The, , OCH3, , 19. Identify correct A , B and C in the reaction, sequence given below., Conc. HNO3, +, Conc. H2SO4, ∆, , value of x is ....... ´ 10- 2. (Nearest integer), Cl2, , A, , Anhyd . AlCl3, , NO2, a. A =, , ,, , Fe/HCl, , NO2, B=, , Cl, , Cl, C=, , NH2, , ,, , NO2, B=, , ,, , Cl, Cl, ,, , C, , [Use log 10 2 = 0.3010, log 10 3 = 0.4771], , 22. 1.22 g of an organic acid is separately, dissolved in 100 g of benzene, , NO2, b. A =, , B, , C=, , (K b = 2.6 K kg mol - 1) and 100 g of acetone, (K b = 1.7 K kg mol - 1). The acid is known to, dimerise in benzene but remain as a, monomer in acetone. The boiling point of, the solution in acetone increases by 0.17°C., The increase in boiling point of solution in, benzene in °C is x ´ 10- 2. The value of x is, ........ (Nearest integer), [Atomic mass : C = 12.0, H = 1.0, O= 16.0], , 23. The value of magnetic quantum number of, OH, , the outermost electron of Zn+ ion is
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62, , ONLINE, , JEE Main 2021 ~ Solved Papers, , 24. The empirical formula for a compound with a, , 28. Sodium oxide reacts with water to produce, , cubic close packed arrangement of anions, and with cations occupying all the octahedral, sites in AxB. The value of x is ........ (Integer, answer), , sodium hydroxide. 20.0 g of sodium oxide, is dissolved in 500 mL of water. Neglecting, the change in volume, the concentration of, the resulting NaOH solution is ....... ´ 10- 1 M., (Nearest integer), [Atomic mass : Na = 23.0, O = 16.0, H = 1.0], , 25. In the electrolytic refining of blister copper,, the total number of main impurities from the, following, removed as anode mud is ……, Pb, Sb, Se, Te, Ru, Ag, Au and Pt, , 29. According to molecular orbital theory, the, 2-, , number of unpaired electron(s) in O2, , 26. The pH of a solution obtained by mixing, , is …… ., , 50 mL of 1 M HCl and 30 mL of 1 M NaOH is, x ´ 10- 4. The value of x is ......... (Nearest, , 30. The transformation occurring in Duma’s, , integer) [log 2.5 = 0.3979], , method is given below, , 27. For the reaction A ® B, the rate constant k, 3, , (in s - 1) is given by log 10 k = 2035, . -, , (2.47 ´ 10 ), , T, The energy of activation in kJ mol - 1 is ........., (Nearest integer), [Given : R = 8.314 J K - 1 mol - 1], , ×, , y, C 2H7N + æç2x + ö÷ CuO ¾® x CO2 +, è, 2ø, y, y, z, H2O + N2 + æç2x + ö÷ Cu, è, 2, 2, 2ø, The value of y is ......... . (Integer answer), , MATHEMATICS, Section A : Objective Type Questions, 1. If a + b + g = 2p , then the system of equations, x + (cos g ) y + (cos b)z = 0, (cos g ) x + y + (cos a) z = 0, (cos b)x + (cos a) y + z = 0, has:, a. no solution, b. infinitely many solution, c. exactly two solutions, d. a unique solution, , 2. Let a, b and c be three vectors mutually, perpendicular to each other and have same, magnitude. If a vector r satisfies., a ´ {(r - b) ´ a} + b ´ {(r - c ) ´ b}, + c ´ {(r - a) ´ c } = 0 , then r is equal to, 1, (a + b + c ), 3, 1, c. (a + b + c ), 2, , a., , 1, (2a + b - c ), 3, 1, d. (a + b + 2c ), 2, , b., , 3. The domain of the function, æ 3x 2 + x - 1ö, æ x - 1ö, ÷ + cos - 1 ç, f (x ) = sin- 1 çç, ÷ is, 2 ÷, è x + 1ø, è ( x - 1) ø, 1, a. é0, ù, ëê 4 ûú, 1 1, c. é , ù È {0}, êë 4 2 úû, , 1 1, b. [ - 2, 0] È é , ù, ëê 4 2 ûú, 1, d. é0, ù, êë 2 úû, , 4. Let S = {1, 2, 3, 4, 5, 6}. Then, the probability, that a randomly chosen onto function g, from S to S satisfies g(3) = 2 g(1) is, 1, 10, 1, c., 5, , 1, 15, 1, d., 30, , a., , b., , 5. Let f :N ® N be a function such that, f ( m + n) = f ( m) + f ( n) for every m, n ÎN. If, f (6) = 18, then f (2) × f (3) is equal to, a. 6, , b. 54, , c. 18, , c. 36
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63, , AUGUST ATTEMPT ~ 31 August 2021, Shift II, 6. The distance of the point (–1, 2, –2) from the, line of intersection of the planes, 2 x + 3 y + 2 z = 0 and x - 2 y + z = 0 is, a., , 1, 2, , b., , 5, 2, , c., , 42, 2, , d., , 34, 2, , 7. Negation of the statement ( p Ú q) Þ (q Ú r) is, a. p Ù ~ q Ù ~ r, c. ~ p Ù q Ù r, , 8., , b. ~ p Ù q Ù ~ r, d. p Ù q Ù r, , tan3 x - tan x, and, If a = lim, p, æ x + p ö÷, x®, 4 cos ç, è, 4ø, b = lim (cos x) cot x are the roots of the, x®0, , equation, ax 2 + bx - 4 = 0, then the ordered, pair (a, b) is, a. (1, – 3), c. (–1, – 3), , b. (– 1, 3), d. (1, 3), , a. 4 f (2), c. 2 f (1), , b. 4 f (1), d. f (1), , 13. The sum of the roots of the equation, , x + 1 - 2 log 2(3 + 2x ) + 2 log 4(10 - 2- x ) = 0 is, a. log 2 14, c. log 2 12, , b. log 2 11, d. log 2 13, , 14. If z is a complex number such that, , joining (– 3, –5) and the points on the ellipse, x2, y2, +, = 1 is, 4, 9, , a. 2 2 - 1, c. 6 2, , b. 3 2, d. 2 2, , 15. Let a1, a 2, a 3 ....... be an A.P. If, a1 + a 2 + ... + a10, a1 + a 2 + .... + a p, , a. 9x + 4 y + 18x + 8 y + 145 = 0, b. 36x 2 + 16 y 2 + 90x + 56 y + 145 = 0, c. 36x 2 + 16 y 2 + 108x + 80 y + 145 = 0, d. 36x 2 + 16 y 2 + 72x + 32 y + 145 = 0, , 2x y + 2 y × 2x, dy, If, , y(0) = 0, then for, = x, dx 2 + 2x + y log e 2, y = 1, the value of x lies in the interval, a. (1, 2), , c. (2, 3 ), , 1, d. æç0, ù, è 2 ûú, , 11. An angle of intersection of the curves,, x2 y2, +, = 1 and x 2 + y 2 = ab, a > b, is, a 2 b2, æa + b ö, a. tan - 1ç, ÷, è ab ø, æa - b ö, c. tan - 1ç, ÷, è ab ø, , 12., , =, , a, 100, , p ¹ 10, then 11 is, 2, a, p, 10, , 19, 21, 21, c., 19, , 100, 121, 121, d., 100, b., , 16. Let A be the set of all points ( a , b) such that, , 2, , 1, b. æç , 1ù, è 2 ûú, , is, , equal to, , 9. The locus of mid–points of the line segments, , 10., , z- 1, , purely imaginary, then the minimum value of, |z - (3 + 3i) | is, , a., , 2, , z-i, , æa - b ö, b. tan - 1ç, ÷, è 2 ab ø, d. tan - 1(2 ab ), , é, æ y2 ö ù, fç 2 ÷ ú, ê 2, èx ø ú, y, dy, If y, ,x > 0 , f > 0, and, = xê 2 +, êx, dx, æ y2 ö ú, f¢ ç 2 ÷ ú, ê, è x ø úû, êë, æ y2 ö, y(1) = - 1, then f ç ÷ is equal to, è 4 ø, , the area of triangle formed by the points, (5, 6), (3, 2) and ( a , b) is 12 sq units. Then, the, least possible length of a line segment, joining the origin to a point in A, is, a., , 4, 5, , b., , 16, 5, , c., , 8, 5, , d., , 12, 5, , 17. The number of solutions of the equation, 2, , 32tan, , x, , + 32sec, , a. 3, , 2, , b. 1, , x, , = 81, 0 £ x £, , p, is, 4, , c. 0, , d. 2, , 18. Let f be any continuous function on [0, 2], and twice differentiable on (0, 2). Iff (0) = 0 ,, f (1) = 1and f (2) = 2, then, a. f ¢¢(x ) = 0 for all x Î(0, 2), b. f ¢¢(x ) = 0 for some x Î(0, 2), c. f ¢ (x ) = 0 for some x Î[0, 2], d. f ¢¢(x ) > 0 for all x Î(0, 2), , 19. If [ x ] is the greatest integer £ x, then, 2, , px ö, ÷ ( x - | x |)[x ]dx is equal to, p 2 ò æç sin, è, 2 ø, 0, a. 2(p - 1), c. 4(p + 1), , b. 4 (p - 1), d. 2(p + 1)
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64, , ONLINE, , tangent to the circle x 2 + y 2 = a, then a is, equal to, , 20. The mean and variance of 7 observations are, 8 and 16 respectively. If two observations are, 6 and 8, then the variance of the remaining 5, observations is, 92, 5, 536, c., 25, , 134, 5, 112, d., 5, , a., , 7, 9, 13 19, +, +, +, + ..., then 160 S is, 5 52 53 54, equal to, , 26. If S =, , b., , 27. The number of elements in the set, ì, ü, æ a bö, ï A = ç 0 d ÷ : a , b and d Î { - 1, 0, 1} ï, è, ø, í, ý,, ïand (I - A) 3 = I - A 3, ï, î, þ, where I is 2 ´ 2 identity matrix, is, , Section B : Numerical Type Questions, 21. If the coefficient of a 7b8 in the expansion of, (a + 2b + 4ab)10 is k × 216, then k is equal to, , 22. Suppose the line, , x -2, a, , +, , y -2, -5, , =, , z+2, 2, , lies on, , 28. If the line y = mx bisects the area enclosed, 3, and the, 2, 2, curve y = 1 + 4 x – x , then 12 m is equal to, , by the lines x = 0 and y = 0, x =, , the plane x + 3 y - 2 z + b = 0. Then, ( a + b) is, equal to, , 23. The number of 4-digit numbers which are, , 29. Let B be the centre of the circle, , neither multiple of 7 nor multiple of 3 is, , 24. If ò, , sin x, sin3 x + cos 3 x, , JEE Main 2021 ~ Solved Papers, , x 2 + y 2 - 2x + 4 y + 1 = 0. Let the tangents at, two points P and Q on the circle intersect at, æ area DAPQ ö, the point A(3, 1). Then 8ç, ÷ is, è area DBPQ ø, , dx =, , a log e| 1 + tan x| + b log e | 1 - tan x + tan2 x|, 2 tan x - 1ö, + g tan- 1 æç, ÷ + C, when C is constant of, è, ø, 3, integration, then the value of 18 (a + b + g 2 ) is, , equal to, , 30. Let f ( x) be a cubic polynomial with f (1) = - 10,, , 25. A tangent line L is drawn at the point (2, – 4), on the parabola y 2= 8x. If the line L is also, , f (- 1) = 6, and has a local minima at x = 1,, and f ¢( x) has a local minima at x = - 1. Then, f (3) is equal to., , Answers, For solutions scan, the QR code, , Physics, 1. (b), 11. (b), 21. 500, , 2. (d), 12. (c), 22. 4, , 3. (c), 13. (d), 23. 250, , 4. (b), 14. (c), 24. 1, , 5. (c), 15. (c), 25. 5, , 6. (a), 16. (c), 26. 52, , 7. (b), 17. (a), 27. 480, , 8. (c), 18. (a), 28. 2, , 9. (d), 19. (d), 29. 5, , 10. (d), 20. (d), 30. 3840, , 3. (a), 13. (b), 23. 0, , 4. (c), 14. (a), 24. 1, , 5. (a), 15. (d), 25. 6, , 6. (b), 16. (b), 26. 6021, , 7. (b), 17. (d), 27. 47, , 8. (c), 18. (b), 28. 13, , 9. (c), 19. (a), 29. 0, , 10. (d), 20. (d), 30. 7, , 6. (d), 16. (c), 26. 305, , 7. (a), 17. (b), 27. 8, , 8. (d), 18. (b), 28. 26, , 9. (c), 19. (b), 29. 18, , 10. (a), 20. (c), 30. 22, , Chemistry, 1. (d), 11. (a), 21. 128, , 2. (c), 12. (b), 22. 13, , Mathematics, 1. (b), 11. (c), 21. 315, , 2. (c), 12. (b), 22. 7, , 3. (c), 13. (b), 23. 5143, , 4. (a), 14. (d), 24. 3, , 5. (b), 15. (c), 25. 2
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65, , S EPT EMB ER AT T EMPT ~ 01 September 2021, Shift II, , JEE Main 2021, 1 SEPTEMBER SHIFT II, PHYSICS, Section A : Objective Type Questions, 1. A cube is placed inside an electric field,, 2$, , E = 150 y j. The side of the cube is 0.5 m and, is placed in the field as shown in the given, figure. The charge inside the cube is, y, , 3. The temperature of an ideal gas in, 3-dimensions is 300 K. The corresponding, de-Broglie wavelength of the electron, approximately at 300 K, is, [m e = mass of electron = 9 × 10−31 kg, h =Planck’s constant = 6.6 × 10−34 Js, K B = Boltzmann constant = 1.38 × 10−23 JK −1], a. 6.26 nm, c. 2.26 nm, , x, , 4. A body of mass m dropped from a height h, reaches the ground with a speed of 0.8 gh., The value of workdone by the air-friction is, a. − 0.68 mgh, c. 1.64 mgh, , z, , a. 3.8 × 10−11 C, −12, , c. 3.8 × 10, , C, , b. 8.3 × 10−11 C, −12, , d. 8.3 × 10, , C, , 2. A square loop of side 20 cm and resistance, 1 Ω is moved towards right with a constant, speed v 0. The right arm of the loop is in a, uniform magnetic field of 5 T. The field is, perpendicular to the plane of the loop and is, going into it. The loop is connected to a, network of resistors each of value 4 Ω. What, should be the value of v 0, so that a steady, current of 2 mA flows in the loop ?, 4Ω, , 4Ω, P, , 4Ω, , b. 8.46 nm, d. 3.25 nm, , Q, , 4Ω, , v0, , a. 1 m/s, c. 102 m/s, , ××××××××, ××××××××, ××××××××, ××××××××, ××××××××, ××××××××, ××××××××, ××××××××, ××××××××, , b. mgh, d. 0.64 mgh, , 5. The ranges and heights for two projectiles, projected with the same initial velocity at, angles 42° and 48° with the horizontal are, R1, R 2 and H1, H 2, respectively. Choose the, correct option., a. R1 > R 2 and H1 = H2, c. R1 < R 2 and H1 < H2, , 6. A block of mass m slides on the wooden, wedge, which in turn slides backward on the, horizontal surface. The acceleration of the, block with respect to the wedge is, [Given, m = 8 kg, M = 16 kg], Assume all the surfaces shown in the figure, to be frictionless., m, M, , 30°, , b. 1 cm/s, d. 10−2 cm/s, , b. R1 = R 2 and H1 < H2, d. R1 = R 2 and H1 = H2, , 4, a. g, 3, , 6, b. g, 5, , c., , 3, g, 5, , d., , 2, g, 3
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66, , ONLINE, , 7. Due to cold weather a 1 m water pipe of, cross–sectional area 1 cm 2 is filled with ice at, –10°C. Resistive heating is used to melt the ice., Current of 0.5 A is passed through 4 kΩ, resistance. Assuming that, all the heat, produced is used for melting, what is the, minimum time required ?, [Given, latent heat of fusion for water/ice, = 333, . × 105 J kg −1, specific heat of ice, = 2 × 103 J kg −1 and density of ice = 103 kg/m 3], a. 0.353 s, c. 3.53 s, , Least count of Observed, value, the equipment, used for, measurement, , Mass (M), , 1g, , 2 kg, , Length of bar (L), , 1 mm, , 1m, , Breadth of bar (b), , 0.1 mm, , 4 cm, , Thickness of bar (d ) 0.01 mm, , 0.4 cm, , Depression (δ), , 5 mm, , 0.01 mm, , Then, the fractional error in the measurement, of Y is, b. 0.0155, d. 0.083, , 9. Two resistors R1 = ( 4 ± 0.8) Ω and R 2 = ( 4 ± 0.4) Ω, are connected in parallel. The equivalent, resistance of their parallel combination will be, a. (4 ± 0.4 ) Ω, c. (2± 0.3) Ω, , versus magnetising field (H) and magnetic, susceptibility (χ) versus temperature (T ), graph, M, , M, , (A), , H, , (B), , χ, , MgL3, elasticity using the formula Y =, . The, 4 bd 3δ, 2, value of g is taken to be 9.8 m/s , without any, significant error, his observations are as, following., , a. 0.0083, c. 0.155, , 11. Following plots show magnetisation (M), , b. 35.3 s, d. 70.6 s, , 8. A student determined Young’s modulus of, , Physical quantity, , JEE Main 2021 ~ Solved Papers, , χ, , (C), , T, , (D), T, , Which of the following combination will be, represented by a diamagnetic material?, a. (A) and (C), , b. (A) and (D), , c. (B) and (D), , d. (B) and (C), , 12. A glass tumbler having inner depth of, 17.5 cm is kept on a table. A student starts, pouring water (µ = 4 / 3) into it while looking, at the surface of water from the above., When he feels that the tumbler is half, filled, he stops pouring water. Up to what, height, the tumbler is actually filled?, a. 11.7 cm b. 10 cm, , c. 7.5 cm, , d. 8.75 cm, , 13. In the given figure, each diode has a, forward bias resistance of 30 Ω and infinite, resistance in reverse bias. The current I1, will be, 130 Ω, , b. (2± 0.4 ) Ω, d. (4 ± 0.3) Ω, , 130 Ω, , 10. The half life period of radioactive element x is, , 130 Ω, , same as the mean life time of another, radioactive element y. Initially they have the, same number of atoms. Then,, a. x will decay faster than y, b. y will decay faster than x, c. x and y have same decay rate initially and later, on different decay rate, d. x and y decay at the same rate always, , H, , I1, , 20 Ω, 200 V, , a. 3.75 A, c. 2 A, , b. 2.35 A, d. 2.73 A
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67, , S EPT EMB ER AT T EMPT ~ 01 September 2021, Shift II, 14. For the given circuit the current i through the, , F, , battery when the key in closed and the, steady state has been reached is, 2Ω, , D, , c., , i, , 0.5mH, , 0.2 H, , 3Ω, , x, , –2N, , 30V, 3Ω, , 3Ω, , F, 2N, , a. 6 A, b. 25 A, , d., , c. 10 A, , x, , d. 0, –2N, , 15. An object of mass m is being moved with a, constant velocity under the action of an, applied force of 2 N along a frictionless, surface with following surface profile., , m, , θ, , θ, D, , The correct applied force versus distance, graph will be, , D, , 16. A mass of 5 kg is connected to a spring. The, potential energy curve of the simple, harmonic motion executed by the system is, shown in the figure. A simple pendulum of, length 4 m has the same period of oscillation, as the spring system. What is the value of, acceleration due to gravity on the planet, where these experiments are performed?, 10, , U(J), , F, , 2N, , a., , 5, , x, , D, , 0, , 4, , 2, x(m), , F, , a. 10 m/s 2, c. 4 m/s 2, , 2N, , b. 5 m/s 2, d. 9.8 m/s 2, , 17. A capacitor is connected to a 20 V battery, x, , b., –2N, , D, , through a resistance of 10 Ω. It is found that, the potential difference across the capacitor, rises to 2 V in 1 µs. The capacitance of the, capacitor in .……… µF., 10, [Given, ln = 0.105 ], 9, a. 9.52, , b. 0.95, , c. 0.105, , d. 1.85
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68, , ONLINE, , 18. Four particles each of mass M, move along a, circle of radius R under the action of their, mutual gravitational attraction as shown in, figure. The speed of each particle is, M, , M, R, , R, , 90°, , R, , R, M, , M, , a., , 1, GM, 2 R(2 2 + 1), , b., , c., , 1 GM, (2 2 − 1), 2 R, , d., , 1 GM, (2 2 + 1), 2 R, GM, R, , 19. Electric field of plane electromagnetic wave, propagating through a non–magnetic, medium is given by, E = 20cos(2 × 1010t − 200x) V/m. The dielectric, constant of the medium is equal to, (Take, µ r = 1), a. 9, , b. 2, , c., , 1, 3, , d. 3, , 20. There are two infinitely long straight current, carrying conductors and they are held at, right angles to each other so that their, common ends meet at the origin as shown, in the figure given below. The ratio of, current in both conductors is 1 : 1. The, magnetic field at point P is, ∞, y, , P(x,y), , θ2, θ1, I, , O, , µ 0I, [, 4 πxy, µ I, b. 0 [, 4 πxy, µ Ixy, c. 0 [, 4π, µ Ixy, d. 0 [, 4π, , a., , I, , x 2 + y 2 + (x + y )], x + y − (x + y )], 2, , 2, , x 2 + y 2 − (x + y )], x 2 + y 2 + (x + y )], , ∞x, , JEE Main 2021 ~ Solved Papers, , Section B : Numerical Type Questions, 21. The temperature of 3.00 mol of an ideal, diatomic gas is increased by 40.0 °C without, changing the pressure of the gas. The, molecules in the gas rotate but do not, oscillate. If the ratio of change in internal, energy of the gas to the amount of, x, workdone by the gas is , then the value of, 10, x (round off to the nearest integer) is ……… ., (Given, R = 8.31 J mol −1 K −1), , 22. The width of one of the two slits in a Young’s, double slit experiment is three times the, other slit. If the amplitude of the light, coming from a slit is proportional to the, slit-width, the ratio of minimum to maximum, intensity in the interference pattern is x : 4, where x is ……… ., , 23. Two satellites revolve around a planet in, coplanar circular orbits in anti-clockwise, direction. Their period of revolutions are 1 h, and 8 h, respectively. The radius of the orbit, of nearer satellite is 2 × 103 km. The angular, speed of the farther satellite as observed, from the nearer satellite at the instant when, π, both the satellites are closest is rad h −1,, x, where x is ……… ., , 24. When a body slides down from rest along a, smooth inclined plane making an angle of, 30° with the horizontal, it takes time T . When, the same body slides down from the rest, along a rough inclined plane making the, same angle and through the same distance,, it takes time αT , where α is a constant, greater than 1. The coefficient of friction, between the body and the rough plane is, 2, 1 α − 1, , where x is ……… ., , x α2 , , 25. The average translational kinetic energy of, N2 gas molecules at ...........°C becomes equal, to the KE of an electron accelerated from, rest through a potential difference of 0.1 V., [Given, K B = 1.38 × 10−23 J/K]
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69, , S EPT EMB ER AT T EMPT ~ 01 September 2021, Shift II, 26. A uniform heating wire of resistance 36 Ω is, connected across a potential difference of, 240 V. The wire is then cut into half and, potential difference of 240 V is applied, across each half separately. The ratio of, power dissipation in first case to the total, power dissipation in the second case would, be 1: x, where x is ……… ., , 27. A steel rod with Y = 2.0 × 1011 Nm −2 and, α = 105 °C −1 of length 4 m and area of, cross-section 10 cm 2 is heated from 0°C to, 400°C without being allowed to extend. The, tension produced in the rod is x × 105 N,, where the value of x is ............. ., , 28. A 2 kg steel rod of length 0.6 m is clamped, on a table vertically at its lower end and is, free to rotate in vertical plane. The upper, end is pushed so that the rod falls under, gravity. Ignoring the friction due to clamping, at its lower end, the speed of the free end of, , rod when it passes through its lowest, position is ........... ms −1., (Take, g = 10 ms −2), , 29. A carrier wave with amplitude of 250 V is, amplitude modulated by a sinusoidal base, band signal of amplitude 150 V. The ratio of, minimum amplitude to maximum amplitude, for the amplitude modulated wave is 50 : x,, then value of x is ........... ., , 30. An engine is attached to a wagon through a, shock absorber of length 1.5 m. The system, with a total mass of 40000 kg is moving with, a speed of 72 kmh −1, when the brakes are, applied to bring it to rest. In the process of, the system being brought to rest, the spring, of the shock absorber gets compressed by, 1.0 m. If 90% of energy of the wagon is lost, due to friction, the spring constant is ……… ×, 105 N/m., , CHEMISTRY, Section A : Objective Type Questions, 1. Water sample is called cleanest on the basis, of which one of the BOD values given below, a. 11 ppm, , b. 15 ppm, , c. 3 ppm, , d. 21 ppm, , 2. Calamine and malachite, respectively, are, , 4. Which one of the following given graphs, represents the variation of rate constant ( k), with temperature (T ) for an endothermic, reaction?, , a. k, , b. k, , the ores of, T, , a. nickel and aluminium, , T, , b. zinc and copper, c. copper and iron, d. aluminium and zinc, , 3. Experimentally reducing a functional group, cannot be done by which one of the, following reagents ?, a. Pt-C/H2, b. Na / H2, c. Pd-C/H 2, d. Zn / H2O, , c. k, , d. k, , T, , T, , 5. Identify A in the following reaction., NH2, K2Cr2O7, , A
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70, , JEE Main 2021 ~ Solved Papers, , ONLINE, , NH2, a., , b., , 9. Monomer units of dacron polymer are, a. ethylene glycol and phthalic acid, b. ethylene glycol and terephthalic acid, , KO, , c. glycerol and terephthalic acid, NO2, b., , NO2, H, , d., , d. glycerol and phthalic acid, , 10. Which one of the following compounds is, aromatic in nature ?, , 6 In the following sequence of reactions a, compound A, (molecular formula C 6H12O2), with a straight chain structure gives a C 4, carboxylic acid. A is, LiAIH4, , a., , b., , CH3, , Oxidation, , A →, B → C 4 carboxylic acid, +, H3 O, , a. CH3 CH2 COO CH2 CH2 CH3, OH, , b. CH3 CH2 C H CH2 O CH == CH2, c. CH3 CH2 CH2 COO CH2 CH3, d. CH3 CH2 CH2 O CH == CH CH2 OH, , 7. Match List-I with List-II., List-I, (Colloid, preparation, method), , List-II, (Chemical reaction), , +, c., , d., , 11. In the given chemical reaction, colours of the, Fe 2+ and Fe 3+ ions, are respectively, 5Fe 2+ + MnO−4 + 8H+ → Mn2+ + 4H 2O + 5Fe 3+, a. yellow, orange, b. yellow, green, c. green, orange, d. green, yellow, , 12. The stereoisomers that are formed by, electrophilic addition of bromine to, trans-but-2-ene is/are, , A. Hydrolysis, , 1., , B. Reduction, , 2. As 2O 3 + 3H2S → As 2S3 (sol), + 3H2O, , b. 2 identical mesomers, , C. Oxidation, , 3. SO 2 + 2H2S → 3S (sol), + 2H2O, , d. 1 racemic and 2 enantiomers, , 2AuCl3 + 3HCHO + 3H2O, → 2Au(sol) + 3HCOOH, + 6HCl, , D. Double, 4. FeCl3 + 3H2O →, Decomposition, Fe(OH) 3 (sol) + 3HCl, , Choose the most appropriate answer from, the options given below., A B C D, a. 1 3 2 4, b. 4 1 3 2, c. 4 2 3 1, d. 1 2 4 3, , 8. The crystal field stabilisation energy (CFSE), and magnetic moment (spin-only) of an, octahedral aqua complex of a metal ion (M + ), are − 0.8 ∆ o and 3.87 BM, respectively., Identify (M 2+ )., a. V 3 +, , b. Cr 3 +, , c. Mn 4 +, , d. Co 2 +, , a. 2 enantiomers and 2 mesomers, c. 2 enantiomers, , 13. Hydrogen peroxide reacts with iodine in, basic medium to give, a. IO −4, , b. IO −, , c. I−, , d. IO −3, , 14. In the following sequence of reactions,, H + /H O, , → B + C, C 3H 6 2→ A KIO, dil. KOH, , The compounds B and C respectively are, a. CI3COOK, HCOOH, b. CI3COOK,CH3I, c. CH3I,HCOOK, d. CHI3 , CH3COOK, , 15. Given below are two statements., Statement I The nucleophilic addition of, sodium hydrogen sulphite to an aldehyde or, a ketone involves proton transfer to form a, stable ion.
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S EPT EMB ER AT T EMPT ~ 01 September 2021, Shift II, Statement II The nucleophilic addition of, hydrogen cyanide to an aldehyde or a ketone, yields amine as final product., In the light of the above statements, choose, the most appropriate answer from the, options given below., a. Both statement I and statement II are true., b. Statement I is false but statement II is true., c. Statement I is true but statement II is false., d. Both statement I and statement II are false., , 16. Which one of the following gives the most, stable diazonium salt ?, NH2, a. CH3—CH2—CH2—NH2, , b., , c. CH3—C—NH2, , NHCH3, d., , prussian blue colour, when added to, b. FeCl2, d. FeCl3, , 18. The oxide without nitrogen-nitrogen bond is, b. N2O 4, d. N2O 5, , 19. Number of paramagnetic oxides among the, following given oxides is, Li2O, Na 2O2 , KO2 , HgO and K 2O, a. 1, , b. 2, , c. 3, , d. 0, , 20. Identify the element for which electronic, configuration in +3 oxidation state is [ Ar ] 3d5., a. Ru, c. Co, , 23. For the reaction,, 2NO 2 ( g ) s N 2O 4 ( g), when, ∆S = − 1760, . JK −1 and ∆H = − 578, . kJ mol −1, the, magnitude of ∆G at 298 K for the reaction is, ……… kJ mol −1. (Nearest integer), , 24. The sum of oxidation states of two silver, ions in [Ag(NH 3) 2 ] [Ag(CN) 2 ] complex is …… ., , (Nearest integer), [Given : NA = 6.02 × 1023 mol −1, Atomic mass of Na = 23.0 u], , 26. If 80 g of copper sulphate CuSO4 ⋅ 5H2O. is, , 17. The potassium ferrocyanide solution gives a, , a. N2O, c. N2O 3, , NaOH solution is x × 10−18 M. The value of x, is ……… (Nearest integer), (Given; The solubility product of Zn(OH)2 is, 2 × 10−20)., , x × 1023. The value of x is ……… ., , H, , a. CoCl3, c. CoCl2, , 22. The molar solubility of Zn(OH)2 in 0.1 M, , 25. The number of atoms in 8 g of sodium is, , CH3, CH3, , 71, , b. Mn, d. Fe, , Section B : Numerical Type Questions, 21. An empty LPG cylinder weight 14.8 kg. When, full, it weight 29.0 kg and shows a pressure, of 3.47 atm. In the course of use at ambient, temperature, the mass of the cylinder is, reduced to 23.0 kg. The final pressure inside, of the cylinder is ……… atm. (Nearest integer), (Assume LPG of be an ideal gas), , dissolved in deionised water to make 5 L of, solution. The concentration of the copper, sulphate solution is x × 10−3 mol L −1. The, value of x is ……… ., [Atomic masses Cu = 63.54 u, S = 32 u,, O = 16 u, H = 1 u], , 27. A 50 watt bulb emits monochromatic red, light of wavelength of 795 nm. The number, of photons emitted per second by the bulb is, x × 1020. The value of x is ……… ., [Given, h = 663, . × 10−34 Js and, c = 30, . × 108 ms −1], , 28. The spin-only magnetic moment value of B+2, species is ……… × 10−2 BM. (Nearest integer), [Given, 3 = 173, . ], , 29. If the conductivity of mercury at 0°C is, , 1.07 × 106 S m −1 and the resistance of a cell, containing mercury is 0.243 Ω, then the cell, constant of the cell is x × 104 m −1. The value, of x is ……… . (Nearest integer), , 30. A peptide synthesised by the reactions of, one molecule each of glycine, leucine,, aspartic acid and histidine will have ………, peptide linkages.
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72, , JEE Main 2021 ~ Solved Papers, , ONLINE, , MATHEMATICS, Section A : Objective Type Questions, 1. Letf : R → R be a continuous function. Then,, , lim, x→, , π, 4, , π, 4, , 2, , sec x, , 6. Two squares are chosen at random on a, chessboard (see figure). The probability that, they have a side in common is, , ∫ f (x) dx, 2, , x −, 2, , π2, 16, , is equal to, , a. f (2 ), c. 2 f ( 2 ), , 64 square, , b. 2f (2), d. 4 f (2), , 2. cos −1(cos( − 5)) + sin−1(sin(6)) − tan−1(tan(12)) is, equal to, (The inverse trigonometric functions take the, principal values), a. 3 π − 11, c. 4 π − 11, , b. 4 π − 9, d. 3 π + 1, , 3. Consider the system of linear equations, − x + y + 2z = 0, 3x − ay + 5 z = 1, 2x − 2 y − az = 7, Let S1 be the set of all a ∈ R for which the, system is inconsistent and S 2 be the set of all, a ∈ R for which the system has infinitely many, solutions. If n( S1) and n( S 2) denote the number, of elements in S1 and S 2 respectively, then, a. n (S1) = 2 and n (S 2 ) = 2, b. n (S1) = 1 and n (S 2 ) = 0, c. n (S1) = 2 and n (S 2 ) = 0, d. n (S1) = 0 and n (S 2 ) = 2, , 1, 18, 1, d., 9, b., , 7. If y = y ( x) is the solution curve of the, 1, , differential equation x 2dy + y − dx = 0 ;, , x, 1, x > 0 and y (1) = 1, then y is equal to, 2, 3, 1, −, 2, e, c. 3 + e, , b. 3 +, , a., , 1, e, , d. 3 − e, , 8. If n is the number of solutions of the, , π, π, , , equation 2cos x 4 sin + x sin − x − 1, 4, , 4, , , , , = 1, x ∈[0, π ] and S is the sum of all these, solutions, then the ordered pair ( n, S) is, b. (2, 2π / 3), d. (3, 5π / 3), , a. (3, 13π/9), c. (2, 8π / 9), , 4. Let the acute angle bisector of the two, , planes x − 2 y − 2z + 1 = 0 and, 2x − 3 y − 6z + 1 = 0 be the plane P. Then,, which of the following points lies on P ?, 1, a. 3, 1, − , , 2, , 1, b. − 2, 0, − , , 2, , c. (0, 2, − 4 ), , d. (4 , 0, − 2 ), , 5. Which of the following is equivalent to the, Boolean expression p ∧ ~ q ?, a. ~ (q → p ), c. ~( p → ~ q ), , 2, 7, 1, c., 7, a., , b. ~ p → ~ q, d. ~ ( p → q ), , 9. The function f ( x) = x 3 − 6x 2 + ax + b is such, that f (2) = f ( 4) = 0. Consider two statements., ( S1) there exists x1, x 2 ∈ (2, 4), x1 < x 2, such, that f ′ ( x1) = −1and f ′ ( x 2) = 0. ( S 2) there exists, x 3 , x 4 ∈ (2, 4) , x 3 < x 4, such that f is, decreasing in (2, x 4), increasing in ( x 4 , 4) and, 2 f ′ ( x ) = 3 f ( x ). Then,, 3, , 4, , a. both (S1) and (S 2 ) are true, b. (S1) is false and (S 2 ) is true, c. both (S1) and (S 2 ) are false, d. (S1) is true and (S 2 ) is false
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73, , S EPT EMB ER AT T EMPT ~ 01 September 2021, Shift II, 1, 2, , xn, dx , ∀ n > m and n, m ∈ N., m, x −1, 0, , 10. Let Jn,m = ∫, , Consider a matrix A = [a ij ]3 × 3 where, J6 + i ,3 − Ji + 3,3 , i ≤ j, . Then,|adj A −1| is, a ii = , 0,, i>j, , a. (15) 2 × 242, c. (105) 2 × 238, , b. (15) 2 × 234, d. (105) 2 × 236, , 11. The area, enclosed by the curves, , y = sin x + cos x and y = |cos x − sin x|and the, π, lines x = 0, x = , is, 2, a. 2 2 ( 2 − 1), c. 4 ( 2 − 1), , b. 2( 2 + 1), d. 2 2 ( 2 + 1), , 12. The distance of line 3 y − 2 z − 1 = 0, = 3x − z + 4 from the piont (2, − 1, 6) is, a. 26, c. 2 6, , b. 2 5, d. 4 2, , 1 3, 13. Consider the parabola with vertex , , , 2 4, 1, and the directrix y = . Let P be the point, 2, 1, where the parabola meets the line x = − . If, 2, the normal to the parabola at P intersects, the parabola again at the point Q, then (PQ) 2, is equal to, 75, 8, 25, c., 2, , a., , 125, 16, 15, d., 2, , b., , 14. The numbers of pairs (a , b) of real numbers,, , such that whenever α is a root of the, equation x 2 + ax + b = 0, α 2 − 2 is also a root, of this equation, is, a. 6, c. 4, , b. 2, d. 8, , 15. Let S n = 1⋅ ( n − 1) + 2⋅( n − 2) + 3 ⋅ ( n − 3) + ... +, ( n − 1) ⋅ 1, n ≥ 4., ∞ 2S, 1 , The sum Σ n −, is equal to, n = 4 n!, ( n − 2) !, e−1, a., 3, e, c., 3, , e−2, b., 6, e, d., 6, , 16. Let P1, P2 , ……, P15 be 15 points on a circle. The, number of distinct triangles formed by, points P$ , P$ and P$ , such that $i + $j + k$ ≠ 15 is, i, , a. 12, c. 443, , j, , k, , b. 419, d. 455, , 17. The range of the function,, , , f ( x) = log, , 5, , , , 3π, 3 + cos , + x, , 4, , π, π, , 3π, + cos + x + cos − x − cos , − x is, 4, , 4, , , 4, b. [ − 2, 2], , a. (0, 5 ), 1, , c. , , 5, , 5, , d. [0, 2], , 18. Let a1, a 2, ……, a 21 be an AP such that, 20, , 1, , Σ, , n = 1 a na, , =, , n+1, , 4, . If the sum of this AP is 189,, 9, , then a 6a16 is equal to, a. 57, c. 48, , b. 72, d. 36, , 19. The function f ( x), that satisfies the condition, π /2, , f ( x) = x +, , ∫ sin x ⋅ cos y, , f ( y ) dy , is, , 0, , 2, ( π − 2) sin x, 3, b. x + ( π + 2) sin x, π, c. x + sin x, 2, d. x + ( π − 2) sin x, , a. x +, , 20. Let θ be the acute angle between the, , x2, y2, +, = 1 and the, 9, 1, circle x 2 + y 2 = 3 at their point of, intersection in the first quadrant. Then, tanθ, is equal to, tangents to the ellipse, , a., , 5, 2 3, , b., , 2, 3, , c., , 4, 3, , d. 2, , Section B : Numerical Type Questions, 21. Let X be a random variable with distribution., x, P (X = x ), , −2, 1, 5, , −1, a, , 3, 1, 3, , 4, 1, 5, , 6, b, , If the mean of X is 2.3 and variance of X is σ 2,, then 100 σ 2 is equal to
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74, , ONLINE, , 22. Let f ( x) = x 6 + 2x 4 + x 3 + 2x + 3, x ∈R. Then,, the natural number n for which, x n f (1) − f ( x), lim, = 44 is, x→1, x −1, , JEE Main 2021 ~ Solved Papers, , English dictionary. Then, the serial number, of the word FARMER in this list is, , 27. If the sum of the coefficients in the, , expansion of ( x + y ) n is 4096, then the, greatest coefficient in the expansion is, , 23. If for the complex numbers z satisfying, , |z − 2 − 2i| ≤ 1, the maximum value of|3 iz + 6|, is attained at a + ib, then a + b is equal to., , 28. Let a = 2i$ − $j + 2k$ and b = $i + 2$j − k$ . Let a, vector v be in the plane containing a and b. If, v is perpendicular to the vector 3i$ + 2$j − k$, and its projection on a is 19 units, then|2v|2, is equal to, , 24. Let the points of intersections of the lines, x − y + 1 = 0, x − 2 y + 3 = 0 and, 2x − 5 y + 11 = 0 are the mid-points of the, sides of a ∆ABC . Then, the area of the, ∆ABC is, , 29. Let [t ] denote the greatest integer ≤ t. The, number of points where the function, π , f ( x) = [ x ]|x 2 − 1| + sin, , [ x ] + 3, , 25. Let f ( x) be polynomial of degree 3 such that, 2, for k = 2, 3, 4, 5. Then, the value of, k, 52 − 10 f (10) is equal to, f ( k) = −, , 26. All the arrangements, with or without, , − [ x + 1], x ∈ ( − 2, 2) is not continuous is, , 30. A man starts walking from the point P( − 3, 4),, touches the X-axis at R, and then turns to, reach at the point Q (0, 2). The man is walking, at a constant speed. If the man reaches the, point Q in the minimum time, then, 50((PR) 2 + (RQ) 2) is equal to, , meaning, of the word FARMER are written, excluding any word that has two R appearing, together. The arrangements are listed, serially in the alphabetic order as in the, , Answers, For solutions scan, the QR code, , Physics, 1. (b), 11. (a), 21. 25, , 2. (b), 12. (b), 22. 1, , 3. (a), 13. (c), 23. 3, , 4. (a), 14. (c), 24. 3, , 5. (b), 15. (b), 25. 500, , 6. (d), 16. (c), 26. 4, , 7. (b), 17. (b), 27. 8, , 8. (b), 18. (b), 28. 6, , 9. (c), 19. (a), 29. 4, , 10. (b), 20. (a), 30. 16, , 8. (d), 18. (d), 28. 173, , 9. (b), 19. (a), 29. 26, , 10. (a,d), 20. (d), 30. 3, , 8. (a), 18. (b), 28. 1494, , 9. (a), 19. (d), 29. 2, , 10. (c), 20. (b), 30. 1250, , Chemistry, 1. (c), 11. (d), 21. 2, , 2. (b), 12. (b), 22. 2, , 3. (b), 13. (c), 23. 5, , 4. (c), 14. (d), 24. 2, , 5. (a), 15. (c), 25. 2, , 6. (c), 16. (b), 26. 64, , 7. (b), 17. (d), 27. 2, , Mathematics, 1. (b), 11. (a), 21. 781, , 2. (c), 12. (c), 22. 7, , 3. (c), 13. (b), 23. 5, , 4. (b), 14. (a), 24. 6, , 5. (d), 15. (a), 25. 26, , 6. (b), 16. (c), 26. 77, , 7. (d), 17. (d), 27. 924
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ONLINE QUESTION PAPER, , JEE Main 2020, (02 September, 2020), TIME 9:30-12:30 (Shift I), , MM : 300, , PHYSICS, 1 eV = 16, . × 10−19 J. The power output of the, reactor is close to, , Objective Type Questions, 1 A gas mixture consists of 3 moles of oxygen, and 5 moles of argon at temperature T., Assuming the gases to be ideal and the, oxygen bond to be rigid, the total internal, energy (in units of RT) of the mixture is, (a) 15, , (b) 13, , (c) 11, , (a) 35 MW, (c) 60 MW, , 4 Interference fringes are observed on a, screen by illuminating two thin slits 1 mm, apart with a light source (λ = 6328, . nm)., The distance between the screen and the, slits is 100 cm. If a bright fringe is, observed on a screen at a distance of 1.27, mm from the central bright fringe, then, the path difference between the waves,, which are reaching this point from the, slits is close to, , (d) 20, , 2, Object, 20, (cm), , 16, , 12, , 8, , (b) 125 MW, (d) 54 MW, , 4, , (b) 1.27 µm, (d) 2.05 µm, , (a) 2 nm, (c) 2.87 nm, , A spherical mirror is obtained as shown in, the above figure from a hollow glass sphere., If an object is in front of the mirror, what, will be the nature and magnification of the, image of the object ? (Figure drawn as, schematic and not to scale), (a), (b), (c), (d), , Erect, virtual and unmagnified, Inverted, real and magnified, Erect, virtual and magnified, Inverted, real and unmagnified, , 3 In a reactor, 2kg of 92 U235 fuel is fully used up, in 30 days. The energy released per fission, is 200 MeV., Given that, the Avogadro number,, N = 6023, × 1026 K −1 mol −1 and, ., , 5, 0, , 25, , 50, , 75, , 100, B, , A, 2m, , Shown in the above figure, a rigid and, uniform 1 m long rod AB held in horizontal, position by two strings tied to its ends and, attached to the ceiling. The rod is of mass, m and has another weight of mass 2 m, hung at a distance of 75 cm from A. The, tension in the string at A is, (a) 1 mg, (c) 0.75 mg, , (b) 2 mg, (d) 0.5 mg
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4, , JEE Main 2020 ~ Solved Papers, , ONLINE, 6 A uniform cylinder of mass M and radius R, is to be pulled over a step of height a (a < R), by applying a force F at its centre O, perpendicular to the plane through the, axes of the cylinder on the edge of the step, (see figure). The minimum value of F, required is, F, , O, R, a, , (a) Mg, , a, R, , (b) Mg 1 −, 2, , R , (c) Mg , −1, R − a, , a2, R2, , R − a, (d) Mg 1 − , , R , , 2, , 7 A plane electromagnetic wave, has, , frequency of 20, . × 1010 Hz and its energy, density is 102, . × 10−8 J / m 3 in vacuum. The, amplitude of the magnetic field of the, wave is close to, Nm 2, 1, = 9 × 109 2 and speed of, (Take,, 4πε 0, C, , (Take, the distance between the tracks as, negligible), (a) 28.5, (c) 29.5, , (b) 30.5, (d) 31.5, , 10 The least count of the main scale of a, vernier callipers is 1 mm. Its vernier scale, is divided into 10th division and coincide, with 9th division of the main scale. When, jaws are touching each other, the 7th, division of vernier scale coincides with a, division of main scale and the zero of, vernier scale is lying right side of the zero, of main scale. When this vernier is used to, measure length of a cylinder the zero of, the vernier scale lies between 3.1 cm and, 3.2 cm and 4th VSD coincides with a main, scale division. The length of the cylinder is, (VSD is vernier scale division), (a) 3.2 cm, (c) 3.07 cm, , (b) 2.99 cm, (d) 3.21 cm, , 11 A charged particle (mass m and charge q), moves along X-axis with velocity v0 . When, it passes through the origin it enters a, region having uniform electric field E = −E$j, which extends upto x = d. Equation of path, of electron in the region (x > d ) is, y, E, , light = 3 × 108 ms−1 ), (a) 190 nT, (c) 180 nT, , O, , (b) 160 nT, (d) 150 nT, , x, , v0, d, , 8 Magnetic materials used for making, permanent magnets (P) and magnets in a, transformer (T) have different properties,, of the following, which property best, matches for the type of magnet required?, (a), (b), (c), (d), , T: Large retentivity, small coercivity, P : Large retentivity, large coercivity, P : Small retentivity, large coercivity, T : Large retentivity, large coercivity, , 9 Trains A and B are running on parallel, tracks in the opposite directions with speeds, of 36 km/h and 72 km/h, respectively. A, person is walking in train A in the opposite, direction to its motion with a speed of, 1.8 km/h. Speed (in ms −1 ) of this person as, observed from train B will be close to, , (a) y =, , qEd, , x, , (b) y =, , (c) y =, , qEd d, , − x, , mv02 2, , (d) y =, , mv02, , qEd, mv02, , (x − d ), , qEd 2, mv02, , x, , 12 An amplitude modulated wave is, represented by the expression, . cos 6280t )sin (211 × 104 t ) volt., Vm = 5(1 + 06, The minimum and maximum amplitudes, of the amplitude modulated wave are,, respectively, (a) 3 V, 5 V, (c), , 3, V, 5 V, 2, , 5, V, 8 V, 2, (d) 5 V, 8 V, (b)
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5, , SEPTEMBER ATTEMPT ~ 02 Sep 2020, Shift I, 13 A beam of protons with speed 4 × 105 ms−1, , 19 A particle of mass m with an initial velocity, , u$i collides perfectly elastically with a mass, 3m at rest. It moves with a velocity v $j after, collision, then v is given by, , enters a uniform magnetic field of 0.3 T at, an angle of 60° to the magnetic field. The, pitch of the resulting helical path of, protons is close to, kg, (Take, mass of the proton = 167, . × 10, and charge of the proton = 1.69 ×10−19 C), (a) 2 cm, (c) 5 cm, , (c) v =, , (b) 4 cm, (d) 12 cm, , y, ω, , (b) T 2 ∝ R 3, 1, (d) T 2 ∝ 3, R, , (c) T ∝ R, 2, , P (a, b), , ω, , 15 A cylindrical vessel, , (b), , 5ω2, 2g, , (c), , 2ω2, 25 g, , h, , (d), , (c) 0.44, , 2ω2, 5g, , 22 When radiation of wavelength λ is used to, illuminate a metallic surface, the stopping, potential is V . When the same surface is, illuminated with radiation of wavelength, V, 3λ, the stopping potential is . If the, 4, threshold wavelength for the metallic, surface is nλ, then value of n will be …… ., , (d) 1.5, , copper, tungsten, mercury and aluminium, with resistivity ρC , ρT , ρ M and ρA ,, respectively. Then,, (b) ρA > ρM > ρC, (d) ρM > ρA > ρC, , 23, , B, C, , 18 If speed V , area A and force F are chosen, as fundamental units, then the dimensional, formula of Young’s modulus will be, (a) [FA2V−3 ], (c) [FA2 V−2 ], , (b) [FA−1V0 ], (d) [FA2V−1 ], , 2gC, ab, , and 1 atm and compresses it adiabatically, to 1/10th of the original volume. Assuming, air to be a diatomic ideal gas made up of, rigid molecules, the change in its internal, energy during this process comes out to be, XkJ. The value of X to the nearest integer, is …… ., , 17 Consider four conducting materials, , (a) ρA > ρT > ρC, (c) ρC > ρA > ρT, , (c) 2 gC (d), , Numerical Type Questions, 21 An engine takes in 5 moles of air at 20° C, , 10 cm, , same material have tensions TX and TZ in, them. If their fundamental frequencies are, 450 Hz and 300 Hz respectively, then the, ratio of TX / TZ is, (b) 2.25, , 2g, C, , (a) 2 2 gC (b), , 16 Two identical strings X and Z made of, , (a) 1.25, , x, , 0, , containing a liquid is rotated, about its axis, so that the, liquid rises at its sides as, shown in the figure. The, radius of vessel is 5 cm and, the angular speed of rotation, is ω red s −1. The difference in, the height h (in cm) of liquid, at the centre of vessel and at, the side will be, 25ω2, 2g, , u, 2, , a wire bent in the shape of a parabola, y = 4Cx2 and rotating with angular speed ω, (see figure). The value of ω is (neglect, friction), , K, over a large distance r from its, varies as, r, centre. In that region, a small star is in a, circular orbit of radius R. Then, the period, of revolution T depends on R as, , (a), , 1, u, 6, u, (d) v =, 3, , (b) v =, , 20 A bead of mass m stays at point P (a , b) on, , 14 The mass density of a spherical galaxy, , (a) T ∝ R, , 2, u, 3, , (a) v =, , −27, , A, , θ, , A small block starts slipping down from a, point B on an inclined plane AB, which is
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6, , JEE Main 2020 ~ Solved Papers, , ONLINE, making an angle θ with the horizontal, section BC is smooth and the remaining, section CA is rough with a coefficient of, friction µ. It is found that the block comes, to rest as it reaches the bottom (point A) of, the inclined plane. If BC = 2AC, the, coefficient of friction is given by µ = k tan θ., Then, the value of k is………, , 24 A circular coil of radius 10 cm is placed in, , a uniform magnetic field of 30, . × 10−5 T with, its plane perpendicular to the field, initially. It is rotated at constant angular, speed about an axis along the diameter of, , coil and perpendicular to magnetic field, so, that it undergoes half of rotation in, 0.2s.The maximum value of emf induced, (in µV) in the coil will be close to the, integer …… ., , 25 A 5 µF capacitor is charged fully by a 220V, supply. It is then disconnected from the, supply and is connected in series to, another uncharged 2.5 µF capacitor. If the, energy change during the charge, X, redistribution is, J, then value of X to, 100, the nearest integer is ……… ., , CHEMISTRY, Objective Type Questions, 1 The statement that is not true about ozone, is, (a) in the stratosphere, CFCs release, chlorine free radicals (Cl), which reacts, with O3 to give chlorine dioxide radicals, (b) in the atmosphere, it is depleted by, CFCs, (c) in the stratosphere, it forms a protective, shield against UV radiation., (d) it is a toxic gas and its reaction with NO, gives NO2, , 2 Which one of the following graphs is not, correct for ideal gas?, , 3 The increasing order of the following, compounds towards HCN addition is, H3CO, (i), , CHO, , CHO, (ii), NO2, , CHO, , O2N, (iv), , (iii), , CHO, , OCH3, , (a), (b), (c), (d), , (i) < (iii) < (iv) < (ii), (iii) < (iv) < (i) < (ii), (iii) < (iv) < (ii) < (i), (iii) < (i) < (iv) < (ii), , 4 The figure that is not a direct manifestation, of the quantum nature of atoms is, Increasing wavelength, , d, , d, , (a), , (I), , T, , T, , (II), , Absorption spectrum, Rb, , d, , d, , (III), , 1/T, , (IV), , p, , d = density, p = pressure, T = temperature, (a) III, , (b) I, , (c) IV, , K, , Kinetic energy of, (b) photoelectrons, , (d) II, , Frequency of incident, radiation, , Na
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7, , SEPTEMBER ATTEMPT ~ 02 Sep 2020, Shift I, 9 If AB4 molecule is a polar molecule, a, (c), , possible geometry of AB4 is, , Internal, energy of, Ar, , (a) square pyramidal (b) square planar, (c) rectangular planar (d) tetrahedral, 300, , 400, , 500, , 600, , 10 Consider that a d 6 metal ion (M 2+ ) forms a, , Temperature (K), , complex with aqua ligands and the spin, only magnetic moment of the complex is, 4.90 BM. The geometry and the crystal, field stabilisation energy of the complex is, , T 2 >T 1, , (d), , Intensity, of black body, radiation, , T1, Wavelength, , 5 An open beaker of water in equilibrium with, water vapour is in a sealed container. When, few grams of glucose are added to the beaker, of water, the rate at which water molecules, (a), (b), (c), (d), , tetrahedral and −1.6∆ t + 1 P, octahedral and −2.4 ∆ 0 + 2 P, octahedral and −1.6 ∆ 0, tetrahedral and −0.6 ∆ t, , 11 The major product in the following reaction, is, H3C, , leaves the solution decreases, leaves the solution increases, leaves the vapour increases, leaves the vapour decreases, , HBr, , HBr, (excess), ∆, , (a), , Zn/H3O+, , OH, CO2H, , C, , (c), , CH3, , CH3, (d), CH3, , 12 For octahedral Mn (II) and tetrahedral Ni, , (b), , CO2H, , Br, (d), , CHO, , CHO, , 7 On heating compound (A) gives a gas (B), which is a constituent of air. This gas, when treated with H2 in the presence of a, catalyst gives another gas (C) which is, basic in nature. (A) should not be, (a) NH4 NO2, (c) NaN3, , (b), , Br, , OH, (c), , CH3, , OH, H3C, , B, , (ii) H+, , O3, , (a), , CH3, , (i) KOH (Alc.), , A, , H3C, , CH3, , following reaction sequence will be, O, , CH==CH2, H3O+, Heat, , 6 The major aromatic product C in the, , (b) (NH4)2 Cr2O7, (d) Pb (NO3 )2, , 8 In general, the property (magnitudes only), that shows an opposite trend in comparison, to other properties across a period is, (a), (b), (c), (d), , (a), (b), (c), (d), , electronegativity, electron gain enthalpy, ionisation enthalpy, atomic radius, , (II) complexes, consider the following, statements :, , (I) Both the complexes can be high spin., (II) Ni(II) complex can very rarely be low, spin., (III) With strong field ligands, Mn(II), complexes can be low spin., (IV) Aqueous solution of Mn(II) ions is, yellow in colour., The correct statements is, (a) (I) and (II) only, (b) (II), (III) and (IV) only, (c) (I), (II) and (III) only, (d) (I), (III) and (IV) only, , 13 The metal mainly used in devising, photoelectric cells is, (a) Na, (c) Cs, , (b) Li, (d) Rb
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8, , ONLINE, , 14 Which of the following compounds will, show retention in configuration on, nucleophilic substitution by OH− ion?, (b) CH3 —CH— CH2Br, , C2H5, Br, , (d) CH3 —C— H, , C6 H13, , (a) CH3 —CH— Br, , C6 H5, (c) CH3 —CH— Br, , CH3, , 15 For the following Assertion and Reason,, the correct option is, , Reason (R) The equilibrium constant of, CuS(s) is high, Cu 2 + (aq) + S2 − (aq), because the solubility product is low., (a) Both (A) and (R) are false., (b) Both (A) and (R) are true and (R) is the, explanation for (A)., (c) Both (A) and (R) are true but (R) is not, the explanation for (A)., (d) (A) is false and (R) is true., , r, , 16 Which of the following is used for the, preparation of colloids?, (a) Bredig’s Arc method (b) Ostwald process, (c) Mond process, (d) van Arkel method, , 17 In Carius method of estimation of halogen, 0.172 g of an organic compound showed, presence of 0.08 g of bromine. Which of, these is the correct structure of the, compound?, (b) H3C — CH2 — Br, NH2, , NH2, Br, (c), , Br, , Br, , 18 Consider the following reactions :, Dry HCl, , (i) Glucose + ROH → Acetal, x eq. of, , y eq.of, , Ni/H2, , → A → Acetyl, (CH3 CO) 2 O, , derivative, z eq.of, (iii) Glucose , → Acetyl derivative, (CH3 CO) 2 O, , x’, ‘y’ and ‘z’ in these reactions are, respectively, (a) 5, 4 and 5, (c) 5, 6 and 5, , (b) 4, 5 and 5, (d) 4, 6 and 5, , 19 The IUPAC name for the following, CHO, CH3, , H3C, , COOH, , (a) 6-formyl-2-methyl-hex-3-enoic acid, (b) 2, 5-diamethyl-6-oxo-hex-3-enoic acid, (c) 2, 5-dimethyl-6-carboxy-hex-3-enal, (d) 2, 5-dimethyl-5-carboxy-hex-3-enal, , 20 While titrating dilute HCl solution with, aqueous NaOH, which of the following will, not be required?, (a) Pipette and distilled water, (b) Burette and porcelain tile, (c) Bunsen burner and measuring cylinder, (d) Clamp and phenolphthalein, , Numerical Type Questions, 21 The Gibbs energy change (inJ) for the, given reaction at, [Cu 2 + ] = [Sn 2 + ] = 1M and 298 K is, Cu (s) + Sn 2 + (aq) → Cu 2+ (aq) + Sn (s);, o, o, = −0.16 V, ECu, = 0.34V,, (E Sn, 2+, 2+, / Sn, / Cu, , Take, F = 96500 C mol −1 ), , 22 The mass of gas adsorbed, x per unit mass, , (d), , → Acetyl derivative, (CH3 CO) 2 O, , (ii) Glucose, , compound is, , Assertion (A) When Cu (II) and sulphide, ions are mixed, they react together, extremely quickly to give a solid., , (a) H3C — Br, , JEE Main 2020 ~ Solved Papers, , of adsorbate, m was measured at various, pressures, p. A graph between, x, log and log p gives a straight line with, m, slope equal to 2 and the intercept equal to, x, 0.4771. The value of at a pressure of, m, 4 atm is (Given, log 3 = 0.4771)
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9, , SEPTEMBER ATTEMPT ~ 02 Sep 2020, Shift I, 23 The number of chiral carbons present in, the molecule given below is …… ., , N, , H3C, , C, HO, , 90 g of water undergoes complete evaporation, at 100°C is ………, (Given : ∆H vap for water, at 373 K = 41kJ/mol, R = 8.314 JK−1mol−1), , 25 The oxidation states of iron atoms in, , O, , H, , 24 The internal energy change (in J) when, , CH3, , compounds (A), (B) and (C), respectively,, are x, y and z. The sum of x, y and z is, Na 4 [Fe (CN)5 (NOS)], Na 4 [FeO4 ], [Fe2 (CO)9 ], (A ), , (C ), , (B), , N, , MATHEMATICS, Objective Type Questions, 1 Let S be the set of all λ∈ R for which the, system of linear equations, 2x − y + 2z = 2, x − 2 y + λz = − 4, x + λy+ z = 4, has no solution. Then the set S, (a) contains more than two elements, (b) contains exactly two elements, (c) is an empty set, (d) is a singleton, , 2 The plane passing through the points, (1, 2, 1), (2, 1, 2) and parallel to the line,, 2x = 3 y, z = 1 also passes through the point, (a) (– 2, 0, 1), (c) (0,–6, 2), , (b) (0,6,–2), (d) (2,0,–1), , 3 Let A be a 2×2 real matrix with entries, , from {0,1} and |A| ≠ 0. Consider the, following two statements, (P) If A ≠ I 2 , then | A|= −1, (Q) If| A| = 1, then tr ( A) = 2,, where I 2 denotes 2×2 identity matrix and, tr(A) denotes the sum of the diagonal, entries of A. Then,, , (a) (P) is false and (Q) is true, (b) Both (P) and (Q) are false, (c) (P) is true and (Q) is false, (d) Both (P) and (Q) are true, , 4 The domain of the function, |x|+ 5, f (x) = sin −1 2, is, x + 1, , (−∞,− a ] ∪ [a , ∞). Then a is equal to, 17 − 1, 2, 17, (d), 2, , 17, +1, 2, 1 + 17, (c), 2, , (b), , (a), , 5 Let α and β be the roots of the equation,, 5x2 + 6x − 2 = 0. If Sn = α n + βn ,, n =1, 2, 3,... then, (a) 5S6 + 6S5 + 2S4 = 0 (b) 6S6 + 5S5 + 2S4 = 0, (c) 6S6 + 5S5 = 2S4, (d) 5S6 + 6S5 = 2S4, , 6 A line parallel to the straight line 2x − y = 0, x2 y2, −, = 1 at, 4, 2, 2, + 5 y1 is equal to, , is tangent to the hyperbola, the point (x1 , y1 ). Then, x12, (a) 10, , (b) 5, , (c) 6, , (d) 8, , 7 Let P (h,k) be a point on the curve, y = x2 + 7x + 2, nearest to the line y = 3x − 3., Then the equation of the normal to the, curve at P is, (a) x − 3 y − 11 = 0, (c) x + 3 y − 62 = 0, , (b) x − 3 y + 22 = 0, (d) x + 3 y + 26 = 0, , 8 Area (in sq. units) of the region outside, |x| | y|, +, = 1 and inside the ellipse, 2, 3, x2 y2, +, = 1 is, 4, 9, (a) 6( π − 2 ), (c) 3 (4 − π ), , (b) 3( π − 2 ), (d) 6 (4 − π ), , 9 Box I contains 30 cards numbered 1 to 30, and Box II contains 20 cards numbered 31, to 50. A box is selected at random and a
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10, , ONLINE, card is drawn from it. The number on the, card is found to be a non-prime number., The probability that the card was drawn, from Box I is, (a), , 8, 17, , (b), , 2, 3, , (c), , 2, 5, , (d), , 4, 17, , JEE Main 2020 ~ Solved Papers, , 16 The sum of the first three terms of a GP is S, and their product is 27. Then all such S lie in, (a) (− ∞ , 9], (c) (− ∞ , − 9]∪[3, ∞ ), , (b) [− 3, ∞ ), (d) (− ∞ , − 3]∪[9, ∞ ), , 17 If a function f (x) defined by, , the maximum value of the term, independent of x in the binomial expansion, 10, 1, 1, − , 9, 6, , , of αx + βx, is 10 k, then k is equal to, , , , , , aex + be− x , −1 ≤ x < 1, , f (x) = cx2, , 1 ≤ x≤3, ax2 + 2cx, , 3 < x≤4, , be continuous for some a , b, c ∈R and, f ′ (0) + f ′ (2) = e, then the value of a is, , (a) 84, , (a), , 10 Let α > 0, β > 0 be such that α3 + β2 = 4. If, , (b) 176, , (c) 352, , (d) 336, , 11 Let X = { x ε N : 1 ≤ x ≤ 17} and, Y = { ax + b : x ∈X and a, b ∈ R, a > 0}. If mean, and variance of elements of Y are 17 and, 216 respectively, then a + b is equal to, (a) 9, , (b) 7, , (c) –7, , (d) –27, , 12 Let y = y(x) be the solution of the, differential equation,, 2 + sin x dy, ⋅, = − cos x, y > 0, y(0) = 1. If, y+1, dx, dy, at x = π is b, then the, y(π ) = a and, dx, ordered pair (a , b) is equal to, (a) (1, 1), , 3, (b) 2, , 2, , (c) (1, − 1), , (d) (2, 1), , 13 If|x|< 1,| y|< 1 and x ≠ y, then the sum to, infinity of the following series, (x + y) + (x2 + xy + y2 ) + (x3 + x2 y + xy2 + y3 ), + … is, , x + y + xy, (1 + x) (1 + y), x + y + xy, (c), (1 − x) (1 − y), (a), , x + y − xy, (1 − x) (1 − y), x + y − xy, (d), (1 + x) (1 + y), (b), , 14 If p(x) be a polynomial of degree three that, has a local maximum value 8 at x = 1 and a, local minimum value 4 at x = 2; then p(0) is, equal to, (a) −24, , (b) 6, , (c) 12, , (d) −12, , 15 If the tangent to the curve y = x + sin y at a, point (a , b) is parallel to the line joining, 1 , 3, 0, and , 2 , then, 2 , 2, (a)|b − a|= 1, (c) b = a, , (b)|a + b|= 1, π, (d) b = + a, 2, , (c), , e, e2 + 3e + 13, 1, e2 − 3e + 13, , (b), (d), , e, e2 − 3e − 13, e, e2 − 3e + 13, , 18 If R = {(x, y): x, y ∈ Z , x2 + 3 y2 ≤ 8} is a, relation on the set of integers Z, then the, domain of R−1 is, (a) {−1, 0,1}, (b) {− 2, − 1,1, 2}, (c) {−2, − 1, 0,1, 2}, (d) {0,1}, , 19 The contrapositive of the statement “If I, reach the station in time, then I will catch, the train” is, (a) If I do not reach the station in time, then, I will catch the train, (b) If I will not catch the train, then I do not, reach the station in time, (c) If I do not reach the station in time, then, I will not catch the train, (d) If I will catch the train, then I reach the, station in time, 3, , 2π, 2π , , + i cos , 1 + sin, 9, 9 is, 20 The value of , 1 + sin 2π − i cos 2π , , 9, 9 , 1, (a) − ( 3 − i ), 2, 1, (c) ( 3 − i ), 2, , 1, (b) − (1 − i 3 ), 2, 1, (d) (1 − i 3 ), 2, , Numerical Type Questions, 21 If the letters of the word ‘MOTHER’ be, permuted and all the words so formed, (with or without meaning) be listed as in, dictionary, then the position of the word, ‘MOTHER’ is…………
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11, , SEPTEMBER ATTEMPT ~ 02 Sep 2020, Shift I, x + x2 + x3 +..+ xn − n, = 820, (n ∈ N), x →1, x−1, then the value of n is equal to ………, , 2, , 22 The integral ∫ ||x − 1|−x|dx is equal to, , 24 If lim, , 0, , 23 The number of integral values of k for, , 25 a, b and c be three unit vectors such that, , which the line, 3x + 4 y = k intersects the, circle, x2 + y2 − 2x − 4 y + 4 = 0 at two, distinct points is……, , | a − b|2 + | a − c|2 = 8. Then, | a + 2b|2 + | a − 2c|2 is equal to …… ., , Answers, Physics, 1., 11., 21., , (a), (c), (4), , 2. (d), 12. (b), 22. (9), , (c), (b), (3), , 3., 13., 23., , (b), (c), (15), , 4., 14., 24., , (a), (a), (4), , 5., 15., 25., , 6. (d), 16. (b), , 7. (b), 17. (d), , 8. (b), 18. (b), , 9., 19., , (c), (c), , 10. (c), 20. (a), , For Detailed Solutions, Visit : http://bit.ly/3dE3VOs, Or Scan :, , Chemistry, 1., (a), 11. (d), 21. (96500), , 2., 12., 22., , (d), (c), (6), , 3., 13., 23., , (d), (c), (5), , 4., (c), 14., (b), 24. (189494), , 5., 15., 25., , (c), (c), (6), , 6. (c), 16. (a), , 7. (d), 17. (c), , 8. (d), 18. (d), , 9. (a), 19. (b), , 10. (d), 20. (c), , For Detailed Solutions, Visit : http://bit.ly/3m1ciXn, Or Scan :, , Mathematics, 1. (b), 11. (c), 21. (309), , 2. (a), 12. (a), 22. (1.5), , 3., 13., 23., , (a), (b), (9), , 4., 14., 24., , (c), (d), (40), , 5., 15., 25., , (d), (a), (2), , 6., 16., , (c), (d), , 7., 17., , (d), (d), , 8., 18., , (a), (a), , 9., 19., , (a), (b), , For Detailed Solutions, Visit : http://bit.ly/2T711bF, Or Scan :, , 10., 20., , (d), (a)
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12, , ONLINE, , JEE Main 2020 ~ Solved Papers, , ONLINE QUESTION PAPER, , JEE Main 2020, (02 September, 2020), TIME 2:30-5:30 (Shift II), , MM : 300, , PHYSICS, Objective Type Questions, 1 A capillary tube made of glass of radius, 0.15 mm is dipped vertically in a beaker, filled with methylene iodide, which rises to, height h in the tube. It is observed that the, two tangents drawn from liquid- glass, interfaces (from opposite sides of the, capillary) make an angle of 60° with one, another. Then, h is close to, (Given, surface tension = 005, . Nm −1,, density = 667 kg m −3 and g = 10 ms −2), (a) 0.049 m, (c) 0.137 m, , (b) 0.087 m, (d) 0.172 m, , 4 The figure shows a region of length l with, a uniform magnetic field of 0.3 T in it and, a proton entering the region with velocity, 4 × 105 ms−1 making an angle 60° with the, field. If the proton completes 10 revolutions, by the time it cross the region shown, l is, close to, (Take, mass of proton = 167, . × 10−27 kg,, charge of the proton = 16, . × 10−19 C), B, , 60º, , 2 An inductance coil has a reactance of 100 Ω., When an AC signal of frequency 1000 Hz, is applied to the coil, the applied voltage, leads the current by 45°. The, self-inductance of the coil is, (a) 11, . × 10−2 H, (c) 5.5 × 10−5 H, , (b) 11, . × 10−1 H, (d) 6.7 × 10−7 H, , 3 The height h at which the weight of a body, will be the same as that at the same depth, h from the surface of the earth is, (Radius of the earth is R and effect of the, rotation of the earth is neglected), 5, (R − R ), 2, 5R − R, (c), 2, (a), , R, 2, 3R − R, (d), 2, (b), , l, , (a) 0.11 m, (c) 0.44 m, , (b) 0.88 m, (d) 0.22 m, , 5 If momentum P, area A and time T are, taken to be the fundamental quantities,, then the dimensional formula for energy is, (a) [P 2AT −2 ], (c) [PA1/2T −1 ], , (b) [PA −1T −2 ], (d) [P 1/2AT −1 ], , 6 When the temperature of a metal wire is, increased from 0°C to 10°C, its length, increases by 0.02%. The percentage change, in its mass density will be closest to, (a) 0.06, (c) 0.008, , (b) 2.3, (d) 0.8
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SEPTEMBER ATTEMPT ~ 02 Sep 2020, Shift II, 7 A 10 µF capacitor is fully charged to a, potential difference of 50 V. After, removing the source voltage it is connected, to an uncharged capacitor in parallel., Now, the potential difference across them, becomes 20 V. The capacitance of the, second capacitor is, (a) 15 µF, (c) 20 µF, , (b) 30 µF, (d) 10 µF, , transition from (n + 1)th level to the nth, level. If n > > 1, the frequency of radiation, emitted is proportional to, , (c), , 1, n, 1, , (b), (d), , n2, , 1, n3, 1, n4, , 9 A heat engine is involved with exchange of, heat of 1915 J, − 40 J, + 125 J and − QJ,, during one cycle achieving an efficiency of, 50.0%. The value of Q is, , (a) 640 J, (c) 980 J, , 11 A particle is moving 5 times as fast as an, electron. The ratio of the de-Broglie, wavelength of the particle to that of the, electron is 1878, ., × 10−4. The mass of the, particle is close to, (a) 4.8 × 10−27 kg, (c) 12, . × 10−28 kg, , (b) 91, . × 10−31 kg, (d) 9.7 × 10−28 kg, , 12 In a plane electromagnetic wave, the, , 8 In a hydrogen atom, electron makes a, , (a), , 13, , directions of electric field and magnetic, field are represented by k$ and 2$i − 2$j,, respectively. What is the unit vector along, direction of propagation of the wave?, 1 $ $, (i + j), 2, 1 $, (c), (i + 2$j), 5, , 1 $ $, ( j + k), 2, 1, (d), (2$i + $j), 5, , (b), , (a), , 13 In the following digital circuit, what will, be the output at Z, when the input (A, B), are (1, 0), (0, 0), (1, 1), (0, 1)?, A, Z, , (b) 40 J, (d) 400 J, , 10 A wire carrying current I is bent in the, shape ABCDEFA as shown, where, rectangle ABCDA and ADEFA are, perpendicular to each other. If the sides of, the rectangles are of lengths a and b, then, the magnitude and direction of magnetic, moment of the loop ABCDEFA is, Z, E, I, I, , F, , C, , D, O, X, , A, , a, , b, , B, , (a) 0, 0, 1, 0, (c) 1, 1, 0, 1, , (b) 1, 0, 1, 1, (d) 0, 1, 0, 0, , 14 A small point mass carrying some positive, charge on it, is released from the edge of a, table. There is an uniform electric field in, this region in the horizontal direction., Which of the following options then, correctly describe the trajectory of the mass?, (Curves are drawn schematically and are, not to scale), , Y, , E, x, , B, , $j, k$ , (a) abI, along , +, , 2, 2, $j, k$ , (b) 2 abI, along , +, , 2, 2, , $j, 2k$ , (c) 2 abI, along , +, , 5, 5, , $j, 2k$ , (d) abI , along , +, , 5, 5, , , y, , y, , y, , (a), , (b), x, , x
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14, , ONLINE, y, , (c), , (d), x, , x, , 15 A potentiometer wire PQ of 1 m length is, connected to a standard cell E1. Another, cell E 2 of emf 1.02 V is connected with a, resistance r and switch S (as shown in, figure). With switch S open, the null, position is obtained at a distance of 49 cm, from Q. The potential gradient in the, potentiometer wire is, E1, , I, , P, , G, , S, , (a) 0.02 V/cm, (b) 0.01 V/cm, (c) 0.03 V/cm, (d) 0.04 V/cm, , 16 In a Young’s double slit experiment,, 16 fringes are observed in a certain, segment of the screen when light of, wavelength 700 nm is used. If the, wavelength of light is changed to 400 nm,, the number of fringes observed in the, same segment of the screen would be, (a) 24, (c) 18, , (R + r ), Q, 2(R 2 + r 2 ), (2R + r ), Q, (R 2 + r 2 ), (R + 2r )Q, 2(R 2 + r 2 ), (R + r ), Q, (R 2 + r 2 ), , 18 The displacement-time graph of a particle, executing SHM is given in figure (sketch is, schematic and not to scale), , O, , 2T/4, T/4, , 3T/4 T, , 5T/4, , Time (s), , Q, , r, , E2, , 1, 4 πε0, 1, (b), 4 πε0, 1, (c), 4 πε0, 1, (d), 4 πε0, (a), , Displacement (m), , y, , JEE Main 2020 ~ Solved Papers, , (b) 30, (d) 28, , 17 A charge Q is distributed over two, concentric conducting thin spherical shells, radii r and R (R > r ). If the surface charge, densities on the two shells are equal, the, electric potential at the common centre is, , r, , Which of the following statement(s) is/are, true for this motion?, 3T, A. The force is zero at t =, ., 4, B. The acceleration is maximum at, t = T., T, C. The speed is maximum at t = ., 4, D. The potential energy is equal to, kinetic energy of the oscillation at, T, t= ., 2, (a) A, B and D, (c) A, B and C, , 19 Two uniform circular discs are rotating, independently in the same direction around, their common axis passing through their, centres. The moment of inertia and angular, velocity of the first disc are 0.1 kg-m 2 and, 10 rad s −1 respectively, while those for the, second one are 0.2 kg-m 2 and 5 rad s −1,, respectively. At some instant they get, stuck together and start rotating as a, single system about their common axis, with some angular speed. The kinetic, energy of the combined system is, 10, J, 3, 5, (c) J, 3, (a), , R, , (b) B, C and D, (d) A and D, , 20, J, 3, 2, (d) J, 3, , (b)
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SEPTEMBER ATTEMPT ~ 02 Sep 2020, Shift II, 20 An ideal gas in a closed container is slowly, heated. As its temperature increases,, which of the following statements are, true?, , 15, a, , value of, X, X (to the nearest integer) is ……… ., remaining portion from O is −, , A. The mean free path of the molecules, decreases., , a, , B. The mean collision time between the, molecules decreases., , O, , C. The mean free path remains, unchanged., , d, l=a/2, , D. The mean collision time remains, unchanged., (a) B and C, (b) A and B, (c) C and D, (d) A and D, , 23 A light ray enters a solid glass sphere of, , Numerical Type Questions, 21 An ideal cell of emf 10 V is connected in, circuit shown in figure. Each resistance is, 2 Ω. The potential difference (in V) across, the capacitor when it is fully charged is, ……… ., R1, , refractive index µ = 3 at an angle of, incidence 60°. The ray is both reflected and, refracted at the farther surface of the, sphere. The angle (in degree) between the, reflected and refracted rays at this surface, is ……… ., , 24 A particle of mass m is moving along the, , X-axis with initial velocity u$i. It collides, elastically with a particle of mass 10 m at, rest and then moves with half its initial, kinetic energy (see figure). If, sin θ1 = n sin θ 2, then value of n is ……… ., , C, , m, R5, , R2, , θ1, , R3, , m, R4, , θ2, , 25 A wire of density 9 × 10−3 kg-cm −3 is, a, is curved, 2, , a, from the centre O of, 2, a uniform circular disc of radius a. If the, distance of the centre of mass of the, out at a distance d =, , 10 m, , 10 m, , 10 V, , 22 A square shaped hole of side l =, , ui^, , stretched between two clamps 1 m apart., The resulting strain in the wire is, 49, . × 10−4. The lowest frequency of the, transverse vibrations in the wire is, (Young’s modulus of wire,Y = 9 × 1010 Nm −2),, (to the nearest integer) ……… .
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16, , ONLINE, , JEE Main 2020 ~ Solved Papers, , CHEMISTRY, Objective Type Questions, 1 If you spill a chemical toilet cleaning liquid, on your hand, your first aid would be, (a) vinegar, (c) aqueous NaHCO3, , (b) aqueous NaOH, (d) aqueous NH3, , 2 An organic compound ‘A’ (C 9H10O ) when, treated with conc. HI undergoes cleavage, to yield compounds ‘B’ and ‘C ’. ‘B ’ gives, yellow precipitate with AgNO3 whereas ‘C’, tautomerism to ‘D’. ‘D’ gives positive, iodoform test. ‘A’ could be, (a), , —O—CH2—CH==CH2, , (b), , —O—CH ==CH—CH3, , (c), , —CH2—O—CH ==CH2, , 5 The major product obtained from, E2-elimination of 3-bromo-2-fluoropentane, is, Br, , (a) CH 3 CH 2 CH CH 2 ==CH 2, (b) CH 3 CH 2 CH== C F, , CH3, F, , (c) CH 3 CH==CH C H CH 3, Br, , (d) CH 3 CH 2 C ==CH CH 3, , 6 Simplified absorption spectra of three, , —O—CH==CH2, , 3 The size of a raw mango shrinks to a much, smaller size when kept in a concentrated, salt solution. Which one of the following, processes can explain this?, (a) Osmosis, (c) Diffusion, , A, B, , (b) Dialysis, (d) Reverse osmosis, , 4 Amongst the following statements regarding, adsorption, those that are valid are:, , (A) ∆H becomes less negative as, adsorption proceeds., (B) On a given adsorbent, ammonia is, adsorbed more than nitrogen gas., (C) On adsorption, the residual force, acting along the surface of the, adsorbent increases., (D) With increase in temperature, the, equilibrium concentration of, adsorbate increases., (a) (D) and (A), (b) (B) and (C), (c) (A) and (B), (d) (C) and (D), , C, , Absorption, , (d) H3C—, , complexes [(i), (ii) and (iii)] of M n + ion are, provided below; their λ max values are, marked as A, B and C respectively. The, correct match between the complexes and, their λ max values is, , λmax, , λmax, λmax, Wavelength (nm), , (i) [M (NCS)6 ]( − 6 + n ), (ii) [M F6 ]( − 6 + n ), (iii) [M (NH3 )6 ]n +, (a) A-(iii), B-(i), C-(ii), (b) A-(ii), B-(i), C-(iii), (c) A-(ii), B-(iii), C-(i), (d) A-(i), B-(ii), C-(iii), , 7 The correct observation in the following, reactions, is, Sucrose Cleavage, → A + B Seliw, anoff's, →, Glycosidic bond, , reagent, , (Hydrolysis)
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SEPTEMBER ATTEMPT ~ 02 Sep 2020, Shift II, (a) Formation of blue colour, (b) Gives no colour, (c) Formation of red colour, (d) Formation of violet colour, , 17, 11 Arrange the following labelled hydrogens, in decreasing order of acidity, NO2 C==C— H a, , 8 Two elements A and B have similar, chemical properties. They don’t form solid, hydrogencarbonates, but react with, nitrogen to form nitrides. A and B,, respectively, are, (a) Na and Rb, (c) Cs and Ba, , (b) Na and Ca, (d) Li and Mg, , 9 The results given in the below table were, obtained during kinetic studies of the, following reaction :, 2A + B → C + D, , COO H b, , d H —O, O— H c, , (a) b > a > c > d, (c) b > c > d > a, , (b) c > b > d > a, (d) c > b > a > d, , 12 Consider the reaction sequence given, below :, Br, , OH, H2O, , OH + Br, , (1), , rate = k [t-BuBr], , Experiment, , [A]/mol, L−1, , [B]/mol, L−1, , Initial, rate/mol L−1, min −1, , I, , 0.1, , 0.1, , 6.00 × 10−3, , II, , 0.1, , 0.2, , 2.40 × 10−2, , III, , 0.2, , 0.1, , . × 10−2, 120, , IV, , X, , 0.2, , 7.20 × 10−2, , V, , 0.3, , Y, , 2.88 × 10−1, , X and Y in the given table are respectively, (a) 0.4, 0.4, (c) 0.3, 0.4, , (b) 0.4, 0.3, (d) 0.3, 0.3, , 10 The major product of the following reaction, is, , CH3, + HOH + Br, , OH, C2H5OH, , (2), , CH3, , H2C, , rate = k [t-BuBr] [OH ], , Which of the following statements is true?, (a) Changing the base from OH È to ÈOR will, have no effect on reaction (2), (b) Changing the concentration of base will, have no effect on reaction (1), (c) Doubling the concentration of base will, double the rate of both the reactions, (d) Changing the concentration of base will, have no effect on reaction (2), , 13 Three elements X , Y and Z are in the 3rd, OH, , CH3, , Conc. HNO3 + conc. H2SO4, , NO2, , OH, , (a) Z < Y < X, (c) X < Z < Y, , OH, NO2, , H3C, , H3C, (b), , (a), O2N, , NO2, , NO2, , OH, , OH, NO2, , H3C, , H3C, (c), , (d), NO2, NO2, , NO2, NO2, , period of the periodic table. The oxides of X,, Y and Z, respectively, are basic, amphoteric, and acidic. The correct order of the atomic, number of X , Y and Z is, (b) X < Y < Z, (d)Y < X < Z, , 14 The one that is not expected to show, isomerism is, (a) [Ni(NH 3 )4 (H 2 O)2 ]2+, (b) [Ni(en)3 ]2+, (c) [Ni(NH 3 )2 Cl 2 ], (d) [Pt(NH 3 )2 Cl 2 ], , 15 Two compounds A and B with same, molecular formula (C 3H6O ) undergo, Grignard’s reaction with methylmagnesium, bromide to give products C and D.
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18, , ONLINE, Products C and D show following chemical, tests., C, , Test, , D, , Ceric, ammonium, nitrate test, , Positive, , Lucas test, , Turbidity obtained Turbidity, after five minutes obtained, immediately, , 18. Match the type of interaction in column A, with the distance dependence of their, interaction energy in column B :, A, , Positive, , Iodoform test Positive, , JEE Main 2020 ~ Solved Papers, , B, , (I), , Ion-ion, , (a), , (II), , Dipole-dipole, , (b), , 1, r, 1, r2, , (III) London dispersion, , (c), , 1, r3, , Negative, (d), , C and D respectively are, , 1, r6, , OH, , (a) C= H 3 C CH 2 CH CH3 ;, CH3, , D = H 3 C C OH, , CH3, (b) C = H 3 C CH 2 CH 2 CH 2 OH;, D = H 3 C CH 2 CH CH 3, , OH, (c) C = H 3 C CH 2 CH 2 CH 2 OH;, CH3, , D = H 3 C C OH, , CH3, CH3, , (d) C=H 3 C C OH; D = H 3 CCH 2 CH CH 3, , , CH3, OH, , 16 Cast iron is used for the manufacture of, (a) wrought iron and pig iron, (b) pig iron, scarp iron and steel, (c) wrought iron, pig iron and steel, (d) wrought iron and steel, , 17 The shape/structure of [XeF5 ]− and XeO 3F2,, respectively, are, (a) pentagonal planar and trigonal, bipyramidal, (b) octahedral and square pyramidal, (c) trigonal bipyramidal and pentagonal, planar, (d) trigonal bipyramidal and trigonal, bipyramidal, , (a) (I)-(b), (II)-(d), (III)-(c), (b) (I)-(a), (II)-(b), (III)-(d), (c) (I)-(a), (II)-(b), (III)-(c), (d) (I)-(a), (II)-(c), (III)-(d), , 19 The molecular geometry of SF6 is, octahedral. What is the geometry of SF4, (including lone pair(s) of electrons, if any)?, (a) Tetrahedral, (b) Trigonal bipyramidal, (c) Pyramidal, (d) Square planar, , 20 The number of subshells associated with, n = 4 and m = −2 quantum numbers is, , (a) 8, , (b) 2, , (c) 16, , (d) 4, , Numerical Type Questions, 21 The work function of sodium metal is, , 441, . × 10−19 J. If photons of wavelength, 300 nm are incident on the metal, the, kinetic energy of the ejected electrons will, be (h = 663, . × 10−34 J s; c = 3 × 108 m/s), ………… × 10−21 J., , 22 The oxidation states of transition metal, atoms in K 2Cr2O7 , KMnO 4 and K 2FeO 4 ,, respectively, are x, y and z. The sum of x, y, and z is ……… ., , 23 For the disproportionation reaction, , 2Cu+ (aq), Cu (s) + Cu 2+ (aq) at 298 K,, In K (where K is the equilibrium constant), is ………× 10−1 ., , c, , ° 2+, Given : (E Cu, = 016, . V,, / Cu +, ° +, E Cu, = 052, . V and, / Cu, , RT, =0025, . ), F
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SEPTEMBER ATTEMPT ~ 02 Sep 2020, Shift II, 24 The ratio of the mass percentages of ‘C’, and H’ and ‘C and O’ of a saturated acyclic, organic compound ‘X’ are 4 : 1 and 3 : 4, respectively. Then, the moles of oxygen gas, required for complete combustion of two, moles of organic compound ‘X’ is ……… ., , 19, 25 The heat of combustion of ethanol into, , carbon dioxides and water is − 327 kcal at, constant pressure. The heat evolved, (in cal) at constant volume and 27°C (if all, gases behave ideally) is (R =2 cal mol −1, K −1) ……… ., , MATHEMATICS, Objective Type Questions, 1 Let A = { X = (x, y, z)T : PX = 0 and, 1 2 1, x2 + y2 + z2 = 1}, where P = −2 3 −4,, , , 1 9 −1, then the set A, (a) is a singleton, (b) is an empty set, (c) contains more than two elements, (d) contains exactly two elements, , 2 Let f : R → R be a function which satisfies, f (x + y) = f (x) + f ( y) ∀ x, y ∈R. If f (1) = 2 and, g(n ) =, , ( n − 1), , Σ, , k =1, , f (k), n ∈N , then the value of n,, , for which g(n ) = 20 is, (a) 5, (c) 4, , (b) 20, (d) 9, , 3 Which of the following is a tautology?, (a) (~ p ) ∧ ( p ∨ q)→ q, (b) (q → p ) ∨ ~ ( p → q), (c) (~ q) ∨ ( p ∧ q) → q, (d) ( p → q) ∧ (q → p ), , point (1, 2), is the solution of the, differential equation, 2x2dy = (2xy + y2 )dx,, 1, then f is equal to, 2, (a), , 1, 1 + log e 2, , (c) 1 + log e 2, , , x → 0, , π, , + x , 4, , , 7 lim tan , (a) e, , (b) 2, , 1/ x, , is equal to, (c) 1, , (d) e2, , 8 The set of all possible values of θ in the, , interval (0, π) for which the points (1, 2), and(sin θ , cos θ) lie on the same side of the, line x + y = 1 is, π 3π , (b) ,, , 4 4, π, (d) 0, , 4, , π, (a) 0, , 2, 3π , (c) 0,, , , 4, , f (x) =, , real solutions for θ, then λ lies in the, interval, 1, (b) − 1, − , , 2 , 3, 5, , (d) − , − , 4 , 2, , 1, log e (1 + x), x ≠ 0. Then the function f, x, , (a) decreases in (−1,0) and increases in (0, ∞), (b) increases in (−1, ∞ ), (c) increases in (− 1, 0) and decreases in (0, ∞ ), (d) decreases in (− 1, ∞ ), , 10 Let a , b, c ∈R be all non-zero and satisfy, a3 + b3 + c3 = 2. If the matrix, a b c, , , A = b c a, c a b, , , , 5 Let f (x) be a quadratic polynomial such, that f (− 1) + f (2) = 0. If one of the roots of, f (x) = 0 is 3, then its other root lies in, (a) (−1, 0), (c) (− 3, − 1), , 1, 1 − log e 2, −1, (d), 1 + log e 2, (b), , 9 Let f : (− 1, ∞) → R be defined by f (0) = 1 and, , 4 If the equation cos4 θ + sin 4 θ + λ = 0 has, 5, (a) − , − 1, , 4, 1, 1, , (c) − , −, 2, 4 , , 6 If a curve y = f (x), passing through the, , (b) (1, 3), (d) (0,1), , satisfies AT A = I ,then a value of abc can be, (a) −, , 1, 3, , (b), , 1, 3, , (c) 3, , (d), , 2, 3
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20, , ONLINE, , each pair of nearest stations is connected, by blue line,whereas all remaining pairs of, stations are connected by red line. If the, number of red lines in 99 times the number, of blue lines, then the value of n is, , 11 The imaginary part of, (3 + 2 −54 ), , 1/ 2, , − (3 − 2 − 54 ), , 1/ 2, , (a) − 6, (c) 6, , can be, , (b) − 2 6, (d) 6, , 12 The equation of the normal to the curve, y = (1 + x)2 y + cos2 (sin −1 x) at x = 0 is, , (a) y + 4x = 2, (c) x + 4 y = 8, , 13 A plane passing through the point (3, 1, 1), contains two lines whose direction ratios, are 1, − 2, 2 and 2, 3, − 1 respectively. If, this plane also passes through the point, (α, − 3, 5), then α is equal to, (b) − 10, (d) − 5, , 14 Let EC denote the complement of an event, E. Let E1 , E 2 and E3 be any pairwise, independent events with P (E1 ) > 0 and, P (E1 ∩ E 2 ∩ E3 ) = 0. Then, P (EC2 ∩ E3C / E1 ) is equal to, (a) P (EC, 2 ) + P (E3 ), , (b) P (E3C ) − P (EC2 ), , (c) P (E3 ) −, , (d) P (E3C ) − P (E2 ), , P (E2C ), , 15 The area (in sq. units) of an equilateral, , triangle inscribed in the parabola y2 = 8x,, with one of its vertices on the vertex of this, parabola, is, , (a) 64 3, (c) 192 3, , (b) 256 3, (d) 128 3, , 16 If the sum of first 11 terms of an AP.,, , a1 , a 2 , a3 , ... is 0 (a1 ≠ 0), then the sum of, the AP., a1 , a3 , a5 ,... , a 23 is ka1, where k is, equal to, , (a) −, , 121, 10, , (b), , 121, 10, , (c), , 72, 5, , (d) −, , 72, 5, , 17 Let S be the sum of the first 9 terms of the, series, { x + ka } + { x2 + (k + 2)a } + { x3 + (k + 4)a }, + { x4 + (k + 6)a } + ... where a ≠0 and x ≠1. If, x10 − x + 45a (x − 1), , then k is equal to, S=, x−1, (a) −5, , (b) 1, , (c) − 3, , (a) 201, , (b) 200, , (c) 101, , (d) 199, , 19 Consider the region R = {(x, y) ∈ R2 :, , (b) y = 4x + 2, (d) 2 y + x = 4, , (a) 5, (c) 10, , JEE Main 2020 ~ Solved Papers, , (d) 3, , 18 Let n > 2 be an integer. Suppose that there, are n Metro stations in a city located along, a circular path. Each pair of stations is, connected by a straight track only. Further,, , x2 ≤ y ≤ 2x }. If a line y = α divides the area, of region R into two equal parts, then, which of the following is true?, (a) α3 − 6α 2 + 16 = 0, (c) 3α 2 − 8α + 8 = 0, , (b) 3α 2 − 8α3 / 2 + 8 = 0, (d) α3 − 6α3 / 2 − 16 = 0, , π, 20 For some θ ∈ 0, , if the eccentric of the, , 2, hyperbola, x2 − y2 sec2 θ = 10 is 5 times the, eccentricity of the ellipse, x2 sec2 θ + y2 = 5 ,, then the length of the latus rectum of the, ellipse, is, , (a) 2 6, , (b) 30, , (c), , 2 5, 3, , (d), , 4 5, 3, , Numerical Type Questions, 21 If y = Σ k cos−1 cos kx − sin kx, then, 6, , k=1, , 3, 5, , 4, 5, , , , dy, at x = 0 is ……… ., dx, 1, 22 For a positive integer n, 1 + is, n, , , x, expanded in increasing powers of x. If, three consecutive coefficients in this, expansion are in the ratio, 2 : 5 : 12, then n, is equal to ……… ., , 23 Let [t ] denote the greatest integer less, than or equal to t. Then the value of, 2, ∫ |2x − [3x]|dx is ……… ., 1, , 24 Let the position vectors of points ‘A’ and ‘ B ’, be $i + $j + k$ and 2$i + $j + 3k$ , respectively. A, point ‘ P ’ divides the line segment AB, internally in the ratio λ : 1 (λ > 0). If O is the, origin and OB ⋅ OP − 3|OA × OP|2 = 6, then, λ is equal to ……… ., , 25 If the variance of the terms in an, increasing AP, b1 , b2 , b3 , ……, b11 is 90,, then the common difference of this AP is, ……… .
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SEPTEMBER ATTEMPT ~ 02 Sep 2020, Shift II, , 21, , Answers, Physics, 1., 11., 21., , (b), (d), (8), , 2. (a), 12. (a), 22. (23), , 3., 13., 23., , (c), (a), (90), , 4., 14., 24., , (c), (d), (10), , 5., 15., 25., , (c), (a), (35), , 6. (a), 16. (d), , 7. (a), 17. (d), , 8. (b), 18. (c), , 9. (c), 19. (b), , 10. (b), 20. (a), , For Detailed Solutions, Visit : http://bit.ly/31hyvZe, Or Scan :, , Chemistry, 1. (c), 11. (c), 21. (222), , 2., 12., 22., , (c), (b), (19), , 3., (a), 13. (b), 23. (144), , 4., 14., 24., , (c), (c), (5), , 5., (b), 15., (a), 25. (–326400), , 6. (a), 16. (d), , 7. (c), 17. (a), , 8. (d), 18. (a), , 9. (c), 19. (b), , 10. (c), 20. (b), , For Detailed Solutions, Visit : http://bit.ly/31lgyc6, Or Scan :, , Mathematics, 1., (d), 11. (b), 21. (91.00), , 2., (a), 12. (c), 22. (118), , 3., 13., 23., , (a), (a), (1), , 4., (b), 14. (d), 24. (0.80), , 5., (a), 15., (c), 25. (3.00), , 6., 16., , (a), (d), , 7., 17., , (d), (c), , 8., 18., , (a), (a), , 9., 19., , (d), (b), , For Detailed Solutions, Visit : http://bit.ly/31m4CqG, Or Scan :, , 10., 20., , (b), (d)
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ONLINE QUESTION PAPER, , JEE Main 2020, (03 September, 2020), TIME 9:30-12:30 (Shift I), , MM : 300, , PHYSICS, Objective Type Questions, 1 In a radioactive material, fraction of, , 3, , active material remaining after time t is, 9/16. The fraction that was remaining, after time t / 2 is, 4, (a), 5, 3, (c), 4, , 3, (b), 5, 7, (d), 8, , 2 An elliptical loop having resistance R, of, semi-major axis a and semi-minor axis b, is placed in a magnetic field as shown in, the figure. If the loop is rotated about the, X-axis with angular frequency ω , then, the average power loss in the loop due to, joule’s heating is, z, b, y, , y, , π 2a 2b2B2ω 2, 2R, πabBω, (c), R, , (a), , x, a, , (b) zero, (d), , π 2a 2b2B2ω 2, R, , 5, RT, 2, 9, (c) RT, 2, (a), , (b), , 3, RT, 2, , (d) 3 RT, , 4 Two isolated conducting spheres S1 and, 2, 1, R and R, have charges, 3, 3, 12 µC and − 3µC respectively, and are at, a large distance from each other. They, are now connected by a conducting wire., A long time after this is done, the charges, on S1 and S 2 respectively, are, , S 2 of radii, , B, , x, , Consider a gas of triatomic molecules., The molecules are assumed to be, triangular and made of massless rigid, rods whose vertices are occupied by, atoms. The internal energy of a mole of, the gas at temperature T is, , (a) 4.5 µC on both, (b) + 4.5 µC and − 4.5 µC, (c) 3 µC and 6 µC, (d) 6 µC and 3 µC
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SEPTEMBER ATTEMPT ~ 03 Sep 2020, Shift I, 5 Moment of inertia of a cylinder of mass, M, length L and radius R about an axis, passing through its centre and, perpendicular to the axis of the cylinder, R 2 L2 , is I = M , + . If such a cylinder is, 12, 4, to be made for a given mass of a material., To have minimum possible moment of, inertia, the ratio L/R for cylinder is, (a), , 2, 3, , (b), , 3, 2, , 3, 2, , (c), , (d), , 2, 3, , 6 A torch battery of length l is to be made, up of a thin cylindrical bar of radius a, and a concentric thin cylindrical shell of, radius b is filled in between with an, electrolyte of resistivity ρ (see figure). If, the battery is connected to a resistance R,, the maximum joule’s heating in R will, takes place for, , 23, 9 A 750 Hz, 20 V (rms) source is connected, to a resistance of 100 Ω, an inductance of, 0.1803 H and a capacitance of 10 µF all in, series combination. The time in which the, resistance (heat capacity 2 J/°C) will get, heated by 10°C is close to., (Assume no loss of heat to the surroundings), (a) 418 s, (c) 365 s, , (b) 245 s, (d) 348 s, , 10 The magnetic field of a plane, electromagnetic wave is, B = 3 × 10−8 sin [200π( y + ct )]$i T,, where c = 3 × 108 ms −1 is the speed of, light. The corresponding electric field is, $ V/m, (a) E = 9 sin [200 π ( y + ct )] k, −6, $ V/m, (b) E = − 10 sin [200 π ( y + ct )] k, $ V/m, (c) E = 3 × 10−8 sin [200 π ( y + ct )] k, $ V/m, (d) E = − 9 sin [200 π ( y + ct )] k, , 11 A charged particle carrying charge 1 µC is, ρ, , l, , a, b, , ρ b, (a) R =, , 2 πl a , ρ, b, (c) R = ln , πl a , , ρ, b, (b) R =, ln , 2 πl a , 2ρ b , (d) R =, ln , πl a , , 7 Magnitude of magnetic field (in SI unit), at the centre of a hexagonal shaped coil of, side 10 cm, 50 turns and carrying current, µ I, I ampere in units of 0 is, π, (a) 250 3, (c) 500 3, , $ ) ms −1., moving with velocity ( 2$i + 3$j + 4k, If an external magnetic field of, $ ) × 10−3 T exists in the region,, ( 5i$ + 3$j − 6k, where the particle is moving, then the, force on the particle is F × 10−9 N. The, vector F is, $, (a) − 0.30$i + 0.32$j − 0.09k, $, (b) − 30i$ + 32$j − 9k, $, $, $, (c) − 300i + 320 j − 90k, $, $, $, (d) − 3.0i + 3.2 j − 0.9k, , 12 In the circuit shown in the figure, the, total charge is 750 µC and the voltage, across capacitor C2 is 20 V. Then, the, charge on capacitor C2 is, , 8 A balloon filled with helium (32°C and, , C3=8 µF, , 1.7 atm) bursts. Immediately afterwards;, the expansion of helium can be considered, as, (a) irreversible isothermal, (b) irreversible adiabatic, (c) reversible adiabatic, (d) reversible isothermal, , C2, , C1=15 µF, , (b) 50 3, (d) 5 3, , + –, V, , (a) 450 µC, (c) 160 µC, , (b) 590 µC, (d) 650 µC
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24, , ONLINE, , 13 In Young’s double slit experiment, light of, , JEE Main 2020 ~ Solved Papers, , 17 When the wavelength of radiation falling, , 500 nm is used to produce an interference, pattern. When the distance between the, slits is 0.05 mm, the angular width (in, degree) of the fringes formed on the, distance screen is close to, , on a metal is changed from 500 nm to, 200 nm, the maximum kinetic energy of, the photoelectrons becomes three times, larger. The work function of the metal is, close to, , (a) 0.17°, (c) 1.7°, , (a) 0.81 eV, (c) 0.52 eV, , (b) 0.57°, (d) 0.07°, , 14 A block of mass m = 1 kg slides with, velocity v = 6 m/s on a frictionless, horizontal surface and collides with a, uniform vertical rod and sticks to it as, shown. The rod is pivoted about O and, swings as a result of the collision, making, angle θ before momentarily coming to, rest. If the rod has mass M = 2 kg and, length l = 1 m, then the value of θ is, approximately, , O, M, l, θ, , (a) 63°, (c) 69°, , v, , m, m, , (b) 55°, (d) 49°, , 50 divisions on its circular scale, the, thickness of an object is measured. It, should correctly be recorded as, (b) 2.124 cm, (d) 2.123 cm, , 16 A uniform thin rope of length 12 m and, mass 6 kg hangs vertically from a rigid, support and a block of mass 2 kg is, attached to its free end. A transverse, short wavetrain of wavelength 6 cm is, produced at the lower end of the rope., What is the wavelength of the wavetrain, (in cm) when it reaches the top of the, rope?, (a) 3, (c) 12, , voltage drop of 0.5 V. The safe limit of, current through the diode is 10 mA. If a, battery of emf 1.5 V is used in the circuit,, the value of minimum resistance to be, connected in series with the diode, so that, the current does not exceed the safe limit is, (a) 300 Ω, (c) 100 Ω, , (b) 50 Ω, (d) 200 Ω, , 19 Pressure inside two soap bubbles are, , (b) 6, (d) 9, , (a) 4 : 1, (c) 8 : 1, , (b) 0.8 : 1, (d) 2 : 1, , 20 A satellite is moving in a low nearly, , 15 Using screw gauge of pitch 0.1 cm and, , (a) 2.121 cm, (c) 2.125 cm, , 18 When a diode is forward biased, it has a, , 1.01 atm and 1.02 atm, respectively. The, ratio of their volume is, , (Take, g = 10 m/s 2), , m, , (b) 1.02 eV, (d) 0.61 eV, , circular orbit around the earth. Its radius, is roughly equal to that of the earth’s, radius Re . By firing rockets attached to it,, its speed is instantaneously increased in, the direction of its motion, so that it, 3, becomes, times larger. Due to this, the, 2, farthest distance from the centre of the, earth that the satellite reaches is R., Value of R is, (a) 4Re, (c) 3Re, , (b) 2.5Re, (d) 2Re, , Numerical Type Questions, 21 An observer can see through a small hole, on the side of a jar (radius 15 cm) at a, point at height of 15 cm from the bottom, (see figure). The hole is at a height of, 45 cm. When the jar is filled with a liquid, up to a height of 30 cm, the same, observer can see the edge at the bottom of, the jar. If the refractive index of the
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SEPTEMBER ATTEMPT ~ 03 Sep 2020, Shift I, liquid is N/100, where N is an integer, the, value of N is .......... ., , 25, rotating about its axis at 5 rpm. The, person now starts moving towards the, centre of the platform. What will be the, rotational speed (in rpm) of the platform, when the person reaches its centre?, , 24 When a long glass capillary tube of radius, 0.015 cm is dipped in a liquid, the liquid, rises to a height of 15 cm within it.If the, contact angle between the liquid and, glass is close to 0°, the surface tension of, the liquid, (in millinewton m −1) to the, nearest integer is, (Take, ρ(liquid) = 900 kgm −3 , g = 10 ms −2), , 45 cm, 15 cm, 15 cm, , 22 A cricket ball of mass 0.15 kg is thrown, vertically up by a bowling machine, so, that it rises to a maximum height of 20 m, after leaving the machine. If the part, pushing the ball applies a constant force, F on the ball and moves horizontally a, distance of 0.2 m, while launching the, ball, the value of F (in N) is, (Take, g = 10 ms −2) ........... ., , 23 A person of 80 kg mass is standing on the, rim of a circular platform of mass 200 kg, , .......... ., , 25 A bakelite beaker has volume capacity of, 500 cc at 30°C. When it is partially filled, with V m volume (at 30°C) of mercury, it is, found that the unfilled volume of the, beaker remains constant as temperature, is varied. If γ (beaker) = 6 × 10−6 °C −1 and, γ ( mercury) = 1.5 × 10−4 °C −1, where γ is the, coefficient of volume expansion, then V m, (in cc) is close to ........... ., , CHEMISTRY, Objective Type Questions, 1 Henry’s constant (in kbar) for four gases, α, β, γ and δ in water at 298 K is given, below :, α, KH, , 50, , β, 2, , γ, 2 × 10, , δ, −5, , 2 Which of the following compounds, produces an optically inactive compound, on hydrogenation?, H, , (a) α has the highest solubility in water at a, given pressure, (b) solubility of γ at 308 K is lower than at, 298 K, (c) The pressure of a 55.5 molal solution of γ, is 1 bar, (d) The pressure of a 55.5 molal solution of δ, is 250 bar, , (c), , H, , CH3, , H, , CH3, , (b), H, , 0.5, , (density of water = 103 kg m −3 at 298 K), This table implies that, , CH3, , (a), CH3, , (d), , 3 An organic compound [A], molecular, formula C10H 20O2 was hydrolysed with, dilute sulphuric acid to give a carboxylic, acid [B] and an alcohol [C]. Oxidation of, [C] with CrO3 H 2SO4 produced [B]., Which of the following structures are not, possible for [A]?
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26, , ONLINE, CH3, , (a) CH3CH2 C H OCOCH2 CH CH2CH3, , CH3, CH3, , (b) CH3CH2 C H COOCH2 CH CH2CH3, , CH3, (c) CH3CH2CH2COOCH2CH2CH2CH3, (d) (CH3 )3 C COOCH2C(CH3 )3, , 4 The mechanism of SN 1 reaction is given, as :, R X → R ⊕ X È →, Ion pair, , R ⊕||X È, , A student writes general characteristics, based on the given mechanism as :, (A) The reaction is favoured by weak, nucleophiles., (B) R⊕ would be easily formed if the, substituents are bulky., (C) The reaction is accompanied by, recemisation., (D) The reaction is favoured by non-polar, solvents., , Which observations are correct?, (a) (A) and (B), (b) (A) and (C), (c) (A), (B) and (C), (d) (B) and (D), , possesses the most acidic hydrogen?, C ≡≡ N, , (c), H3 C, , O, , (d), CH3, , (a) 100 mL of 0.1 M CH3COOH and 100 mL, of 0.1 M NaOH, (b) 100 mL of 0.1 M HCl and 200 mL of, 0.1 M NaCl, (c) 100 mL of 0.1 M CH3COOH and 200 mL, of 0.1 M NaOH, (d) 100 mL of 0.1 M HCl and 200 mL of, 0.1 M CH3COONa, , (a) less than 300 K, (b) equal to 373 K, (c) more than 373 K, (d) greater than 300 K but less than 373 K, , 9 Tyndall effect is observed when, (a) the diameter of dispersed particles is, much larger than the wavelength of light, used, (b) the diameter of dispersed particles is, much smaller than the wavelength of, light used, (c) the refractive index of dispersed phase is, greater than that of the dispersion, medium, (d) the diameter of dispersed particles is, similar to the wavelength of light used, , MeO, , O, H, , O, , (a) fractional distillation, (b) differential extraction, (c) steam distillation, (d) distillation under reduced pressure, , 11 The electronic spectrum of [Ti(H 2O)6 ]3 +, , (b) H3C—C ≡≡ C—H, H, O, , 7 An acidic buffer is obtained on mixing, , 10 Glycerol is separated in soap industries by, , 5 Which one of the following compounds, , H, , (a) acid rain, (b) blue baby syndrome, (c) ozone layer depletion, (d) eutrophication, , boiling point of H 2S will be, , È, , (a), , 6 Thermal power plants can lead to, , 8 If the boiling point of H 2O is 373 K, the, , Solvent, Separated ion, pair, , Y, →, R Y + X È, , N ≡≡ C, , JEE Main 2020 ~ Solved Papers, , OMe, , OMe, , shows a single broad peak with a, maximum at 20,300 cm −1. The crystal, field stabilisation energy (CFSE) of the, complex ion, in kJ mol −1, is, (1 kJ mol −1 = 83.7 cm −1), (a) 145.5, (c) 83.7, , (b) 242.5, (d) 97
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SEPTEMBER ATTEMPT ~ 03 Sep 2020, Shift I, , 18 In a molecule of pyrophosphoric acid, the, , 12 The Kjeldahl method of nitrogen, estimation fails for which of the following, reaction products?, NO2, Sn/HCl, , LiAlH4, , II., , (i) SnCl2+HCl, (ii) H2O, , (a) III and IV, (c) I, III and IV, , NH2, , IV., , NaNO2, HCl, , (b) I and IV, (d) II and III, , 13 The atomic number of the element, unnilennium is, (a) 109, (c) 108, , (a) a second order reaction is always a, multistep reaction, (b) a zero order reaction is a multistep, reaction, (c) a first order reaction is always a single, step reaction, (d) a zero order reaction is a single step, reaction, , 15 Let CNaCl and CBaSO4 be the conductances, (in S) measured for saturated aqueous, solutions of NaCl and BaSO4,, respectively, at a temperature T., Which of the following is false?, (a) Ionic mobilities of ions from both salts, increase with T., (b) C BaSO4 (T2) > C BaSO4 (T1 ) for T2 > T1, (c) C NaCl (T2) > C NaCl (T1 ) for T2 > T1, (d) C NaCl >> C BaSO4 at a given T, , 16 The complex that can show optical, activity is, , (a) trans-[Cr(Cl2)(ox)2]3 −, (b) trans-[Fe(NH3 )2(CN)4 ]−, (c) cis-[Fe(NH3 )2(CN)4 ]−, (d) cis-[CrCl2(ox)2]3 − (ox = oxalate), , 17 Aqua-regia is used for dissolving noble, metals (Au, Pt, etc.). The gas evolved in, this process is, (b) N2O5 (c) N2, , 19 The antifertility drug “Novestrol” can, (a) ZnCl2 / HCl; FeCl3 ; alcoholic HCN, (b) Br2 /water; ZnCl2 / HCl; FeCl3, (c) alcoholic HCN; NaOCl; ZnCl2 / HCl, (d) Br2 /water; ZnCl2 / HCl; NaOCl, , Numerical Type Questions, 20 Of the species, NO, NO+ , NO2+ and NO− ,, the one with minimum bond strength is, , (a) NO+, , (b) NO, , (c) NO2+, , (d) NO−, , 21 The mole fraction of glucose (C6H12O6 ) in, , (b) 102, (d) 119, , 14 It is true that, , (a) NO, , (b) 3, 3, and 3, (d) 4, 2, and 1, , react with, , CH2CN, , III., , number of P OH, P == O and P O P, bonds/moiety(ies) respectively are, , (a) 2, 4 and 1, (c) 4, 2, and 0, , CN, , I., , 27, , (d) N2O3, , an aqueous binary solution is 0.1. The, mass percentage of water in it, to the, nearest integer, is ......... ., 22 The photoelectric current from Na (work, function, w0 = 2.3 eV) is stopped by the, output voltage of the cell, Pt( s)|H 2( g, 1 bar)|HCl ( aq. , pH = 1), |AgCl( s)| Ag( s)., The pH of aqueous HCl required to stop the, photoelectric current from K ( w0 = 2.25 eV),, all other conditions remaining the same,, is ........... × 10−2 (to the nearest integer)., RT, Given, 2.303, = 0.06 V;, F, °, EAgCl|Ag|, = 0.22 V, Cl −, , 23 An element with molar mass, , 2.7 × 10−2 kg mol −1 forms a cubic unit cell, with edge length 405 pm. If its density is, 2.7 × 103 kg m −3 , the radius of the, element is approximately ............ × 10−12, m (to the nearest integer)., 24 The total number of monohalogenated, organic products in the following, (including stereoisomers) reaction is ...... ., A, , (Simplest optically, active alkene), , (i) H / Ni/ ∆, , 2, , →, , (ii) X 2/ ∆, , 25 The volume strength of 8.9 M H 2O2, solution calculated at 273 K and 1 atm is, .......... . (R = 0.0821 L atm K −1 mol −1), (rounded off to the nearest integer).
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28, , ONLINE, , JEE Main 2020 ~ Solved Papers, , MATHEMATICS, Objective Type Questions, , 7 Consider the two sets, , π π, 1 If y 2 + loge (cos2 x ) = y, x ∈ − , , then, 2 2, (a) y′′ (0) = 0, (c)| y′′ (0)| = 2, , , , equal to, , 2 2π − sin−1, (a), , π, 2, , (b)| y′ (0)| + | y′′ (0)| = 1, (d)| y′ (0)|+ | y′ ′ (0)| = 3, , 4, 5, 16 , + sin−1, + sin−1 is, 5, 13, 65, , (b), , 5π, 4, , (c), , 3π, 2, , (d), , 7π, 4, , 3 If the first term of an AP is 3 and the sum, of its first 25 terms is equal to the sum of, its next 15 terms, then the common, difference of this AP is, (a), , 1, 6, , (b), , 1, 5, , (c), , 1, 4, , (d), , 1, 7, , 4 A hyperbola having the transverse axis of, length 2 has the same foci as that of the, ellipse 3x 2 + 4 y 2 = 12, then this hyperbola, does not pass through which of the, following points?, 1 , (a) , , 0, 2 , , 3 , (b) − , 1, 2 , , 1, , (c) 1, −, , , 2, , 3 1, (d) , ,, , 2 2, , and N be the foot of the perpendicular, drawn from P on the axis of the parabola., A line is now drawn through the, mid-point M and PN , parallel to its axis, which meets the parabola at Q. If the, 4, y-intercept of the line NQ is , then, 3, 1, 4, , (d) PN = 3, , 9, (9 + q2), 4, 9, (c) (9 + p2), 4, , 9, (9 − q2), 4, 9, (d) (9 − p2), 4, , (a), , x−2, , (b), , 2x − 3, , 9 If ∆ = 2x − 3 3x − 4, , 3x − 4, 4x − 5, , =, , 3x − 5 5x − 8 10x − 17, (b) 1, (d) 9, , {( x , y ) : 0 ≤ y ≤ x 2 + 1, 0 ≤ y ≤ x + 1,, 1, ≤ x ≤ 2} is, 2, , 6 Let P be a point on the parabola, y = 12x, , (c) MQ =, , 1, 1, and are the roots, α, β, of the equation 2x 2 + 2qx + 1 = 0, then, 1 , 1 , 1 , 1, , α − β − α + β + is equal to, , α , β , β , α, x 2 + px + 2 = 0 and, , 10 The area (in sq. units) of the region, , 2, , 1, 3, , 8 If α and β are the roots of the equation, , (a) − 1, (c) − 3, , (b) (~ p) ∨ q, (d) (~ p) ∨ (~ q), , (b) MQ =, , (a) A − B = (− ∞ , − 3) ∪ (5, ∞ ), (b) A ∩ B = { − 3}, (c) B − A = (− 3, 5), (d) A ∪ B = R, , Ax + Bx 2 + Cx + D, then B + C is equal to, , equivalent to, , (a) PN = 4, , B = [− 3, 5)., Which of the following is not true?, , 3, , 5 The proposition p → ~ ( p ∧ ~ q ) is, (a) q, (c) (~ p) ∧ q, , A = { m ∈ R : both the roots of, x 2 − ( m + 1)x + m + 4 = 0 are real} and, , 23, 16, 79, (c), 16, (a), , 79, 24, 23, (d), 6, (b), , 11 The foot of the perpendicular drawn from, the point (4, 2, 3) to the line joining the, points (1, −2, 3) and (1, 1, 0) lies on the, plane, (a) 2x + y − z = 1, (c) x − 2 y + z = 1, , (b) x − y − 2z = 1, (d) x + 2 y − z = 1
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SEPTEMBER ATTEMPT ~ 03 Sep 2020, Shift I, 12 The solution curve of the differential, dy, equation, (1 + e− x )(1 + y 2 ), = y 2, which, dx, passes through the point (0, 1) is, , , 1 + e, (a) y2 + 1 = y log e , + 2, 2 , , , , the scores appearing on the die is, observed to be a multiple of 4. Then the, conditional probability that the score 4, has appeared atleast once is, , 14, , 1, 8, , (d), , 1, 9, , π, , ∫− π|π −|x||dx is equal to, (a), , 2π 2, , (b) 2π 2, , (c) π 2, , (d), , π2, 2, , 15 For the frequency distribution, Variate ( x ) : x1 x2 x3K x15, Frequency ( f ) : f1 f2 f3K f15, where 0 < x1 < x2 < x3 < K < x15 = 10 and, 15, , Σ fi > 0, the standard deviation cannot be, , i =1, , (a) 4, , (b) 1, , (b) 1 + (51)!, (d) 1, , 14 , 3 , (a) (− ∞ , 0) ∪ , , ∞ (b) (− ∞ , 0) ∪ , ∞, 15 , 7 , 14, 14, , , (d) − ∞ , − ∪ (0, ∞ ), (c) − ∞ , , , , 15, 15, , 13 A die thrown two times and the sum of, , (c), , 18 The value of ( 2 ⋅ 1P0 − 3 ⋅ 2P1 + 4 ⋅ 3 P2 − ..., , increasing for all x lying in, , 1 + e− x , (d) y2 = 1 + y log e , , 2 , , 1, 3, , (d) 0, , 19 The function, f ( x ) = ( 3x − 7) x 2/ 3 , x ∈ R, is, , 1 + ex , (c) y2 = 1 + y log e , , 2 , , (b), , (b) 2, , (a) 1 − 51(51)!, (c) 1 + (52)!, , , , 1 + ex , (b) y + 1 = y log e , + 2, 2, , , , , 2, , 1, 4, , (a) 1, 1, (c), 2, , up to 51th term) + (1 ! − 2 ! + 3 ! − ... up to, 51th term) is equal to, , −x , , (a), , 29, , (c) 6, , (d) 2, , 16 The lines, $ ) and, r = ( $i − $j) + l( 2i$ + k, $), r = ( 2$i − $j) + m ( i$ + $j − k, (a) do not intersect for any values of l and m, (b) intersect for all values of l and m, 1, (c) intersect when l = 2 and m =, 2, (d) intersect when l = 1 and m = 2, , 17 Let [t ] denote the greatest integer ≤ t. If, for some λ ∈ R − { 0, 1},, 1 − x +|x|, lim, = L, then L is equal to, x → 0 λ − x + [x ], , 20 If the number of integral terms in the, 1, 1, expansion of 3 2 + 5 8 is exactly 33,, , , , , then the least value of n is, n, , (a) 264, (c) 256, , (b) 128, (d) 248, , Numerical Type Questions, 21 The value of, , 1, , 1, 1, log 2.5 +, +, + ... to ∞ , 3 3 2 33, , , ( 016, . ), ......... ., , is equal to, , x 1, , 4, 22 Let A = , , x ∈ R and A = [aij ]. If, 1 0, , a11 = 109, then a22 is equal to .......... ., , 23 The diameter of the circle, whose centre, lies on the line x + y = 2 in the first, quadrant and which touches both the, lines x = 3 and y = 2, is ............ ., m/ 2, , n/3, , 1 + i, 1 + i, =, = 1, ( m , n ∈N ), , , 1 − i, 1 − 1, then the greatest common divisor of the, least values of m and n is ........... ., , 24 If , , 25 If lim, , x→0, , 1 , x2, x2, x2, x2 , cos , − cos, + cos, 8 1 − cos, 2, 4, 2, 4 , x , −k, = 2 , then the value of k is .......... .
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30, , ONLINE, , JEE Main 2020 ~ Solved Papers, , Answers, Physics, 1., (c), 11. (b), 21. (158), , 2. (a), 12. (b), 22. (150), , 3., 13., 23., , (d), (b), (9), , 4., 14., 24., , (d), (a), (101), , 5., 15., 25., , (c), (b), (20), , 6. (d), 16. (c), , 7. (c), 17. (d), , 8. (b), 18. (c), , 9. (d), 19. (c), , 10. (d), 20. (d), , For Detailed Solutions, Visit : http://bit.ly/34bgKNd, Or Scan :, , Chemistry, 1. (d), 11. (d), 21. (47), , 2. (d), 12. (a), 22. (58.3), , 3., 13., 23., , (a,c), (a), (143.00), , 4., 14., 24., , (c), (b), (8), , 5., (d), 15. (c), 25. (100), , 6. (a), 16. (d), , 7. (d), 17. (a), , 8. (a), 18. (d), , 9. (d), 19. (b), , 10. (d), 20. (d), , For Detailed Solutions, Visit : http://bit.ly/34biZA7, Or Scan :, , Mathematics, 1., (c), 11. (a), 21. (4.00), , 2., (c), 12., (c), 22. (10.00), , 3. (a), 13. (d), 23. (3.00), , 4., (d), 14. (c), 24. (4.00), , 5., (b), 15. (c), 25. (8.00), , 6., 16., , (c), (a), , 7., 17., , (a), (b), , 8., 18., , (d), (c), , 9., 19., , (c), (a), , For Detailed Solutions, Visit : http://bit.ly/2ICwtwf, Or Scan :, , 10., 20., , (b), (c)
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ONLINE QUESTION PAPER, , JEE Main 2020, (03 September, 2020), TIME 2:30-5:30 (Shift II), , MM : 300, , PHYSICS, s, , Objective Type Questions, 1 Concentric metallic hollow spheres of radii, R and 4R hold charges Q1 and Q2 ,, respectively. Given that, surface charge, densities of the concentric spheres are, equal. The potential difference, V (R) − V (4R) is, (a), (c), , 3Q2, 4 πε0 R, 3Q1, 4 πε0 R, , (b), , 3Q1, 16 πε0 R, , (d), , Q2, 4πε0 R, , 2 The mass density of a planet of radius R, , s, , (a), , (b), , t, , t, , s, , s, , (c), , (d), , t, , t, , 4 Two resistors 400 Ω and 800 Ω are, , varies with the distance r from its centre, , r2 , as ρ(r ) = ρ0 1 − 2 . Then, the, R , , , connected in series across a 6 V battery., The potential difference measured by a, voltmeter of 10 kΩ across 400 Ω resistor is, close to, , gravitational field is maximum at, , (a) 1.95 V, (c) 1.8 V, , (a) r =, (c) r =, , 3, R, 4, 5, R, 9, , (b) r = R, , (b) 2 V, (d) 2.05 V, , 5 A perfectly diamagnetic sphere has a small, (d) r =, , 1, R, 3, , 3 A particle is moving unidirectionally on a, horizontal plane under the action of a, constant power supplying energy source., The displacement (s)-time (t) graph that, describes the motion of the particle is, (graphs are drawn schematically and are, not to scale), , spherical cavity at its centre,which is filled, with a paramagnetic substance. The whole, system is placed in a uniform magnetic, field B. Then, the field inside the, paramagnetic substance is, , P
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32, , JEE Main 2020 ~ Solved Papers, , ONLINE, (a) much larger than|B|and parallel to B, (b) B, (c) zero, (d) much larger than| B|but opposite to B, , 11 To raise the temperature of a certain mass, of gas by 50°C at a constant pressure,, 160 cal of heat is required. When the same, mass of gas is cooled by 100°C at constant, volume, 240 cal of heat is released. How, many degrees of freedom does each molecule, of this gas have (assume gas to be ideal)?, , 6 Two light waves having the same, , wavelength λ in vacuum are in phase, initially. Then, the first wave travels a, path L1 through a medium of refractive, index n1 while the second wave travels a, path of length L2 through a medium of, refractive index n2. After this, the phase, difference between the two waves is, , (a), (c), , 2π, (n1 L1 − n2L2 ), λ, 2 π L2 L1 , −, , , λ n1 n2 , , (b), , 2 π L1 L1 , −, , , λ n1 n2 , , (d), , 2π, (n2L1 − n1 L2 ), λ, , (a) 5, , (a), , 2, , (b), , 1, 2, , (c), , 1, 2, , (a), , (b) 3.2 g, , (c) 2.6 g, , atom are accelerated from rest, through, the same potential difference. The ratio of, final speeds of hydrogen and helium ions is, close to, (b) 10 : 7, , (c) 2 : 1, , in 300 s. If atmospheric temperature, around is 20°C, then the sphere’s, temperature after the next 5 min will be, close to, (b) 35°C, (d) 33°C, , (d), , 1, 500, , electromagnetic wave propagating along, the x-direction in vacuum is, E = E 0$j cos(ωt − kx). The magnetic field B,, at the moment t = 0 is, , (a) B = E0 µ 0 ε0 cos(kx) $j, E0, (b) B =, cos(kx)$j, µ 0 ε0, E0, $, (c) B =, cos(kx)k, µ 0 ε0, $, (d) B = E µ ε cos(kx)k, 0, , 0 0, , 14, FV, , ω, , FH, l, θ, , (d) 5 : 7, , 10 A metallic sphere cools from 50°C to 40°C, , (a) 31°C, (c) 28°C, , (b) 500, , (d) 4 g, , 9 Hydrogen ion and singly ionised helium, , (a) 1 : 2, , (d) 3, , 13 The electric field of a plane, , 8 A calorimeter of water equivalent 20 g, , (a) 2 g, , 1, 250, , (c) 250, , (d) 1, , contains 180 g of water at 25°C. ‘ m ’ grams, of steam at 100°C is mixed in it till the, temperature of the mixture is 31°C. The, value of m is close to, (Take, latent heat of water = 540 cal g −1,, specific heat of water = 1 cal g −1 °C −1), , (c) 6, , wavelength 1 nm and visible light of, wavelength 500 nm, respectively. Both the, sources emit light of the same power 200 W., The ratio of the number density of photons, of X-rays to the number density of photons, of the visible light of the given, wavelengths is, , 7 A block of mass m attached to a massless, spring is performing oscillatory motion of, amplitude A on a frictionless horizontal, plane. If half of the mass of the block, breaks off when it is passing through its, equilibrium point, the amplitude of, oscillation for the remaining system, becomes fA. The value of f is, , (b) 7, , 12 Two sources of light emit X-rays of, , A uniform rod of length l is pivoted at one, of its ends on a vertical shaft of negligible, radius. When the shaft rotates at angular, speed ω, the rod makes an angle θ with it, (see figure). To find θ, equate the rate of, change of angular momentum (direction, ml2 2, going into the paper), ω sin θ cos θ about, 12
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33, , SEPTEMBER ATTEMPT ~ 03 Sep 2020, Shift II, the centre of mass to the torque provided, by the horizontal and vertical forces FH, and FV about the centre of mass. The, value of θ is then such that, g, , (a) cosθ =, (c) cosθ =, , lω 2, 2g, 3lω2, , g, , (b) cosθ =, , 2lω2, 3g, , (d) cosθ =, , 2lω2, , 15 A block of mass 1.9 kg is at rest at the edge, of a table of height 1 m. A bullet of mass, 0.1 kg collides with the block and sticks to it., If the velocity of the bullet is 20 m/s in the, horizontal direction just before the collision,, then the kinetic energy just before the, combined system strikes the floor, is, (Take, g = 10 m/s 2 and assume there is no, rotational motion and loss of energy after, the collision is negligible), (a) 20 J, (c) 21 J, , (b) 19 J, (d) 23 J, , 16 Amount of solar energy received on the, earth’s surface per unit area per unit time, is defined as solar constant. Dimensional, formula of solar constant is, −2, , (a) [MLT ], (c) [M2L0 T −1 ], , 0, , −3, , (b) [ML T ], (d) [ML2T −2], , 17 If a semiconductor photodiode can detect a, photon with a maximum wavelength of, 400 nm, then its band gap energy is, (Take, Planck’s constant, h = 663, . × 10−34 J-s, and speed of light, c = 3 × 108 m/s), (a) 1.5 eV, (c) 3.1 eV, , (b) 1.1 eV, (d) 2.0 eV, , 18 A uniform magnetic field B exists in a, direction perpendicular to the plane of a, square loop made of a metal wire. The wire, has a diameter of 4 mm and a total length, of 30 cm. The magnetic field changes with, time at a steady rate dB / dt = 0032, Ts −1., ., The induced current in the loop is close to, (Take, resistivity of the metal wire, . × 10−8 Ωm), = 123, (a) 0.61 A, (c) 0.53 A, , (b) 0.43 A, (d) 0.34 A, , 19 Which of the following will not be observed, when a multimeter (operating in, resistance measuring mode) probes, , connected across a component, are just, reversed?, (a) Multimeter shows no deflection in both, cases, i.e. before and after reversing the, probes if the chosen component is metal, wire., (b) Multimeter shows an equal deflection in, both cases, i.e. before and after reversing, the probes if the chosen component is, resistor., (c) Multimeter shows no deflection in both, cases, i.e. before and after reversing the, probes if the chosen component is, capacitor., (d) Multimeter shows a deflection,, accompanied by a splash of light out of, connected component in one direction and, no deflection on reversing the probes if the, chosen component is LED., , 20 The radius R of a nucleus of mass number, A can be estimated by the formula, . × 10−15 ) A1/ 3 m. It follows that the, R = (13, mass density of a nucleus is of the order of, ~M, ~ . × 10−27 kg), (M proton =, neutron − 167, (a) 1017 kg m −3, (c) 1010 kg m −3, , (b) 1024 kg m −3, (d) 103 kg m −3, , Numerical Type Questions, 21 A galvanometer coil has 500 turns and each, , turn has an average area of 3 × 10−4 m 2. If, a torque of 1.5 N-m is required to keep this, coil parallel to a magnetic field when a, current of 0.5 A is flowing through it, the, strength of the field (in T) is ........... ., , 22 A block starts moving up an inclined plane, of inclination 30° with an initial velocity of, v0. It comes back to its initial position with, v, velocity 0 . The value of the coefficient of, 2, kinetic friction between the block and the, I, inclined plane is close to, , the nearest, 1000, integer to I is .......... ., , 23 If minimum possible work is done by a, refrigerator in converting 100 g of water at, 0°C to ice, how much heat (in cal) is, released to the surroundings at, temperature 27°C to the nearest integer, …… ?, (Take, latent heat of ice = 80 cal/g)
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34, , ONLINE, X, , 24 A massless equilateral, , F, , triangle EFG of side a, (as shown in figure), has three particles of, mass m situated at its, vertices. The moment, of inertia of the, a, E, system about the line, EX perpendicular to EG in the plane of, , JEE Main 2020 ~ Solved Papers, , N, ma 2, where N is an integer. The, 20, value of N is ............ ., EFG is, , 25 When an object is kept at a distance of, G, , 30 cm from a concave mirror, the image is, formed at a distance of 10 cm from the, mirror. If the object is moved with a speed, of 9 cms −1, the speed (in cms −1) with which, image moves at that instant is ........... ., , CHEMISTRY, Objective Type Questions, 1 The decreasing order of reactivity of the, following compounds towards nucleophilic, substitution (SN 2) is, CH2Cl, , 4 100 mL of 0.1M HCl is taken is a beaker, , CH2Cl, , (I), , and to it 100 mL of 0.1 M NaOH is added, in steps of 2 mL and the pH continuously, measured. Which of the following graphs, correctly depicts the change in pH?, , NO2, , (II), , NO2, CH2Cl, , (III), , (a) (i)-(a); (ii)-(c); (iii)-(b); (iv)-(e), (b) (i)-(e); (ii)-(a); (iii)-(c); (iv)-(d), (c) (i)-(d); (ii)-(a); (iii)-(b); (iv)-(c), (d) (i)-(d); (ii)-(c); (iii)-(a); (iv)-(e), , CH2Cl, , (IV), NO2, , (a) pH 7, , O2N, , NO2, , (a), (b), (c), (d), , (b) pH 7, , NO2, , vol. of NaOH, , vol. of NaOH, , (II) > (III) > (IV) > (I), (IV) > (II) > (III) > (I), (III) > (II) > (IV) > (I), (II) > (III) > (I) > (IV), , (c) pH 7, , (d) pH 7, , 2 The five successive ionisation enthalpies of, an element are 800, 2427, 3658, 25024 and, 32824 kJ mol −1. The number of valence, electrons in the element is, (a) 3, (c) 4, , vol. of NaOH, , 5 The strengths of 5.6 volume hydrogen, , (b) 5, (d) 2, , 3 Match the following drugs with their, therapeutic actions :, , peroxide (of density 1 g/mL) in terms of, mass percentage and molarity (M),, respectively, are, (Take molar mass of hydrogen peroxide as, 34 g/mol), , (i), , Ranitidine, , (a), , Antidepressant, , (ii), , Nardil (Phenelzine), , (b), , Antibiotic, , (c), , Antihistamine, , (b) 0.85 and 0.5, , Antacid, , (c) 1.7 and 0.5, , (iii) Chloramphenicol, , (iv) Dimetane, (d), (Brompheniramine), (e), , vol. of NaOH, , Analgesic, , (a) 0.85 and 0.25, , (d) 1.7 and 0.25
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36, , JEE Main 2020 ~ Solved Papers, , ONLINE, (c) In manganate and permanganate ions, the, π-bonding takes place by overlap of, p-orbitals of oxygen and d-orbitals of, manganese., (d) Manganate and permanganate ions are, tetrahedral., , 12 Among the statements (I-IV), the correct, ones are :, (I) Be has smaller atomic radius compared, to Mg., (II) Be has higher ionisation enthalpy, than Al., (III) Charge/radius ratio of Be is greater, than that of Al., (IV) Both Be and Al form mainly covalent, compounds., (a) (II), (III) and (IV) (b) (I), (II) and (IV), (c) (I), (III) and (IV), (d) (I), (II) and (III), , 13 The major product in the following, reaction is, I, t-BuOH, Heat, , N, , CH3, , 3, 2, , 16 For the reaction 2 A + 3B + C → 3P, which, statement is correct?, dnA, dt, dnA, (b), dt, dnA, (c), dt, dnA, (d), dt, (a), , 2 dnB, 3 dt, 3 dnB, =, 2 dt, dnB, =, =, dt, 2 dnB, =, 3 dt, =, , (d), , the azimuthal quantum number, l takes, values 0, 1, 2, …… n + 1, where n is the, principle quantum number. Then, the, element with atomic number, (a) 8 is the first noble gas, (b) 13 has a half-filled valence subshell, (c) 9 is the first alkali metal, (d) 6 has a 2p-valence subshell, , 17 The incorrect statement(s) among (A) – (D), regarding acid rain is (are) :, (A) It can corrode water pipes., (B) It can damage structures made up of stone., (C) It cannot cause respiratory ailments in, animals., (D) It is not harmful for trees., , 19 Consider the following reaction :, OHc, dHO, , H3 C, , CH3, , (b) liquid diethyl ether to aqueous NaCl, solution, , CH3, OHb, , SO4–, , N, , (b) (A), (C) and (D), (d) (A), (B) and (D), , (a) [Cr(H2O)4 Cl 2 ]Cl ⋅ 2H2O, (b) [Cr(H2O)6 ]Cl3, (c) [Cr(H2O)5 Cl]Cl 2 ⋅ H2O, (d) [Cr(H2O)3 Cl3 ]⋅ 3H2O, , OHa, , Chromic, → ‘P’, , 15 An ionic micelle is formed on the addition of, N, , 3 dnC, 4 dt, 3 dnC, =, 4 dt, dnC, dt, 4 dnC, =, 3 dt, =, , H12O6Cl3Cr. If the complex on treatment, with conc. H2SO4 loses 13.5% of its original, mass, the correct molecular formula of ( A), is [Given : atomic mass of Cr = 52 amu and, Cl = 35 amu], , 14 Consider the hypothetical situation where, , (a), , PF6, , N, , H3 C, , 18 Complex ( A) has a composition of, , (b), , (c), , (d), , (a) (C) and (D), (c) (C) only, , O t-Bu, (a), , (c) sodium stearate to pure toluene excess, water to liquid, , anhydride, , The product ‘P’ gives positive, ceric ammonium nitrate test. This is, because of the presence of which of these, OH group(s)?, (a) (b) and (d), (c) (b) only, , (b) (d) only, (d) (c) and (d)
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37, , SEPTEMBER ATTEMPT ~ 03 Sep 2020, Shift II, 20 The increasing order of the reactivity of, the following compounds in nucleophilic, addition reaction is :, Propanal, Benzaldehyde, Propanone,, Butanone, (a) Benzaldehyde < Butanone < Propanone <, Propanal, (b) Butanone < Propanone < Benzaldehyde <, Propanal, (c) Propanal < Propanone < Butanone <, Benzaldehyde, (d) Benzaldehyde < Propanal < Propanone <, Butanone, , Numerical Type Questions, 21 6023, ., × 1022 molecules are present in 10 g, of a substance ‘x’. The molarity of a, solution containing 5 g of substance ‘x’ in 2, L solution is ........... × 10−3 ., , 22 The volume (in mL) of 0.1 N NaOH, , 23 The number of, , C == O groups present in, , a tripeptide Asp-Glu-Lys is ........... ., , 24 An acidic solution of dichromate is, electrolysed for 8 minutes using 2A, current. As per the following equation, Cr2O72− + 14H+ + 6e− → 2Cr3 + + 7H2O, The amount of Cr3 + obtained was 0.104 g., The efficiency of the process(in %) is, (Take : F = 96000 C, atomic mass of, chromium =52) ........... ., , 25 If 250 cm3 of an aqueous solution, containing 0.73 g of protein A is isotonic, with one litre of another aqueous solution, containing 1.65 g of a protein B, at 298 K,, the ratio of the molecular masses of A and, B is ........... × 10−2 (to the nearest integer)., , required to neutralise 10 mL of 0.1 N, phosphonic acid is ............ ., , MATHEMATICS, 4 Let a , b, c ∈R be such that a 2 + b2 + c2 = 1., , Objective Type Questions, x , dx = A(x) tan −1 ( x ) +, 1 + x, B(x) + C, where C is a constant of, integration, then the ordered pair, ( A(x), B(x)) can be, , 2π , 4π , , , If a cos θ = b cos θ +, = c cosθ +, ,, , , 3, 3, π, where θ = , then the angle between the, 9, $ and b$i + c$j + ak, $ is, vectors a$i + b$j + ck, , (a) (x − 1, x ), (c) (x + 1, − x ), , (a), , , , 1 If ∫ sin −1 , , (b) (x + 1, x ), (d) (x − 1, − x ), , 2 If the term independent of x in the, 9, , 1, 3, expansion of x2 − is k, then 18 k is, 2, 3x, equal to, (a) 5, (c) 9, , 3 lim, , x→ a, , (b) 7, (d) 11, , (a + 2x)1/ 3 − (3x)1/ 3, (3a + x)1/ 3 − (4x)1/ 3, , 2, (a) , 3, , 4/3, , 2 2, (c) , 9 3, , 1/3, , (b) 0, , (c), , 2π, 3, , (d), , π, 9, , 5 Suppose f (x) is a polynomial of degree four,, having critical points at − 1, 0, 1. If, T = { x ∈ R} f (x) = f (0), then the sum of, squares of all the elements of T is, (a) 2, , (b) 4, , (c) 8, , (d) 6, , 6 Let xi (1 ≤ i ≤ 10) be ten observations of a, 10, , (a ≠ 0) is equal to, , 2, (b) , 9, , π, 2, , i =1, , 10, , Σ (xi − p) = 9 p where 0 ≠ p ∈R, then the, 2, , i =1, , 4/3, , 2 2, (d) , 3 9, , random variable X. If Σ (xi − p) = 3 and, , standard deviation of these observation is, 1./3, , (a), , 9, 10, , (b), , 3, 5, , (c), , 7, 10, , (d), , 4, 5
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38, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 7 If the sum of the series, , 4, 1, 3, + 19 + 18 + ... upto nth term is, 5, 5, 5, 488 and the nth term is negative, then, , 20 + 19, , (a) nth term is − 4, , (b) nth term is − 4, , (c) n = 60, , (d) n = 41, , 2, 5, , 8 The probability that a randomly chosen, 121, 104, , (b), , 134, 104, , (c), , 150, 104, , (d), , 10 Let the latus rectum of the parabola, , y2 = 4x be the common chord to the circles, C1 and C 2 each of them having radius 2 5., Then, the distance between the centres of, the circles C1 and C 2 is, (c) 8 5, , (d) 12, , 11 The set of all real values of λ for which the, , quadratic equations, (λ2 + 1)x2 − 4λx + 2 = 0, always have exactly one root in the, interval (0, 1) is, , (a) (0, 2), , (b) (− 3, − 1) (c) (2, 4], , (d) (1, 3], , 12 Let e1 and e2 be the eccentricities of the, x2, y2, ellipse,, + 2 = 1 (b < 5) and the, 25 b, x2 y2, hyperbola,, −, = 1 respectively, 16 b2, satisfying e1e2 = 1. If α and β are the, distances between the foci of the ellipse, and the foci of the hyperbola respectively,, then the ordered pair (α , β) is equal to, (a) (8, 12), 20, (c) , 12, 3, , , (b) (8, 10), 24, (d) ,10, 5, , , 13 The plane which bisects the line joining, , the points (4,− 2, 3) and (2, 4, − 1) at right, angles also passes through the point, , (a) (0, − 1, 1), (c) (4, 0, 1), , (b) (4, 0, − 1), (d) (0, 1, − 1), , 15 If z1 , z2 are complex numbers such that, , (a), , (b) F, T, F, (d) T, T, T, , (b) 4 5, , (b) (− 3, 3), 3, 3, (d) , − , 5, 5, , 104, , the truth value of ( p ∧ q) → (~ q ∨ r ) is F., Then the truth values of p, q, r are, respectively., , (a) 8, , (a) ( 3, − 3), 3 3, (c) − , , 5 5, , 135, , 9 Let p, q, r be three statements such that, , (a) T, F, T, (c) T, T, F, , and C(5, − 5), then its orthocentre has, coordinates, , Re(z1 ) =|z1 − 1|, Re(z2 ) =|z2 − 1|and, π, arg(z1 − z2 ) = , then Im(z1 + z2 ) is equal to, 6, , 5-digit number is made from exactly two, digits is, (a), , 14 If a ∆ABC has vertices A (− 1, 7), B (− 7, 1), , 3, 2, , (b), , 1, 3, , 2, 3, , (c), , (d) 2 3, , 16 Let A be a 3 × 3 matrix such that, , 2 −1 1 , adj A = −1 0 2 and, , , 1 −2 −1, B = adj (adj A), If| A| = λ and|(B−1 )T| = µ, then the ordered, pair, (|λ|, µ ) is equal to, 1, (b) 9, (c) 9,, 81, , , (a) (3, 81), , 1, , 9, , 1, (d) 3, , 81, , 17 If the surface area of a cube is increasing, at a rate of 3.6 cm2/sec, retaining its, shape; then the rate of change of its, volume (in cm3 /sec), when the length of a, side of the cube is 10 cm, is, (a) 18, , (b) 10, , (c) 9, , (d) 20, , 18 Let R1 and R2 be two relations defined as, follows, R1 = {(a , b) ∈ R2 : a 2 + b2 ∈Q} and, R2 = {(a , b) ∈ R2 : a 2 + b2 ∉Q}, where Q is, the set of all rational numbers. Then, (a) R1 and R2 are both transitive, (b) Neither R1 nor R2 is transitive, (c) R1 is transitive but R2 is not transitive, (d) R2 is transitive but R1 is not transitive, , 19 If x3 dy + xy dx = x2dy + 2 y dx; y(2) = e and, x > 1, then y(4) is equal to, (a), , e, 2, , (b), , 3, +, 2, , e (c), , 3, e, 2, , (d), , 1, +, 2, , 20 If the value of the integral, 1/ 2, , ∫0, , x2, (1 − x ), , 2 3/ 2, , (a) 3 2 + π, (c) 2 3 + π, , k, dx is , then k is equal to, 6, (b) 2 3 − π, (d) 3 2 − π, , e
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39, , SEPTEMBER ATTEMPT ~ 03 Sep 2020, Shift II, , such that 15 ≤ x2 + y2 + z2 ≤ 150. Then, the, number of elements in the set S is equal to, ............ ., , Numerical Type Questions, 21 The total number of 3-digit numbers,, whose sum of digits is 10, is ............ ., , 22 If the tangent to the curve, y = ex at a point, , 24 Let a plane P contain two lines, , r = $i + λ ($i + $j), λ ∈R and, $ ), µ ∈R. If Q(α , β, γ) is the, r = − $j + µ ($j − k, foot of the perpendicular drawn from the, point M (1, 0, 1) to P, then 3(α + β + γ), equals ............ ., , c, , (c, e ) and the normal to the parabola,, y2 = 4x at the point (1, 2) intersect at the, same point the X-axis, then the value of c, is .......... ., , 23 Let S be the set of all integer solutions,, , 25 If m arithmetic means (AMs) and three, , (x, y, z), of the system of equations, x − 2 y + 5z = 0, − 2x + 4 y + z = 0, − 7x + 14 y + 9z = 0, , geometric means (GMs) are inserted, between 3 and 243 such that 4th AM is, equal to 2nd GM, then m is equal to, , Answers, Physics, 1., 11., 21., , (b), (c), (20), , 2. (c), 12. (b), 22. (346), , 3., (a), 13., (d), 23. (8791), , (a), (d), (25), , 4., 14., 24., , 5., 15., 25., , (c), (c), (1), , 6. (a), 16. (b), , 7. (c), 17. (c), , 8. (a), 18. (a), , 9. (c), 19. (c), , 10. (d), 20. (a), , For Detailed Solutions, Visit : http://bit.ly/3lYCqlE, Or Scan :, , Chemistry, 1. (a), 11. (b), 21. (25), , 2., 12., 22., , (a), (b), (10), , 3., 13., 23., , (c), (b), (5), , 4., (a), 14. (b), 24. (60), , 5., (c), 15., (a), 25. (2 × 10 −2 ), , 6. (a), 16. (d), , 7. (b), 17. (c), , 8. (d), 18. (a), , 9., 19., , (c), (c), , 10. (a), 20. (b), , For Detailed Solutions, Visit : http://bit.ly/34by8S4, Or Scan :, , Mathematics, 1., 11., 21., , (c), (d), (54), , 2., 12., 22., , (b), (b), (4), , 3., 13., 23., , (d), (b), (8), , 4., 14., 24., , (a), (b), (5), , 5., 15., 25., , (b), (d), (39), , 6., 16., , (a), (d), , 7., 17., , (a), (c), , 8., 18., , (d), (b), , 9., 19., , (c), (c), , For Detailed Solutions, Visit : http://bit.ly/3m0jBOY, Or Scan :, , 10., 20., , (a), (b)
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ONLINE QUESTION PAPER, , JEE Main 2020, (04 September, 2020), TIME 9:30-12:30 (Shift I), , MM : 300, , PHYSICS, Objective Type Questions, 1 A beam of plane polarised light of large, cross-sectional area and uniform intensity, of 3.3 Wm −2 falls normally on a polariser,, which rotates about its axis with an, angular speed of 31.4 rad/s. The energy of, light passing through the polariser per, revolution is close to, (Take, cross-sectional area = 3 × 10−4 m 2 ), (b) 5.0 × 10−4 J, (d) 1.0 × 10−5 J, , (a) 1.5 × 10−4 J, (c) 1.0 × 10−4 J, , 2 Two point charges 4q and − q are fixed on, , −d, d, and x = , respectively., 2, 2, If a third point charge q is taken from the, origin to x = d along the semi-circle as, shown in the figure, the energy of the, charge will, , the X-axis at x =, , 4q, , –q, , 3 A small bar magnet placed with its axis at, 30° with an external field of 0.06 T, experiences a torque of 0.018 Nm. The, minimum work required to rotate it from, its stable to unstable equilibrium position is, (a), (b), (c), (d), , 9.2 × 10 −3 J, 7.2 × 10 −2 J, 6.4 × 10 −2 J, 11.7 × 10 −3 J, , 4 A small bar magnet is moved through a, coil at constant speed from one end to the, other. Which of the following series of, observations will be seen on the, galvanometer G attached across the coil?, G, , a, Magnet, , c, , b, , Three positions shown describe: (i) the, magnet’s entery (ii) magnet is completely, inside and (iii) magnet’s exit., (i), , 2q2, 4q2, (b) decrease by, (a) increase by, 3 πε0 d, 3 πε0 d, (c) increase by, , 3q2, q2, (d) decrease by, 4 πε0 d, 4πε0 d, , (a), , (ii), , (iii)
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41, , SEPTEMBER ATTEMPT ~ 04 Sep 2020, Shift I, (i), , (ii), , (iii), , 7 Take the breakdown voltage of the zener, diode used in the given circuit as 6V. For the, input voltage shown in figure below, the time, variation of the output voltage is (Graphs are, drawn schematically and on not to scale), , (b), , (i), , (ii), , R1, , (iii), 10 V, Vin, , V=0, , (c), , Vo, , –10 V, , (i), , (ii), , V, , (iii), , (a), , t, , (d), V, , 5 Two charged thin infinite plane sheets of, , (b), , uniform surface charge densities σ + and, σ − , where|σ +|>|σ −|, intersect at right, angle. Which of the following best, represents the electric field lines for this, system?, σ–, , V, (c), , σ–, , σ+ (b), , (a), , t, , t, , V, , σ+, , (d), , σ–, , σ–, , σ+ (d), , (c), , σ+, , an upward acceleration 9.8 cm s −2. The, density of water is 1 g/cm3 and water, offers negligible drag force on the bubble., The mass of the bubble is, (Take, g = 980 cm/s 2), 1.52 g, 4.51 g, 4.15 g, 3.15 g, , m, moving along, 2, the X-axis with velocity v0 collides, elastically with another particle B at rest, m, having mass mB = . If both particles, 3, move along the X-axis after the collision,, the change ∆ λ in de-Broglie wavelength of, particle A, in terms of its de-Broglie, wavelength λ 0 before collision is, , 8 Particle A of mass mA =, , 6 An air bubble of radius 1 cm in water has, , (a), (b), (c), (d), , t, , (a) ∆ λ =, , 5, λ0, 2, , (c) ∆ λ = 2 λ 0, , (b) ∆ λ = 4λ 0, (d) ∆ λ =, , 3, λ0, 2, , 9 Dimensional formula for thermal, conductivity is, (Here, K denotes the temperatuere), (a) [MLT −2 K], (c) [MLT −3 K −1 ], , (b) [MLT −2K −2], (d) [MLT −3 K]
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42, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 10 A tennis ball is released from a height h, , 13 Choose the correct option relating, , and after freely falling on a wooden floor,, h, it rebounds and reaches height . The, 2, velocity versus height of the ball during its, motion may be represented graphically by, (Graphs are drawn schematically and on, not to scale), v, , v, h/2, , (a), , h, , h, , h(v) (b), , h/2, , h(v), , wavelengths of different parts of, electromagnetic wave spectrum, (a), (b), (c), (d), , λ X-rays < λ microwaves < λ radio waves < λ visible, λ visible > λ X − rays > λ radio waves > λ microwaves, λ radio waves > λ microwaves > λ visible > λ X − rays, λ visible < λ microwaves < λ radio waves < λ X − rays, , 14 A wire A, bent in the shape of an arc of a, circle, carrying a current of 2 A and having, radius 2 cm and another wire B, also bent, in the shape of arc of a circle, carrying a, current of 3 A and having radius of 4 cm,, are placed as shown in the figure. The, ratio of the magnetic fields due to the, wires A and B at the common centre O is, , v, , v, , A, , h, , (c), , h/2, , h/2, , h(v) (d), , h, , h(v), , O, , B, , 90º, 60º, , 11 For a transverse wave travelling along a, straight line, the distance between two, peaks (crests) is 5 m, while the distance, between one crest and one trough is 1.5 m., The possible wavelengths (in metre) of the, waves are, 1 1 1, , , ,....., 1 3 5, 1 1 1, (d) , , , ....., 2 4 6, , (a) 1, 2, 3,......, , (b), , (c) 1, 3, 5,....., , 12 Blocks of masses m, 2m, 4m and 8m are, arranged in a line on a frictionless floor., Another block of mass m, moving with speed, v along the same line (see figure) collides, with mass m in perfectly inelastic manner., All the subsequent collisions are also, perfectly inelastic. By the time, the last, block of mass 8m starts moving, the total, energy loss is p% of the original energy., Value of p is close to, v, m, , (a) 77, , m, , (b) 87, , 2m, , 4m, , (c) 94, , 8m, , (d) 37, , (a) 4 : 6, (c) 6 : 5, , (b) 6 : 4, (d) 2 : 5, , 15 On the X-axis and at a distance x from the, origin, the gravitational field due to a, Ax, mass distribution is given by 2, in, (x + a 2 )3/ 2, the x-direction. The magnitude of, gravitational potential on the X-axis at a, distance x, taking its value to be zero at, infinity, is, (a), , A, (x + a 2 )1/ 2, 2, , (b) A (x2 + a 2 )3 / 2, A, (c), (x2 + a 2 )3 / 2, (d) A (x2 + a 2 )1/ 2, , 16 A battery of 3.0 V is connected to a resistor, dissipating 0.5 W of power. If the terminal, voltage of the battery is 2.5 V, the power, dissipated within the internal resistance is, (a) 0.072 W, , (b) 0.125 W, , (c) 0.50 W, , (d) 0.10 W
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43, , SEPTEMBER ATTEMPT ~ 04 Sep 2020, Shift I, 17 Match the C p/CV ratio for ideal gases with, different type of molecules:, C p /CV, , Molecule type, (A) Monatomic molecules, , I., , 7/5, , (B) Diatomic rigid molecules, , II., , 9/7, , (C) Diatomic non-rigid, molecules, , III., , 4/3, , (D) Triatomic rigid molecules, , IV., , 5/3, , (a), (b), (c), (d), , A B, IV I, III IV, II III, IV II, , C, II, II, I, I, , D, III, I, IV, III, , rotating about its axis with angular speed, ω1. If another stationary disc having, R, radius and same mass M is dropped, 2, co-axially on to the rotating disc., Gradually, both discs attain constant, angular speed ω 2. The energy lost in the, process is p% of the initial energy. Value of, p is ..........., , 22 ABC is a plane lamina of the shape of an, , 18 The following figure shows few data points, in a photoelectric effect experiment for a, certain metal. The minimum energy for, ejection of electron from its surface is, (Take, Planck’s constant, h = 662, . × 10−34 J-s), Y, , VStop (V), , Numerical Type Questions, 21 A circular disc of mass M and radius R is, , equilateral triangle. D, E are mid-points of, AB, AC and G is the centroid of the, lamina. Moment of inertia of the lamina, about an axis passing through G and, perpendicular to the plane ABC is I 0. If, part ADE is removed, the moment of, inertia of the remaining part about the, NI 0, , where N is an integer., same axis is, 16, Value of N is …… ., A, , C, , (6, V), , B (5.5, 0), A, 5, , (a) 1.93 eV, (c) 2.27 eV, , D, G, , X, F(10, , 14, , Hz), , B, , (b) 2.59 eV, (d) 2.10 eV, , 19 The specific heat of water = 4200 J kg −1K −1, −1, , and the latent heat of ice = 34, . × 10 J kg ., 100 g of ice at 0°C is placed in 200 g of water, at 25°C. The amount of ice that will melt as, the temperature of water reaches 0°C is, close to (in grams), 5, , (a) 63.8, (c) 64.6, , (b) 69.3, (d) 61.7, , 20 Starting from the origin at time t = 0, with, , initial velocity 5$j ms −1, a particle moves in, the xy-plane with a constant acceleration, of (10$i + 4$j) ms −2. At time t, its coordinates, are (20 m, y0 m). The values of t and y0, respectively, are, , (a) 2 s and 18 m, (c) 2 s and 24 m, , E, , (b) 5 s and 25 m, (d) 4 s and 52 m, , C, , 23 In a compound microscope, the magnified, virtual image is formed at a distance of, 25 cm from the eye-piece. The focal length, of its objective lens is 1 cm. If the, magnification is 100 and the tube length of, the microscope is 20 cm, then the focal, length of the eye-piece lens (in cm) is, ……… ., , 24 A closed vessel contains 0.1 mole of a, monatomic ideal gas at 200 K. If 0.05 mole, of the same gas at 400 K is added to it, the, final equilibrium temperature (in K) of the, gas in the vessel will be close to …… ., , 25 In the line spectra of hydrogen atom,, difference between the largest and the, shortest wavelengths of the Lyman series is, 304 Å. The corresponding difference for the, Paschan series (in Å) is ……… .
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44, , ONLINE, , JEE Main 2020 ~ Solved Papers, , CHEMISTRY, Objective Type Questions, 1 The elements with atomic numbers 101, and 104 belong to, respectively,, (a), (b), (c), (d), , actinoids and group 4, actinoids and group 6, group 6 and actinoids, group 11 and group 4, , 7 When neopentyl alcohol is heated with an, acid, it slowly converted into an 85 : 15, mixture of alkenes A and B, respectively., What are these alkenes?, (a), , COOH, , (a), , CH3, , (b), , (c), CH3, , CH3, , (d), , infrared, ultraviolet, microwave, visible, , (b) 2, , (c) 4, , (d) 1, , 5 On heating, lead (II) nitrate gives a, brown gas (A). The gas (A) on cooling, changes to a colourless solid/liquid (B)., (B) on heating with NO changes to a blue, solid (C). The oxidation number of, nitrogen in solid (C) is, (b) + 4, , (c) + 2, , (d) + 3, , 6 On combustion of Li, Na and K in excess, of air, the major oxides formed,, respectively, are, (a), (b), (c), (d), , CH3, , H3C, , H3 C, , Li 2O, Na 2O and K 2O 2, Li 2O, Na 2O 2 and K 2O, Li 2O, Na 2O 2 and KO 2, Li 2O 2, Na 2O 2 and K 2O 2, , CH2, , and, H3 C, CH3, , H3 C, , CH2, , and, H3 C, , CH2, , 8 The decreasing order of reactivity of the, following organic molecules towards AgNO3, solution is, Cl, , (A), , [Pt(en)(NO 2) 2] is, , (a) + 5, , H2C, , Cl, , 4 The number of isomers possible for, , CH3, , and, , (d) H3C, , spectrum where the Balmer series lines, appear is, , (a) 3, , H3 C, , H3C, , 3 The region in the electromagnetic, , (a), (b), (c), (d), , CH2, , H3C, , CH2COOH, , COOH, (c), , CH2, , H3C, , COOH, , (b), , H3 C, , and, H3C, , 2 [P] on treatment with Br 2/FeBr3 in CCl 4, , produced a single isomer C8H7 O2 Br while, heating [P] with sodalime gave toluene., The compound [P] is, , CH3, , CH3, , H3C, , (B), OMe, , (C) CH3 CHCH3, , Cl, (a), (b), (c), (d), , (D) CH3 CHCH2 NO2, , Cl, , (A) > (B) > (C) > (D), (C) > (D) > (A) > (B), (B) > (A) > (C) > (D), (A) > (B) > (D) > (C), , 9 Among statements (A)-(D), the correct ones, are :, (A) Limestone is decomposed to CaO during, the extraction of iron from its oxides., (B) In the extraction of silver, silver is, extracted as an anionic complex., (C) Nickel is purified by Mond’s process., (D) Zr and Ti are purified by van-Arkel, method.
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45, , SEPTEMBER ATTEMPT ~ 04 Sep 2020, Shift I, , Interatomic distance (pm), 0, , 50, , 100, , 13 For the equilibrium A r B , the, variation of the rate of the forward (a) and, reverse (b) reaction with time is given by, , 150, , –100, , (a), , –200, , Potential, –300, Energy, (kJ mol–1), –400, –500, , A–D, A–C, , A–A, , (b), , A–B, , –600, , (a) A-B has the stiffest bond, (b) D is more electronegative than other, atoms, (c) A-A has the largest bond enthalpy, (d) A-D has the shortest bond length, , (c), , 11 What are the functional groups present in, the structure of maltose?, (a) One ketal and one hemiketal, (b) One acetal and one ketal, (c) One acetal and one hemiacetal, (d) Two acetals, , 12, , (d), , Eext, , Rate of reaction, , the molecules A, B, C and D given below, suggests that:, , Rate of reaction, , 10 The intermolecular potential energy for, , (b) If E ext = 1.1 V, no flow of electrons or, current occurs., (c) If E ext > 1.1 V, electrons flows from Cu to Zn., (d) If E ext < 1.1 V, Zn dissolves at anode and, Cu deposits at cathode., , a, Equilibrium, b, Time, a, Equilibrium, b, Time, , Rate of reaction, , (A), (B), (C) and (D), (A), (C) and (D) only, (C) and (D) only, (B), (C) and (D) only, , a, Equilibrium, b, Time, , Rate of reaction, , (a), (b), (c), (d), , a, Equilibrium, b, Time, , 14 The ionic radii of O2− , F− , Na + and Mg2+, are in the order, , Zn rod, –ve, 1M, ZnSO4, solution, , Salt, Bridge, , Cu rod, +ve, 1M, CuSO4, solution, , (a), (b), (c), (d), , O2− > F − > Mg 2+ > Na +, Mg 2+ > Na + > F − > O2−, O2− > F − > Na + > Mg 2+, F − > O2− > Na + > Mg 2+, , 15 The IUPAC name of the following compound is, CH3 O, C—OH, , E°, , = + 0 . 34 V, , E°, , = − 0 . 76 V, , Cu 2+ |Cu, Zn 2+ |Zn, , Identify the incorrect statement from the, options below for the above cell., (a) If E ext > 1.1 V, Zn dissolves at Zn, electrode and Cu deposits at Cu, electrode., , Br, , (a) 3-bromo-5-methylcyclopentane, carboxylic acid, (b) 3-bromo-5-methylcyclopentanoic acid, (c) 5-bromo-3-methylcyclopentanoic acid, (d) 4-bromo-2-methylcyclopentane, carboxylic acid
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46, , ONLINE, , 16 For one mole of an ideal gas, which of, these statements must be true?, (A) U and H each depends only on, temperature., (B) Compressibility factor Z is not equal to 1., (C) C p,m − CV,m = R, (D) dU = CV dT for any process., (a), (b), (c), (d), , (B), (C) and (D), (A) and (C), (A), (C) and (D), (C) and (D), , the same magnetic moment (spin only) is, [Mn(H2O)6 ]2+ and [Cr(H2O)]2+, [Cr(H2O)6 ]2+ and [Fe(H2O)6 ]2+, [Co(OH)4 ]2− and [Fe(NH3 )6 ]2+, [Cr(H2O)6 ]2+ and [CoCl 4 ]2−, , CHCl3 + alc. KOH?, , Adenine and lysine, Thymine and proline, Adenine and thymine, Adenine and proline, , 19 An organic compound (A) (molecular, formula C6H12O2) was hydrolysed with dil., H2SO4 to give a carboxylic acid (B) and an, alcohol (C). ‘C’ gives white turbidity, immediately when treated with anhydrous, ZnCl2 and conc. HCl. The organic, compound (A) is, O, (a), , (b), , O, (c), , O, , 23 If 75% of a first order reaction was, completed in 90 minutes, 60% of the same, reaction would be completed in, approximately (in minutes) ........... ., (Take : log 2 = 030, . ; log 25, . = 040, . ), , 25 The number of chiral centres present in [B], is ............. ., O, , —CH—C≡≡N, CH3, , 20 Match the following:, I. Foam, II. Gel, , containing 1 mole of n-hexane and 3 moles, of n-heptane is 550 mm of Hg. At the same, temperature, if one more mole of, n-heptane is added to this solution, the, vapour pressure of the solution increases, by 10 mm of Hg. What is the vapour, pressure in mm Hg of n-heptane in its, pure state ........... ?, , when 2.8 kg of dinitrogen quantitatively, reacts with 1 kg of dihydrogen is ......... ., , O, O, , (d), , H2O2 reacts completely with 0.316 g of, KMnO4 in acid solution. The purity of, H2O2 (in%) is ............. (molecular weight of, H2O2 = 34; molecular weight of, KMnO4 = 158)., , 24 The mass of ammonia in grams produced, , O, O, , (C) Jellies, (D) Rubber, (E) Froth, (F) Milk, (a) (I)-(D), (II)-(B), (III)-(A), (IV)-(E), (b) (I)-(B), (II)-(C), (III)-(E), (IV)-(D), (c) (I)-(E), (II)-(C), (III)-(A), (IV)-(F), (d) (I)-(D), (II)-(B), (III)-(E), (IV)-(F), , 22 At 300 K, the vapour pressure of a solution, , 18 Which of the following will react with, (a), (b), (c), (d), , III. Aerosol, IV. Emulsion, , Numerical Type Questions, 21 A 20.0 mL solution containing 0.2g impure, , 17 The pair in which both the species have, (a), (b), (c), (d), , JEE Main 2020 ~ Solved Papers, , (A) Smoke, (B) Cell fluid, , (i) C2H5MgBr, (ii) H3O+, , [A], , (i) CH3MgBr, [B], (ii) H2O
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47, , SEPTEMBER ATTEMPT ~ 04 Sep 2020, Shift I, , MATHEMATICS, Objective Type Questions, 1 If (a + 2b cos x) (a − 2b cos y) = a 2 − b2,, where a > b > 0, the, (a), , a−b, a+ b, , (b), , a+ b, a−b, , dx π π , at , is, dy 4 4 , (c), , 2a + b, a − 2b, (d), 2a − b, a + 2b, , 2 The mean and variance of 8 observations, are 10 and 13.5 respectively. If 6 of these, observations are 5,7,10, 12, 14, 15, then, the absolute difference of the remaining, two observations is, (a) 9, , (b) 3, , (c) 7, , (d) 5, , 3 If 1 + (1 − 22 ⋅ 1) + (1 − 42 ⋅ 3) + (1 − 62 ⋅ 5) +, L + (1 − 202 ⋅ 19) = α − 220β, then an, ordered pair (α , β) is equal to, (a) (11, 97), (c) (10, 97), , (b) (10, 103), (d) (11, 103), , 4 A survey shows that 63% of the people in a, city read newspaper A whereas 76% read, newspaper B. If x% of the people read both, the newspapers, then a possible value of x, can be, (a) 55, (c) 65, , (b) 29, (d) 37, , 5 Given the following two statements:, , (S1 ) : (q ∨ p) → ( p ↔~ q) is a tautology., (S2 ) : ~ q ∧ (~ p ↔ q) is a fallacy. Then, (a) both (S1 ) and (S 2) are not correct, (b) only (S1 ) is correct, (c) both (S1 ) and (S 2) are correct, (d) only (S 2) is correct, , 6 Two vertical poles AB = 15 m and CD = 10 m, are standing apart on a horizontal ground, with points A and C on the ground. If P is, the point of intersection of BC and AD, then, the height of P (in meters) above the line AC, is, (a) 20/3, (c) 10/3, , (b) 6, (d) 5, , 7 Let f be a twice differentiable function on, (1, 6). If f (2) = 8, f ' (2) = 5, f ' (x) ≥ 1 and, f ′ ′ (x) ≥ 4, for all x ∈(1, 6), then, , (a) f (5) + f '(5) ≥ 28, (c) f (5) + f '(5) ≤ 26, , (b) f (5) ≤ 10, (d) f '(5) + f ''(5) ≤ 20, , 20, , 8 The value of, , ∑ 50− r C 6, , is equal to, , r=0, , (a) 50 C7 −, (c) 51 C7 +, , 30, , C7, C7, , 30, , cos θ, , 9 If A = , i sin θ, , (b) 51 C7 − 30C7, (d) 50 C6 − 30C6, , i sin θ , π, , θ = and, cos θ , 24, , a b , A5 = , , where i = −1, then which one, c d, of the following is not true?, , (a) a 2 − d 2 = 0, 1, (c) a 2 − b2 =, 2, , (b) a 2 − c2 = 1, (d) 0 ≤ a 2 + b2 ≤ 1, , 10 Let α and β be the roots of x2 − 3x + p = 0, and γ and δ be the roots of x2 − 6x + q = 0. If, α , β, γ, δ form a geometric progression., Then ratio (2q + p) : (2q − p) is, (a) 9 : 7, (c) 5 : 3, , x2, , (b) 3 : 1, (d) 33 : 31, , +, , y2, , = 1 (a > b) be a given ellipse,, a 2 b2, length of whose latus rectum is 10. If its, eccentricity is the maximum value of the, 5, function, φ(t) =, + t − t 2, then a 2 + b2 is, 12, equal to, , 11 Let, , (a) 145, (c) 126, , (b) 116, (d) 135, , 12 A triangle ABC lying in the first quadrant, has two vertices as A(1, 2) and B(3, 1). If, ∠BAC = 90°, and ar (∆ABC ) = 5 5 sq. units,, then the abscissa of the vertex C is, (a) 2 + 5, (c) 2 5 − 1, , (b) 1 + 2 5, (d) 1 + 5, , 13 Let P(3, 3) be a point on the hyperbola,, x2, , −, , y2, , = 1. If the normal to it at P, a 2 b2, intersects the X-axis at (9, 0) and e is its, eccentricity, then the ordered pair (a 2,e2 ), is equal to, 9, (a) , 3, 2 , 9, (c) , 2, 2 , , 3, (b) , 2, 2 , (d) (9, 3)
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48, , ONLINE, , JEE Main 2020 ~ Solved Papers, , 2, , x, dx is equal, , x sin x + cos x, , 14 The integral ∫ , , to (where C is a constant of integration), x tan x, +C, x sin x + cos x, x tan x, (b) sec x +, +C, x sin x + cos x, x sec x, (c) tan x −, +C, x sin x + cos x, x sec x, (d) tan x +, +C, x sin x + cos x, (a) sec x −, , 19 Let y = y(x) be the solution of the, differential equation,, xy'− y = x2 (x cos x + sin x), x > 0. If y(π ) = π,, π, π, then y' ' + y is equal to, 2, 2, π π2, +, 2, 4, π π2, (c) 1 + +, 2, 4, , (a) 2 +, , π, 2, π, (d) 2 +, 2, (b) 1 +, , 20 Let f (x) =|x − 2|and g(x) = f ( f (x)), x ∈ [0, 4]., 3, , 15 Let f (x) = ∫, , x, , dx (x ≥ 0). Then, , (1 + x)2, f (3) − f (1) is equal to, , 3, 2, (c) 0, , π 1, 3, + +, 6 2, 4, π 1, 3, (b) − + +, 12 2, 4, π 1, 3, (c) + −, 6 2 4, π 1, 3, (d), + −, 12 2 4, , 21 Let (2x2 + 3x + 4)10 =, , 20, , ∑ a r xr . Then a 7, a, , r=0, , is, , 13, , equal to ............. ., , 22 If the equation of a plane P, passing, , 2z + i, , z = x + iy and k > 0. If the, z − ki, curve represented by Re(u ) + Im(u ) = 1, intersects the Y -axis at the points P and Q, where PQ = 5 , then the value of k is, (b) 4, (d) 3/2, , 17 Let x0 be the point of local maxima of, f (x) = a ⋅ (b × c), where, $ , b = −2i$ + x$j − k, $ and, a = x i$ − 2$j + 3k, $, $, $, c = 7i − 2 j + xk. Then the value of, a ⋅ b + b ⋅ c + c ⋅ a at x = x0 is, , (b) − 4, (d) − 30, , 18 Let [t ] denote the greatest integer ≤ t. Then, the equation in x, [x]2 + 2[x + 2] − 7 = 0 has, (a), (b), (c), (d), , 1, 2, (d) 1, (b), , Numerical Type Questions, , 16 Let u =, , (a) 14, (c) − 22, , 0, , (a), , (a) −, , (a) 1/2, (c) 2, , Then ∫ ( g(x) − f (x)) dx is equal to, , infinitely many solutions, exactly four integral solutions, no integral solution, exactly two solutions, , through the intersection of the planes,, x + 4 y − z + 7 = 0 and 3x + y + 5z = 8 is, ax + by + 6z = 15 for some a , b ∈R, then the, distance of the point (3, 2, − 1) from the, plane P is ........... ., , 23 The probability of a man hitting a target is, 1, . The least number of shots required, so, 10, that the probability of his hitting the, 1, target at least once is greater than , is, 4, ........... ., , 24 Suppose a differentiable function f (x), satisfies the identity, f (x + y) = f (x) + f ( y) + xy2 + x2 y, for all real, f (x), x and y. If lim, = 1, then f ' (3) is equal, x→ 0 x, to ............ ., , 25 If the system of equations, x − 2 y + 3z = 9, 2x + y + z = b, x − 7 y + az = 24, has infinitely many, solutions, then a − b is equal to ............. .
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SEPTEMBER ATTEMPT ~ 04 Sep 2020, Shift I, , Answers, Physics, 1., 11., 21., , (c), (b), (20), , 2. (b), 12. (c), 22. (11), , 3., 13., 23., , (b), (c), (6), , 4., 14., 24., , (b), (c), (266), , 5., (c), 15., (a), 25. (10553), , 6. (c), 16. (d), , 7. (c), 17. (a), , 8. (b), 18. (c), , 9. (c), 19. (d), , 10. (c), 20. (a), , For Detailed Solutions, Visit : http://bit.ly/31nOYv7, Or Scan :, , Chemistry, 1. (a), 11. (c), 21. (85), , 2., (b), 12. (a), 22. (600), , 3., 13., 23., , (d), (a), (60), , 4., (a), 14., (c), 24. (3400), , 5., 15., 25., , (d), (d), (2), , 6., 16., , (c), (c), , (a), (b), , 7., 17., , 8., 18., , (c), (a), , 9., 19., , (a), (b), , 10., 20., , (a), (c), , 10., 20., , (a), (d), , For Detailed Solutions, Visit : http://bit.ly/3dGGXGv, Or Scan :, , Mathematics, 1., 11., 21., , (b), (c), (8), , 2., 12., 22., , (c), (b), (3), , 3., 13., 23., , (d), (a), (3), , 4., 14., 24., , (a), (c), (10), , 5., 15., 25., , (a), (d), (5), , 6., 16., , (b), (c), , 7., 17., , (a), (c), , 8., 18., , (b), (a), , 9., 19., , (c), (d), , For Detailed Solutions, Visit : http://bit.ly/3jca2L1, Or Scan :
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ONLINE QUESTION PAPER, , JEE Main 2020, (04 September, 2020), TIME 2:30-5:30 (Shift II), , MM : 300, , PHYSICS, Objective Type Questions, 1 The value of current i1 flowing from A to C, in the circuit diagram is, , 8V, i, , B, 2Ω, , 5Ω, 4Ω, , 4 Ω i1, , 2Ω, , A, , i, , C, 5Ω, , 2Ω, , 2Ω, , D, , (a) 1A, (c) 2 A, , (b) 5 A, (d) 4 A, , 2 Find the binding energy per nucleon for, 120, 50 Sn., , Mass of proton m p = 100783, u, mass, ., , u and mass of tin, of neutron mn = 100867, ., nucleus mSn = 119902199, u., ., (Take, 1 u = 931 MeV), (a) 9.0 MeV, (c) 8.0 MeV, , (b) 7.5 MeV, (d) 8.5 MeV, , 3 A series L-R circuit is connected to a, battery of emf V. If the circuit is switched, ON at t = 0, then the time at which the, , 1, energy stored in the inductor reaches , n, times of its maximum value, is, (a), , L n + 1, ln , , R n − 1, , (c), , L n − 1, ln , , R , n , , L , n , ln , , R n + 1, L , n , (d) ln , , R n − 1, (b), , 4 Consider two uniform discs of same, , thickness and different radii R1 = R and, R2 = αR made of the same material. If the, ratio of their moments of inertia I1 and I 2, respectively, about their axes is, I1 : I 2 = 1 : 16, then the value of α is, , (a) 2, (c) 4, , (b) 2 2, (d) 2, , 5 The electric field of a plane, electromagnetic wave is given by, E = E 0 (x$ + y$ )sin(kz − ωt ), Its magnetic field will be given by, E0 $, (x + y$ ) sin(kz − ωt ), c, E, (b) 0 (− x$ + y$ ) sin(kz − ωt ), c, E, (c) 0 (x$ − y$ ) sin(kz − ωt ), c, E0 $ $, (d), (x − y ) cos(kz − ωt ), c, (a)
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51, , SEPTEMBER ATTEMPT ~ 04 Sep 2020, Shift II, 6 Match the thermodynamic processes, taking place in a system with the correct, conditions. In the table, ∆Q is heat, supplied, ∆W is work done and ∆U is, change in internal energy of the system., Process, Adiabatic, , (A) ∆W = 0, , (II), , Isothermal, , (B) ∆Q = 0, , (III) Isochoric, , (C) ∆U ≠ 0, ∆W ≠ 0, and ∆Q ≠ 0, , (IV) Isobaric, , (D) ∆U = 0, , (a), (b), (c), (d), , 7, , Condition, , (I), , I, B, A, B, A, , II, A, A, D, B, , y, , III IV, D C, B C, A C, D D, , applied along the vertical, it starts, rotating around its horizontal diameter., The angular speed of the coil, acquired, after rotating by 60°, will be, (a) 10 rad s −1, (c) 10π rad s −1, , (b) 20π rad s −1, (d) 20 rad s −1, , 10 A particle of charge q and mass m is, subjected to an electric field E = E 0 (1 − ax2 ), in the x-direction, where a and E 0 are, constants. Initially, the particle was at rest, at x = 0. Other than the initial position, the, kinetic energy of the particle becomes zero, when the distance of the particle from the, origin is, 1, a, 3, a, , (a), (c), , O′, , (b) a, (d), , 2, a, , 11 A capacitor C is fully charged with voltage, O, , 80 cm, , x, 60 cm, , For a uniform rectangular sheet, shown in, the above figure, the ratio of moments of, inertia about the axes perpendicular to the, sheet and passing through O (the centre of, mass) and O′ (corner point) is, (a) 1/8, (c) 1/4, , (b) 2/3, (d) 1/2, , 8 A paramagnetic sample shows a net, magnetisation of 6 A/m, when it is placed, in an external magnetic field of 0.4 T at a, temperature of 4 K. When the sample is, placed in an external magnetic field of, 0.3 T at a temperature of 24 K, then the, magnetisation will be, (a) 4 A/m, (c) 1 A/m, , (b) 0.75 A/m, (d) 2.25 A/m, , 9 A circular coil has moment of inertia, 2, , 0.8 kg m around any diameter and is, carrying current to produce a magnetic, moment of 20 Am2. The coil is kept, initially in a vertical position and it can, rotate freely around a horizontal diameter., When a uniform magnetic field of 4 T is, , V0. After disconnecting the voltage source,, it is connected in parallel with another, C, uncharged capacitor of capacitance . The, 2, energy loss in the process after the charge, is distributed between the two capacitors, is, 1, (a) CV 02, 3, 1, (c) CV 02, 2, , 1, (b) CV 02, 6, 1, (d) CV 02, 4, , 12 A small ball of mass m is thrown upward, with velocity u from the ground. The ball, experiences a resistive force mkv2, where v, is its speed. The maximum height attained, by the ball is, (a), , ku 2 , 1, , tan −1 , k, 2g , , (c), , 1 , ku 2 , , ln 1 +, k , 2 g , , 1 , ku 2 , , ln 1 +, 2k , g , ku 2 , 1, , (d), tan −1 , 2k, g , (b), , 13 A body is moving in a low circular orbit, about a planet of mass M and radius R., The radius of the orbit can be taken to be, R itself. Then, the ratio of the speed of this, body in the orbit to the escape velocity, from the planet is, (a) 1, (c) 2, , 1, 2, (d) 2, , (b)
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52, , ONLINE, , 14 Two identical cylindrical vessels are kept, on the ground and each contains the same, liquid of density d. The area of the base of, both vessels is S but the height of liquid in, one vessel is x1 and in the other, x2. When, both cylinders are connected through a, pipe of negligible volume very close to the, bottom, the liquid flows from one vessel to, the other until it comes to equilibrium at a, new height. The change in energy of the, system in the process is, 3, gdS (x2 − x1 )2, 4, 1, (d) gdS (x2 − x1 )2, 4, , (a) gdS (x22 + x12 ), , (b), , (c) gdS (x2 + x1 )2, , JEE Main 2020 ~ Solved Papers, , (a) graph does not change, (b) straight line shifts to left, (c) slope of the straight line get more steep, (d) straight line shifts to right, , 18 A cube of metal is subjected to a, hydrostatic pressure of 4 GPa. The, percentage change in the length of the side, of the cube is close to, (Take bulk modulus of metal, B = 8 × 1010 Pa), (a) 1.67, , (b) 0.6, , (c) 20, , (d) 5, , 19 Identify the operation performed by the, circuit given below., A, , 15 The driver of a bus approaching a big wall, notices that the frequency of his bus’s horn, changes from 420 Hz to 490 Hz, when he, hears it after it gets reflected from the, wall. Find the speed of the bus if speed of, the sound is 330 ms −1., (a) 81 kmh −1, (b) 91 kmh −1, (c) 71 kmh −1, (d) 61 kmh −1, , B, C, , (a) AND, (c) NOT, , (b) NAND, (d) OR, , 20 A quantity x is given by x =, , 16 A person pushes a box on a rough, horizontal platform surface. He applies a, force of 200 N over a distance of 15 m., Thereafter, he gets progressively tired and, his applied force reduces linearly with, distance to 100 N. The total distance, through which the box has been moved is, 30 m. What is the work done by the person, during the total movement of the box?, (a) 5250 J, (c) 3280 J, , (b) 2780 J, (d) 5690 J, , 17 In a photoelectric effect experiment, the, graph of stopping potential V versus, reciprocal of wavelength (1 /λ ) obtained is, shown in the figure., V, , IFv2, WL4, , where, I is moment of inertia, F is force, v, is work and L is length. The dimensional, formula for x is same as that of, (a) Planck’s constant, (b) force constant, (c) coefficient of viscosity, (d) energy density, , Numerical Type Questions, 21 Orange light of wavelength 6000 × 10−10 m, , illuminates a single slit of width 06, . × 10−4 m., The maximum possible number of, diffraction minima produced on both sides, of the central maximum is ……… ., , 22 The change in the magnitude of the, , θ, , 1/λ, , As the intensity of incident radiation is, increased,, , volume of an ideal gas when a small, additional pressure ∆p is applied at a, constant temperature, is the same as the, change when the temperature is reduced, by a small quantity ∆T at constant, pressure. The initial temperature and, pressure of the gas are 300 K and 2 atm,, respectively. If|∆T | = C|∆p|, then value of, C (in K/atm) is ……… .
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53, , SEPTEMBER ATTEMPT ~ 04 Sep 2020, Shift II, B, , 23, 40 Ω, , positions is 40 cm. If the power of the lens, N , is close to , D, where N is an integer., 100, Then, the value of N is ……… ., , 60 Ω, , A, , C, , 90 Ω, , 25 The speed versus time graph for a particle, , 110 Ω, , is shown in the figure. The distance, travelled (in metre) by the particle during, the time interval t = 0 s to t = 5 s will be, ……… ., , D, 40 V, , Four resistances 40 Ω, 60 Ω, 90 Ω and 110 Ω, make the arms of a quadrilateral ABCD., Across AC is a battery of emf 40 V and, internal resistance negligible. The potential, difference across BD (in volt) is ……… ., , 10, 8, Speed 6, (in ms–1), 4, , 24 The distance between an object and a, , 2, , screen is 100 cm. A lens can produce real, image of the object on the screen for two, different positions between the screen and, the object. The distance between these two, , 0, , 1, , 2, , 3 4, Time, (in s), , 5, , CHEMISTRY, 1 The crystal field stabilisation energy, (CFSE) of [CoF3 (H2O)3 ] (∆ 0 < P ) is, , (a) −0.8 ∆ 0, (c) −0.4∆ 0, , (b) −0.8∆ 0 + 2P, (d) −0.4∆ 0 + P, , 2 The processes of calcination and roasting, in metallurgical industries, respectively,, can lead to, (a) global warming and acid rain, (b) global warming and photochemical smog, (c) photochemical smog and ozone layer, depletion, (d) photochemical smog and global warming, , 5 A sample of red ink (a colloidal, suspension) is prepared by mixing eosin, dye, egg white, HCHO and water. The, component which ensures stability of the, ink sample is, (a) egg white, (c) HCHO, , 6 The major product [R] in the following, sequence of reactions is, (i) LiNH2/ ether, , HC ≡≡ CH → [P ], (ii) H3C, , CH Br, , 3 The mechanism of action of ‘‘Terfenadine’’, , (CH3 ) 2CH, , (Seldane) is, (a) Inhibits the secretion of histamine, (b) Inhibits the action of histamine receptor, (c) Helps in the secretion of histamine, (d) Activates the histamine receptor, , (i) HgSO 4 / H 2SO 4, , (a) −RT ln V 2 / V1, (c) CV (T2 − T1 ), , (b) − RT (V 2 − V1 ), (d) zero, , Conc. H SO, , 2, 4, → [Q] →, [ R], , (ii) NaBH 4, , (a), , 4 Five moles of an ideal gas at 1 bar and, 298 K is expanded into vacuum to double, the volume. The work done is, , (b) eosin dye, (d) water, , H3C, , C== CH—CH3, , (CH3)2CH, , (b), , H3C, , CH—CH==CH2, , (CH3)2CH, , ∆
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54, , JEE Main 2020 ~ Solved Papers, , ONLINE, , (c), , H3C, , 12 250 mL of a waste solution obtained from, C==C(CH3)2, , the workshop of a goldsmith contains, 0.1 M AgNO3 and 0.1 M AuCl. The solution, was electrolysed at 2 V by passing a, current of 1 A for 15 minutes. The, metal/metals electrodeposited will be, , H3CCH2, H2C, , (d), , C—CH2—CH3, , (CH3)2CH, , (E °, , Ag + / Ag, , 7 The molecule in which hybrid MOs involve, only one d-orbital of the central atom is, 3−, , (a) XeF4, (c) BrF5, , (b) [CrF6 ], (d) [Ni(CN)4 ]2−, , 8 The major product [B] in the following, reactions is, , H SO, , HI, 2, 4, [ A] alcohol →, [B], →, ∆, , Heat, , (a) only silver, (b) silver and gold in equal mass proportion, (c) only gold, (d) silver and gold in proportion to their, atomic weights, , 420 K, (b) H2 SO4 + NaCl →, Disproportionation, , (c) H3 PO2 →, +, , nature is, (a) O− ( g ) + e− → O2− ( g ), (b) Na ( g ) → Na + ( g ) + e−, (c) H( g ) + e− → H− ( g ), (d) Ar( g ) + e− → Ar− ( g ), , CH3, , (c) CH3 CH2 C == CH2, (d) CH3 CH2 CH == CH CH3, , 9 The shortest wavelength of H atom in the, , Lyman series is λ1. The longest, wavelength in the Balmer series of He+ is, , 36λ1, (a), 5, 9λ, (c) 1, 5, , the underlined atom is affected is, (a) XeF4 + SbF5 →, , 14 The process that is not endothermic in, , (b) CH2 == CH2, , 5λ, (b) 1, 9, 27λ1, (d), 5, , 15 In the following reaction sequence, [C ] is, NH2, (i) NaNO2 + HCl, 0-5ºC, Cl, [A] 2 [B], hν, (ii) Cu2Cl2 + HCl, Na+dry ether, , CH3, , 10 If the equilibrium constant for, , (a) Cl—, , —CH2—CH2—, , —Cl, , P is, , (2), (a) K (1), eq / K eq, , (2), (b) K (1), eq + K eq, , (2), (c) K (1), eq K eq, , (1), (d) K (2), eq − K eq, , 11 An alkaline earth metal ‘M’ readily forms, water soluble sulphate and water insoluble, hydroxide. Its oxide MO is very stable to, heat and does not have rock-salt structure., M is, (b) Ca, , (c) Be, , (d) Mg, , (b) CH3—, , (c) Cl—, , (d) CH2—, Cl, , [C], , (Major, product), , (1 ), and that of B + C = P, B + C is K eq, , ( 2), , the equilibrium constant for, is K eq, , (a) Sr, , = 1.69 V), , H, (d) NH3 →, , CH3, , (a) CH3 CH == C CH3, , Aq, , Au + / Au, , 13 The reaction in which the hybridisation of, , CH3, , CH3 CH2 C H CH2 OCH2 CH3, , Aq, , = 0.80 V, E °, , —, , —CH3, , —CH2—, , —, , —CH2—Cl, , —CH2, Cl
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55, , SEPTEMBER ATTEMPT ~ 04 Sep 2020, Shift II, Br, , 16 The incorrect statement(s) among (1)-(3) is, (are), , 1. W(VI) is more stable than Cr(VI)., 2. in the presence of HCl,, permanganate titrations provide, satisfactory results., , Br, , 3. some lanthanoid oxides can be used, as phosphors., (a) 2 and 3 only, (c) 1 only, , D, , (c), , (b) 2 only, (d) 1 and 2 only, , (d), D, , 20 Among the following compounds, which, one has the shortest C—Cl bond?, , 17 Which of the following compounds will, , Cl, , form the precipitate with aq. AgNO3, solution most readily?, Br, , (a) H3C—Cl, , N, , (c), (b), , (a), , (c), , O, , Br, , 18 The one that can exhibit highest, paramagnetic behaviour among the, following is, gly = glycinato; bpy = 2, 2′-bipyridine, (a) [Pd(gly)2 ], (b) [Fe(en)(bpy)(NH3 )2 ]2+, (c) [Co(OX)2 (OH)2 ]− (∆ 0 > P ), (d) [Ti(NH3 )6 ]3 +, , 2MnO−4 + 6H+ + 5H2O2 →, , (i)NaBH 4, , CH2 == CH CHO → [ A], (ii) SOCl 2, , Br, D, D, , (b), Br, , CH2, , 2Fe2+ + H2O2 → xA + yB, (in basic medium), , reaction sequence will be, , (a), , Cl, , 24 Consider the following equations :, , 19 The major product [C ] of the following, , Anhy. AlCl3, , (d) HC, , of Na 2CO3 ⋅ xH2O. The normality of the, solution is 0.1 N. The value of x is ……… ., (The atomic mass of Na is 23 g/mol), 22 The number of chiral centres present in, threonine is ……… ., 23 The number of molecules with energy, greater than the threshold energy for a, reaction increases five fold by a rise of, temperature from 27 °C to 42 °C. Its, energy of activation in J/mol is ……… ., (Take ln 5 = 16094, ; R = 8314, J mol −1 K −1), ., ., , (d), , Br, , H3 C, H3C——Cl, CH3, , Numerical Type Questions, 21 A 100 mL solution was made by adding 1.43 g, , OCH3, N, , CH, CH2, , Br, , N, , (b), , [B ], , DBr, , [C], , x′ C + y′ D + z′ E, (in acidic medium), The sum of the stoichiometric coefficients, x, y, x′ , y′ and z′ for products A, B, C, D and, E, respectively, is ……… ., 25 The osmotic pressure of a solution of NaCl, is 0.10 atm and that of a glucose solution, is 0.20 atm. The osmotic pressure of a, solution formed by mixing 1 L of the, sodium chloride solution with 2 L of the, glucose solution is x × 10−3 atm. x is ………, (nearest integer).
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56, , JEE Main 2020 ~ Solved Papers, , ONLINE, , MATHEMATICS, 1 If for some positive integer n, the, coefficients of three consecutive terms in, the binomial expansion of (1 + x)n + 5 are in, the ratio 5 : 10 : 14, then the largest, coefficient in this expansion is, (a) 330, (c) 792, , (b) 462, (d) 252, , 2 The circle passing through the intersection, of the circles, x2 + y2 − 6x = 0 and, x2 + y2 − 4 y = 0, having its centre on the, line, 2x − 3 y + 12 = 0, also passes through, the point, , (a) (−1, 3), (c) (1, − 3), , (b) (−3, 1), (d) (−3, 6), , x+ y+ z =2, , has infinitely many solutions, then, (b) 2λ − µ = 5, (d) λ + 2µ = 14, , 4 The minimum value of 2sin x + 2cos x is, −1 +, , (c) 2, , 1, 2, , (b) 21 −, 1−, , (d) 2, , 2, 1, 2, , 5 Let a1 , a 2 , … , a n be a given AP. Whose, common difference is an integer and, Sn = a1 + a 2 + … + a n . If a1 = 1, a n = 300, and 15 ≤ n ≤ 50, then the ordered pair, (Sn − 4 , a n − 4 ) is equal to, (a) (2490, 249), (b) (2480, 249), (c) (2480, 248), (d) (2490, 248), , 7, 18, 9, (d), 2, (b), , 8 Let f : (0, ∞) → (0, ∞) be a differentiable, function such that f (1) = e and, t 2 f 2 (x) − x2 f 2 (t ), = 0., lim, t→ x, t−x, If f (x) = 1, then x is equal to, 1, e, 1, (d), 2e, , (b), , 1, centre is at origin and its eccentricity is ., 2, If P(1, β), β > 0 is a point on this ellipse,, then the equation of the normal to it at P, is, (a) 8x − 2 y = 5, (b) 4x − 3 y = 2, (c) 7x − 4 y = 1, (d) 4x − 2 y = 1, , 10 Let, , 50, , n, , i =1, , i =1, , U X i = U Yi = T, where each X i, , contains 10 elements and each Y i contains, 5 elements. If each element of the set T is, an element of exactly 20 of sets X i ′ s and, exactly 6 of sets Y i ′ s, then n is equal to, (a) 50, (c) 45, , 6 The angle of elevation of a cloud C from a, point P, 200 m above a still lake is 30°. If, the angle of depression of the image of C in, the lake from the point P is 60°, then PC, (in m) is equal to :, (a) 100, (c) 200 3, , + 3 tan x ⋅ sin 6x) dx is equal to, 1, 9, 1, (c) −, 18, (a) −, , 9 Let x = 4 be a directrix to an ellipse whose, , 3x + 2 y + λ z = µ, , 2, , tan3 x ⋅ sin 2 3x(2 sec2 x ⋅ sin 2 3x, , (c) e, , 2x + 4 y − z = 6, , (a) 2−1 +, , π /3, , ∫π / 6, , (a) 2e, , 3 If the system of equations, , (a) 2λ + µ = 14, (c) λ − 2µ = − 5, , 7 The integral, , (b) 400, (d) 400 3, , (b) 15, (d) 30, , 11 If the perpendicular bisector of the line, segment joining the points P(1, 4) and, Q(k, 3) has y-intercept equal to −4, then a, value of k is, (a) 15, (c) 14, , (b) −4, (d) −2
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57, , SEPTEMBER ATTEMPT ~ 04 Sep 2020, Shift II, 12 Suppose the vectors x1 , x2 and x3 are the, , solutions of the system of linear equations,, Ax = b when the vector b on the right side, is equal to b1, b2 and b3 respectively. If, 1, 0, 0, 1, 0, x1 = 1, x2 = 2, x3 = 0, b1 = 0, b2 = 2, , , , , , 1, 1, 1, 0, 0, 0, and b3 = 0, then the determinant of A is, , 2, equal to, , (a), , 3, 2, , (b) 2, , (c), , 1, 2, , (d) 4, , 13 The solution of the differential equation, dy, y + 3x, + 3 = 0 is, −, dx log e ( y + 3x), , (where C is a constant of integration), (a) x − log e ( y + 3x) = C, 1, (b) y + 3x − (log e x)2 = C, 2, (c) x − 2 log e ( y + 3x) = C, 1, (d) x − (log e ( y + 3x))2 = C, 2, , plane x − y + z = 5 measured parallel to the, x y, z, is, = =, 2 3 −6, , line, , 1, 7, , (c) 7, , (b) 1, (d), , 7, 5, , 15 In a game two players A and B take turns, in throwing a pair of fair dice starting with, player A and total of scores on the two, dice, in each throw is noted. A wins the, game if he throws a total of 6 before B, throws a total of 7 and B wins the game if, he throws a total of 7 before A throws a, total of six. The game stops as soon as, either of the players wins. The probability, of A winning the game is, 31, 61, 5, (c), 31, , (a), , 30, 61, 5, (d), 6, , (b), , (2 + α )4 = a + bα, where α =, a + b is equal to, (a) 24, (c) 9, , −1 + i 3, , then, 2, , (b) 33, (d) 57, , 17 Contrapositive of the statement, ‘If a function f is differentiable at a, then it, is also continuous at a’, is, (a) If a function f is not continuous at a, then, it is differentiable at a, (b) If a function f is continuous at a, then it is, differentiable at a, (c) If a function f is continuous at a, then it is, not differentiable at a, (d) If a function f is not continuous at a, then, it is not differentiable at a, , 18 Let λ ≠ 0 be in R. If α and β are the roots of, the equation, x2 − x + 2λ = 0 and α and γ are, the roots of the equation,, βγ, is equal to, 3x2 − 10x + 27λ = 0, then, λ, , 14 The distance of the point (1, −2, 3) from the, , (a), , 16 If a and b are real numbers such that, , (a) 36, , (b) 9, , (c) 27, , (d) 18, , π, + tan −1 x |x| ≤ 1, 4, 19 The function f (x) = , is, 1, (|x| − 1), |x| > 1, 2, (a) both continuous and differentiable on, R − {1}, (b) both continuous and differentiable on, R − {−1}, (c) continuous on R − {−1} and differentiable on, R − {−1, 1}, (d) continuous on R − {1} and differentiable on, R − {−1, 1}, , 20 The area (in sq. units) of the largest, rectangle ABCD whose vertices A and B lie, on the X-axis and vertices C and D lie on, the parabola, y = x2 − 1 below the X-axis, is, 4, 3 3, 1, (c), 3 3, (a), , 2, 3 3, 4, (d), 3, (b)
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58, , JEE Main 2020 ~ Solved Papers, , ONLINE, , Numerical Type Questions, 21 Let PQ be a diameter of the circle, , 24 Let { x} and [x] denote the fractional part of, x and the greatest integer ≤ x respectively, n, n, of a real number x. If ∫ (x)dx,∫ [x]dx and, , x + y = 9. If α and β are the lengths of the, perpendiculars from P and Q on the, straight line, x + y = 2 respectively, then, the maximum value of αβ is ……… ., 22 If a = 2i$ + $j + 2k$ , then the value of, |i$ × (a × i$ )|2 + |$j × (a × $j )|2 + |k$ × (a × k$ )|2 is, 2, , 2, , 0, , 0, , 10(n 2 − n ), (n ∈ N , n > 1) are three, consecutive terms of a GP, then n is equal, to ………… ., , 25 If the variance of the following frequency, distribution :, , equal to ……… ., , 23 A test consists of 6 multiple choice, questions, each having 4 alternative, answers of which only one is correct. The, number of ways, in which a candidate, answers all six questions such that exactly, four of the answers are correct, is ……… ., , Class, , 10-20, , 20-30, , 30-40, , Frequency, , 2, , x, , 2, , is 50, then x is equal to ……… ., , Answers, Physics, 1., (a), 11. (b), 21. (198), , 2. (d), 12. (b), 22. (150), , 3., 13., 23., , (d), (b), (2), , 4., 14., 24., , (a), (d), (476), , 5., 15., 25., , (b), (b), (20), , 6. (c), 16. (a), , 7. (c), 17. (a), , 8. (b), 18. (a), , 9. (d), 19. (a), , 10. (c), 20. (d), , For Detailed Solutions, Visit : http://bit.ly/3dFmba9, Or Scan :, , Chemistry, 1. (c), 11. (c), 21. (10), , 2., 12., 22., , (a), (c), (2), , 3., (b), 13., (a), 23. (84297.47), , 4., 14., 24., , (d), (c), (19), , 5., (a), 15. (a), 25. (167), , 6. (c), 16. (b), , 7. (d), 17. (b), , 8. (a), 18. (d), , 9. (c), 19. (c), , 10. (c), 20. (b), , For Detailed Solutions, Visit : http://bit.ly/3jbinPb, Or Scan :, , Mathematics, 1., 11., 21., , (b), (b), (7), , 2., 12., 22., , (d), (b), (18), , 3. (a), 13. (d), 23. (135), , 4., 14., 24., , (d), (b), (21), , 5., 15., 25., , (d), (b), (4), , 6., 16., , (b), (c), , 7., 17., , (c), (d), , 8., 18., , (b), (d), , 9., 19., , (d), (d), , For Detailed Solutions, Visit : http://bit.ly/3j9HGAZ, Or Scan :, , 10., 20., , (d), (a)
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ONLINE QUESTION PAPER, , JEE Main 2020, (05 September, 2020), TIME 9:30-12:30 (Shift I), , MM : 300, , PHYSICS, Objective Type Questions, 1 Three different processes that can occur in, an ideal monoatomic gas are shown in the, p versus V diagram. The paths are labelled, as A → B, A → C and A → D. The change in, internal energies during these process are, taken as E AB , E AC and E AD and the, work done as W AB , W AC and W AD ., The correct relation between these, parameters are, , of a perfect monoatomic gas at some, temperature T and at a pressure of 2 cm of, mercury is close to, (Given, mean kinetic energy of a molecule, at T is 4 × 10−14 erg, g = 980 cm/s 2, density, of mercury = 136, . g/cm3 ), (a) 5.8 × 1016, (c) 4.0 × 1018, , 4 For a concave lens of focal length f, the, , f, T2, , v, =, , v, , B, , u, , T 1 >T 2, C, A, , (b) 4.0 × 1016, (d) 5.8 × 1018, , relation between object and image, distances u and v, respectively, from its, pole can best be represented by (u = v is, the reference line), , D, P, , 3 Number of molecules in a volume of 4 cm3, , (a), , V, , = EAC < EAD , WAB > 0, WAC = 0, WAD < 0, = EAC = EAD ,WAB > 0,WAC = 0, WAD > 0, < EAC < EAD , WAB > 0, WAC > WAD, > EAC > EAD , WAB < WAC < WAD, , 2 An electrical power line, having a total, resistance of 2 Ω, delivers 1 kW at 220 V., The efficiency of the transmission line is, approximately, (a) 91%, , (b) 85%, , (c) 96%, , (d) 72%, , u, , v, f, , v, , f, , =, , EAB, EAB, EAB, EAB, , u, , (a), (b), (c), (d), , (b), , f, , u
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60, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 7 A physical quantity z depends on four, , u, , =, , v, , v, f, , observables a, b, c and d, as z =, , . The, cd3, percentages of error in the measurement of, a , b, c and d are 2%, 15, . %, 4% and 25, . %, respectively. The percentage of error in z is, , (c), , u, , f, , (a) 13.5%, (c) 14.5%, , u, , f, , 8 An electron is constrained to move along, the Y -axis with a speed of 01, . c (c is the, speed of light) in the presence of, electromagnetic wave, whose electric field is, E = 30$j sin(15, . × 107 t − 5 × 10−2 x) V/m., , (d), , u, , f, , 5 A balloon is moving up in air vertically, above a point A on the ground. When it is, at a height h1, a girl standing at a distance, d (point B ) from A (see figure) sees it at an, angle 45° with respect to the vertical., When the balloon climbs up a further, height h2, it is seen at an angle 60° with, respect to the vertical if the girl moves, further by a distance 2.464 d (point C)., Then, the height h2 is, (Given, tan 30° = 05774, ., ), , h2, , d, , B, , 60º, 2.464 d, , C, , (b) d, (d) 0.732 d, , 6 A bullet of mass 5g, travelling with a, speed of 210 m/s, strikes a fixed wooden, target. One-half of its kinetic energy is, converted into heat in the bullet while the, other half is converted into heat in the, wood. The rise of temperature of the, bullet, if the specific heat of its material is, cal g −1 ° C−1, is close to, 0030, ., (a) 87.5° C, (c) 119.2° C, , (Given, c = 3 × 108 ms −1 and electron charge, . × 10−19 C), = 16, (a), (b), (c), (d), , 2.4 × 10−18 N, 4.8 × 10−19 N, 16, . × 10−19 N, 3.2 × 10−18 N, , 9 A galvanometer of resistance G is, converted into a voltmeter of range 0-1V, by connecting a resistance R1 in series with, it. The additional resistance that should be, connected in series with R1 to increase the, range of the voltmeter to 0-2V will be, (b) R1, (d) R1 − G, , 10 A wheel is rotating freely with an angular, 45º, , (a) 1464, d, ., (c) 0.464 d, , The maximum magnetic force experienced, by the electron will be, , (a) R1 + G, (c) G, , h1, , A, , (b) 16.5%, (d) 12.25%, , =, , v, , u, , a 2b2/ 3, , (b) 83.3° C, (d) 38.4° C, , speed ω on a shaft. The moment of inertia, of the wheel is I and the moment of inertia, of the shaft is negligible. Another wheel of, moment of inertia 3I initially at rest is, suddenly coupled to the same shaft. The, resultant fractional loss in the kinetic, energy of the system is, (a), , 3, 4, , (c) 0, , 5, 6, 1, (d), 4, (b), , 11 Two capacitors of capacitances C and 2C, are charged to potential differences V and, 2V respectively. These are then connected, in parallel in such a manner that the, positive terminal of one is connected to the
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61, , SEPTEMBER ATTEMPT ~ 05 Sep 2020, Shift I, In R, , negative terminal of the other. The final, energy of this configuration is, 9, CV 2, 2, 25, (c), CV 2, 6, , (a), , (b), , 6, , 3, CV 2, 2, , 4, 2, , (d) zero, , 0, , 12 The value of the acceleration due to gravity, R, (where, R = radius of, 2, the earth) from the surface of the earth. It, is again equal to g1 at a depth d below the, d, surface of the earth. The ratio equals, R, is g1 at a height h =, , 7, 9, 4, (c), 9, , 1, 3, 5, (d), 9, , (b), , (a), , 13 A helicopter rises from rest on the ground, vertically upwards with a constant, acceleration g. A food packet is dropped, from the helicopter when it is at a height, h. The time taken by the packet to reach, the ground is close to (Here, g is the, acceleration due to gravity)., (a) t =, , 2 h, 3 g, , (b) t = 18, ., , h, g, , (c) t =, , 2h, 3g, , (d) t = 3.4, , h, g, , 14 A square loop of side 2a and carrying, current I is kept in xy-plane with its centre, at origin. A long wire carrying the same, current I is placed parallel to the Z-axis, and passing through the point (0, b, 0),, (b >> a ). The magnitude of the torque on, the loop about Z-axis is given by, (a), , 2 µ 0 I 2a3, , (c), , µ 0 I 2a3, , πb, , 2, , 2 πb, , 2, , (b), , 2 µ 0 I 2a 2, πb, , (d), , µ 0 I 2a 2, 2 πb, , 15 Activities of three radioactive substances, A, B and C are represented by the curves, A, B and C in the figure. Then, their, half-lives T1/ 2 ( A): T1/ 2 (B): T1/ 2 (C ) are in the, ratio, , (a) 4 : 3 : 1, (c) 2 : 1 : 1, , A, C, , B, 5, , 10, , t, (yr), , (b) 3 : 2 : 1, (d) 2 : 1 : 3, , 16 In a resonance tube experiment, when the, tube is filled with water up to a height of, 17.0 cm from bottom, it resonates with a, given tuning fork. When the water level is, raised, the next resonance with the same, tuning fork occurs at a height of 245, . cm. If, the velocity of sound in air is 330 m/s, the, tuning fork frequency is, (a) 1100 Hz, (c) 2200 Hz, , (b) 3300 Hz, (d) 550 Hz, , 17 Assume that the displacement of air is, , proportional to the pressure difference ∆p, created by a sound wave. Displacement, further depends on the speed of sound v,, density of air ρ and the frequency f. If, ∆p ~ 10Pa, v ~ 300 m/s, ρ ∼ 1 kg/m3 and, f ~ 1000 Hz, then s will be of the order of, (Take the multiplicative constant to be 1.), , (a) 10 mm, 1, mm, (c), 10, , (b) 1 mm, 3, mm, 100, , (d), , 18 With increasing biasing voltage of a, photodiode, the photocurrent magnitude, (a) increases initially and after attaining, certain value, it decreases, (b) increases initially and saturates finally, (c) remains constant, (d) increases linearly, , 19 A hollow spherical shell at outer radius R, floats just submerged under the water, surface. The inner radius of the shell is r., If the specific gravity of the shell material, 27, with respect to water, the value of r is, is, 8, 8, R, 9, 2, (c) R, 3, (a), , 1, R, 3, 4, (d) R, 9, (b)
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62, , ONLINE, , 20 A solid sphere of radius R carries a charge, Q + q distributed uniformly over its, volume. A very small point-like piece of it, of mass m gets detached from the bottom of, the sphere and falls down vertically under, gravity. This piece carries charge q. If it, acquires a speed v when it has fallen, through a vertical height y (see figure),, then (Assume the remaining portion to be, spherical.), , Q, , R, , q, , y, v, , JEE Main 2020 ~ Solved Papers, , The first maximum intensity occurs at, θ = 60°. Then, E (in eV) is …… ., (Given, Planck’s constant, h = 664, . × 10−34 Js,, 1 eV = 16, . × 10−19 J and, electron mass, m = 91, . × 10−31 kg, , 22 A compound microscope consists of an, objective lens of focal length 1 cm and an, eye piece of focal length 5 cm with a, separation of 10 cm. The distance between, an object and the objective lens, at which, n, the strain on the eye is minimum is, cm., 40, The value of n is …… ., , 23 A particle of mass 200 MeV/c 2 collides, with a hydrogen atom at rest. Soon after, the collision, the particle comes to rest and, the atom recoils and goes to its first, excited state. The initial kinetic energy of, N, the particle (in eV) is . The value of N, 4, is ……… ., (Given, the mass of the hydrogen atom to, be 1 GeV/c 2), , , , qQ, (a) v2 = y , + g, 2, 4 πε0 R ym, , , , qQ, (b) v2 = 2 y , + g, , 4 πε0 R (R + y)m, , , qQ, 2, (c) v = y , + g, , 4 πε0 R (R + y)m, , , qQR, 2, (d) v = 2 y , + g, 3, , 4 πε0 (R + y) m, , Numerical Type Questions, 21 A beam of electrons of energy E scatters, from a target having atomic spacing of 1Å., , 24 Two concentric circular coils C1 and C 2 are, placed in the xy-plane. C1 has 500 turns, and radius of 1 cm. C 2 has 200 turns and, radius of 20 cm. C 2 carries a time, dependent current I (t ) = (5t 2 − 2t + 3)A,, where t is in second. The emf induced in C1, 4, (in mV), at the instant t = 1 s is . The, x, value of x is …… ., $ ) N acts at a point, 25 A force F = (i$ + 2$j + 3k, $, $, $, (4i + 3 j − k) m. Then, the magnitude of, $ )m will be, torque about the point ($i + 2$j + k, x N-m. The value of x is …… .
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63, , SEPTEMBER ATTEMPT ~ 05 Sep 2020, Shift I, , CHEMISTRY, 1 The condition that indicates a polluted, environment is, (a) pH of rain water to be 5.6, (b) eutrophication, (c) BOD value of 5 ppm, (d) 0.03% of CO 2 in the atmosphere, , 2 The potential energy curve for the H2, molecule as a function of internuclear, distance is, Energy, , 4 Consider the following reaction:, N2O4 ( g) q, , 2NO2 ( g); ∆H ° = + 58 kJ, , For each of the following cases (A, B ), the, direction in which the equilibrium shifts is, (A) temperature is decreased., (B) pressure is increased by adding N2 at, constant T., (a), (b), (c), (d), , (A) towards product, (B) towards reactant, (A) towards reactant, (B) no change, (A) towards reactant, (B) towards product, (A) towards product, (B) no change, , 5 A diatomic molecule X 2 has a body-centred, , (a), Internuclear, distance, Energy, , cubic (bcc) structure with a cell edge of, 300 pm. The density of the molecule is, 6.17 g cm −3 . The number of molecules, present in 200 g of X 2 is, (Avogadro constant (N A ) = 6 × 1023 mol −1), (b) 2N A, (d) 4N A, , (a) 40N A, (c) 8N A, , (b), Internuclear, distance, , 6 In the sixth period, the orbitals that are, filled are, (a) 6s, 5f , 6d , 6 p, (c) 6s, 5d , 5f , 6 p, , Energy, , (c), , (b) 6s, 4f , 5d , 6 p, (d) 6s, 6 p , 6d , 6f, , 7 The most appropriate reagent for, Internuclear, distance, Energy, , conversion of C2H5CN into CH3CH2CH2NH2, is, (a) Na(CN)BH3, (c) NaBH4, , (b) LiAlH4, (d) CaH2, , 8 The increasing order of the acidity of the, , (d), , α-hydrogen of the following compounds is, Internuclear, distance, , O, , 3 The values of the crystal field stabilisation, , (A), , (B ), , O, , O, , (d) −0.4∆ 0 and −0.6∆ t, , Ph, , OMe, , (a) −0.4∆ 0 and −0.27∆ t, (c) −2.4∆ 0 and −0.6∆ t, , O, , Ph, , energies for a high spin d 6 metal ion in, octahedral and tetrahedral fields, respectively, are, (b) −1.6∆ 0 and −0.4∆ t, , O, , (C), , (a), (b), (c), (d), , (D ) < (C ) < (A ) < (B ), (C ) < (A ) < (B ) < (D ), (A ) < (C ) < (D ) < (B ), (B ) < (C ) < (A ) < (D ), , NMe2, (D)
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64, , ONLINE, , 9 The structure of PCl5 in the solid state is, +, , −, , (a) tetrahedral [PCl 4 ] and octahedral [PCl 6 ], (b) trigonal bipyramidal, (c) square planar [PCl 4 ]+ and octahedral, [PCl 6 ]−, (d) square pyramidal, , 10 The equation that represents the, water-gas shift reaction is, 1270 K, , (a) C(s) + H2O( g ) ———→ CO( g ) + H2 ( g ), , JEE Main 2020 ~ Solved Papers, , (d) the conditions of pH and potential under, which a species is thermodynamically, stable., , 15 The correct electronic configuration and, , spin-only magnetic moment (BM) of Gd3 +, (Z = 64), respectively, are, , (a), (b), (c), (d), , [Xe] 4f 7 and 7.9, [Xe] 5f 7 and 7.9, [Xe] 5f 7 and 8.9, [Xe] 4f 7 and 8.9, , 16 Which of the following derivative of, , 1273 K, , (b) 2C(s) + O2 ( g ) + 4N2 ( g ) ———→, 2 CO( g ) + 4N2 ( g ), 673 K, , (c) CO( g ) + H2O( g ) ———→ CO2 ( g ) + H2 ( g ), Catalyst, , alcohols is unstable in an aqueous base?, (b) RO, , (a), O, , RO, 1270 K, , (d) CH4 ( g ) + H2O( g ) ———→ CO( g ) + 3H2 ( g ), , O, , Ni, , 11 Which of the following is not an essential, , (c), , amino acid?, (a) Leucine, (c) Lysine, , following compounds is, N, , (A), , (a), (b), (c), (d), , N, , N, , N, , H, , H, , H, , (B), , (C), , (D), , (A) < (B) < (C) < (D), (D) < (A) < (B) < (C), (B) < (A) < (D) < (C), (B) < (A) < (C) < (D), , 13 The difference between the radii of 3rd and, 4th orbits of Li2+ is ∆R1. The difference, between the radii of 3rd and 4th orbits of, He+ is ∆R2. Ratio ∆R1 : ∆R2 is, , (a) 3 : 2, (c) 2 : 3, , Me, , 17 A flask contains a mixture of compounds A, , (b) Valine, (d) Tyrosine, , 12 The increasing order of basicity of the, , N, , (d) RO—CMe3, RO, , (b) 8 : 3, (d) 3 : 8, , 14 An Ellingham diagram provides information, , and B. Both compounds decompose by, first-order kinetics. The half-life for A and, B are 300 s and 180 s, respectively. If the, concentrations of A and B are equal, initially, the time required for the, concentration of A to be four times that of, B (in s) is (Use ln 2 = 0693, . ), (a) 120, (c) 300, , (b) 180, (d) 900, , 18 If a person is suffering from the deficiency, of nor-adrenaline, what kind of drug can, be suggested?, (a) Antihistamine, (c) Antidepressant, , (b) Analgesic, (d) Anti-inflammatory, , 19 Identify the correct molecular picture, showing what happens at the critical, micellar concentration (CMC) of an, aqueous solution of a surfactant ( polar, head; ~~ non-polar tail; • water)., (A), , (B), , (C), , (D), , (a) (C ), (c) (D ), , (b) (B ), (d) (A ), , about, (a) the kinetics of the reduction process., (b) the pressure dependence of the standard, electrode potentials of reduction reactions, involved in the extraction of metals., (c) the temperature dependence of the, standard Gibbs energies of formation of, some metal oxides.
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65, , SEPTEMBER ATTEMPT ~ 05 Sep 2020, Shift I, , Numerical Type Questions, 21 The total number of coordination sites in, , 20 In the following reaction sequence the, major products A and B are, , ethylenediaminetetraacetate [EDTA 4− ] is, …… ., , O, +, , O, , Anhydrous, AlCl3, , A, , 22 A soft drink was bottled with a partial, , (1) Zn–Hg/HCl, (2) H3PO4, , O, , B, , O, (a) A =, , ;B=, CO2H, , O, , O, (b) A =, , (First dissociation constant of, . × 10−7 ) log 2 = 03, . ; density of the, H2CO3 = 40, , ;B=, , soft drink = 1 g mL −1), , CO2H, , 23 An oxidation-reduction reaction in which, 3 electrons are transferred has a ∆G° of, °, 1737, . kJ mol −1 at 25° C. The value of E cell, , O, (c) A =, , pressure of CO2 of 3 bar over the liquid at, room temperature. The partial pressure of, CO2 over the solution approaches a value, of 30 bar when 44 g of CO2 is dissolved in, 1 kg of water at room temperature. The, approximate pH of the soft drink is, …… ×10−1., , (in V) is …… ×10−2., , ;B=, , (1 F = 96,500 C mol −1), , CO2H, , O, , O, , 24 The number of chiral carbon(s) present in, peptide, Ile-Arg-Pro, is …… ., , (d) A =, , ;B=, CO2H, , 25 The minimum number of moles of O2, O, , required for complete combustion of 1 mole, of propane and 2 moles of butane is …… ., , MATHEMATICS, 1 The mean and variance of 7 observations, are 8 and 16, respectively. If five, observations are 2, 4, 10, 12, 14, then the, absolute difference of the remaining two, observations is, (a) 1, (c) 4, , (b) 3, (d) 2, , 2 If the coordinates of two points A and B, are ( 7 , 0) and (− 7 , 0) respectively and P, is any point on the conic, 9x2 + 16 y2 = 144,, then PA + PB is equal to, (a) 16, (c) 6, , (b) 8, (d) 9, , 3 The product of the roots of the equation, 9x2 − 18|x|+ 5 = 0, is, (a), , 5, 27, , (b), , 25, 9, , (c), , 5, 9, , (d), , 25, 81, , 4 If 32sin 2α −1, 14 and 34− 2sin 2α are the first, three terms of an AP for some α, then the, sixth term of this AP is, (a) 81, , (b) 65, , (c) 78, , (d) 66, , 5 If 2 + 2 ⋅ 3 + 2 ⋅ 3 + .... + 2 ⋅ 3 + 310, 10, , 9, , 1, , 8, , 2, , 9, , = S − 211, then S is equal to, 311, + 210, 2, (c) 2 ⋅ 311, , (a), , (b) 311, (d) 311 − 212
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66, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 6 If ∫ (e2x + 2ex − e− x − 1)e( e, , x, , + e−x ), , 12 If α is the positive root of the equation,, , dx, , −x, , = g(x)e( e + e ) + c, where c is a constant of, integration, then g(0) is equal to, x, , (a) 2, , (b) e2, , (c) e, , (d) 1, , (a), , 7 If the minimum and the maximum values, π π , of the function f : , → R,, 4 2 , − sin θ, , 1, , defined by f (θ ) = − cos2 θ −1 − cos2 θ 1, 12, 10, −2, are m and M respectively, then the ordered, pair (m, M ) is equal to, (b) (−4, 4), , (c) (0, 4), , (d) (−4, 0), , x ↔~ y is equivalent to, (a) (~ x ∧ y) ∨ (~ x∧ ~ y), (b) (x ∧ y) ∨ (~ x∧ ~ y), (d) (x ∧ y) ∧ (~ x∨ ~ y), , 9 If the volume of a parallelopiped, whose, coterminus edges are given by the vectors, $ , b = 2$i + 4$j − nk, $ and, a = $i + $j + nk, $ (n ≥ 0), is 158 cu units, then, c = i$ + n$j + 3k, (a) n = 9, , (b) b ⋅ c = 10, , (c) a ⋅ c = 17, , (d) n = 7, , series, 1, 1, 1, tan −1 + tan −1 + tan −1 , 3, 7, 13, , 11 The value of ∫, π, 2, , (c) π, , π/2, −π/ 2 1, , (c), , 10, 11, , 1, + esin x, , dx is, , π, 4, 3π, (d), 2, , (b), , (d), , 3, 2, , (b) 21, , (c) 48, , (d) 36, , 14 If (a , b, c) is the image of the point, (1, 2, − 3) in the line, a + b + c is equal to, (a) 3, , (b) 2, , x+ 1 y−3, z, = , then, =, 2, −2, −1, (c) −1, , (d) 1, , working in an office like coffee, whereas, 65% like tea. If x denotes the percentage of, them, who like both coffee and tea, then x, cannot be, , (d), , (b) 38, , (c) 36, , (d) 54, , k (x − π )2 − 1, x ≤ π, 16 If the function f (x) = 1, x>π, k2 cos x,, is twice differentiable, then the ordered, pair (k1 , k2 ) is equal to, , 1, (a) (1, 1) (b) , 1, 2 , , 1, (c) (1, 0) (d) , − 1, 2, , , y2 = 4x and x2 = 4 y also touches the circle,, x2 + y2 = c2, then c is equal to, 1, 2, , (b), , 1, 4, , (c), , 1, 2, , (d), , 1, 2 2, , 18 If the four complex numbers z, z, z − 2 Re( z ), , 1, + tan −1 + .... , then tan(S) is equal to, 21, , (a), , (a) 29, , (a), , 5, 6, , 3, 2, , 17 If the common tangent of the parabolas,, , 10 If S is the sum of the first 10 terms of the, , (b), , (c), , 13 If the point P on the curve, 4x2 + 5 y2 = 20 is, , (a) 63, , (c) (x∧ ~ y) ∨ (~ x ∧ y), , 6, 5, , 1, 2, , 15 A survey shows that 73% of the persons, , 8 The negation of the Boolean expression, , (a), , (b), , is equal to, 2, , (a) (0, 2 2 ), , 1, 2, , farthest from the point Q(0, − 4), then PQ 2, , −1 − sin θ, , 2, , p(x) = x2 − x − 2 = 0, then, 1 − cos( p(x)), is equal to, lim, +, x+ α −4, x→ α, , 5, 11, , and z − 2 Re(z) represent the vertices of a, square of side 4 units in the argand plane,, then|z|is equal to, (a) 4 2, , (b) 2, , (c) 2 2, , (d) 4, , 19 If y = y(x) is the solution of the differential, 5 + ex dy, ⋅, + ex = 0 satisfying, 2 + y dx, y(0) = 1, then a value of y(log e 13) is, , equation, (a) 0, , (b) −1, , (c) 1, , (d) 2
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67, , SEPTEMBER ATTEMPT ~ 05 Sep 2020, Shift I, 20 Let λ ∈R. The system of linear equations, , 4 letters at a time from the letters of the, work ‘SYLLABUS’ such that two letters are, distinct and two letters are alike, is …… ., , 2x1 − 4x2 + λx3 = 1, x1 − 6x2 + x3 = 2, , λx1 − 10x2 + 4x3 = 3, , 23 The natural number m, for which the, coefficient of x in the binomial expansion of, 22, 1, m, x + 2 is 1540, is …… ., , x , , is inconsistent for, (a), (b), (c), (d), , exactly two values of λ, exactly one positive value of λ, every value of λ, exactly one negative value of λ, , 1, 5, , 24 If the line, 2x − y + 3 = 0 is at a distance, , 2, from the lines 4x − 2 y + α = 0 and, 5, 6x − 3 y + β = 0, respectively, then the sum, of all possible values of α and β is …… ., , Numerical Type Questions, , and, , x, 21 Let f (x) = x , for −10 < x < 10, where [t ], 2 , denotes the greatest integer function., Then, the number of points of, discontinuity of f is equal to …… ., , 25 Four fair dice are thrown independently, 27 times. Then, the expected number of, times, at least two dice show up a three or, a five, is …… ., , 22 The number of words, with or without, meaning, that can be formed by taking, , Answers, Physics, 1., 11., 21., , (*), (b), (50), , 2. (c), 12. (d), 22. (50), , 3., 13., 23., , (c), (d), (51), , (b), (b), (5), , 4., 14., 24., , 5., 15., 25., , (b), (d), (195), , 6. (a), 16. (c), , 7. (c), 17. (d), , 8. (b), 18. (b), , 9. (a), 19. (d), , 10. (a), 20. (d), , For Detailed Solutions, Visit : http://bit.ly/2FENPaG, Or Scan :, , Chemistry, 1., 11., 21., , (b), (d), (6), , 2., 12., 22., , (c), (c), (37), , 3., 13., 23., , (d), (c), (–6), , 4., 14., 24., , (b), (c), (4), , 5., 15., 25., , (d), (a), (18), , 6., 16., , (b), (c), , 7., 17., , (b), (d), , 8., 18., , (a), (c), , 9., 19., , (a), (d), , 10., 20., , (c), (d), , For Detailed Solutions, Visit : http://bit.ly/3dC354S, Or Scan :, , Mathematics, 1. (d), 11. (a), 21. (8.00), , 2., (b), 12., (c), 22. (240.00), , 3., (d), 13. (d), 23. (13.00), , Note (*) None of the option is correct., , 4., (d), 14., (b), 24. (30.00), , 5., (b), 15., (c), 25. (11.00), , 6. (a), 16. (b), , 7. (d), 17. (a), , 8. (b), 18. (c), , 9. (b), 19. (b), , For Detailed Solutions, Visit : http://bit.ly/31r6vma, Or Scan :, , 10. (b), 20. (d)
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ONLINE QUESTION PAPER, , JEE Main 2020, (05 September, 2020), TIME 2:30-5:30 (Shift II), , MM : 300, , PHYSICS, Objective Type Questions, 1 A spaceship in space sweeps stationary, interplanetary dust. As a result, its mass, dM (t ), increases at a rate, = bv2 (t ), where v(t ), dt, is its instantaneous velocity. The, instantaneous acceleration of the satellite is, (a) −bv3 (t ), (c) −, , 2bv3, M (t ), , bv3, M (t ), bv3, (d) −, 2M (t ), , (b) −, , 2 Ten charges are placed on the circumference, , 3 An infinitely long straight wire carrying, current I, one side opened rectangular, loop and a conductor C with a sliding, connector are located in the same plane,, as shown in the figure. The connector has, length l and resistance R. It slides to the, right with a velocity v. The resistance of, the conductor and the self-inductance of, the loop are negligible. The induced, current in the loop, as a function of, separation r between the connector and, the straight wire is, , of a circle of radius R with constant angular, separation between successive charges., Alternate charges 1, 3, 5, 7, 9 have charge, +q each, while 2, 4, 6, 8, 10 have charge −q, each. The potential V and the electric field E, at the centre of the circle respectively, are, (Take, V = 0 at infinity), 10q, ;E=0, 4 π ε0 R, 10q, (b) V = 0 ; E =, 4 π ε0 R 2, , One side opened long, conducting wire loop, , C, R, , I, , v, l, , r, , (a) V =, , (c) V = 0 ; E = 0, 10q, 10q, (d) V =, ;E=, 4 π ε0 R, 4 π ε0 R 2, , µ 0 Ivl, 4 π Rr, 2 µ 0 Ivl, (c), π Rr, (a), , µ 0 Ivl, π Rr, µ 0 Ivl, (d), 2 π Rr, , (b)
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69, , SEPTEMBER ATTEMPT ~ 05 Sep 2020, Shift II, 4 In the circuit shown, charge on the 5µF, capacitor is, , 2 µF, , L2 and respective temperature coefficients, of linear expansion α1 and α 2, are joined, end-to-end. Then the effective temperature, coefficient of linear expansion is, , 4 µF, , α1 L1 + α 2L2, L1 + L2, α1 + α 2, (c), 2, , 5 µF, , 6V, , (b) 10.90 µC, (d) 5.45 µC, , (d) 4, , detecting the null point in electrical, experiments. If on passing a current of, 6 mA, it produces a deflection of 2°, its, figure of merit is close to, , motion is shown in the figure. The point S, is at 4.333 s. The total distance covered by, the body in 6 s is, v (in m/s) 4, , (b) 6 × 10−3 A/div, (d) 3 × 10−3 A/div, , A, , B, , 2, , 3, , 2, 0, , 6 The correct match between the entries in, , –2, , S, 1, , 4, , (A) Microwaves, , Column II, (Wavelength), (I), , 100 m, −15, , (B) γ-rays, , (II) 10, , (C) AM radiowaves, , (III) 10−10 m, , (D) X-rays, , (IV) 10−3 m, , A, (a) II, (c) III, , B, I, II, , C D, IV III, I IV, , A, (b) I, (d) IV, , C, IV, I, , D, II, III, , produce sound waves of the same, wavelength λ = 1 m, in phase. S1 and S2 are, placed 1.5 m apart (see figure). A listener,, located at L, directly in front of S2 finds, that the intensity is at a minimum when, he is 2 m away from S2. The listener moves, away from S1, keeping his distance from S2, fixed. The adjacent maximum of intensity, is observed when the listener is at a, distance d from S1. Then, d is, 2m, 2m, , L, , d, , (d), , 49, m, 4, , small spherical ball of radius r and density, ρ falls under gravity through a distance h, in air before entering a tank of water. If, the terminal velocity of the ball inside, water is same as its velocity just before, entering the water surface, then the value, of h is proportional to, (Ignore viscosity of air), (a) r 4, (c) r3, , (b) r, (d) r 2, , 11 A parallel plate capacitor has plate of, length l, width w and separation of plates, is d. It is connected to a battery of emf V . A, dielectric slab of the same thickness d and, of dielectric constant k = 4 is being inserted, between the plates of the capacitor. At, what length of the slab inside plates, will, the energy stored in the capacitor be two, times the initial energy stored?, 2l, 3, , (b), , l, 3, , (c), , l, 4, , (d), , l, 2, , 12 A driver in a car, approaching a vertical, , S1, , (b) 5 m, , (c) 11 m, , (a), , 1.5 m, , (a) 12 m, , (b) 12 m, , 10 In an experiment to verify Stoke’s law, a, , 7 Two coherent sources of sound S1 and S2,, , S2, , t (in s), , 6, , C, , 37, m, (a), 3, , m, , B, III, II, , D, 5, , table are :, Column I, (Radiation), , L2L1, α1α 2, α1 + α 2 (L2 + L1 )2, , 9 The v-t graph of a body in a straight line, , 5 A galvanometer is used in laboratory for, , (a) 333° A/div, (c) 666° A/div, , (b) 2 α1α 2, , (a), , 6V, , (a) 18.00 µC, (c) 16.36 µC, , 8 Two different wires having lengths L1 and, , (c) 2 m, , (d) 3 m, , wall notices that the frequency of his car, horn, has changed from 440 Hz to 480 Hz,, when it gets reflected from the wall. If the
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70, , ONLINE, speed of sound in air is 345 m/s, then the, speed of the car is, (a) 54 km/h, (c) 18 km/h, , (b) 36 km/h, (d) 24 km/h, , 13 A ring is hung on a nail. It can oscillate, without slipping or sliding, (i) in its plane with a time period T1 and, (ii) back and forth in a direction, perpendicular to its plane, with a period, T2., T, The ratio 1 will be, T2, 2, 3, , (a), , (b), , 2, 3, , 3, 2, , (c), , (d), , 2, 3, , 14 Two zener diodes (A and B) having breakdown, voltages of 6 V and 4 V respectively, are, connected as shown in the circuit below. The, output voltage Vout variation with input, voltage linearly increasing with time, is, given by (Vin = 0 V at t = 0), (figures are qualitative), A, Vin, , 6V, , B, , RL=400 Ω, , 4V, , JEE Main 2020 ~ Solved Papers, , 15 A radioactive nucleus decays by two, different processes. The half-life for the, first process is 10 s and that for the, second is 100 s. The effective half-life of, the nucleus is close to, (a) 9 s, , (b) 6 s, , (c) 55 s, , (d) 12 s, , E, 1, , y = and, 16 The quantities x =, B, µ 0ε 0, l, are defined, where C is, z=, CR, capacitance, R is resistance, l is length,, E is electric field, B is magnetic field, ε 0, is free space permittivity and µ 0 is, permeability, respectively. Then,, (a), (b), (c), (d), , x, y and z have the same dimension, Only x and z have the same dimension, Only x and y have the same dimension, Only y and z have the same dimension, , 17 In an adiabatic process, the density of a, diatomic gas becomes 32 times of its, initial value. The final pressure of the, gas is found to be n times the initial, pressure. The value of n is, (a) 32, , (b) 326, , (c) 128, , (d), , Vout, , 100 Ω, , 1, 32, , 18 The acceleration due to gravity on the, , Vout, 4V, , (a), Time, , 6V, , Vout, , 4V, , (b), , earth’s surface at the poles is g and, angular velocity of the earth about the, axis passing through the pole is ω. An, object is weighed at the equator and at a, height h above the poles by using a, spring balance. If the weights are found, to be same, then h is (h << R, where R is, the radius of the earth), (a), , R 2ω2, 2g, , (b), , R 2ω2, g, , (c), , R 2ω2, 4g, , (d), , R 2ω2, 8g, , 19 In the given circuit, currents in different, Time, , branches and value of one resistor are, shown. Then, potential at point B with, respect to the point A is, , 6V, , Vout, , 4V, , (c), , 2V, D, , E, 1A, , Time, , 2Ω, , 6V, , Vout, , A, , (d), , 1V, , Time, , B, , (a) +2 V, , C, , (b) −2 V, , 2A, , (c) −1V, , F, , (d) +1V
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71, , SEPTEMBER ATTEMPT ~ 05 Sep 2020, Shift II, 20 An iron rod of volume 10−3 m3 and relative, permeability 1000 is placed as core in a, solenoid with 10 turns/cm. If a current of, 0.5 A is passed through the solenoid, then, the magnetic moment of the rod will be, (a) 50 × 102 Am 2, (c) 500 × 102 Am 2, , (b) 5 × 102 Am 2, (d) 0.5 × 102 Am 2, , Numerical Type Questions, 21 A body of mass 2 kg is driven by an engine, delivering a constant power of 1 J/s. The, body starts from rest and moves in a, straight line. After 9 s, the body has moved, a distance (in m) ……… ., , 22 Nitrogen gas is at 300°C temperature. The, , 24 The surface of a metal is illuminated, , alternately with photons of energies E1 = 4 eV, and E 2 = 25, . eV respectively. The ratio of, maximum speeds of the photoelectrons, emitted in the two cases is 2. The work, function of the metal (in eV) is ……… ., , 25 A thin rod of mass 0.9 kg and length 1 m is, suspended at rest from one end, so that it, can freely oscillate in the vertical plane., A particle of mass 0.1 kg moving in a, straight line with velocity 80 m/s hits the, rod at its bottom-most point and sticks to, it (see figure). The angular speed (in rad/s), of the rod immediately after the collision, will be ………, , temperature (in K) at which the rms speed, of a H2 molecule would be equal to the rms, speed of a N2 molecule is ………, (Molar mass of N2 gas is 28 g.), , 1m, , 23 A prism of angle A = 1° has a refractive, v, , index µ = 15, . . A good estimate for the, minimum angle of deviation (in degree) is, close to N/10. Value of N is ……… ., , CHEMISTRY, Objective Type Questions, 1 The final major product of the following, reaction is, , CH2, , CHCl, , (a), , Me, , (b), , CH3, , (i) Ac2O/Pyridine, (ii) Br2, FeCl3, (iii) OH–/∆, , Cl, CHCl, , CHCl, , NH2, , Me, , Me, , Br, , Br, NH2, , NH2, Br, , Me, (c), , (d), , H3C, , (b), , (a), , (c), , Me, , CH3, , 3 Adsorption of a gas follows Freundlich, adsorption isotherm. If x is the mass of the, gas adsorbed on mass m of the adsorbent,, x, the correct plot of versus p is, m, , (d), , Br, , 200 K, , NH2, , NH2, , x, (a) m, , 250 K, 270 K, , 2 Among the following compounds,, geometrical isomerism is exhibited by, , p
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72, , JEE Main 2020 ~ Solved Papers, , ONLINE, 270 K, 250 K, , x, (b) m, , 200 K, p, 200 K, 250 K, , x, (c) m, , 700 K, , 7 The correct order of the ionic radii of O2− ,, N3 − , F− , Mg 2+ , Na + and Al3 + is, , (a), (b), (c), (d), , N3 − < O2− < F− < Na + < Mg 2+ < Al3 +, Al3 + < Na + < Mg 2+ < O2− < F− < N3 −, Al3 + < Mg 2+ < Na + < F− < O2− < N3 −, N3 − < F− < O2− < Mg 2+ < Na + < Al3 +, , 8 Which one of the following polymers is not, obtained by condensation polymerisation?, (a) Nylon 6, 6, (c) Bakelite, , p, , (b) Buna-N, (d) Nylon 6, , 9 The major product of the following reaction, 270 K, , is, HO, , x, (d) m, , CH2CH3, , 250 K, 200 K, , H2SO4, , O, , p, , 4 An element crystallises in a face-centred, cubic (fcc) unit cell with cell edge a. The, distance between the centres of two, nearest octahedral voids in the crystal, lattice is, (a), , a, 2, , (b) a, , (c), , 2a, , (d), , (a) both (A) and (B) cannot be optically active, , (b) (A) can be optically active, but (B) cannot, be optically active, (c) both (A) and (B) can be optically active, , (d) (A) cannot be optically active, but (B) can, be optically active, , 6 The increasing order of boiling points of, the following compounds is, OH, , (b), , O, , O, , CH==CH2, , CHCH3, (d), , O, , [Co(en)2Cl2 ]+ (A) and cis-[Co(en)2Cl2 ]+ (B)., The correct statement regarding them is, , OH, , (a), , (c), , a, 2, , 5 Consider the complex ions, trans-, , OH, , CH2CH3, , CH2CH3, , O, , 10 Hydrogen peroxide, in the pure state, is, (a), (b), (c), (d), , non-planar and almost colourless, linear and blue in colour, linear and almost colourless, planar and blue in colour, , 11 The rate constant (k) of a reaction is, measured at different temperature (T ), and, the data are plotted in the given figure., The activation energy of the reaction in, kJ mol −1 is (R is gas constant), , OH, , 10, In k, 5, , (a), (b), (c), (d), , CH3, , NO2, , (I), , (II), , I < III < IV < II, I < IV < III < II, IV < I < II < III, III < I < II < IV, , NH2, (III), , OCH3, (IV), , 0, , (a), , 2, R, , 1, , (b), , 2 3, 103/T, , 1, R, , 4, , (c) R, , 5, , (d) 2R
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73, , SEPTEMBER ATTEMPT ~ 05 Sep 2020, Shift II, 12 Lattice enthalpy and enthalpy of solution, of NaCl are 788 kJ mol −1 and 4 kJ mol −1,, respectively. The hydration enthalpy of, NaCl is, , (a) −780 kJ mol −1, (c) −784 kJ mol −1, , (b) 780 kJ mol −1, (d) 784 kJ mol −1, , The electrolyte X is, (a) HCl, (c) KNO3, , (b) NaCl, (d) CH3 COOH, , 19 The following molecule acts as an, N, , 13 The one that is not suitable for the, , N, , (CH2)2, , removal of permanent hardness of water is, (a), (b), (c), (d), , 14 The compound that has the largest, , H M H bond angle (M = N, O, S, C) is, , (a) H2O, , (b) NH3, , (c) H2S, , (d) CH4, , 15 Boron and silicon of very high purity can, be obtained through, (a), (b), (c), (d), , liquation, zone refining, vapour phase refining, electrolytic refining, , 16 The correct statement about probability, density (except at infinite distance from, nucleus) is, (a), (b), (c), (d), , it can be zero for 1s orbital, it can be negative for 2p orbital, it can be zero for 3p orbital, it can never be zero for 2s orbital, , 17 The major product formed in the following, reaction is, HBr, , CH3CH == CHCH(CH3 )2 →, (a), (b), (c), (d), , (Brompheniramine), , Clark’s method, Ion-exchange method, Calgon’s method, Treatment with sodium carbonate, , CH3 CH(Br)CH2CH(CH3 )2, CH3 CH2CH(Br)CH(CH3 )2, Br(CH2 )3 CH(CH3 )2, CH3 CH2CH2C(Br)(CH3 )2, , 18 The variation of molar conductivity with, concentration of an electrolyte (X ) in, aqueous solution is shown in the given, figure., , Molar, Conductivity, , Br, , (a) antiseptic, (c) anti-bacterial, , (b) anti-depressant, (d) anti-histamine, , 20 Reaction of ammonia with excess Cl2 gives, (a), (b), (c), (d), , NH4 Cl and N2, NH4 Cl and HCl, NCl3 and NH4 Cl, NCl3 and HCl, , Numerical Type Questions, 21 The volume, in mL, of 0.02 M K 2Cr2O7, solution required to react with 0.288 g of, ferrous oxalate in acidic medium is …… ., (Molar mass of Fe = 56 g mol −1), , 22 For a dimerisation reaction, 2 A( g) → A2 ( g),, at 298 K, ∆U s = − 20 kJ mol −1,, ∆S È = − 30 JK −1 mol −1, then the ∆Gs will, be ……… J., , 23 Considering that ∆ 0 > P, the magnetic, moment (in BM) of [Ru(H2O)6 ]2+ would be, ……… ., , 24 For a reaction,, X + Y = 2Z, 1.0 mol of X, 1.5 mol ofY , and 0.5 mol of Z ,, were taken in a 1 L vessel and allowed to, react. At equilibrium, the concentration of, Z was 1.0 mol L−1. The equilibrium, x, constant of the reaction is ……… . The, 15, value of x is ……… ., , 25 The number of chiral carbons present in, sucrose is ……… ., √c
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74, , ONLINE, , JEE Main 2020 ~ Solved Papers, , MATHEMATICS, Objective Type Questions, 1 If the system of linear equations, , −1 + i 3 , , 1−i , , 6 The value of , , x + y + 3z = 0, x + 3 y + k2 z = 0, , (a) −215, (c) −215 i, , 3x + y + 3z = 0, , (b) 9, , (c) 3, , (d) −9, , 2 If α and β are the roots of the equation,, 7x2 − 3x − 2 = 0, then the value of, α, β, is equal to, +, 2, 1 −α, 1 − β2, (a), , 27, 32, , (b), , 1, 24, , (c), , 3, 8, , (d), , 27, 16, , 3 If x = 1 is a critical point of the function, f (x) = (3x2 + ax − 2 − a )ex , then, 2, are local minima of f, 3, 2, (b) x = 1and x = − are local maxima of f, 3, 2, (c) x = 1is a local maxima and x = − is a local, 3, minima of f, 2, (d) x = 1is a local minima and x = − is a local, 3, maxima of f, (a) x = 1and x = −, , 4 The area (in sq. units) of the region, , A = {(x, y) : (x − 1)[x] ≤ y ≤ 2 x, 0 ≤ x ≤ 2},, where [t ] denotes the greatest integer, function, is, , 8, 1, 2−, 3, 2, 8, (c), 2−1, 3, , (a), , 4, 2+1, 3, 1, 4, (d), 2−, 2, 3, , (b), , 5 If the sum of the second, third and fourth, terms of a positive term GP is 3 and the, sum of its sixth, seventh and eighth terms, is 243, then the sum of the first 50 terms, of this GP is, 1 49, (a), (3 − 1), 26, 2 50, (c), (3 − 1), 13, , is, , (b) 215 i, (d) 6 5, , π, 2 π, − sin and, 16, 8, 2 π , 2 π, M = cos − sin , then, 16, 8, , 7 If L = sin 2 , , has a non-zero solution (x, y, z) for some, y, k ∈ R, then x + is equal to, z, (a) −3, , 30, , 1 50, (b), (3 − 1), 26, 1 50, (d), (3 − 1), 13, , π, 1, 1, + cos, 2 2 2, 8, π, 1, 1, (b) L =, − cos, 4 2 4, 8, π, 1, 1, (c) M =, + cos, 4 2 4, 8, π, 1, 1, (d) M =, + cos, 2 2 2, 8, (a) L = −, , 8 If a + x = b + y = c + z + 1, where a , b, c, x, y,, z are non-zero distinct real numbers,, x a + y x + a, then y b + y y + b is equal to, , , z c + y z + c, (a) y(b − a ), (c) 0, , (b) y(a − b), (d) y(a − c), , 9 If the line y = mx + c is a common tangent, x2, y2, −, = 1 and the circle, 100 64, x2 + y2 = 36, then which one of the, following is true?, to the hyperbola, , (a) c2 = 369, (c) 4c2 = 369, , (b) 5m = 4, (d) 8m + 5 = 0, , 10 Which of the following points lies on the, , tangent to the curve x4e y + 2 y + 1 = 3 at, the point (1, 0)?, , (a) (2, 2), (c) (2, 6), , (b) (2, 6), (d) (−2, 4), , 11 The statement, ( p → (q → p)) → ( p → ( p ∨ q)) is, (a), (b), (c), (d), , equivalent to ( p ∧ q) ∨ (~ q), a contradiction, equivalent to ( p ∨ q) ∧ (~ p ), a tautology
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75, , SEPTEMBER ATTEMPT ~ 05 Sep 2020, Shift II, ( 1 + x 2 + x 4 − 1)/ x, , 12 lim, , x(e, , x→ 0, , − 1), , 1 + x2 + x4 − 1, , (a) is equal to e, (c) is equal to 0, , (b) is equal to 1, (d) does not exist, , 13 If the sum of the first 20 terms of the, series log (71/ 2 ) x + log (71/ 3 ) x + log (71/ 4 ) x + …, (b) 71/ 2, (d) 746/ 21, , 1 + x2 − 1, with, , , x, , , 2x 1 − x2 , at x = 1 is, respect to tan −1 , 1 − 2x2 , 2, , , , 14 The derivative of tan −1 , , 2 3, 5, 2 3, (c), 3, , 3, 12, 3, (d), 10, , (a), , 15 If ∫, , (b), , cos θ, 5 + 7 sin θ − 2 cos2 θ, , dθ, , = A log e|B(θ )| + C , where C is a constant of, B(θ ), can be, integration, then, A, , 2 sin θ + 1, sin θ + 3, 5(sin θ + 3), (c), 2 sin θ + 1, (a), , 2 sin θ + 1, 5(sin θ + 3), 5(2 sin θ + 1), (d), sin θ + 3, , (b), , 16 Let y = y(x) be the solution of the, dy, + 2 y sin x, dx, π, π, π, = sin 2x, x ∈ 0, . If y = 0, then y is, 3, 4, 2, equal to, differential equation cos x, , (a) 2 −, (c), , 2, , 2−2, , (b) 2 + 2, 1, (d), −1, 2, , 17 If the length of the chord of the circle,, , x2 + y2 = r 2 (r > 0) along the line, y − 2x = 3, is r, then r 2 is equal to, , 9, 5, 24, (c), 5, (a), , (b) 12, (d), , the data 3, 5, 7, a , b are 5 and 2, respectively, then a and b are the roots of, the equation, (a) x2 − 10x + 18 = 0, (c) x2 − 10x + 19 = 0, , (b) 2x2 − 20x + 19 = 0, (d) x2 − 20x + 18 = 0, , 19 If for some α ∈R, the lines, x+ 1 y−2 z −1, and, =, =, −1, 2, 1, x+2 y+1 z+1, are coplanar, then, =, =, L2 :, α, 5 −α, 1, the line L2 passes through the point, L1 :, , is 460, then x is equal to, (a) 72, (c) e2, , 18 If the mean and the standard deviation of, , 12, 5, , (a) (10, 2, 2), (c) (10, −2, −2), , (b) (2, −10, −2), (d) (−2, 10, 2), , 20 There are 3 sections in a question paper, and each section contains 5 questions. A, candidate has to answer a total of 5, questions, choosing at least one question, from each section. Then the number of, ways, in which the candidate can choose, the questions, is, (a) 3000, , (b) 1500, , (c) 2255, , (d) 2250, , Numerical Type Questions, 21 The coefficient of x4 in the expansion of, , (1 + x + x2 + x3 )6 in powers of x, is ……… ., , 22 In a bombing attack, there is 50% chance, that a bomb will hit the target. At least, two independent hits are required to, destroy the target completely. Then the, minimum number of bombs, that must be, dropped to ensure that there is at least, 99% chance of completely destroying the, target, is ………, , 23 If the lines x + y = a and x − y = b touch the, curve y = x2 − 3x + 2 at the points where, a, the curve intersects the X-axis, then is, b, equal to …… ., , 24 Let the vectors a , b, c be such that|a| = 2,, |b| = 4 and|c| = 4. If the projection of b on a, is equal to the projection of c on a and b is, perpendicular to c, then the value of, |a + b − c|is ……… ., , 25 Let A = { a , b, c} and B = {1, 2, 3, 4}. Then the, number of elements in the set, C = { f : A → B|2 ∈ f ( A) and f is not, one-one} is ……… .
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76, , ONLINE, , JEE Main 2020 ~ Solved Papers, , Answers, Physics, 1., 11., 21., , (b), (b), (18), , 2. (c), 12. (a), 22. (41), , 3., 13., 23., , (d), (a), (5), , 4., 14., 24., , (c), (c), (2), , 5., 15., 25., , (d), (a), (20), , 6. (d), 16. (a), , 7. (d), 17. (c), , 8. (a), 18. (a), , 9. (a), 19. (d), , 10. (a), 20. (b), , For Detailed Solutions, Visit : http://bit.ly/3o6TQOY, Or Scan :, , Chemistry, 1. (d), 11. (d), 21. (50), , 2., (b), 12., (c), 22. (–13537.57), , 3., 13., 23., , (a), (b), (0), , 4., 14., 24., , (a), (d), (16), , 5., (d), 15. (b), 25. (9.00), , 6. (b), 16. (c), , 7. (c), 17. (d), , 8. (b), 18. (d), , 9. (a), 19. (d), , 10. (a), 20. (d), , For Detailed Solutions, Visit : http://bit.ly/2T42qQh, Or Scan :, , Mathematics, 1., (a), 11., (d), 21. (120.00), , 2., (d), 12., (b), 22. (11.00), , 3. (d), 13. (a), 23. (0.5), , 4. (a), 14. (d), 24. (6.00), , 5., (b), 15., (d), 25. (19.00), , 6., 16., , (c), (c), , 7., 17., , (d), (d), , 8., 18., , (b), (c), , 9., 19., , (c), (b), , For Detailed Solutions, Visit : http://bit.ly/37oS5H4, Or Scan :, , 10., 20., , (c), (d)
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ONLINE QUESTION PAPER, , JEE Main 2020, (06 September, 2020), TIME 9:30-12:30 (Shift I), , MM : 300, , PHYSICS, Objective Type Questions, 1 A screw gauge has 50 divisions on its, circular scale. The circular scale is 4 units, ahead of the pitch scale marking, prior to, use. Upon one complete rotation of the, circular scale, a displacement of 0.5 mm is, noticed on the pitch scale. The nature of, zero error involved and the least count of, the screw gauge, are respectively, (a) negative, 2 µm, (c) positive, 0.1 mm, , straight track with speed v and is emitting, sound of frequency ν o (see figure). An, observer is standing at a finite distance, at, the point O, from the track. The time, variation of frequency heard by the, observer is best represented by, (Here, t0 represents the instant when the, distance between the source and observer, is minimum.), , (a) νo, , t0 t, , (b) νo, , ν, , t0 t, , (c) νo, , (b) positive, 10 µm, (d) positive, 0.1 µm, , 2 A sound source S is moving along a, , ν, , ν, , t0 t, ν, (d) νo, , t0 t, , 3 In the given figure, P and Q are two, equally intense coherent sources emitting, radiation of wavelength 20 m. The, separation between P and Q is 5 m and the, phase of P is ahead of that of Q by 90°. A, B, and C are three distinct points of, observation, each equidistant from the, mid-point of PQ. The intensities of, radiation at A, B and C will be in the ratio
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78, , ONLINE, B, , JEE Main 2020 ~ Solved Papers, M (R 2 + H 2 ), 4, MR 2, (d), 3, , MR 2, 2, MH 2, (c), 3, , (a), , C, , P, , Q, , (a) 0 : 1 : 4, (c) 0 : 1 : 2, , A, , 8 Four point masses, each of mass m are, , (b) 2 : 1 : 0, (d) 4 : 1 : 0, , 4 If the potential energy between two, A, B, , then, +, r 6 r12, at equilibrium, separation between, molecules and the potential energy are, , molecules is given by U = −, , 2B , (c) , , A , , 1/ 6, , 1/ 6, , fixed at the corners of a square of side l., The square is rotating with angular, frequency ω , about an axis passing, through one of the corners of the square, and parallel to its diagonal, as shown in, the figure. The angular momentum of the, square about this axis is, , 1/ 6, , ,−, , A2, 2B, , B, (b) , A, , ,−, , A2, 4B, , 2B , (d) , , A , , ,0, Ax, is, , B, (a) , , 2A , , (b), , 1/ 6, , ,−, , A2, 2B, , 5 An AC circuit has R = 100 Ω, C = 2 µF and, L = 80 mH connected in series. The quality, factor of the circuit is, (a) 2, , (b) 0.5, , (c) 20, , (d) 400, , 6 Charges Q1 and Q2 are at points A and B, of a right angle triangle OAB (see figure)., The resultant electric field at point O is, perpendicular to the hypotenuse, then, Q1 / Q2 is proportional to, A, , (a) ml2ω, (c) 3 ml2ω, , (b) 4 ml2ω, (d) 2 ml2ω, , 9 For the given input voltage waveform, Vin (t ), the output voltage waveform Vout (t ),, across the capacitor is correctly depicted, by, 1 kΩ, +5 V, , Q1, , 5 µs, , Vout (t), , 10 nF, , x1, , 0V, 0, , O, , (a), , x13, x23, , (b), , Q2, B, , x2, , x2, x1, , (c), , x1, x2, , 5 µs, , t, , Vout (t), , (d), , x22, x1 2, , (a), , 3V, 2V, , 7 Shown in the figure is a hollow icecream, cone (it is open at the top). If its mass is M,, radius of its top R and height H, then its, moment of inertia about its axis is, , 5 µs 10 µs, , 15 µs, , t, , 5 µs 10 µs, , 15 µs, , t, , Vout (t), 2V, (b), , R, , H
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79, , SEPTEMBER ATTEMPT ~ 06 Sep 2020, Shift I, , 15 You are given that mass of 73 Li = 70160, ., u,, , Vout (t), (c), , mass of 42 He = 40026, ., u, , 2V, , and mass of 11 H = 10079, ., u., 5 µs 10 µs 15 µs, , t, , Vout (t), (d), , 2V, , 5 µs 10 µs, , 15 µs, , t, , 10 A particle of charge q and mass m is, moving with a velocity −v$i (v ≠ 0) towards a, large screen placed in the yz-plane at a, distance d. If there is a magnetic field, $ , the minimum value of v for which, B = B0k, the particle will not hit the screen is, qdB0, (a), 3m, , 2qdB0, qdB0, (b), (c), m, m, , qdB0, (d), 2m, , 11 An insect is at the bottom of a, hemispherical ditch of radius 1 m. It, crawls up the ditch but starts slipping, after it is at height h from the bottom. If, the coefficient of friction between the, ground and the insect is 0.75, then h is, (Take, g = 10 ms−2 ), , When 20g of 73 Li is converted into 42 He by, proton capture, the energy liberated, (in kWh), is, [Mass of nucleon = 1 GeV/c 2], (a) 4.5 × 105, (c) 6.82 × 105, , (b) 8 × 106, (d) 133, . × 106, , 16 A point like object is placed at a distance of, 1 m in front of a convex lens of focal length, 0.5 m. A plane mirror is placed at a, distance of 2 m behind the lens. The, position and nature of the final image, formed by the system is, (a), (b), (c), (d), , 2.6 m from the mirror, real, 1 m from the mirror, virtual, 1 m from the mirror, real, 2.6 m from the mirror, virtual, , 17 Identify the correct output signal Y in the, given combination of gates (as shown) for, the given inputs A and B., B, Y, , A, , (a) 0.20 m (b) 0.45 m (c) 0.60 m (d) 0.80 m, , 12 A satellite is in an elliptical orbit around a, planet P. It is observed that the velocity of, the satellite when it is farthest from the, planet is 6 times less than that when it is, closest to the planet. The ratio of distances, between the satellite and the planet at, closest and farthest points is, (a) 1 : 6, , (b) 1 : 3, , (c) 1 : 2, , (d) 3 : 4, , 13 An electron, a doubly ionised helium ion, (He + +) and a proton are having the same, kinetic energy. The relation between their, respective de-Broglie wavelengths λ e ,, λ He + + and λ p is, , (a) λ e > λ He + + > λ p, (c) λ e > λ p > λ He + +, , (b) λ e < λ He + + = λ p, (d) λ e < λ p < λ He + +, , 14 A clock has a continuously moving second’s, hand of 0.1 m length. The average, acceleration of the tip of the hand (in ms −2), is of the order of, , (a) 10−3, , (b) 10−4, , (c) 10−2, , (d) 10−1, , A, , B, 5, , 10, , 15, , 20, , t, , (a), 5, , 10, , 15, , 20, , 5, , 10, , 15, , 20, , 5, , 10, , 15, , 20, , 5, , 10, , 15, , 20, , t, , (b), t, , (c), t, , (d), t
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80, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 18 Molecules of an ideal gas are known to, have three translational degrees of, freedom and two rotational degrees of, freedom. The gas is maintained at a, temperature of T., The total internal energy U of a mole of, Cp, this gas, and the value of γ =, are, CV , given respectively, by, 5, 6, 7, RT and γ = (b) U = 5RT and γ =, 2, 5, 5, 5, 7, 6, (c) U = RT and γ = (d) U = 5RT and γ =, 2, 5, 5, , (a) U =, , 19 An object of mass m is suspended at the, end of a massless wire of length L and area, of cross-section A. Young modulus of the, material of the wire is Y . If the mass is, pulled down slightly its frequency of, oscillation along the vertical direction is, 1, 2π, 1, (c) f =, 2π, , (a) f =, , mL, YA, mA, YL, , 1 YA, 2π mL, 1 YL, (d) f =, 2π mA, , (b) f =, , 20 An electron is moving along +x-direction, , with a velocity of 6 × 106 ms −1. It enters a, region of uniform electric field of 300 V/cm, pointing along + y-direction. The, magnitude and direction of the magnetic, field set up in this region such that the, electron keeps moving along the x-direction, will be, , (a), (b), (c), (d), , 3 × 10−4 T, along + z-direction, 5 × 10−3 T, along − z-direction, 5 × 10−3 T, along + z-direction, 3 × 10−4 T, along − z-direction, , Numerical Type Questions, 21 The density of a solid metal sphere is, determined by measuring its mass and its, diameter. The maximum error in the, , x , density of the sphere is , %. If the, 100, relative errors in measuring the mass and, the diameter are 6.0% and 1.5%, respectively, the value of x is ........, 22 Two bodies of the same mass are moving, with the same speed, but in different, directions in a plane. They have a, completely inelastic collision and move, together thereafter with a final speed, which is half of their initial speed. The, angle between the initial velocities of the, two bodies (in degree) is ............, , 23 Suppose that intensity of a laser is, , 315, 2, W/m . The rms electric field (in V/m), , π , associated with this source is close to the, nearest integer is ....... ., (Take, ε 0 = 886, . × 10−12 C2Nm−2 and, c = 3 × 108 ms −1), , 24 Initially a gas of diatomic molecules is, contained in a cylinder of volume V1 at a, pressure p1 and temperature 250 K., Assuming that 25% of the molecules get, dissociated causing a change in number of, moles. The pressure of the resulting gas at, temperature 2000 K, when contained in a, volume 2V1 is given by p2. The ratio p2 /p1, is ..........., , 25 A part of a complete circuit is shown in the, figure. At some instant, the value of, current I is 1 A and it is decreasing at the, rate of 102 As−1. The value of the potential, difference VP − VQ (in volt) at that instant,, is ..........., L=50 mH, , R=2Ω, , P, , Q, 30 V
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81, , SEPTEMBER ATTEMPT ~ 06 Sep 2020, Shift I, , CHEMISTRY, Objective Type Questions, 1 The correct statement with respect to, dinitrogen is, (a), (b), (c), (d), , N2 is paramagnetic in nature., it can combine with dioxygen at 25°C., liquid dinitrogen is not used in cryosurgery., it can be used as an inert diluent for, reactive chemicals., , 2 Consider the following reactions:, Ozonolysis, , ( A) → (B) + (C ), (I2 + NaOH), ∆, , yellow ppt., , Ag2O, , Silver mirror, , ∆, , (I2 + NaOH), , (C ), , ∆, , no yellow ppt., , Anhydrous ZnCl2, LiAlH4, (D), ∆, and conc. HCl, , Gives white, turbidity within, 5 minutes, , (A) is, (a), , (b), , (c), , (d), , O, , OCH3, , (d), O2N, , moles of the 1st component and n2 moles of, the 2nd component is prepared. M1 and M 2, are the molecular weights of component 1, and 2 respectively. If d is the density of the, solution in g mL −1, C 2 is the molarity and, χ 2 is the mole-fraction of the 2nd component,, then C 2 can be expressed as, , 1000 χ 2, M1 + χ 2 (M2 − M1 ), dχ 2, (b) C2 =, M2 + χ 2 (M2 − M1 ), (a) C2 =, , 1000 dχ 2, M1 + χ 2 (M2 − M1 ), dχ1, (d) C2 =, M2 + χ 2 (M2 − M1 ), , following reaction is, —C, , O, , O2N, , (c) C2 =, , 3 The major product obtained from the, O2N—, , (c), , 4 A solution of two components containing n1, , (C7 H14 ), , ‘ B’, , OH, , 5 The incorrect statement is, (a) bronze is an alloy of copper and tin., , Hg2+/H+, —OCH3, H2O, , C—, , OCH3, (a), , (b) cast iron is used to manufacture wrought, iron., (c) german silver is an alloy of zinc, copper, and nickel., (d) brass is an alloy of copper and nickel., , below., O, , (b), O2N, , 6 Consider the Assertion and Reason given, , O, , O2N, , OH, , Assertion (A) Ethene polymerised in the, presence of Ziegler Natta catalyst at high, temperature and pressure is used to make, buckets and dustbins., Reason (R) High density polymers are, closely packed and are chemically inert.
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82, , JEE Main 2020 ~ Solved Papers, , ONLINE, Choose the correct answer from the following:, (a) (A) is correct but (R) is wrong., (b) Both (A) and (R) are correct but (R) is not the, correct explanation of (A)., (c) Both (A) and (R) are correct and (R) is the, correct explanation of (A)., (d) (A) and (R) both are wrong., , 7 Arrange the following solutions in the, decreasing order of pOH., (A) 0.01 M HCl, (B) 0.01 M NaOH, (C) 0.01 M CH3 COONa (D) 0.01 M NaCl, (a) (A) > (C) > (D) > (B), (b) (A) > (D) > (C) > (B), (c) (B) > (C) > (D) > (A), (d) (B) > (D) > (C) > (A), , 8 Among the sulphates of alkaline earth, metals, the solubilities of BeSO4 and MgSO4, in water, respectively, are, (a) poor and poor, (c) high and high, , (b) high and poor, (d) poor and high, , H 3C, , CH3, , Br, , Br, , (a), , (b), Br, , Br, , NO2, , NO2, , CH3, , Br, , CH3, , Br, (c), , (d), Br, , Br, NO2, , NO2, , 11 The presence of soluble fluoride ion upto, 1 ppm concentration in drinking water, is, (a) harmful for teeth, (c) harmful to bones, , (b) harmful to skin, (d) safe for teeth, , 12 The increasing order of pK b values of the, following compounds is, , N(CH3)2 N(CH3)2 NHCH3, , NHCH3, , 9 The major products of the following reaction are, CH3, t, , ( i ) KO Bu / ∆, CH3 CH CH CH3 →, ( ii ) O3 / H2O 2, , OSO2CH3, CH3, + CH3CHO, , (a), CH3, , CH3, + CH3COOH, CH3, , O, , + HCHO, CHO, CH3, , (a) II < IV < III < I, (c) II < I < III < IV, , (IV), , (b) I < II < IV < III, (d) I < II < III < IV, , 13 Which of the following compounds shows, (a) 2-methylpent-2-ene, (b) 4-methylpent-2-ene, (c) 4-methylpent-1-ene, (d) 2-methylpent-1-ene, , only transition elements, is, (a) 37, 42, 50, 64, (c) 9, 17, 34, 38, , (b) 21, 25, 42, 72, (d) 21, 32, 53, 64, , 15 The variation of equilibrium constant, + HCOOH, , (d), CH3, , (III), , 14 The set that contains atomic numbers of, , CH3, (c), CH3, , (II), , geometrical isomerism?, , O, , (b), , OH, , CN, OCH3, (I), , COOH, , with temperature is given below:, Temperature, , 10 The major product of the following reaction is, CH3, 2HBr, , Equilibrium constant, , T1 = 25°C, , K1 = 10, , T2 = 100°C, , K 2 = 100, , The values of ∆H °, ∆G° at T1 and ∆G° at, T2 (in kJ mol −1) respectively, are close to, [use R = 8314, JK −1 mol −1], ., , NO2
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83, , SEPTEMBER ATTEMPT ~ 06 Sep 2020, Shift I, (a), (b), (c), (d), , 28.4, − 714, ., 0.64, − 714, ., 28.4, − 5.71, 0.64, − 5.71, , and − 5.71, and − 5.71, and − 14. 29, and − 14. 29, , Among the following, the correct sequence, for the order of the reactions is, , 16 Kraft temperature is the temperature, (a) below which the aqueous solution of, detergents starts freezing, (b) below which the formation of micelles takes, place, (c) above which the aqueous solution of, detergents starts boiling, (d) above which the formation of micelles takes, place, , 17 For the reaction,, Fe2N(s) +, , 3, H ( g) s, 2 2, , 2Fe(s) + NH3 ( g), , (a) KC = K p (RT ), , (b) KC = K p (RT )−1/ 2, , (c) KC = K p (RT )1/ 2, , (d) KC = K p (RT )3 / 2, , 18 The species that has a spin-only magnetic, moment of 5.9 BM, is (Td = tetrahedral), , (a), (b), (c), (d), , [Ni(CN)4 ]2− (square planar), [NiCl 4 ]2− (Td ), [Ni(CO)4 ](Td ), [MnBr4 ]2− (Td ), , oxidation state is, , Numerical Type Questions, 21 In an estimation of bromine by Carius, method, 1.6 g of an organic compound gave, 1.88 g of AgBr. The mass percentage of, bromine in the compound is ....... . (Atomic, mass, Ag = 108, Br = 80 g mol−1), , 22 Potassium chlorate is prepared by the, electrolysis of KCl in basic solution, 6 OH− + Cl− → ClO3− + 3H2O + 6e− . If only, 60% of the current is utilised in the, reaction, the time (rounded to the nearest, hour) required to produce 10 g of KClO3, using a current of 2 A is ........ ., , 23 The number of Cl == O bonds in perchloric, acid is ‘‘..........’’., , 24 The elevation of boiling point of 0.10 m, , (b) Ce, , (c) Eu, , (d) Tb, , 20 Consider the following reactions, A → P1; B → P2; C → P3; D → P4,, The order of the above reactions are a , b, c, and d, respectively. The following graph is, obtained when log[rate] vs log[conc.] are, plotted:, [D], , D>A>B>C, A>B>C>D, C>A>B>D, D>B>A>C, , (Given : F = 96,500 C mol−1; molar mass of, KClO3 = 122 g mol−1), , 19 The lanthanoid that does not show + 4, (a) Dy, , (a), (b), (c), (d), , aqueous CrCl3 ⋅ xNH3 solution is two times, that of 0.05 m aqueous CaCl2 solution. The, value of x is ....... ., [Assume 100% ionisation of the complex, and CaCl2, coordination number of Cr as, 6, and that all NH3 molecules are present, inside the coordination sphere], , 25 A spherical balloon of radius 3 cm, , [B], , log [rate], , [A], [C], , log [conc.], , containing helium gas has a pressure of, 48 × 10−3 bar. At the same temperature,, the pressure, of a spherical balloon of, radius 12 cm containing the same amount, of gas will be ............ × 10−6 bar.
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84, , JEE Main 2020 ~ Solved Papers, , ONLINE, , MATHEMATICS, Objective Type Questions, 1 If α and β be two roots of the equation, x − 64x + 256 = 0. Then, the value of, 2, , 3, , α, 5 , β , , 1/ 8, , β , + 5 , α , 3, , 1/ 8, , (a), , A = {(x, y):|x|+| y|≤ 1, 2 y ≥|x|} is, 2, , 1, 3, 1, (c), 6, , 7, 6, 5, (d), 6, , (b), , (a), , dy, equation 1 + x + y + x y + xy, = 0 is, dx, (where C is a constant of integration), 2, , 2 2, , 1 + x2 + 1, 1, +C, log e , , , 2, 2, 1 + x − 1, , (a), , 1 + y2 + 1 + x2 =, , (b), , 1 + x2 + 1, 1, +C, 1 + y2 − 1 + x2 = log e , , , 2, 2, 1 + x − 1, , (c), , 1 + y2 + 1 + x2 =, , 1 + x2 − 1, 1, +C, log e , , , 2, 1 + x2 + 1, , (d), , 1 + y2 − 1 + x2 =, , 1 + x2 − 1, 1, +C, log e , , , 2, 1 + x2 + 1, , 4 Let L1 be a tangent to the parabola, y2 = 4(x + 1) and L2 be a tangent to the, parabola y = 8(x + 2) such that L1 and L2, intersect at right angles. Then, L1 and L2, meet on the straight line, 2, , (a) x + 3 = 0, (c) x + 2 = 0, , (b) 2x + 1 = 0, (d) x + 2 y = 0, , 5 If f (x + y) = f (x) f ( y) and, , ∞, , ∑ f (x) = 2, x,, , y ∈N , where N is the set of all natural, f (4), is, numbers, then the value of, f (2), (c), , 1, 3, , (d), , 15, 101, , 5050, 5049, , (c), , 5050, 5051, , (d), , 5051, 5050, , 4, 9, , (b), , 5, 101, , (c), , 5, 33, , (d), , 10, 99, , 8 A ray of light coming from the point, (2, 2 3 ) is incident at an angle 30° on the, line x = 1 at the point A. The ray gets, reflected on the line x = 1 and meets X-axis, at the point B. Then, the line AB passes, through the point, 1 , (a) 3, −, , , 3, , , 3, (b) 4, −, , 2 , , , (c) (3, − 3 ), , (d) (4, − 3 ), , 9 Which of the following points lies on the, locus of the foot of perpendicular drawn, x2 y2, upon any tangent to the ellipse,, +, =1, 4, 2, from any of its foci?, (a) (−2, 3 ), (c) (−1, 3 ), , (b) (−1, 2 ), (d) (1, 2), , 10 The region represented by, , {z = x + iy ∈C :|z|−Re(z) ≤ 1} is also given by, the inequality, , (a) y2 ≥ 2(x + 1), (c) y2 ≤ x +, , x =1, , 1, 9, , (b), , three numbers are selected at random, (without repetition), then the probability, that they are in AP with positive common, difference, is, (a), , 3 The general solution of the differential, 2, , 5049, 5050, , 7 Out of 11 consecutive natural numbers if, , 2 The area (in sq. units) of the region, , (b), , I 2 = ∫ (1 − x50 )101 dx such that I 2 = αI1, then, , α equals to, , is, (b) 3, (d) 4, , 2, 3, , 1, , 0, , 0, , (a) 2, (c) 1, , (a), , 1, , 6 If I1 = ∫ (1 − x50 )100 dx and, , 1, 2, , 1, (b) y2 ≤ 2 x + , , 2, (d) y2 ≥ x + 1, , 11 The position of a moving car at time t is, , given by f (t ) = at 2 + bt + c, t > 0, where a, b, and c are real numbers greater than 1., Then, the average speed of the car over the, time interval [t1 , t2 ] is attained at the point, , (a) (t2 − t1 ) / 2, (c) (t1 + t2 ) / 2, , (b) a (t2 − t1 ) + b, (d) 2a (t1 + t2 ) + b
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85, , SEPTEMBER ATTEMPT ~ 06 Sep 2020, Shift I, ( x − 1) 2, , t cos(t 2 ) dt , ∫0, 12 lim, , x →1, (x − 1)sin(x − 1) , , , 1, (a) is equal to, 2, (c) is equal to −, , (a) (−3, 3), (c) (−4, − 1), , 19 Let a , b, c, d and p be any non-zero distinct, , (b) is equal to 1, 1, 2, , (d) does not exist, , n, , n, , i =1, , i =1, , 13 If ∑ (xi − a ) = n and ∑ (xi − a )2 = na,, (n, a > 1), then the standard deviation of n, observations x1 , x2 , K , xn is, (b) n a − 1, , (a) a − 1, (c), , n (a − 1), , a −1, , (d), , 14 If {p } denotes the fractional part of the, 3200 , number p, then , is equal to, 8 , 5, (a), 8, , 7, (b), 8, , 3, (c), 8, , 1, (d), 8, , 15 The shortest distance between the lines, x−1 y+ 1 z, = and x + y + z + 1 = 0,, =, 0, 1, −1, 2x − y + z + 3 = 0 is, (a) 1, , (b), , 1, 3, , (c), , 1, 2, , 1, (d), 2, , 16 The negation of the Boolean expression, p ∨ (~ p ∧ q) is equivalent to, , (a) p ∧ ~ q, , (b) ~ p ∧ ~ q, , (c) ~ p ∨ ~ q, , (d) ~ p ∨ q, , 17 Two families with three members each and, one family with four members are to be, seated in a row. In how many ways can, they be seated so that the same family, members are not separated?, (a) 2! 3! 4!, (c) (3!)2 ⋅ (4!), , (b) (−3, − 1), (d) (1, 3), , (b) (3!)3 ⋅ (4!), (d) 3! (4!)3, , 18 Let m and M be respectively the minimum, and maximum values of, 1 + sin 2 x, cos2 x, sin 2x, 2, 2, 1 + cos x, sin x, sin 2x . Then, the, 1 + sin 2x, cos2 x, sin 2 x, ordered pair (m, M) is equal to, , real numbers such that (a 2 + b2 + c2 ) p2 − 2, (ab + bc + cd ) p + (b2 + c2 + d 2 ) = 0. Then,, (a) a , c, p are in AP, (b) a , c, p are in GP, (c) a , b, c, d are in GP (d) a , b, c, d are in AP, , 20 The value of λ and µ for which the system, of linear equations, x + y + z = 2, x + 2 y + 3z = 5, x + 3 y + λz = µ, has infinitely many solutions are,, respectively, (a) 6 and 8, (c) 5 and 8, , (b) 5 and 7, (d) 4 and 9, , Numerical Type Questions, 21 Set A has m elements and Set B has n, elements. If the total number of subsets of, A is 112 more than the total number of, subsets of B, then the value of m ⋅ n is ....., , 22 Let f : R → R be defined as, 5, 1, 2, x sin x + 5x , x < 0, , f (x) = , x=0, 0,, 5, 1, 2, x cos x + λx , x > 0, , The value of λ for which f ′′ (0) exists, is ....., , 23 If a and b are unit vectors, then the, , greatest value of 3|a + b|+|a − b|is ......., , 24 Let AD and BC be two vertical poles at A, and B respectively on a horizontal ground., If AD = 8 m, BC = 11 m and AB = 10 m;, then the distance (in meters) of a point M, on AB from the point A such that, MD 2 + MC 2 is minimum is ........, , 25 The angle of elevation of the top of a hill, from a point on the horizontal plane, passing through the foot of the hill is found, to be 45°. After walking a distance of 80 m, towards the top, up a slope inclined at an, angle of 30° to the horizontal plane, the, angle of elevation of the top of the hill, becomes 75°. Then, the height of the hill, (in meters) is ..........
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86, , ONLINE, , JEE Main 2020 ~ Solved Papers, , Answers, Physics, 1., (b), 11. (a), 21. (1050), , 2. (b), 12. (a), 22. (120), , 3., (b), 13. (c), 23. (194), , 4., 14., 24., , (c), (a), (5), , 5., 15., 25., , (a), (d), (33), , 6. (c), 16. (a), , 7. (a), 17. (b), , 8. (c), 18. (c), , 9. (a), 19. (b), , 10. (c), 20. (c), , For Detailed Solutions, Visit : http://bit.ly/3kbXJ2P, Or Scan :, , Chemistry, 1. (d), 11. (d), 21. (50), , 2., (d), 12. (b), 22. (11.00), , 3., 13., 23., , (a), (b), (3), , 4., 14., 24., , (c), (b), (5), , 5., 15., 25., , (d), (c), (750), , 6., 16., , (c), (d), , 7., 17., , (b), (c), , 8., 18., , (c), (d), , 9., 19., , (d), (c), , 10., 20., , (d), (d), , 10., 20., , (b), (c), , For Detailed Solutions, Visit : http://bit.ly/2IGUXVb, Or Scan :, , Mathematics, 1., (a), 11., (c), 21. (28.00), , 2. (d), 12. (*), 22. (5.00), , 3., (a), 13. (d), 23. (4.00), , 4., (a), 14. (d), 24. (5.00), , 5., (d), 15., (b), 25. (80.00), , 6., 16., , (c), (b), , 7., 17., , (c), (b), , 8., 18., , (c), (b), , 9., 19., , (c), (c), , For Detailed Solutions, Note. (*) None of the option is correct., , Visit : http://bit.ly/31o8Xty, Or Scan :
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87, , SEPTEMBER ATTEMPT ~ 06 Sep 2020, Shift II, , ONLINE QUESTION PAPER, , JEE Main 2020, (06 September, 2020), TIME 2:30-5:30 (Shift II), , MM : 300, , PHYSICS, Objective Type Questions, 5Ω, 1, 10 Ω, , 10 V, , 20 V, 2Ω, , 4Ω, , (a) 0.71 A from positive to negative terminal, (b) 0.42 A from positive to negative terminal, (c) 0.21 A from positive to negative terminal, (d) 0.36 A from negative to positive terminal, , 2 A charged particle going around in a circle, can be considered to be a current loop. A, particle of mass m carrying charge q is, moving in a plane with speed v under the, influence of magnetic field B. The, magnetic moment of this moving particle, mv2B, , (c) −, , 2, , 2B, mv2B, B2, , (b) −, (d) −, , K2, , K1, , In above figure shown, the current in the, 10 V battery is close to, , (a), , (see figure). One end of the long rod is, maintained at 100°C and the other at 0°C, (see figure). If the joints of the rod are at, 70°C and 20°C in steady state and there is, no loss of energy from the surface of the, rod, the correct relationship between, K1, K 2 and K3 is, , mv2B, 2 πB 2, mv2B, 2B 2, , 3 Three rods of identical cross-section and, lengths are made of three different, materials of thermal conductivity K1 , K 2, and K3 , respectively. They are joined, together at their ends to make a long rod, , K3, 0ºC, , 100ºC, 70ºC, , 20ºC, , (a) K1 : K3 = 2 :3; K 2 : K3 = 2 : 5, (b) K1 < K 2 < K3, (c) K1 : K 2 = 5 : 2; K1 : K3 = 3 : 5, (d) K1 > K 2 > K3, , 4 Two identical electric point dipoles have, , dipole moments p1 = p i$ and p2 = − p $i are, held on the X-axis at distance a from each, other. When released, they move along the, X-axis with the direction of their dipole, moments remaining unchanged. If the, mass of each dipole is m, their speed when, they are infinitely far apart is, , (a), , p, a, , 1, π ε0 ma, , (b), , p, 1, a 2 π ε0 ma, , (c), , p, a, , 2, πε0 ma, , (d), , p, 3, a 2 πε0 ma
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88, , ONLINE, , 5 For a plane electromagnetic wave, the, magnetic field at a point x and time t is, B(x, t ) = [12, . × 10−7 sin(05, . × 103 x, $]T, + 15, . × 1011 t )k, The instantaneous electric field E, corresponding to B is, (Given, speed of light, c = 3 × 108 m/s), V, (a) E(x, t ) = [−36 sin(0.5 × 103 x + 15, . × 1011 t )$j ], m, V, (b) E(x, t ) = [36 sin(1 × 103 x + 0.5 × 1011 t )$j], m, $] V, (c) E(x, t ) = [36 sin(0.5 × 103 x + 15, . × 1011 t )k, m, 3, 11 $ V, (d) E(x, t ) = [36 sin(1 × 10 x + 15, . × 10 t ) j], m, , 6 Two planets have masses M and 16 M and, their radii are a and 2a, respectively. The, separation between the centres of the, planets is 10a. A body of mass m is fired, from the surface of the larger planet, towards the smaller planet along the line, joining their centres. For the body to be, able to reach at the surface of smaller, planet, the minimum firing speed needed, is, GM, (a) 2, a, (c), , GM 2, ma, , GM, (b) 4, a, (d), , 3 5GM, 2, a, , 7 A particle moving in the xy-plane, experiences a velocity dependent force, F = k(vy $i + vx $j), where vx and vy are the x, and y components of its velocity v., If a is the acceleration of the particle, then, which of the following statements is true, for the particle?, (a) Quantity v × a is constant in time., (b) F arises due to a magnetic field., (c) Kinetic energy of particle is constant in time., (d) Quantity v ⋅ a is constant in time., , 8 Particle A of mass m1 moving with velocity, , ( 3 i$ + $j)ms−1 collides with another particle, B of mass m2 which is at rest initially. Let, v1 and v2 be the velocities of particles A and, B after collision, respectively. If m1 = 2m2, , JEE Main 2020 ~ Solved Papers, , and after collision v1 = ($i + 3$j) ms−1, then, the angle between v1 and v2 is, (a) 15°, , (b) 60°, , (c) −45°, , (d) 105°, , 9 When a car is at rest, its driver sees rain, drops falling on it vertically. When driving, the car with speed v, he sees that rain, drops are coming at an angle 60° from the, horizontal. On further increasing the, speed of the car to (1 + β)v, this angle, changes to 45°. The value of β is close to, (a) 0.50, , (b) 0.41, , (c) 0.37, , (d) 0.73, , 10 Given the masses of various atomic, , particles m p = 10072, ., u,mn = 10087, ., u,, u,, ., u,mν = 0, md = 20141, ., me = 0000548, where p = proton, n = neutron, e = electron, ν = antineutrino and d = deuteron. Which, of the following process is allowed by, momentum and energy conservation?, (a) n + n → deuterium atom (electron bound to, the nucleus), (b) p → n + e+ + ν, (c) n + p → d + ν, (d) e+ + e− → γ, , 11 A circuit to verify Ohm’s law uses, ammeter and voltmeter in series or, parallel connected correctly to the resistor., In the circuit,, (a) ammeter is always used in parallel and, voltmeter in series, (b) Both ammeter and voltmeter must be, connected in parallel, (c) ammeter is always connected in series and, voltmeter in parallel, (d) Both ammeter and voltmeter must be, connected in series, , 12 Consider the force F on a charge q due to a, uniformly charged spherical shell of radius, R carrying charge Q distributed uniformly, over it. Which one of the following, statement is true for F, if q is placed at, distance r from the centre of the shell ?, 1 Qq, (for r < R ), 4 π ε0 R 2, 1 Qq, (b), > F > 0 (for r < R ), 4 π ε0 R 2, 1 Qq, (c) F =, (for r > R ), 4 π ε0 r 2, 1 Qq, (for all r), (d) F =, 4 π ε0 R 2, (a) F =
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89, , SEPTEMBER ATTEMPT ~ 06 Sep 2020, Shift II, 13 A student measuring the diameter of a, pencil of circular cross-section with the, help of a vernier scale records the, following four readings; 5.50 mm, 5.55, mm, 5.45 mm and 5.65 mm. The average, of these four readings is 5.5375 mm and, the standard deviation of the data is, 0.07395 mm. The average diameter of the, pencil should be therefore recorded as, (a) (5.5375 ± 0.0739) mm, (b) (5.5375 ± 0.0740) mm, (c) (5.538 ± 0.074) mm, (d) (5.54 ± 0.07) mm, , y(t ) = y0 sin 2 ωt, where y is measured from, the lower end of unstretched spring. Then ω, is, (a), , 1 g, 2 y0, , (b), , g, y0, , (c), , g, 2 y0, , (d), , 2g, y0, , 18 In a dilute gas at pressure p and, temperature T, the mean time between, successive collisions of a molecule varies, with T as, (a) T, , (b), , 14 A double convex lens has power P and, , (a) 2R, , (b), , R, 2, , (c), , 3R, 2, , (d), , R, 3, , 15 A square loop of side 2a and carrying, current I is kept in xz-plane with its centre, at origin. A long wire carrying the same, current I is placed parallel to Z-axis and, passing through point (0, b, 0), (b >> a ). The, magnitude of torque on the loop about, Z-axis will be, (a), (c), , 2µ 0 I 2a 2, πb, , (b), , µ 0 I 2a 2b, 2 π (a + b ), 2, , 2, , (d), , 2µ 0 I 2a 2b, π (a 2 + b2 ), µ 0 I 2a 2, 2 πb, , 16 A fluid is flowing through a horizontal pipe, of varying cross-section with speed v ms−1, at a point where the pressure is p Pa., p, At another point, where pressure is, 2, Pa its speed is V ms−1. If the density of the, fluid is ρ kg m−3 and the flow is, streamline, then V is equal to, , (a), , p, + v, ρ, , (b), , 2p, + v2, ρ, , (c), , p, + v2, 2ρ, , (d), , p, + v2, ρ, , 17 When a particle of mass m is attached to a, vertical spring of spring constant k and, released, its motion is described by, , (c), , 1, T, , (d) T, , 19 Assuming the nitrogen molecule is moving, with rms velocity at 400 K, the de-Broglie, wavelength of nitrogen molecule is close to, (Given, weight of N2 molecule, = 464, . × 10−26 kg, Boltzmann constant, . × 10−23 J/K and Planck’s constant, = 138, . × 10−34 J-s), = 663, (a) 0.24Å, (c) 0.34Å, , (b) 0.20Å, (d) 0.44Å, , 20 The linear mass density of a thin rod AB of, length L varies fromA to B as, x, λ (x) = λ 0 1 + , where x is the distance, , L, from A. If M is mass of the rod, then its, moment of inertia about an axis passing, through A and perpendicular to the rod is, 5, ML2, 12, 2, (c) ML2, 5, , 7, ML2, 18, 3, (d) ML2, 7, , (a), , (b), , Numerical Type Questions, 21 The output characteristics of a transistor, is shown in the figure. When VCE is 10V, and IC = 40, . mA, then value of βac is, (IB), 60 µA, 50 µA, , 8, , (IC) in mA, , same radii of curvature R of both the, surfaces. The radius of curvature of a, surface of a plano-convex lens made of the, same material with power 1.5 P is, , 1, T, , 6, , 40 µA, 30 µA, 20 µA, 10 µA, , 4, 2, 2, , 4, , 6 8 10 12 14, (VCE) in volt
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90, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 22 The centre of mass of a solid hemisphere of, radius 8 cm is x cm from the centre of the, flat surface. Then, value of x is …… ., , 23 An engine operates by taking a monatomic, ideal gas through the cycle shown in the, figure. The percentage efficiency of the, engine is close to ……… ., , 3p0, , B, , A, , D, , V0, , 2V0, , performed using monochromatic light of, wavelength λ. The intensity of light at a, point on the screen, where the path, difference is λ, is K units. The intensity of, light at a point where the path difference, λ, nK, is given by, , where n is an integer., is, 6, 12, The value of n is ……… ., , 25 In a series L-R circuit, power of 400W is, , C, , dissipated from a source of 250 V, 50 Hz., The power factor of the circuit is 0.8. In, order to bring the power factor to unity, a, capacitor of value C is added in series to, the L and R. Taking the value of C as, n µF, then value of n is ……… ., , 3π , , 2p0, p0, , 24 A Young’s double slit experiment is, , CHEMISTRY, Objective Type Questions, 1 For a reaction,, 4M(s) + nO 2( g) → 2M 2O n (s), The free energy change is plotted as a, function of temperature. The temperature, below which the oxide is stable could be, inferred from the plot as the point at, which, (a) the slope changes from negative to positive, (b) the free energy change shows a change, from negative to positive value, (c) the slope changes from positive to negative, (d) the slope changes from positive to zero, , 2 The average molar mass of chlorine is, , . g mol −1. The ratio of 35 Cl to 37 Cl in, 355, naturally occurring chlorine is close to, (a) 4 : 1, , (b) 3 : 1, , (c) 2 : 1, , (d) 1 : 1, , 3 Which one of the following statements is, not true?, (a) Lactose contains α-glycosidic linkage, between C1 of galactose and C4 of glucose., (b) Lactose is a reducing sugar and it gives, Fehling’s test., (c) Lactose (C11 H 22 O11 ) is a disaccharide and it, contains 8 hydroxyl groups., , (d) On acid hydrolysis, lactose gives one, molecule of D(+ ) - glucose and one molecule, of D (+ ) - galactose, , 4 The value of KC is 64 at 800 K for the, reaction,, N2( g) + 3H2( g), , - 2NH ( g), 3, , The value of KC for the following reaction is, 1, 3, NH3( g), N2( g) + H2( g), 2, 2, , -, , (a) 1/64, (c) 1/4, , (b) 8, (d) 1/8, , 5 Dihydrogen of high purity (> 99.95%) is, obtained through, (a) the reaction of Zn with dilute HCl, (b) the electrolysis of acidified water using Pt, electrodes, (c) the electrolysis of brine solution, (d) the electrolysis of warm Ba(OH)2 solution, using Ni electrodes., , 6 The reaction of NO with N2O 4 at 250 K, gives, (a) N 2 O, (c) N 2 O3, , (b) NO2, (d) N 2 O5
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91, , SEPTEMBER ATTEMPT ~ 06 Sep 2020, Shift II, 7 The correct match between Item-I (starting, , 12 Match the following compounds, , material) and Item-II (reagent) for the, preparation of benzaldehyde is, , (Column -I) with their uses (Columns -II)., Column -I, , Item - I, I, , Benzene, , Item - II, (P) HCl and SnCl 2 ,, H3O +, , II, , Benzonitrile, , (Q) H2 , Pd-BaSO 4 , S, and quinoline, , III, , Benzoyl chloride (R) CO, HCl and AlCl 3, , (a) (I) - (Q), (II) - (R) and (III) - (P), (b) (I) - (P), (II) - (Q) and (III) - (R), (c) (I) - (R), (II) - (P) and (III) - (Q), (d) (I) - (R), (II) - (Q) and (III) - (P), , 8 A crystal is made up of metal ions M1 and, , (I), , (II) NaCl, , (B) White wash, , (III) CaSO4 ⋅ 1 H 2O (C) Antacid, 2, (IV) CaCO3, , (b) +1, + 3, (d) +4, + 2, , 9 The element that can be refined by, distillation is, (a) nickel, (c) tin, , (b) zinc, (d) gallium, , 10 For a d 4 metal ion in an octahedral field,, the correct electronic configuration is, (a) t32g e1g when ∆ 0 < P, (c), , t24g eg0, , when ∆ 0 < P, , (b) t32g e1g when ∆ 0 > P, (d), , tg2e22g, , when ∆ 0 < P, , 13 The IUPAC name of the following, compounds is, OH, NH2, O2N, CHO, , (a) 2-nitro-4-hydroxymethyl-5-amino, benzaldehyde, (b) 3-amino-4-hydroxymethyl-1-5nitrobenzaldehyde, (c) 5-amino-4-hydroxymethyl, 1-2-nitrobenzaldehyde, (d) 4-amino-2-formyl-5-hydroxymethyl, -nitrobenzene, , 14 Which of the following compounds can be, prepared in good yield by Gabriel, phthalimide synthesis?, , 11 Match the following :, Test / Method, , CH2NH2, Reagent, , I., , Lucas test, , (A) C6H5SO 2Cl /aq. KOH, , II., , Dumas method, , (B) HNO 3 /AgNO 3, , (a), (b) CH3 CH2 NHCH3, , III. Kjeldahl’s method (C) CuO /CO 2, IV. Hinsberg test, , (D) Washing soda preparation, , (a) (I)-(D), (II)-(A), (III)-(C), (IV)-(B), (b) (I)-(B), (II)-(D), (III)-(A), (IV)-(C), (c) (I)-(B), (II)-(C), (III)-(D), (IV)-(A), (d) (I)-(C), (II)-(D), (III)-(B), (IV)-(A), , M 2 and oxide ions. Oxide ions form a ccp, lattice structure. The cation M1 occupies, 50% of octahedral voids and the cation M 2, occupies 12.5% of tetrahedral voids of oxide, lattice. The oxidation numbers of M1 and, M 2 are, respectively, (a) +2, + 4, (c) +3, + 1, , Column - II, (A) Casts of statues, , Ca(OH)2, , O, , (D) Conc. HCl and ZnCl 2, (E) H 2SO4, , (a) (I)-(D), (II)-(C), (III)-(B), (IV)-(E), (b) (I)-(B), (II)-(D), (III)-(E), (IV)-(A), (c) (I)-(D), (II)-(C), (III)-(E), (IV)-(A), (d) (I)-(B), (II)-(A), (III)-(C), (IV)-(D), , CH2—C—NH2, (c), NH2, (d)
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92, , ONLINE, , 15 A set of solutions is prepared using 180 g of, water as a solvent and 10 g of different, non-volatile solutes A, B and C. The relative, lowering of vapour pressure in the presence, of these solutes are in the order, [Given, molar mass of A =100 g mol −1;, B = 200 g mol −1; C =10,000 g mol −1], (a) B > C > A, (c) A > B > C, , (b) C > B > A, (d) A > C > B, , 16 For the given cell;, Cu(s)|Cu 2+ (C1M)||Cu 2+ (C 2M)|Cu(s), change in Gibbs energy (∆G) is negative, if, C1, 2, (d) C2 = 2 C1, , (b) C2 =, , (a) C1 = C2, (c) C1 = 2C2, , 17 Reaction of an inorganic sulphite X with, dilute H2SO 4 generates compound Y ., Reaction of Y with NaOH gives X. Further,, the reaction of X with Y and water affords, compound Z. Y and Z respectively, are, (a) SO2 and Na2 SO3, (b) SO3 and NaHSO3, (c) SO2 and NaHSO3, (d) S and Na2 SO3, , of the major products A, B and C of the, following reactions will be, O, , + HBr, , II., III., , (C6H5CO)2, , A, , + HBr, , B, , + HBr, , (a) II < III < I, (c) I < II < III, , 20 The correct match between Item - I and, Item - II is :, Item - I, , Item - II, , (A) Natural rubber (I), (B) Neoprene, , 1,3- butadiene + styrene, , (II) 1,3- butadiene +, acrylonitrile, , (C) Buna -N, , (III) Chloroprene, , (D) Buna -S, , (IV) Isoprene, , (a) (A)-(III), (B)-(IV), (C)-(I), (D)-(II), (b) (A)-(III), (B)-(IV), (C)-(II), (D)-(I), (c) (A)-(IV), (B)-(III), (C)-(II), (D)-(I), (d) (A)-(IV), (B)-(III), (C)-(I), (D)-(II), , Numerical Type Questions, 21 If the solubility product of AB2 is, , 3.20 × 10−11 M3 , then the solubility of AB2, in pure water is ……… ×104 mol L−1, , [Assuming that neither kind of ion reacts, with water], , 22 For Freundlich adsorption isotherm, a plot, , 18 The increasing order of the boiling points, , I., , JEE Main 2020 ~ Solved Papers, , C, , (b) III < I < II, (d) I < III < II, , 19 Mischmetal is an alloy consisting mainly of, (a) lanthanoid metals, (b) actinoid and transition metals, (c) lanthanoid and actinoid metals, (d) actinoid metals, , x, of log (y-axis) and log p (x-axis) gives a, m, straight line. The intercept and slope for, the line is 0.4771 and 2, respectively. The, mass of gas, adsorbed per gram of, adsorbent if the initial pressure is 0.04 atm,, is ……… × 10−4g. (log 3 = 04771, ), ., , 23 A solution of phenol in chloroform when, treated with aqueous NaOH gives, compound P as a major product. The mass, percentage of carbon in P is ……… ., (to the nearest integer), (Atomic mass: C =12; H = 1; O = 16), , 24 The atomic number of unnilunium is …… ., 25 The rate of a reaction decreased by 3.555, times when the temperature was changed, from 40° C to 30° C. The activation energy, (in kJ mol −1) of the reaction is …… ., (Take; R = 8314, J mol −1K −1, ln 3.555 = 1.268), .
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93, , SEPTEMBER ATTEMPT ~ 06 Sep 2020, Shift II, , MATHEMATICS, Objective Type Questions, 2 x, e, 1, , 1 The integral ∫, (a) e(4e + 1), (c) e(4e − 1), , ⋅ x (2 + log e x)dx equals, x, , (b) 4e2 − 1, (d) e(2e − 1), , 2 The area (in sq. units) of the region, , enclosed by the curves y = x2 − 1 and, y = 1 − x2 is equal to, , 4, 3, 7, (c), 2, , 8, 3, 16, (d), 3, , (a), , (b), , 3 The angle of elevation of the summit of a, mountain from a point on the ground is, 45°. After climbing up one km towards the, summit at an inclination of 30° from the, ground, the angle of elevation of the, summit is found to be 60°. Then, the height, (in km) of the summit from the ground is, (a), , 3 −1, 3 +1, , (b), , 3 +1, 3 −1, , (c), , 1, 3 −1, , (d), , 1, 3 +1, , 4 The set of all real values of λ for which the, function f (x) = (1 − cos2 x). (λ + sin x),, π π, x ∈ − , , has exactly one maxima and, 2 2, exactly one minima, is, , 1, (a) − ,, 2, , 1, − {0}, 2, 1 1, (c) − , , 2 2, , 3, (b) − ,, 2, , 3, , 2, 3 3, (d) − , − {0}, 2 2, , 5 If α and β are the roots of the equation, 2x(2x + 1) = 1, then β is equal to, (a) 2α (α + 1), (c) 2α (α − 1), , (b) −2α (α + 1), (d) 2α 2, , 6 For all twice differentiable functions, f : R → R, with f (0) = f (1) = f ′ (0) = 0, (a) f ′ ′ (x) ≠ 0 at every point x ∈ (0, 1), (b) f ′ ′ (x) = 0 at every point x ∈ (0, 1), (c) f ′ ′ (0) = 0, (d) f ′ ′ (x) = 0 at every point x ∈ (0, 1), , 7 If y = x − 1 cosec x is the solution of the, 2, π, , differential equation,, π, 2, dy, + p(x) y = cosec x, 0 < x < , then the, 2, dx, π, functionp(x) is equal to, , (a) cot x, (c) secx, , (b) cosecx, (d) tan x, , 8 Let L denote the line in the xy-plane with x, and y intercepts as 3 and 1 respectively., Then, the image of the point (−1, − 4) in, this line is, 11 28, (a) , , 5 5, 8 29, (c) , , 5 5 , , 29 8, (b) , , 5 5, 29 11, (d) , , 5 5, , 9 If the tangent to the curve, y = f (x) = x loge x,, (x > 0) at a point (c, f (c)) is parallel to the, line segment joining the point (1, 0) and, (e, e) then c is equal to, (a), , e−1, e, , 1 , , , , (b) e e − 1 , , 1 , , , , (c) e 1 − e , , (d), , 1, e −1, , 10 Let f : R → R be a function defined by, f (x) = max { x, x2 }. Let S denote the set of all, points in R, where f is not differentiable., Then,, (a) {0, 1}, (c) φ {an empty set}, , (b) {0}, (d) {1}, , π, cos θ sin θ , and A = , . If, 5, − sin θ cos θ , B = A + A4, then det (B), , 11 Let θ =, , (a) is one, (b) line in (2, 3), (c) is zero, (d) lies in (1, 2), , 12 A plane P meets the coordinate axes at, A, B and C respectively. The centroid of, ∆ABC is given to be (1, 1, 2). Then, the, equation of the line through this centroid, and perpendicular to the plane P is
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94, , ONLINE, x−1, =, 2, x−1, (b), =, 1, x−1, (c), =, 2, x−1, (d), =, 1, (a), , y − 1 z −2, =, 1, 1, y − 1 z −2, =, 1, 2, y − 1 z −2, =, 2, 1, y − 1 z −2, =, 2, 2, , 19 Consider the statement “For an integer n if, n3 − 1 is even, then n is odd”. The, contrapositive statement of this statement, is, , 13 The common difference of the AP, b1 , b2 , K , bm is 2 more than the common, difference of AP a1 , a 2 ,... , a n . If, a 40 = − 159, a100 = − 399 and b100 = a70, then, b1 is equal to, (a) 81, , (b) −127, , (c) −81, , (d) 127, , 14 If the normal at an end of a latus rectum of, an ellipse passes through an extremity of, the minor axis, then the eccentricity e of, the ellipse satisfies, (a) e4 + 2e2 − 1 = 0, (c) e4 + e2 − 1 = 0, , (b) e2 + e2 − 1 = 0, (d) e2 + 2e − 1 = 0, , 15 For a suitable chosen real constant a, let a, functin f : R − { a } → R be defined by, a −x, . Further suppose that for any, f (x) =, a+x, real number x ≠ −a and f (x) ≠ −a,, 1, ( fof )(x) = x. Then, f − is equal to, 2, , (a), , 1, 3, , (b) −, , 1, 3, , (c) −3, , (d) 3, , 16 If the constant term in the binomial, k, , expansion of x − 2 , , x , equals, (a) 9, , (b) 1, , 10, , is 405, then|k|, , (c) 3, , (d) 2, , 17 The centre of the circle passing through, the point (0, 1) and touching the parabola, y = x2 at the point (2, 4) is, −53 16 , (a) , , , 10 5 , 3 16, (c) , , 10 5 , , 6 53, (b) , , 5 10 , 16 53, (d) − , , 5 10 , , 18 Let z = x + iy be a non-zero complex, number such that z2 = i|z|2, where i = −1,, then z lies on the, (a) line y = − x, (c) line y = x, , JEE Main 2020 ~ Solved Papers, , (b) imaginary axis, (d) real axis, , (a) For an integer n, if n is even, then n3 − 1 is, odd, (b) For an integer n, if n3 − 1 is not even, then, n is not odd, (c) For an integer n, if n is even, then n3 − 1 is, even, (d) For an integer n, if n is odd, then n3 − 1 is, even, , 20 The probabilities of three events A, B and, C are given by P ( A) = 06,, . P (B) = 04, . and, P (C ) = 05., . If P ( A ∪ B) = 08,, . P ( A ∩ C ) = 03,, ., P ( A ∩ B ∩ C ) = 0.2, P (B ∩ C ) =β and, P ( A ∪ B ∪ C ) =α , where 085, . ≤ α ≤ 095, . ,, then β lies in the interval, (a) [ 0.35, 0.36], (b) [0.25, 0.35], (c) [0.20, 0.25], (d) [0.36, 0.40], , Numerical Type Questions, 21 Suppose that a function f : R → R satisfies, f (x + y) = f (x) f ( y) for all x, y ∈ R and, n, , f (1) = 3. If Σ f (i ) = 363, then n is equal to, i =1, , 22 The sum of distinct values of λ for which, the system of equations, (λ − 1)x + (3λ + 1) y + 2λz = 0, (λ − 1)x + (4λ − 2) y + (λ + 3)z = 0, 2x + (3λ + 1) y + 3(λ − 1) = 0, has non-zero solutions, is, , 23 If x and y be two non-zero vectors such, that|x + y| =|x|and 2x + λy is, perpendicular to y, then the value of λ is, 24 Consider the data on x taking the values, 0, 2, 4, 8, ……, 2n with frequencies, n, C 0 , n C1 ,n C 2 ,.... , n C n respectively. If the, 728, mean of this data is n , then n is equal to, 2, 25 The number of words (with or without, meaning) that can be formed from all the, letters of the word “LETTER” in which, vowels never come together is
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95, , SEPTEMBER ATTEMPT ~ 06 Sep 2020, Shift II, , Answers, Physics, 1., (c), 11. (c), 21. (150), , 2. (d), 12. (c), 22. (3), , 3., 13., 23., , (a), (d), (19), , (b), (d), (9), , 4., 14., 24., , 5., 15., 25., , (a), (a), (400), , 6. (d), 16. (d), , 7. (a), 17. (c), , 8. (d), 18. (b), , 9. (d), 19. (a), , 10. (c), 20. (b), , For Detailed Solutions, Visit : http://bit.ly/31lbmFq, Or Scan :, , Chemistry, 1., 11., 21., , (b), (c), (2), , 2., 12., 22., , (b), (b), (48), , 3., 13., 23., , (a), (c), (69), , 4., 14., 24., , (d), (a), (101), , 5., 15., 25., , (d), (c), (100), , 6., 16., , (c), (d), , 7., 17., , (c), (c), , 8., 18., , (a), (a), , 9., 19., , (b), (a), , 10., 20., , (a), (c), , 10., 20., , (a), (b), , For Detailed Solutions, Visit : http://bit.ly/37lYQJG, Or Scan :, , Mathematics, 1., (c), 11. (d), 21. (5.00), , 2., (b), 12. (c), 22. (3.00), , 3., (c), 13. (c), 23. (1.00), , 4., (d), 14. (c), 24. (6.00), , 5., (b), 15., (d), 25. (120.00), , 6., 16., , (b), (c), , 7., 17., , (a), (d), , 8., 18., , (a), (c), , 9., 19., , (b), (a), , For Detailed Solutions, Visit : http://bit.ly/3jit8yZ, Or Scan :
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ONLINE QUESTION PAPER, , JEE Main 2020, (07 January, 2020), TIME 9:30-12:30 (Shift I), , MM : 300, , PHYSICS, Objective Type Questions, 1 Consider a circular coil of wire carrying, constant current I, forming a magnetic, dipole. The magnetic flux through an, infinite plane that contains the circular, coil and excluding the circular coil area is, given by φi . The magnetic flux through the, area of the circular coil area is given by φ o ., Which of the following option is correct ?, (a) φ i > φ o (b) φi < φ o (c) φi = φo (d) φi = − φo, , 2 A satellite of mass m is launched vertically, upwards with an initial speed u from the, surface of the earth. After it reaches height, R (R = radius of the earth), it ejects a, m, rocket of mass , so that subsequently the, 10, satellite moves in a circular orbit. The, kinetic energy of the rocket is (G is the, gravitational constant M, is the mass of, the earth), (a), , 3m , u +, 8 , , 5 GM , , 6R , 2, , 2, , m, 2GM , , u −, 20 , 3R , m 2 113 GM , (c), u +, , 20 , 200 R , 119 GM , (d) 5m u 2 −, , , 200 R , , (b), , 3 If the magnetic field in a plane, electromagnetic wave is given by, B = 3 × 10−8 sin(16, . × 103 x + 48 × 1010 t )$jT,, then what will be expression for electric, field?, $ V/m, (a) E = 60 sin(16, . × 103 x + 48 × 1010 t )k, (b) E = 3 × 10−8 sin(16, . × 103 x + 48 × 1010 t ) $i V/m, (c) E = 3 × 10−8 sin(16, . × 103 x + 48 × 1010 t ) $jV/m, $V/m, (d) E = 9 sin(16, . × 103 x + 48 × 1010 t )k, , 4 Visible light of wavelength 6000 × 10−8 cm, falls normally on a single slit and, produces a diffraction pattern. It is found, that the second diffraction minimum is, at 60° from the central maximum. If the, first minimum is produced at θ1, then θ1 is, close to, (a) 25°, (c) 20°, , (b) 30°, (d) 45°, , 5 An L-C-R circuit behaves like a damped, harmonic oscillator. Comparing it with a, physical spring-mass damped oscillator, having damping constant b, the correct, equivalence would be, 1, 1, 1, (a) L ↔ , C ↔ , R ↔, b, m, k, 1, (b) L ↔ m, C ↔ , R ↔ b, k, (c) L ↔ m, C ↔ k, R ↔ b, (d) L ↔ k, C ↔ b, R ↔ m
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4, , ONLINE, 6 As shown in the figure, a bob of mass m is, tied by a massless string whose other end, portion is wound on a flywheel (disc) of, radius r and mass m. When released from, rest the bob starts falling vertically. When, it has covered a distance of h, the angular, speed of the wheel will be, , JEE Main 2020 ~ Solved Papers, , (a) 0.25, (c) 0.5, , (b) 0.4, (d) 0.2, , 10 Which of the following gives a reversible, operation?, (a), , (b), , (c), , (d), , m, r, , (a), , 1 2 gh, 1 4 gh, 3, 3, (b) r, (d) r, (c), r, 3, r, 3, 4 gh, 2 gh, , 7 Speed of a transverse wave on a straight, wire (mass 6.0 g, length 60 cm and area of, cross-section 1.0 mm 2) is 90 ms −1. If the, Young’s modulus of wire is 16 × 1011 Nm −2,, the extension of wire over its natural, length is, (a) 0.01 mm, (c) 0.03 mm, , (b) 0.04 mm, (d) 0.02 mm, , 8 Two infinite planes each with uniform, , surface charged density +σ are kept in, such a way that the angle between them is, 30°. The electric field in the region shown, between them is given by, +σ, , y, , 30º, , +σ, , x, , $, , 3 $ x, y − , 1 −, 2 , 2, , , (a), , σ, 2 ε0, , , (1 +, , , $, σ, x, 3 )y$ − (b), 2, 2 ε0, , (c), , σ, 2 ε0, , , (1 +, , , $, $, x, σ , 3 $, x, 3 )y$ + (d), y + , 1 +, ε0 , 2 , 2, 2, , 9 The current I1 (in ampere) flowing through, 1Ω resistor in the following circuit is, I1 1Ω, 2Ω, 1Ω, , 2Ω, 1V, , 5, = are, CV 3, mixed with 3 mol of another ideal gas with, Cp 4, Cp, for the mixture is, = . The value of, CV 3, CV, , 11 Two moles of an ideal gas with, , m, , (a) 1.42, (c) 1.50, , Cp, , (b) 1.47, (d) 1.45, , 12 The time period of revolution of electron in, its ground state orbit in a hydrogen atom is, . × 10−16 s. The frequency of revolution of, 16, the electron in its first excited state (in Hz ) is, (a), (b), (c), (d), , 16, . × 1014, 5.6 × 1012, 6.2 × 1015, 7.8 × 1014, , 13 A parallel plate capacitor has plates of, area A separated by distance d between, them. It is filled with a dielectric which, has a dielectric constant that varies as, k(x) = K (1 + αx), where x is the distance, measured from one of the plates. If, (αd ) << 1, the total capacitance of the, system is best given by the expression, , AK ε0, (1 + αd ), d, 2, A ε0 K , αd , (b), 1 + , , 2 , d , AK ε0 , αd , (c), 1 +, , d , 2, A ε0 K , α 2d 2 , , 1 +, (d), d , 2 , , (a)
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5, , JANUARY ATTEMPT ~ 07 Jan 2020, Shift I, 2.5 kg, , 14 If we need a magnification of 375 from a, compound microscope of tube length, 150 mm and an objective of focal length, 5 mm, the focal length of the eyepiece, should be close to, , 4 cm, , 5 cm, , (a) 22 mm (b) 2 mm (c) 12 mm (d) 33 mm, , 15 A litre of dry air at STP expands, , adiabatically to a volume of 3 L. If γ = 140, . ,, the work done by air is (31. 4 = 46555, ., ), [Take, air to be an ideal gas], , (a) 100.8 J (b) 90.5 J (c) 48 J, , (d) 60.7 J, , 16 A 60 HP electric motor lifts an elevator, having a maximum total load capacity of, 2000 kg. If the frictional force on the, elevator is 4000 N, the speed of the, elevator at full load is close to (Take, 1 HP, = 746 W, g = 10 ms −2), (a) 2.0 ms −1, (c) 1.9 ms −1, , (b) 1.5 ms −1, (d) 1.7 ms −1, , 17 A polariser-analyser set is adjusted such, that the intensity of light coming out of the, analyser is just 10% of the original, intensity., Assuming, that, the, polariser-analyser set does not absorb any, light, the angle by which the analyser need, to be rotated further to reduce the output, intensity to be zero, is, (a) 71.6°, , (b) 90°, , (c) 45°, , (d) 18.4°, , 18 A long solenoid of radius R carries a time, , (t )-dependent current I (t ) = I 0t (1 − t ). A ring, of radius 2R is placed coaxially near its, middle. During the time interval 0 ≤ t ≤ 1,, the induced current (I R ) and the induced, EMF(VR ) in the ring change as ;, (a) Direction of IR remains unchanged and, VR is maximum at t = 0.5s, (b) At t = 0.25s direction of IR reverses and, VR is maximum, (c) Direction of IR remains unchanged and, VR is zero at t = 0.25s, (d) At t = 0.5 direction of IR reverses and VR, is zero, , 19 Three point particles of masses 1.0 kg,, 1.5 kg and 2.5 kg are placed at three corners, of a right angle triangle of sides 4.0 cm,, 3.0 cm and 5.0 cm as shown in the figure., The centre of mass of the system is at a, point, , 1.0 kg, , (a), (b), (c), (d), , 1.5 kg, , 3 cm, , 2.0 cm right and 0.9 cm above 1 kg mass, 0.6 cm right and 2.0 cm above 1 kg mass, 1.5 cm right and 1.2 cm above 1 kg mass, 0.9 cm right and 2.0 cm above 1 kg mass, , 20 The radius of gyration of a uniform rod of, length l, about an axis passing through a, l, point away from the centre of the rod, 4, and perpendicular to it, is, (a), , 1, l, 8, , (b), , 3, l, 8, , (c), , 7, l, 48, , (d), , 1, l, 4, , Numerical Type Questions, 21 A loop ABCDEFA of straight edges has six, corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0),, D(0, 5, 0), E(0, 5, 5) and F (0, 0, 5). The, magnetic field in this region is, $ )T. The quantity of flux through, B = (3i$ + 4k, the loop ABCDEFA (in Wb) is ………… ., , 22 A beam of electromagnetic radiation of, , intensity 64, . × 10−5 W/cm 2 is comprised of, wavelength λ = 310 nm. It falls normally, on a metal (work function φ = 2 eV) of, surface area of 1 cm 2. If one in 103 photons, ejects an electron, total number of, electrons ejected in 1 s is 10x ., (hc = 1240 eVnm, 1 eV = 16, . × 10−19 J), then, x is ……… ., , 23 A Carnot engine operates between two, reservoirs of temperatures 900 K and, 300 K. The engine performs 1200 J of work, per cycle. The heat energy (in J) delivered, by the engine to the low temperature, reservoir in a cycle, is ……… ., , 24 A non-isotropic solid metal cube has, coefficients of linear expansion as :, 5 × 10−5 /°C along the X-axis and 5 × 10−6/°C, along the Y and the Z-axis. If the, coefficient of volume expansion of the solid, is C × 10−6/°C, then the value of C is ……… .
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6, , ONLINE, , JEE Main 2020 ~ Solved Papers, , 25 A particle (m = 1 kg) slides down a frictionless, , Height, , A, , track ( AOC ) starting from rest at a point A, (height 2 m). After reaching C, the particle, continues to move freely in air as a projectile., When it reaching its highest point P (height, 1 m), the kinetic energy of the particle (in J), is : (Figure drawn is schematic and not to, scale; take g = 10 ms −2) ……… ., , P, 2m, , C, 2m, O, , CHEMISTRY, Objective Type Questions, 1 The number of orbitals associated with, 1, quantum numbers n = 5, ms = + is, 2, , (a) 25, (c) 15, , (b) 50, (d) 11, , 2 The dipole moments of CCl4 , CHCl3 and, CH4 are in the order, (a), (b), (c), (d), , CCl 4 < CH4 < CHCl3, CH4 < CCl 4 < CHCl3, CH4 == CCl 4 < CHCl3, CHCl3 < CH4 == CCl 4, , 5 The theory that can completely/ properly, explain the nature of bonding in [Ni(CO)4 ] is :, (a), (b), (c), (d), , Werner’s theory, Crystal field theory, Valence bond theory, Molecular orbital theory, , 6 The increasing order of pK b for the, following compounds will be :, N, , NH2 CH NH,, (A ), , 3 What is the product of following reaction?, (i) NaBH, , 4, ?, Hex - 3 - ynal →, , (ii) PBr3, (iii) Mg/ ether, (iv) CO 2/ H 3O +, , (a), , COOH, , NH, CH3 NH CH3, (C), , N, (B), , (a), (b), (c), (d), , (B) < (C) < (A), (C) < (A) < (B), (A) < (B) < (C), (B) < (A) < (C), , 7 Consider the following reaction :, (b), , COOH, N, , (c), , COOH, , CH3, , + Na SO3—, , —N2 Cl, , CH3, OH –, , → X, (d), , COOH, , 4 The IUPAC name of the complex, [Pt(NH3 )2Cl(NH2CH3 )]Cl is, (a) diammine (methanamine) chlorido, platinum (II) chloride, (b) diamminechlorido (methanamine), platinum (II) chloride, (c) diamminechlorido (aminomethane), platinum (II) chloride, (d) bisammine (methanamine) chlorido, platinum (II) chloride, , The product ‘X’ is used, (a) in acid base titration as an indicator, (b) in protein estimation as an alternative to, ninhydrin, (c) as food grade colourant, (d) in laboratory test for phenols, , 8 Oxidation number of potassium in K 2O,, K 2O2 and KO2, respectively, is, , (a) +1, +4 and +2, , (c) +1, + 1 and +1, , (b) +1, + 2 and +4, 1, (d) +2, + 1 and +, 2
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7, , JANUARY ATTEMPT ~ 07 Jan 2020, Shift I, 9 The electron gain enthalpy (in kJ/mol) of, fluorine, chlorine, bromine and iodine,, respectively, are, (a), (b), (c), (d), , −333, −325, −349 and −296, −296, −325, −333 and −349, −333, −349, −325 and −296, −349, −333, −325 and −296, , 10 Consider the following reactions :, Conc. H SO, , 2, 4, (A) (CH3 )3 CCH(OH)CH3 →, , Alc. KOH, , (B) (CH3 )2CHCH(Br)CH3 →, (CH 3 ) 3 O È K ⊕, , (C) (CH3 )2CHCH(Br)CH3 →, ∆, , (D) (CH3 )2 C CH2 CHO →, |, OH, Which of these reaction(s) will not, produce Saytzeff product?, (a), (b), (c), (d), , (A), (C) and (D), (B) and (D), (C) Only, (D) Only, , 11 1-methyl ethylene oxide when treated, with an excess of HBr produces :, Br, , (a) Br, , Br, , (b), Br, , CH3, , (c), , (i), , Riboflavin, , (A), , Beriberi, , (ii), , Thiamine, , (B), , Scurvy, , (iii), , Pyridoxine, , (C), , Cheilosis, , (iv), , Ascorbic acid, , (D), , Convulsions, , (a), (b), (c), (d), , (i)-(C), (ii)-(D), (iii)-(A), (iv)-(B), (i)-(C), (ii)-(A), (iii)-(D), (iv)-(B), (i)-(D), (ii)-(B), (iii)-(A), (iv)-(C), (i)-(A), (ii)-(D), (iii)-(C), (iv)-(B), , 14 At 35°C, the vapour pressure of CS2 is, 512 mm Hg and that of acetone is 344 mm, Hg. A solution of CS2 in acetone has a total, vapour pressure of 600 mm Hg. The false, statement amongst the following is, (a) Raoult’s law is not obeyed by this system, (b) CS 2 and acetone are less attracted to each, other than to themselves, (c) a mixture of 100 mL CS 2 and 100 mL, acetone has a volume < 200 mL, (d) heat must be absorbed in order to, produce the solution at 35°C, , 15 Given that the standard potentials (E°) of, , Cu 2+ /Cu and Cu + /Cu are 0.34 V and, 0.522 V respectively, the E° of Cu 2+ /Cu + is, (a) −0158, V, ., (c) −0182, V, ., , (b) +0158, V, ., (d) 0182, V, ., , 16 The purest form of commercial iron is, CH3, , Br, , 13 Match the following :, , Br, , (d), CH3, , 12 Among the following statements, that, which was not proposed by Dalton was, (a) chemical reactions involve, reorganisation of atoms. These are, neither created nor destroyed in a, chemical reaction., (b) when gases combine or reproduced in a, chemical reaction they do so in a simple, ratio by volume provided all gases are, at the same T and P., (c) all the atoms of a given element have, identical properties including identical, mass. Atoms of different elements differ, in mass., (d) matter consists of indivisible atoms., , (a) cast iron, (c) wrought iron, , (b) scrap iron and pig iron, (d) pig iron, , 17 The atomic radius of Ag is closest to, (a) Hg, (c) Ni, , (b) Au, (d) Cu, , 18 The relative strength of, interionic/intermolecular forces in, decreasing order is, (a), (b), (c), (d), , dipole-dipole > ion-dipole > ion-ion, ion-ion > ion-dipole > dipole-dipole, ion-dipole > ion-ion > dipole-dipole, ion-dipole > dipole-dipole > ion-ion, , 19 A solution of m-chloroaniline,, m-chlorophenol and m-chlorobenzoic acid in, ethyl acetate was extracted initially with a, saturated solution of NaHCO3 to give, fraction A.
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8, , JEE Main 2020 ~ Solved Papers, , ONLINE, The left over organic phase was, extracted with dilute NaOH solution to, give fraction B. The final organic layer, was labelled as fraction C. Fractions A, B, and C contain respectively, (a) m-chlorobenzoic acid, m-chloroaniline, and m-chlorophenol, (b) m-chlorophenol, m-chlorobenzoic acid, and m-chloroaniline, (c) m-chlorobenzoic acid, m-chlorophenol, and m-chloroaniline,, (d) m-chlorobenzoic acid and, m-chlorophenol, , 20 In comparison to the zeolite process for, the removal of permanent hardness, the, synthetic resins method is, (a) more efficient as it can exchange only, cations, (b) less efficient as it exchanges only, anions, (c) less efficient as the resins cannot be, regenerated, (d) more efficient as it can exchange both, cations as well as anions, , Numerical Type Questions, 21 For the reaction; A(l) → 2B( g), ∆U = 21, . kcal, ∆S = 20 cal K −1 at 300 K., Hence, ∆G in kcal is …… ., , 22 Chlorine reacts with hot and concentrated, NaOH and produces compounds (X ) and (Y )., Compound (X ) gives white precipitate with, silver nitrate solution. The average bond, order between Cl and O atoms in (Y ) is …… ., , 23 The number of chiral carbons in, chloramphenicol is …… ., , 24 Two solutions, A and B, each of 100 L was, made by dissolving 4 g of NaOH and 9.8 g of, H2SO4 in water, respectively. The pH of the, resultant solution obtained from mixing 40 L, of solution A and 10 L of solution B is……… ., , 25 During the nuclear explosion, one of the, , products is 90Sr with half-life of 6.93 years., If 1 µg of 90Sr was absorbed in the bones of a, newly born baby in place of Ca, how much, time, in years, is required to reduce it by, 90% if it is not lost metabolically ……… ., , MATHEMATICS, , 2x + 3by + bz = 0, , tan α + cot α , 1, +, ,, 2, 1 + tan α sin 2 α, dy, 5π, 3π , at α =, is, α ∈, , π , then, 4, , dα, 6, , 2x + 4cy + cz = 0, , (a) −, , Objective Type Questions, 1 If the system of linear equations, 2x + 2ay + az = 0, , where a, b, c ∈ R are non-zero and, distinct; has a non-zero solution, then, 1 1 1, (a) a + b + c = 0, (b) , , are in A.P., a b c, (c) a , b, c are in A.P. (d) a , b, c are in G.P., , 2 Let α be a root of the equation, , x2 + x + 1 = 0 and the matrix, 1 1 1 , 1 , A=, 1 α α 2 , then the matrix A31, , 3, 2, 4, 1 α α , is equal to, , (a) A3, (c) A 2, , (b) I3, (d) A, , 3 If y(α ) = 2, , 1, 4, , (b), , 4, 3, , (c) −4, , (d) 4, , 4 The area of the region, enclosed by the circle, , x2 + y2 = 2 which is not common to the region, bounded by the parabola y2 = x and the, straight line y = x, is, , 1, (12 π − 1), 3, 1, (c) (24 π − 1), 6, (a), , 1, (12 π − 1), 6, 1, (d) (6 π − 1), 3, (b), , 5 If y = mx + 4 is a tangent to both the, parabolas, y2 = 4x and x2 = 2by, then b is, equal to, (a) −32, , (b) −128, , (c) −64, , (d) 128
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9, , JANUARY ATTEMPT ~ 07 Jan 2020, Shift I, 6 If g(x) = x2 + x − 1 and ( gof ), , 14 The greatest positive integer k, for which, , 5, (x) = 4x − 10x + 5, then f is equal to, 4, 2, , 3, (b), 2, , 1, (a) −, 2, , 3, (c) −, 2, , 1, (d), 2, , 7 The logical statement ( p ⇒ q) ∧ (q ⇒ ~ p) is, (a) ~ p, (c) p, , (b) q, (d) −q, , 8 Let xk + yk = a k, (a , k > 0) and, 1, , dy y 3, + = 0, then k is, dx x, 4, 3, , (b), , 3, 2, , (c), , 2, 3, , (d), , 1, 3, , 9 If y = y(x) is the solution of the differential, dy, , equation, e y , − 1 = ex such that y(0) = 0,, dx, , then y(1) is equal to, (a) 2 + log e 2, (c) 1 + log e 2, , (b) 2e, (d) log e 2, , 10 If the distance between the foci of an, ellipse is 6 and the distance between its, directrices is 12, then the length of its, latus rectum is, (a) 3 2, , (b), , 3, , (c) 2 3, , (d), , 3, 2, , 11 Let P be a plane passing through the, points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R, be any point (2, 1, 6). Then the image of R, in the plane P is, (a) (6, 5, 2), (c) (6, 5, −2), , (b) (4, 3, 2), (d) (3, 4, −2), , 12 An unbiased coin is tossed 5 times. Suppose, that a variable X is assigned the value k, when k consecutive heads are obtained for, k = 3, 4, 5, otherwise X takes the value −1., Then the expected value of X, is, 3, (a) −, 16, , 3, (b), 16, , 1, (c), 8, , 1, (d) −, 8, , 13 Total number of 6-digit numbers in which, only and all the five digits 1, 3, 5, 7 and 9, appear, is, (a) 6!, (c), , 1, (6!), 2, , 49125 + 49124 + … + 492 + 49 + 1, is, (a) 32, (c) 65, , (b) 63, (d) 60, , z −1 , = 1, where z = x + iy, then the, 2z + i , point (x, y) lies on a, 2, (a) straight line whose slope is − ., 3, 3, 1, (b) circle whose centre is at − , − ., 2, 2, 3, (c) straight line whose slope is ., 2, 5, (d) circle whose diameter is, ., 2, , 15 If Re, , equivalent to, , (a), , 49k + 1 is a factor of the sum, , (b), , 5, (6!), 2, , (d) 56, , 16 Five numbers are in A.P., whose sum is 25, and product is 2520. If one of these five, 1, numbers is − , then the greatest number, 2, amongst them is, (a) 7, (c) 27, , (b) 16, 21, (d), 2, , 17 If f (a + b + 1 − x) = f (x), for all x, where a, and b are fixed positive real numbers, then, b, 1, x( f (x) + f (x + 1))dx is equal to, ∫, a+b a, b+1, , (a), , ∫a + 1 f (x + 1)dx, , (c), , ∫a − 1 f (x + 1)dx, , b −1, , b+1, , (b), , ∫a + 1 f (x)dx, , (d), , ∫a − 1 f (x)dx, , b −1, , 18 A vector a = αi$ + 2 $j + βk$ (α , β ∈R) lies in, the plane of the vectors, b = i$ + $j and, c = i$ − $j + 4k$ . If a bisects the angle between, b and c, then, (a) a ⋅ i$ + 3 = 0, (c) a ⋅ i$ + 1 = 0, , (b) a ⋅ k$ + 2 = 0, (d) a ⋅ k$ + 4 = 0, , 19 Let α and β be two real roots of the, equation (k + 1) tan 2 x − 2 ⋅ λ tan x, = (1 − k), where k(≠ − 1) and λ are real, numbers. If tan 2 (α + β) = 50, then a value, of λ is, (a) 5 2, (c) 10 2, , (b) 10, (d) 5
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10, , ONLINE, , 3, 2, , 20 Let the function, f : [−7, 0] → R be, , vertices of a triangle ABC. If P is a point, inside the triangle ABC such that the, triangles APC, APB and BPC have equal, areas, then the length of the line segment, 1, 7, PQ, where Q is the point − , − , is, 6, 3, ……… ., , (b) [−3, 11], (d) (−∞ , 20], , Numerical Type Questions, 21 If the sum of the coefficients of all even, , 24 Let S be the set of points where the, , powers of x in the product, (1 + x + x + … + x )(1 − x + x − x + … + x, is 61, then n is equal to …… ., 2, , , , , 23 Let A(1, 0), B(6, 2) and C , 6 be the, , continuous on [−7, 0] and differentiable on, (−7, 0). If f (−7) = − 3 and f ′ (x) ≤ 2, for all, x ∈ (−7, 0), then for all such functions f,, f (−1) + f (0) lies in the interval, (a) (−∞ , 11], (c) [−6, 20], , JEE Main 2020 ~ Solved Papers, , 2n, , 2, , 3, , 2n, , function, f (x) =|2 −|x − 3||, x ∈ R, is not, differentiable. Then ∑ f ( f (x)) is equal to, x ∈S, ………. ., , ), , 22 If the variance of the first n natural, numbers is 10 and the variance of the first, m even natural numbers is 16, then m + n, is equal to ……… ., , 25 lim, , x→ 2, , 3x + 33 − x − 12, 3− x / 2 − 31 − x, , is equal to ……… ., , Answers, Physics, 1. (d), 11. (a), 21. (175), , 2., 12., 22., , (d), (d), (11), , 3. (d), 13. (c), 23. (600), , 4., 14., 24., , (a), (a), (60), , 5., 15., 25., , (b), (b), (10), , 6., 16., , (c), (c), , 7., 17., , (c), (d), , 8., 18., , (b), (d), , 9., 19., , (d), (d), , 10., 20., , (d), (c), , 10., 20., , (c), (d), , 10., 20., , (a), (d), , For Detailed Solutions, Visit : http://bit.ly/35770Tm, Or Scan :, , Chemistry, 1., (a), 11. (a), 21. (–2.70), , 2. (c), 12. (b), 22. (1.67), , 3. (d), 13. (b), 23. (2.0), , 4., (b), 14., (c), 24. (10.60), , 5., (d), 15., (b), 25. (23.03), , 6., 16., , (d), (c), , 7., 17., , (a), (b), , 8., 18., , (c), (b), , 9., 19., , (c), (c), , For Detailed Solutions, Visit : http://bit.ly/3jiwN04, Or Scan :, , Mathematics, 1., 11., 21., , (b), (c), (30), , 2., 12., 22., , (a), (c), (18), , 3., 13., 23., , (d), (b), (05), , 4., 14., 24., , (b), (b), (03), , 5., 15., 25., , (b), (d), (36), , 6., 16., , (a), (b), , 7., 17., , (a), (c), , 8., 18., , (c), (b), , 9., 19., , (c), (b), , For Detailed Solutions, Visit : http://bit.ly/3o8ST8W, Or Scan :
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ONLINE QUESTION PAPER, , JEE Main 2020, (07 January, 2020), TIME 2:30-5:30 (Shift II), , MM : 300, , PHYSICS, $, If its instantaneous velocity at (t = 0) is v0k, , Objective Type Questions, , , the force acting on it due to the wave is, , 1 A thin lens made of glass (refractive index, = 15, . ) of focal length f = 16 cm in immersed, in a liquid of refractive index 142, . . If its, focal length in liquid is f1, then the ratio, f1 / f is closest to the integer, (a) 1, , (b) 5, , (c) 9, , (a) zero, $i + $j, 2, $i + $j, (c) parallel to, 2, $, (d) parallel to k, (b) antiparallel to, , (d) 17, , 2 A mass of 10 kg is suspended by a rope of, length 4 m, from the ceiling. A force F is, applied horizontally at the mid-point of the, rope such that the top half of the rope, makes an angle of 45° with the vertical., Then, F equals (Take, g = 10 ms −2 and the, rope to be massless), (a) 75 N, , (b) 70 N, , 5, , B (T), 2.0, , 1.0, , (c) 100 N (d) 90 N, , –150, , 3 A box weighs 196 N on a spring balance at, , 50, , the north pole. Its weight recorded on the, same balance, if it is shifted to the equator, is close to (Take, g = 10 ms −2 at the north, pole and the radius of the earth = 6400 km), (a) 195.66 N, (c) 194.66 N, , 150, , H A/m, , –1.0, , (b) 195.32 N, (d) 194.32 N, , 4 The electric field of a plane, , –50, , –2.0, , electromagnetic wave is given by, $i + $j, cos (kz + ωt ), E = E0, 2, , The figure gives experimentally measured, B versusH variation in a ferromagnetic, material. The retentivity, coercivity and, saturation respectively of the material are, , At t = 0, a positively charged particle is at, π, , the point (x, y, z) = 0, 0, ., , k, , (a), (b), (c), (d), , 1.0 T, 50 A/m and 1.5 T, 150 A/m, 1.0 T and 1.5 T, 1.5 T, 50 A/m and 1.0 T, 1.5 T, 50 A/m and 1.0 T
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12, , ONLINE, 6 In the figure, potential difference between, , 30 V, , 10 In a building, there are 15 bulbs of 45 W,, 15 bulbs of 100 W, 15 small fans of 10 W and, 2 heaters of 1 kW. The voltage of electric, main is 220 V. The minimum fuse capacity, (rated value) of the building will be, , A and B is, 10 kΩ, , JEE Main 2020 ~ Solved Papers, , A, , 10 kΩ, , 10 kΩ, , (a) 25 A, , (b) 10 A, , (c) 20 A, , (d) 15 A, , 11 Two ideal Carnot engines operate in, B, , (a) zero, (c) 5 V, , (b) 10 V, (d) 15 V, , 7 An elevator in a building can carry a, maximum of 10 persons with the average, mass of each person being 68 kg. The mass, of the elevator itself is 920 kg and it moves, with a constant speed of 3 m/s. The, frictional force opposing the motion is, 6000 N. If the elevator is moving up with, its full capacity, the power delivered by the, motor to the elevator (g = 10 m/s 2) must be, at least, (a) 62360 W, (c) 56300 W, , (b) 48000 W, (d) 66000 W, , 8 A stationary observer receives sound from, two identical tuning forks, one of which, approaches and the other one recedes with, the same speed (much less than the speed, of sound). The observer hears 2 beats/s., The oscillation frequency of each tuning, fork is ν 0 = 1400 Hz and the velocity of, sound in air is 350 m/s. The speed of each, tuning fork is close to, (a), , 1, m/s, 8, , 1, m/s, 2, 1, (d) m/s, 4, , (b), , (c) 1 m/s, , the same energy E in the range of a few, electron volt. The ratio of the de Broglie, wavelength associated with the electron, and the wavelength of the photon is (c =, speed of light in vacuum), 1/ 2, , (c) c (2mE )1/ 2, , (a) T = 0, (c) T = T1 T2, , 2T1T2, T1 + T2, T + T2, (d) T = 1, 2, , (b) T =, , 12 In a Young’s double slit experiment, the, separation between the slits is 0.15 mm. In, the experiment, a source of light of, wavelength 589 nm is used and the, interference pattern is observed on a, screen kept 1.5 m away. The separation, between the successive bright fringes on, the screen is, (a) 4.9 mm (b) 3.9 mm (c) 6.9 mm (d) 5.9 mm, , 13 The dimension of, , B2, , where B is magnetic, 2µ 0, , field and µ 0 is the magnetic permeability of, vacuum, is, , 9 An electron (of mass m) and a photon have, , E , (a) , , 2m , , cascade (all heat given up by one engine is, used by the other engine to produce work), between temperatures T1 and T2. The, temperature of the hot reservoir of the, first engine is T1 and the temperature of, the cold reservoir of the second engine is, T2. T is temperature of the sink of first, engine which is also the source for the, second engine. How is T related to T1 and, T2, if both the engines perform equal, amount of work?, , 1/ 2, , (b), , 1 2E , , , c m, , (d), , 1 E , , , c 2m , , 1/ 2, , (a) [ML−1 T −2], (c) [ML2T −1 ], , (b) [MLT −2], (d) [ML2T −2], , 14 Mass per unit area of a circular disc of, radius a depends on the distance r from its, centre as σ(r ) = A + Br. The moment of, inertia of the disc about the axis,, perpendicular to the plane and passing, through its centre is, A B, (a) 2 πa 4 + , 4, 5, aB , 4 A, (c) πa +, , 4, 5 , , aA B , (b) 2 πa 4 , + , 4, 5, aB , 4 A, (d) 2 πa +, , 4, 5
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13, , JANUARY ATTEMPT ~ 07 Jan 2020, Shift II, 15 Under an adiabatic process, the volume of, an ideal gas gets doubled. Consequently,, the mean collision time between the gas, Cp, molecule changes from τ1 to τ 2. If, =γ, CV, τ, for this gas, then a good estimate for 2 is, τ1, given by, 1, (a) , 2, , γ+1, 2, , (c) 2, , 1, (b), 2, , 20 An emf of 20 V is applied at time t = 0 to a, circuit containing in series 10 mH inductor, and 5Ω resistor. The ratio of the currents, at time t = ∞ and at t = 40 s is close to, (Take, e2 = 7389, ., ), (a) 1.06, , 1, (d) , 2, , 20 V supply. It is then disconnected from, the supply and is connected to another, uncharged 60 pF capacitor in parallel. The, electrostatic energy that is lost in this, process by the time, the charge is, redistributed between them is (in nJ), ………… ., , γ, , 22 The balancing length for a cell is 560 cm in, a potentiometer experiment. When an, external resistance of 10Ω is connected in, parallel to the cell, the balancing length, changes by 60 cm. If the internal, N, resistance of the cell is, Ω, where N is an, 10, integer, then value of N is ………… ., , (b) 2.5 s and 5.0 s, (d) 5.0 s and 7.5 s, , 17 A particle of mass m and charge q has an, initial velocity v = v0$j. If an electric field, E = E 0i$ and magnetic field B = B0i$ act on, , 23 The sum of two forces P and Q is R such, that|R| =|P|. The angle θ (in degrees) that, the resultant of 2P and Q will make with Q, is, ……… ., , the particle, its speed will double after a, time, 3mv0, qE0, , 2mv0, (c), qE0, , (d) 0.84, , 21 A 60 pF capacitor is fully charged by a, , magnetic field. Initially at t = 0, the plane, of the loop is perpendicular to the, magnetic field. If it rotates with a period of, 10s about an axis in its plane, then the, magnitude of induced emf will be, maximum and minimum respectively at, , (a), , (c) 1.46, , Numerical Type Questions, , 16 A planar loop of wire rotates in a uniform, , (a) 2.5 s and 7.5 s, (c) 5.0 s and 10.0 s, , (b) 1.15, , (b), , 3mv0, qE0, , (d), , 2mv0, qE0, , 24, , F, , 18 The activity of a radioactive sample falls, from 700s −1 to 500s −1 in 30 min. Its, half-life is close to, , (a) 62 min, (c) 72 min, , (b) 66 min, (d) 52 min, , 19 An ideal fluid flows (laminar flow) through, a pipe of non-uniform diameter. The, maximum and minimum diameters of the, pipes are 6.4 cm and 4.8 cm, respectively., The ratio of the minimum and the, maximum velocities of fluid in this pipe is, 9, (a), 16, 3, (c), 2, , 81, (b), 256, 3, (d), 4, , Consider a uniform cubical box of side a on a, rough floor that is to be moved by applying, minimum possible force F at a point b above, its centre of mass (see figure). If the, coefficient of friction is µ = 04, . , the maximum, b, for box not to, possible value of 100 ×, a, topple before moving is ………, ., , 25 M grams of steam at 100°C is mixed with, 200 g of ice at its melting point in a, thermally insulated container. If it, produces liquid water at 40°C [heat of, vaporisation of water is 540 cal/g and heat, of fusion of ice is 80 cal/g], the value of M, is ……… .
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16, , ONLINE, , 15 In the following reaction sequence,, structures of A and B, respectively will be, O, HBr, ∆, , Na, , A Ether (Intramolecular product) B, , (a) 100 mL of 0.2 N HCl, (b) 200 mL of 0.4 N HCl, (c) 200 mL of 0.2 N HCl, (d) 100 mL of 0.1 N HCl, , 19 The refining method used when the metal, and the impurities have low and high, melting temperatures, respectively, is, , CH2Br, , Br, , CH2Br, OH, , (a), , JEE Main 2020 ~ Solved Papers, , (a), (b), (c), (d), , and, , CH2Br, , O, , distillation, zone refining, liquation, vapour phase refining, , 20 Among the statements (A)-(D), the, OH, , OH, Br, , (b), , and, , CH2Br, Br, , Br, OH, , (c), , and, , O, , CH2Br, OH, , OH, Br, , (d), , and, , incorrect ones are, (A) octahedral Co(III) complexes with, strong, field ligands have very high, magnetic moments, (B) When ∆ 0 < P, the d-electron, configuration of Co(III) in an octahedral, 4, complex is teg, , eg2, (C) Wavelength of light absorbed by, [Co(en)3 ]3 + is lower than that of [CoF6 ]3 −, (D) If the ∆ 0 for an octahedral complex of, Co(III) is 18,000 cm −1, the ∆ t for its, tetrahedral complex with the same, ligand will be 16,000 cm −1, (a) B and C only, (c) C and D only, , (b) A and B only, (d) A and D only, , CH2Br, , 16 Within each pair of elements F and Cl, S, and Se, and Li and Na, respectively, the, elements that release more energy upon, an electron gain are, (a) F, Se and Na, (c) Cl, S and Li, , (b) F, S and Li, (d) Cl, Se and Na, , 17 Which of the following statements is, correct?, (a) Gluconic acid is obtained by oxidation of, glucose with HNO3, (b) Gluconic acid is a dicarboxylic acid, (c) Gluconic acid can form cyclic, (acetal/hemiacetal) structure, (d) Gluconic acid is a partial oxidation, product of glucose, , 18 The ammonia (NH3 ) released on, quantitative reaction of 0.6 g urea, (NH2CONH2 ) with sodium hydroxide, (NaOH) can be neutralised by, , Numerical Type Questions, 21 The number of sp2-hybridised carbons, present in “aspartame” is …………, , 22 3 g of acetic acid is added to 250 mL of 0.1, M HCl and the solution made up to, 1, 500 mL. To 20 mL of this solution mL of, 2, 5 M NaOH is added. The pH of the, solution is …………, [Given : pK a of acetic acid = 4.75, molar, mass of acetic acid = 60 g/mol,, ], log 3 = 04771, ., Neglect any changes in volume., 0, 23 The standard heat of formation (∆ f H 298, ) of, , ethane (in kJ / mol), if the heat of, combustion of ethane, hydrogen and, graphite are −1560,−3935, . and, −286 kJ / mol, respectively is ………
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17, , JANUARY ATTEMPT ~ 07 Jan 2020, Shift II, 24 Consider the following reactions :, , 25 The flocculation value of HCl for arsenic, , NaCl + K 2Cr2O7 + H2SO4 → ( A) + side, products (conc.), ( A) + NaOH → (B) + side products, (B) + H2SO4 + H2O2 → (C ) + side products, (dilute), The sum of the total number of atoms in, one molecule each of (A), (B) and (C) is, …………, , sulphide sol. is 30 m mol L −1. If H2SO4 is, , used for the flocculation of arsenic, sulphide, the amount in grams of H2SO4 is, 250 mL required for the above purpose is, …………, (molecular mass of H2SO4 = 98 g / mol), , MATHEMATICS, Objective Type Questions, , (a), , 1 Let α and β be the roots of the equation, x2 − x − 1 = 0. If pk = (α )k + (β)k , k ≥ 1, then, which one of the following statements is, not true?, (a), (b), (c), (d), , p3 = p5 − p4, ( p1 + p2 + p3 + p4 + p5 ) = 26, p5 = p2. p3, p5 = 11, , 2 The number of ordered pairs (r , k) for, which 6 ⋅ 35C r = (k2 − 3) ⋅ 36C r + 1, where k is, an integer, is, (a) 4, , (b) 3, , (c) 2, , (d) 6, , 3 The value of c in the Lagrange’s mean, value theorem for the function, f (x) = x3 − 4x2 + 8x + 11, when x ∈[0, 1] is, 7−2, (a), 3, 4− 5, (c), 3, , 2, (b), 3, 4− 7, (d), 3, , 4 The value of α for which 4α ∫, (a) log e, (c) log e 2, , 2, , 2 − α|x|, e, −1, , π 1, +, 3 6, , (b), , π, 3, , (c), , 2π, 3, , (d), , π, 9, , 6 In a workshop, there are five machines, and the probability of any one of them to, 1, be out of service on a day is . If the, 4, probability that at most two machines will, 3, 3, be out of service on the same day is k,, 4, then k is equal to, (a) 4, , (b), , 17, 4, , (c), , 17, 8, , (d), , 17, 2, , 7 Let A = [a ij ] and B = [bij ] be two 3 × 3 real, matrices such that bij = (3)( i +, , j − 2), , a ji ,, , where i , j = 1, 2, 3. If the determinant of B is, 81, then the determinant of A is, 1, 9, 1, (c), 81, , (a), , (b) 3, (d), , 1, 3, , 8 The locus of the mid-points of the, dx = 5, is, , 3, (b) log e , 2, 4, (d) log e , 3, , 5 If θ1 and θ 2 be respectively the smallest, and the largest values of θ in (0, 2π ) − { π }, which satisfy the equation,, θ2, 5, + 4 = 0, then ∫ cos2 3θdθ is, 2 cot2 θ −, θ, 1, sin θ, equal to, , perpendiculars drawn from points on the, line, x = 2 y to the line x = y is, (a) 5x − 7 y = 0, (c) 3x − 2 y = 0, , (b) 2x − 3 y = 0, (d) 7x − 5 y = 0, , 9 Let a , b and c be three unit vectors such, that a + b + c = 0. If λ = a ⋅ b + b ⋅ c + c ⋅ a, and d = a × b + b × c + c × a, then the, ordered pair, (λ , d ) is equal to, , 3, (a) , 3 b × c, 2, , 3, (c) , 3a × c, 2, , , 3, (b) − , 3c × b, 2, , 3, (d) − , 3a × b, 2,
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18, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 10 Let the tangents drawn from the origin to, the circle, x + y − 8x − 4 y + 16 = 0 touch, it at the points A and B. The ( AB)2 is, equal to, 2, , 2, , 56, 5, 64, (c), 5, , 52, 5, 32, (d), 5, , (a), , (b), , 11 The coefficient of x7 in the expression, (1 + x)10 + x(1 + x)9 + x2 (1 + x)8 + ... + x10 is, (a) 420, (c) 210, , (b) 330, (d) 120, , 12 If 3x + 4 y = 12 2 is a tangent to the ellipse, x2, , y2, = 1 for some a ∈ R, then the, 9, a2, distance between the foci of the ellipse is, +, , (a) 2 7, (c) 2 2, , 13 If the sum of the first 40 terms of the, series, 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + ..., is (102)m, them m is equal to, (b) 25, (d) 20, , 14 Let y = y(x) be the solution curve of the, dy, = 1,, dx, satisfying y(0) = 1. This curve intersects the, x-axis at a point whose abscissa is, differential equation, ( y2 − x), , (b) 2 − e, (d) 2 + e, , (a) 2, (c) −e, , {(x, y) ∈ R2 |4x2 ≤ y ≤ 8x + 12} is, 125, (b), 3, , 127, (c), 3, , 128, (d), 3, , 16 Let A, B, C and D be four non-empty sets., The contrapositive statement of “If A ⊆ B, and B ⊆ D, then A ⊆ C ” is, (a), (b), (c), (d), , If A ⊆/ C, then A ⊆/ B or B ⊆/ D, If A ⊆ C, then B ⊂ A or D ⊂ B, If A ⊆/ C, then A ⊆/ B or B ⊆ D, If A ⊆/ C, then A ⊆ B or B ⊆ D, , 17 Let f (x) be a polynomial of degree 5 such, that x = ± 1 are its critical points. If, f (x), , lim 2 + 3 = 4, then which one of the, x→ 0, x , following is not true?, , 3, (b) − tan −1 , 4, 3, (d) π − tan −1 , 4, , 19 Let a1 , a 2 , a3 , ... be a G.P. such that a1 < 0,, a1 + a 2 = 4 and a3 + a 4 = 16. If, , 9, , ∑ a i = 4λ,, , i =1, , (a) − 171, 511, (c), 3, , (b) 171, (d) − 513, , 20 Let y = y(x) be a function of x satisfying, y 1 − x2 = k − x 1 − y2 where k is a, dy, 1, 1, 1, constant and y = − . Then, at x = ,, 2, 4, dx, 2, is equal to, (a), , 5, 2, , (b) −, , 5, 2, , (c), , 2, 5, , (d) −, , 5, 4, , Numerical Type Questions, , 15 The area (in sq. units) of the region, 124, (a), 3, , 4, (a) π − tan −1 , 3, 4, (c) tan −1 , 3, , then λ is equal to, , (b) 4, (d) 2 5, , (a) 10, (c) 5, , (a) f is an odd function., (b) x = 1 is a point of minima and x = − 1 is a, point of maxima of f., (c) f (1) − 4 f (−1) = 4., (d) x = 1 is a point of maxima and x = − 1 is a, point of minimum of f., 3 + i sin θ, 18 If, , θ ∈ [0, 2π ], is a real number,, 4 − i cos θ, then an argument of sin θ + i cos θ is, , 21 If the mean and variance of eight numbers, 3, 7, 9, 12, 13, 20, x and y be 10 and 25, respectively, then x ⋅ y is equal to …… ., , 22 If the system of linear equations,, x+ y+ z =6, , x + 2 y + 3z = 10, , 3x + 2 y + λ z = µ, has more than two solutions, then µ − λ2 is, equal to ………… ., 1 1, 23 If the function f defined on − , by, 3 3, 1, 1 + 3x, , when x ≠ 0, log e , f (x) = x, 1 − 2x , k, , when x = 0, , is continuous, then k is equal to ………… .
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19, , JANUARY ATTEMPT ~ 07 Jan 2020, Shift II, 24 If the foot of the perpendicular drawn from, , 25 Let X = { n ∈ N : 1 ≤ n ≤ 50}. If A = { n ∈ X : n, is multiple of 2} and B = { n ∈ X : n is a, multiple of 7}, then the number of, elements is the smallest subset of X, containing both A and B is ………… ., , the point (1, 0, 3) on a line passing through, 5 7 17, (α , 7, 1) is , , , then α is equal to, 3 3 3 , ………… ., , Answers, Physics, 1., 11., 21., , (c), (d), (6), , 2. (c), 12. (d), 22. (12), , 3. (b), 13. (a), 23. (90°), , 4. (b), 14. (d), 24. (75), , 5., (a), 15. (a), 25. (40 g), , 6., 16., , (b), (b), , 7., 17., , (d), (b), , 8., 18., , (d), (a), , 9., 19., , (d), (a), , 10., 20., , (c), (a), , 10., 20., , (a), (d), , 10., 20., , (c), (b), , For Detailed Solutions, Visit : http://bit.ly/3kboTqx, Or Scan :, , Chemistry, 1. (d), 11. (b), 21. (9), , 2. (c), 12. (c), 22. (5.23), , 3., (a), 13., (a), 23. (−192.50), , 4., (b), 14., (a), 24. (18.00), , 5., (a), 15. (d), 25. (0.37), , 6., 16., , (c), (c), , 7., 17., , (a), (d), , 8., 18., , (c), (a), , 9., 19., , (a), (c), , For Detailed Solutions, Visit : http://bit.ly/3dQvUuB, Or Scan :, , Mathematics, 1. (c), 11. (b), 21. (54), , 2. (a), 12. (a), 22. (13), , 3. (d), 13. (d), 23. (05), , 4., 14., 24., , (c), (b), (04), , 5. (b), 15. (d), 25. (29), , 6., 16., , (c), (a), , 7., 17., , (a), (d), , 8., 18., , (a), (a), , 9., 19., , (d), (a), , For Detailed Solutions, Visit : http://bit.ly/2Hg47HZ, Or Scan :
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ONLINE QUESTION PAPER, , JEE Main 2020, (08 January, 2020), TIME 9:30-12:30 (Shift I), , MM : 300, , PHYSICS, Objective Type Questions, 1 A leak proof cylinder of length 1 m, made, , (a) 1.26, (c) 1.01, , (b) 1.03, (d) 1.04, , 2 The magnifying power of a telescope with, tube length 60 cm is 5. What is the focal, length of its eyepiece?, (a) 10 cm, (c) 30 cm, , (b) 20 cm, (d) 40 cm, , 3 The plot that depicts the behaviour of the, mean free time τ (time between two, successive collisions) for the molecules of, an ideal gas, as a function of temperature, (T ), qualitatively is (graphs are schematic, and not drawn to scale), , (b), √T, , 1, T, , τ, , (d), 1, √T, , T, , 4 Consider two solid spheres of radii R1 = 1 m,, R2 = 2 m and masses M1 and M 2,, respectively. The gravitational field due to, sphere 1 and 2 are shown. The value of, M1, is, M2, 4, 3, 2, , 2, , 1, , 1, 0, , 1, 3, 1, (c), 6, (a), , τ, , (a) τ, , τ, (c), , Gravitational field (E), , of a metal which has very low coefficient of, expansion is floating vertically in water at, 0 °C such that its height above the water, surface is 20 cm. When the temperature of, water is increased to 4°C, the height of the, cylinder above the water surface becomes, 21 cm. The density of water at T = 4 °C,, relative to the density at T = 0 °C is close to, , 1, , 2, , 3, , 4, , 1, 2, 2, (d), 3, (b), , 5, Radius (R)
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21, , JANUARY ATTEMPT ~ 08 Jan 2020, Shift I, 5 A particle of mass m is fixed to one end of a, light spring having force constant k and, unstretched length l. The other end is fixed., The system is given an angular speed ω, about the fixed end of the spring such that, it rotates in a circle in gravity free space., Then, the stretch in the spring is, mlω2, (a), k + mω, (c), , mlω, , (b), , 2, , charged particles A, C and centre O of the, circle formed an equilateral triangle as, shown in figure. Electric field at O along, x-direction is, y, 2q, B, , mlω2, , – 4q, A, d, , k + mω2, mlω, k − mω, , d, 30º, 30º, d, , 150º, , 2, , (d), , k − mω2, , O, , x, C, – 2q, , 6 A thermodynamic cycle xyzx is shown on a, V - T diagram., V, , (a), , y, , z, , 2 3q, πε0 d 2, , (b), , 3q, 4 πε0 d 2, , (c), , 3 3q, 4πε0 d 2, , (d), , 3q, πε0 d 2, , 9 In finding the electric field using Gauss, law the formula|E| =, , x, T, , The p - V diagram that best describes this, cycle is (diagrams are schematic and not to, scale), p, , p, , y, , x, , x, (b), , (a), y, , z, , z, , V, , V, , p, , p, z, , x, , x, , y, , z, , y, , V, , V, , 7 Consider a solid sphere of radius R and, , , r2 , mass density ρ( r ) = ρ0 1 − 2 , 0 < r ≤ R., R , , The minimum density of a liquid in which, it will float is, , (a), , ρ0, 3, , (b), , 2 ρ0, 5, , (c), , In the formula, ε 0 is permittivity of free, space, A is the area of Gaussian surface, and qenc is charge enclosed by the, Gaussian surface. This equation can be, used in which of the following situation?, (a) Only when the Gaussian surface is an, equipotential surface and|E|is constant, on the surface., (b) Only when the Gaussian surface is an, equipotential surface., (c) For any choice of Gaussian surface., (d) Only when|E| = constant on the surface., , 10 At time t = 0 magnetic field of 1000 gauss, , (d), , (c), , qenc, is applicable., ε 0| A|, , 2 ρ0, 3, , (d), , ρ0, 5, , is passing perpendicularly through the, area defined by the closed loop shown in, the figure. If the magnetic field reduces, linearly to 500 gauss, in the next 5 s, then, induced emf in the loop is, 16 cm, , 4 cm, , 2 cm, , 8 Three charged particles A, B and C with, charges − 4q, 2q and − 2q are present on the, circumference of a circle of radius d. The, , (a) 48 µV, (c) 56 µV, , (b) 28 µV, (d) 36 µV
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22, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 11 The dimension of stopping potential V0 in, photoelectric effect in units of Planck’s, constant h, speed of light c and, gravitational constant G and ampere A is, / −1/3 4/3, (a) h −23, c G A −1, 2 3 / 2 1/3, (c) h G c A −1, , / 1/3, (b) h1/3 G 23, c A −1, 23, / 5 /3 1/3, (d) h c G A −1, , 12 When photon of energy 4.0 eV strikes the, surface of a metal A, the ejected, photoelectrons have maximum kinetic, energy TA eV and de-Broglie wavelength, λ A . The maximum kinetic energy of, photoelectrons liberated from another, metal B by photon of energy 4.50 eV is, TB = (TA − 15, . ) eV. If the de-Broglie, wavelength of these photoelectrons, λ B = 2λ A , then the work function of metal, B is, (a) 4 eV, (c) 1.5 eV, , (b) 2 eV, (d) 3 eV, , 13 Effective capacitance of parallel, combination of two capacitors C1 and C 2 is, 10 µF. When these capacitors are, individually connected to a voltage source, of 1 V, the energy stored in the capacitor, C 2 is 4 times that of C1. If these capacitors, are connected in series, then their effective, capacitance will be, (a) 4.2 µF (b) 3.2 µF (c) 1.6 µF (d) 8.4 µF, , 14 Proton with kinetic energy of 1 MeV moves, from south to north. It gets an acceleration, of 1012 m/s 2 by an applied magnetic field, (west to east). The value of magnetic field, (rest mass of proton is 16, . × 10−27 kg), (a) 71 mT, (c) 0.71 mT, , and length l pivoted about its centre. A, mass m moving with velocity v making, π, angle θ = to the rod’s long axis collides, 4, with one end of the rod and sticks to it., The angular speed of the rod-mass system, just after the collision is, 3 2v, 7 l, 3v, (c), 7 l, , specific wavelength, if the medium has, relative permittivity 3 and relative, 4, permeability for this wavelength,will be, 3, (a) 45°, (c) 15°, , (b) 60°, (d) 30°, , 17 Boolean relation at the output stage Y for, the following circuit is, +5 V, A, Output-Y, B, , 5V, , (a) A ⋅ B, (c) A + B, , (b) A + B, (d) A ⋅ B, , 18 The length of a potentiometer wire is, 1200 cm and it carries a current of 60 mA., For a cell of emf 5 V and internal, resistance of 20 Ω, the null point on it is, found to be at 1000 cm. The resistance of, whole wire is, (a) 80 Ω, (c) 60 Ω, , (b) 100 Ω, (d) 120 Ω, , 19 The graph which depicts the results of, Rutherford gold foil experiment with, α-particles is, θ : Scattering angle, Y : Number of scattered α-particles detected, (plots are schematic and not to scale), , (b) 0.071 mT, (d) 7.1 mT, , 15 Consider a uniform rod of mass M =4 m, , (a), , 16 The critical angle of a medium for a, , 4v, 7 l, 3 v, (d), 7 2 l, , (a), , Y, , (b), 0, , θ, , Y, , π, , 0, , θ, , π, , 0, , θ, , π, , (d) Y, , (c) Y, , (b), , 0, , θ, , π
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23, , JANUARY ATTEMPT ~ 08 Jan 2020, Shift I, 20 The coordinates of centre of mass of a, uniform flag shaped lamina (thin flat, plate) of mass 4 kg. (The coordinates of the, same are shown in figure) are, (0, 3), , (0, 0), , 23 A particle is moving along the x-axis with, , (2, 3), , its coordinate with the t given by, x(t ) = 10 + 8t − 3t 2. Another particle is, moving along the y-axis with its coordinate, as a function of time given by y(t ) = 5 − 8t3 ., At t = 1 s, the speed of the second particle, as measured in the frame of the first, particle is given as v. Then v (in m/s) is, ……… ., , (2, 2), , (1, 2), , (1, 0), , (a) (1.25 m, 1.50 m), (c) (0.75 m, 0.75 m), , Assuming the speed of sound in air at STP, is 300 m/s, the frequency difference, between the fundamental and second, harmonic of this pipe is …… Hz., , (b) (1 m, 1.75 m), (d) (0.75 m, 1.75 m), , Numerical Type Questions, 21 Four resistances of 15 Ω, 12 Ω, 4 Ω and, , 10 Ω respectively in cyclic order to form, Wheatstone’s network. The resistance that, is to be connected in parallel with the, resistance of 10 Ω to balance the network, is ……… Ω ., , 22 A one metre long (both ends open) organ, pipe is kept in a gas that has double the, density of air at STP., , 24 A point object in air is in front of the, curved surface of a plano-convex lens. The, radius of curvature of the curved surface is, 30 cm and the refractive index of the lens, material is 1.5, then the focal length of the, lens (in cm) is ……… ., , 25 A body A, of mass m = 01, . kg has an initial, velocity of 3$i ms −1. It collides elastically, with another body, B of the same mass, which has an initial velocity of 5$j ms −1., After collision, A moves with a velocity, v = 4($i + $j). The energy of B after collision, x, is written as, J. The value of x is ……… ., 10, , CHEMISTRY, Objective Type Questions, 1 A graph of vapour pressure and, , Vapour pressure, (mm Hg), , temperature for three different liquids X,, Y , and Z is shown below :, X, , 800, , Z, , Y, , 500, , The following inference are made :, A. X has higher intermolecular, interactions compared to Y ., B. X has lower intermolecular interactions, compared to Y ., C. Z has lower intermolecular interactions, compared to Y ., The correct inference(s) is/are :, , 400, , (a) (C), (c) (A), , 200, 0 293, , 313, , 333, Temp, , 353, , (b) (B), (d) (A) and (C), , 2 The third ionisation enthalpy is minimum, for :, (a) Mn, , (b) Ni, , (c) Co, , (d) Fe
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24, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 3 The most suitable reagent for the given, conversion is, CONH2, , CH3, C==O, ?, , (a) I, II, IV, (c) I, III, IV, , HO2C, CN, , (III) The lines of longest wavelength, corresponds to n2 = 3, (IV) The ionisation energy of hydrogen can, be calculated from wave number of, these lines, , CONH2, , (b) II, III, IV, (d) I, II, III, , 8 The major products A and B in the, COCH3, , following reactions are :, CN, , Peroxide, Heat, , [A], , HOH2C, [A] +, , CN, , (a) B2H6, (c) NaBH4, , (b) LiAlH4, (d) H2 / Pd, , (a), , A=, , •, , B, , CN, , 4 The rate of a certain biochemical reaction, at physiological temperature (T ) occurs 106, times faster with enzyme than without., The change in the activation energy upon, adding enzyme is :, (a) + 6 RT, (c) + 6 (2.303) RT, , and B =, , (b), , (b) − 6(2.303) RT, (d) − 6 RT, , A=, , CN, •, , CN, , CN, , and B =, , 5 The number of bonds between sulphur and, oxygen atoms in S2O2−, 8 and the number of, bonds between sulphur and sulphur atoms, in rhombic sulphur, respectively, are, , (a) 4 and 6, (c) 4 and 8, , (c) A=, , and 3-methylpentane. One of the liquids, boils at 63°C while the other boils at 60°C., What is the best way to separate the two, liquids and which one will be distilled out, first?, (a) Fractional distillation 3-methylpentane, (b) Fractional distillation, isohexane, (c) Simple distillation, 3-methylpentane, (d) Simple distillation, isohexane, , 7 For the Balmer series in the spectrum of H, 1, 1 , atom, v = RH 2 − 2 , the correct, n1 n2 , statements among (I) to (IV) are :, (I) As wavelength decreases, the lines in, the series converge, (II) The integer n1 is equal to 2, , CN, , and B =, , (b) 8 and 8, (d) 8 and 6, , 6 A flask contains a mixture of isohexane, , •, , (d), , A=, , CN, •, , CN, , and B =, , CN, , 9 Among the gases (a)-(e), the gases that, cause greenhouse effect are :, (a) CO2, (b) H2O, (c) CFCs, (d) O2, (e) O3, (a) (a), (b), (c) and (d), (c) (a), (b), (c) and (e), , (b) (a) and (d), (d) (a), (c), (d) and (e), , 10 The complex that can show fac- and, mer-isomers is :, (a) [Pt(NH3 )2 Cl 2 ], (b) [Co(NH3 )3 (NO2 )3 ], (c) [Co(NH3 )4 Cl 2 ]+, (d) [CoCl 2 (en )2 ]
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26, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 19 Which of the following statement is not, true for glucose?, (a) The pentaacetate of glucose does not, react with hydroxylamine to give oxime, (b) Glucose exists in two crystalline forms, α and β, (c) Glucose gives Schiff’s test for aldehyde, (d) Glucose reacts with hydroxylamine to, form oxime, , 23 The magnitude of work done by a gas that, undergoes a reversible expansion along the, path ABC shown in the figure is ……… ., Pressure, (Pa) 10, A, , 8, 6, 4, , 20 When gypsum is heated to 393 K, it forms :, (a) Dead burnt plaster, (b) CaSO4 .0.5H2O, , (2, 2), , (c) CaSO4 .5H2O, , B, , 4, , 6, , 8, , 10, , C, 12, , Volume, (m3), , 24 What would be the electrode potential for, , (d) Anhydrous CaSO4, , the given half-cell reaction at pH = 5 ?, ……… ., , Numerical Type Questions, 21 The number of chiral centres in penicillin, is ……… ., , 22 Ferrous sulphate heptahydrate is used to, fortify foods with iron. The amount (in, grams) of the salt required to achieve, 10 ppm of iron in 100 kg of wheat is ……… ., Atomic weight : Fe = 5585, . ; S = 3200, . ;, O = 1600, ., , 0, 2H2O → O2 + 4H⊕ + 4e− ; E red, = 123, . V, , (R = 8314, J mol −1 K −1; Temp = 298 K;, ., oxygen under std. atm. pressure of 1 bar), , 25 The volume (in mL) of 0.125 M AgNO3, required to quantitatively precipitate chloride, ions in 0.3 g of [Co(NH3 )6 ]Cl3 is ……… ., M[Co(NH 3 ) 6 ]Cl 3 = 267.46 g/mol, M AgNO3 = 16987, . g/mol, , MATHEMATICS, Objective Type Questions, π π, , ,, 2 2 , then which of the following is true?, π , (a) f′ is decreasing in − , 0 and, 2 , increasing, π, in 0, , 2, π , (b) f′ is increasing in − , 0 and decreasing, 2 , π, in 0, , 2, (c) f is not differentiable at x = 0, π, (d) f′ (0) = −, 2, , 1 Let f (x) = x cos−1 (− sin|x |), x ∈ −, , 2 Let y = y(x) be a solution of the differential, equation,, dy, 1 − x2, + 1 − y2 = 0,|x| < 1., dx, 3, 1, , then, If y =, 2, 2, (a), , 3, 2, , (b) −, , 3, 2, , −1 , y is equal to, 2, (c) −, , 1, 2, , (d), , 1, 2, , 3 The inverse function of, f (x) =, , 8 2 x − 8 −2 x, 8 2 x + 8 −2 x, , , x ∈ (− 1, 1) is, , (a), , 1− x, 1− x, 1, 1, (log 8 e) log e , (b) log e , , 4, 4, 1 + x, 1 + x, , (c), , 1 + x, 1 + x, 1, 1, (log 8 e) log e , (d) log e , , 4, 4, 1− x, 1− x
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27, , JANUARY ATTEMPT ~ 08 Jan 2020, Shift I, 4 If c is a point at which Rolle’s theorem, , x2 + α , , holds for the function, f (x) = log e , 7x , in the interval [3, 4], where α ∈R, then, f ′ ′ (c) is equal to, , (a) −, , 1, 24, , (b) −, , 1, 12, , (c), , 1, 12, , 3, 7, , (d), , 5 If the equation,x2 + bx + 45 = 0 (b ∈R) has, conjugate complex roots and they satisfy, |z + 1| = 2 10, then, (a) b2 + b = 72, (c) b2 − b = 30, , (b) b2 + b = 12, (d) b2 − b = 42, , conterminous edges are given by, $ , v = i$ + $j + 3k, $ and, u = $i + $j + λk, $ be 1 cu. unit. If θ be the, w = 2i$ + $j + k, angle between the edges u and w, then, cos θ can be, 5, 3 3, , (b), , 7, 6 3, , (c), , 7, 6 6, , (d), , 5, 7, , 7 The locus of a point which divides the line, segment joining the point (0, − 1) and a, point on the parabola, x2 = 4 y, internally in, the ratio 1 : 2, is, (a) 4x2 − 3 y = 2, (c) 9x2 − 12 y = 8, , 3x2 + 2 , , (b) x2 − 3 y = 2, (d) 9x2 − 3 y = 2, , 1/ x 2, , , 8 lim 2, x → 0 7 x + 2, , (a) e2, , (b) e, , (c), , 1, 2, , (d), , 1, e, , x−3 y−8 z −3, x+ 3 y+ 7 z −6, and, =, =, =, =, −1, −3, 3, 1, 2, 4, is, (b) 2 30, , (c), , 7, 30, 2, , (d) 3, , 10 Let the line y = mx and the ellipse, 2x2 + y2 = 1 intersect at a point P in the, first quadrant. If the normal to this ellipse, at P meets the co-ordinate axes at, 1, , , , 0 and (0, β), then β is equal to, −, 3 2 , 2 2, 3, , (b), , 2, 3, , 5π, 6, , (b) −, , π, 6, , (c), , 2π, 3, , (d), , π, 3, , 12 Let A and B be two independent events, 1, 1, and P (B) = . Then,, 3, 6, which of the following is TRUE?, such that P ( A) =, , (c) P (A / B ′ ) =, , 1, 4, , 1, 3, , 1, 3, 2, (d) P (A / B ) =, 3, , (b) P (A ′/B ′ ) =, , 13 Which one of the following is a tautology?, (a) (P ∧ (P → Q )) → Q, (b) P ∧ (P ∨ Q ), (c) P ∨ (P ∧Q ), (d) Q → (P ∧ (P → Q ), , 14 The mean and the standard deviation (s.d.), of 10 observations are 20 and 2, respectively. Each of these 10 observations, is multiplied by p and then reduced by, q,where p ≠ 0 and q ≠ 0. If the new mean, and new s.d. become half of their original, values, then q is equal to, (b) − 10, , (a) 10, 19, , 9 The shortest distance between the lines, , (a), , (a), , (c) − 5, , (d) − 20, , 15 If a , b and c are the greatest values of, is equal to, , e, , (a) 3 30, , dy 1 d, (sin −1 ( f (x))) and, =, dx 2 dx, π, y( 3 ) = , then y(− 3 ) is equal to, 6, , |x| > 1. If, , (a) P (A / (A ∪ B )) =, , 6 Let the volume of a parallelopiped whose, , (a), , 11 Let f (x) = (sin (tan −1 x) + sin(cot−1 x))2 − 1,, , (c), , 2, 3, , (d), , 2, 3, , Cp, , 20, , C q and, , 21, , C r respectively, then, , a, b, c, (a), =, =, 10 11 42, a, b, c, (c), =, =, 10 11 21, , a, =, 11, a, (d), =, 11, (b), , b, =, 22, b, =, 22, , c, 21, c, 42, , 16 For a > 0, let the curves C1 : y2 = ax and, C 2 : x2 = ay intersect at origin O and a, point P. Let the line x = b (0 < b < a ), intersect the chord OP and the x-axis at, points Q and R, respectively. If the line, x = b bisects the area bounded by the, curves, C1 and C 2, and the area of, 1, ∆OQR = , then ‘a’ satisfies the equation, 2, (a) x6 + 6x3 − 4 = 0, (b) x6 − 12x3 + 4 = 0, (c) x6 − 6x3 + 4 = 0, (d) x6 − 12x3 − 4 = 0
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28, , ONLINE, , Numerical Type Questions, , 17 For which of the following ordered pairs, (µ, δ), the system of liner equations, , 21 The number of all 3 × 3 matrices A, with, , x + 2 y + 3z = 1, 3x + 4 y + 5z = µ, , enteries from the set { − 1, 0, 1} such that, the sum of the diagonal elements of AAT is, 3, is ……… ., , 4x + 4 y + 4z = δ is inconsistent?, (a) (4, 6), , (b) (4, 3), , (c) (1, 0), , (d) (3, 4), , 18 Let two points be A(1, − 1) and B(0, 2). If a, , 22 Let the normal at a point P on the curve, y2 − 3x2 + y + 10 = 0 intersect the y-axis at, 3, 0, . If m is the slope of the tangent at P, 2, to the curve, then|m|is equal to ……… ., , point P (x′ , y′ ) be such that the area of, ∆PAB = 5 sq. units and it lies on the line,, 3x + y − 4λ = 0, then a value of λ is, (b) − 3, , (a) 1, , (c) 3, , (d) 4, , 19 Let f : R → R be such that for all x ∈R, , 23 An urn contains 5 red marbles, 4 black, , (21 + x + 21 − x ), f (x) and (3x + 3− x ) are in, A.P, then the minimum value of f (x) is, (a) 4, , (b) 3, , (c) 2, , marbles and 3 white marbles. Then the, number of ways in which 4 marbles can be, drawn so that at the most three of them, are red is ……… ., , (d) 0, , 20 If, , 20, , cos x dx, , ∫ sin3 x(1 + sin6 )x)2/ 3, , = f (x) (1 + sin 6 x)1/ λ + c, , (b) −, , 9, 8, , (c) − 2, , (d), , 24 The sum Σ (1 + 2 + 3 + K + k) is, k=1, , 25 The least positive value of ‘a’ for which the, , where c is a constant of integration, then, is equal to, (a) 2, , JEE Main 2020 ~ Solved Papers, , equation, 2x2 + (a + 10)x +, , 9, 8, , 33, = 2a has real, 2, , roots is ……… ., , Answers, Physics, 1. (c ), 11. ( *), 21. (10), , 2., (a), 12., (a), 22. (106.06), , 3. (c ), 13. (c), 23. (580), , 4., (c), 14. (c), 24. (60), , 5., 15., 25., , (c), (a), (1), , 6., 16., , (b), (d), , 7., 17., , (b), (d), , 8., 18., , (d), (b), , 9., 19., , (a), (b), , 10., 20., , (c), (d), , 10., 20., , (b), (b), , 10., 20., , (b), (c), , For Detailed Solutions, Visit : http://bit.ly/3o4skkW, Or Scan :, , Chemistry, 1. (b), 11. (d), 21. (3.00), , 2. (d), 12. (c), 22. (4.97), , 3., (a), 13. (c), 23. (48.00), , 4., (b), 14., (b), 24. (−0. 94), , 5., (b), 15. (d), 25. (26.92), , 6., 16., , (b), (a), , 7., 17., , (d), (c), , 8., 18., , (c), (c), , 9., 19., , (c), (c), , For Detailed Solutions, Visit : http://bit.ly/3kfmeMg, Or Scan :, , Mathematics, 1. (a), 11. (b), 21. (672), , 2., 12., 22., , (d), (c), (4), , 3. (c), 13. (a), 23. (490), , Note (*) None of the options is correct., , 4., (c), 14. (d), 24. (1540), , 5., 15., 25., , (c), (d), (8), , 6., 16., , (b), (b), , 7., 17., , (c), (b), , 8., 18., , (c), (c), , 9., 19., , (a), (b), , For Detailed Solutions, Visit : http://bit.ly/3dHcd84, Or Scan :
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ONLINE QUESTION PAPER, , JEE Main 2020, (08 January, 2020), TIME 2:30-5:30 (Shift II), , MM : 300, , PHYSICS, Objective Type Questions, L, 1, , ε, , ground with a speed of 2gh. If they, collide head-on completely inelastically,, then the time taken for the combined mass, h, is, to reach the ground, in units of, g, , R, , S, , As shown in the figure, a battery of emf ε, is connected to an inductor L and, resistance R in series. The switch is closed, at t = 0. The total charge that flows from, the battery, between t = 0 and t = tc (tc is, the time constant of the circuit) is, (a), (c), , εL , 1 −, R2 , εR, 2, , eL, , 1, , e, , (b), (d), , (a), (c), , 1, 2, 3, 2, , 1, 2, 3, (d), 4, (b), , 4, R, , εL, , 1, , R2, εL, eR, , G, , C, , O, , 2, , 2 A simple pendulum is being used to, determine the value of gravitational, acceleration g at a certain place. The length, of the pendulum is 25.0 cm and a stop, watch with 1s resolution measures the, time taken for 40 oscillations to be 50 s., The accuracy in g is, (a) 2.40%, (c) 4.40%, , (b) 5.40%, (d) 3.40%, , 3 A particle of mass m is dropped from a, height h above the ground. At the same, time another particle of the same mass is, thrown vertically upwards from the, , As shown in figure, when a spherical, cavity (centred at O) of radius 1 is cut out, of a uniform sphere of radius R (centred at, C), the centre of mass of remaining, (shaded) part of sphere is at G, i.e. on the, surface of the cavity. R can be determined, by the equation, (a), (b), (c), (d), , (R 2 + R + 1) (2 − R ) = 1, (R 2 + R − 1) (2 − R ) = 1, (R 2 − R − 1) (2 − R ) = 1, (R 2 − R + 1) (2 − R ) = 1
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30, , ONLINE, , 5 A plane electromagnetic wave of frequency, 25 GHz is propagating in vacuum along, the z-direction. At a particular point in, space and time, the magnetic field is given, by B = 5 × 10− 8 $j T. The corresponding, electric field E is (speed of light,, c = 3 × 108ms− 1), , JEE Main 2020 ~ Solved Papers, , (graphs are drawn schematically and are, not to scale), m, m, 1, , 1, (a), , f, , 2f, , x (b), , (a) − 1.66 × 10− 16 $i V / m (b) 1.66 × 10− 16 $i V / m, (c) − 15 $i V / m, (d) 15 $i V / m, , 2f, , f, , 2f, , x, , m, m, 1, , 6 A particle of mass m and charge q is, released from rest in a uniform electric, field. If there is no other force on the, particle, the dependence of its speed v on, the distance x travelled by it is correctly, given by (graphs are schematic and not, drawn to scale), , f, , (c), , 1, f, , 2f, , x (d), , x, , 8 A uniform sphere of mass 500 g rolls, (a), , without slipping on a plane horizontal, surface with its centre moving at a speed, of 5.00 cm/s. Its kinetic energy is, , v, , x, , (a) 6.25 × 10− 4 J, (c) 8.75 × 10− 4 J, , (b) 113, . × 10− 3 J, (d) 8.75 × 10− 3 J, , 9 A particle moves such that its position, (b), , vector r (t ) = cos ωti$ + sin ωt$j, where ω is a, constant and t is time. Then, which of the, following statements is true for the velocity, v(t ) and acceleration a(t ) of the particle?, , v, , x, , (c), , v, , x, , (d), , v, , x, , 7 An object is gradually moving away from, the focal point of a concave mirror along, the axis of the mirror. The graphical, representation of the magnitude of linear, magnification (m) versus distance of the, object from the mirror (x) is correctly, given by, , (a) v and a both are parallel to r., (b) v is perpendicular to r and a is directed, away from the origin., (c) v and a both are perpendicular to r., (d) v is perpendicular to r and a is directed, towards the origin., , 10 A transverse wave travels on a taut steel, wire with a velocity of v when tension in it, is 206, . × 104 N. When the tension is, changed to T, the velocity changed to v / 2., The value of T is close to, (a), (b), (c), (d), , 10.2 × 102 N, 515, . × 103 N, 2.50 × 104 N, 30.5 × 104 N, , 11 A very long wire ABDMNDC is shown in, figure carrying current I. AB and BC parts, are straight, long and at right angle. At D, wire forms a circular turn DMND of radius, R. AB, BC parts are tangential to circular, turn at N and D. Magnetic field at the, centre of circle is
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31, , JANUARY ATTEMPT ~ 08 Jan 2020, Shift II, M, , wavelength of electron, then its de Broglie, wavelength at time t is given by, , N, B, , D, , λ0, , (a), , .........., , 1+, , C, , 1+, , A, , µ I, (b) 0, 2R, µ 0I , 1 , (d), π −, , 2 πR , 2, , (a) 0.568, , (b) 0.853, , e2E02t 2, , λ0, , (b), 2+, , m2v02, , λ0 2, , (d), , 1+, , 2m2v02, , e2E02t 2, , e2E02t 2, m2v02, , 1, 10, is being used as a refrigerator. If the work, done on the refrigerator is 10 J, then the, amount of heat absorbed from the, reservoir at lower temperature is:, , 16 A Carnot engine having an efficiency of, , 12 In a double-slit experiment, at a certain, point on the screen the path difference, 1, between the two interfering waves is th, 8, of a wavelength. The ratio of the intensity, of light at that point to that at the centre, of a bright fringe is, , e E02t 2, m2v02, λ0, , (c), , µ I, 1 , (a) 0 π +, , 2 πR , 2, µ I, (c) 0 ( π + 1), 2 πR, , 2, , (a) 99 J, , (b) 100 J, , (c) 90 J, , (d) 1 J, , 17 In the given circuit, value of Y is, 1, , (c) 0.760 (d) 0.672, , Y, , 13 A galvanometer having a coil resistance, , 100 Ω gives a full scale deflection when a, current of 1 mA is passed through it. What, is the value of the resistance which can, convert this galvanometer into a voltmeter, giving full scale deflection for a potential, difference of 10 V?, , 0, , (a), (b), (c), (d), , (a) 8.9 kΩ (b) 10 kΩ (c) 9.9 kΩ (d) 7.9 kΩ, , 14 A capacitor is made of two square plates, , each of side a making a very small angle α, between them, as shown in figure. The, capacitance will be close to, , toggles between 0 and 1, 1, 0, will not execute, , 18, , M, 5m, , V1, , N, , α, , 5m, , d, a, , ε0 a 2 , αa , 1 −, , d , 4d , 2, ε a, αa , (c) 0 1 −, , d , 2d , , (a), , O, , V2, , ε0 a 2, d, ε0 a 2, (d), d, , (b), , 1 + αa , , , , d, 1 − 3αa , , , , 2d , , 15 An electron (mass m) with initial velocity, v = v0i$ + v0$j is in an electric field, $ . If λ is initial de-Broglie, E = − E0 k, 0, , Two liquids of densities ρ1 and ρ2 (ρ2 = 2 ρ1 ), are filled up behind a square wall of side, 10 m as shown in figure. Each liquid has a, height of 5 m. The ratio of the forces due to, these liquids exerted on upper part MN to, that at the lower part NO is (assume that, the liquids are not mixing), (a) 1/2, (c) 1/4, , (b) 2/3, (d) 1/3
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32, , JEE Main 2020 ~ Solved Papers, , ONLINE, , 19 Consider a mixture of n moles of helium gas, and 2n moles of oxygen gas (molecules, taken to be rigid) as an ideal gas. Its, C p / CV value will be, (a) 40/27, , (b) 23/15, , (c) 19/13 (d) 67/45, , 20 Consider two charged metallic spheres S1 and, S2 of radii R1 and R2, respectively. The, electric fields E1 (on S1) and E 2 (on S2 ) on, their surfaces are such that, E1 / E 2 = R1 / R2. Then the ratio V1(on S1)/V2, (on S2) of the electrostatic potentials on, each sphere is, R , (a) 1 , R2 , , 3, , (b) R2 / R1 (c) R1 / R2 (d) (R1 / R2 )2, , Numerical Type Questions, 21 The series combination of two batteries, both, of the same emf 10 V, but different internal, resistance of 20 Ω and 5 Ω, is connected to the, parallel combination of two resistors 30 Ω, and R Ω. The voltage difference across the, battery of internal resistance 20 Ω is zero,, the value of R(in Ω) is ............... ., , 22 Three containers C1, C 2 and C3 have water, at different temperatures. The table below, shows the final temperature T when, different amounts of water (given in liters), are taken from each container and mixed, (assume no loss of heat during the process), , C1, , C2, , C3, , T, , 1l, , 2l, , –, , 60°C, , −, , 1l, , 2l, , 30°C, , 2l, , –, , 1l, , 60°C, , 1l, , 1l, , 1l, , θ, , The value of θ (in °C to the nearest integer), is ...... ., , 23 A ball is dropped from the top of a 100 m, , 1, s, 2, before hitting the ground, it covers a, distance of 19 m. Acceleration due to, gravity (in ms− 2) near the surface on that, planet is ........... ., high tower on a planet. In the last, , 24 An asteroid is moving directly towards, the centre of the earth. When at a, distance of 10 R (R is the radius of the, earth) from the earth’s centre, it has a, speed of 12 km/s. Neglecting the effect of, earth’s atmosphere, what will be the, speed of the asteroid when it hits the, surface of the earth (escape velocity from, the earth is 11.2 km/s)? Give your answer, to the nearest integer in km/s ............, , 25 The first member of the Balmer series of, hydrogen atom has a wavelength of 6561 Å., The wavelength of the second member of, the Balmer series (in nm) is ..... ., , CHEMISTRY, Objective Type Questions, 1 Arrange the following bonds according to, their average bond energies in descending, order, C Cl, C Br, C F, C I, (a), (b), (c), (d), , C F > C Cl > C Br > C I, C Br > C I > C Cl > C F, C I > C Br > C Cl > C F, C Cl > C Br > C I > C F, , 2 Two monomers in maltose are, (a), (b), (c), (d), , α-D-glucose and α-D-glucose, α-D-glucose and α-D-galactose, α-D-glucose and β-D-glucose, α-D-glucose and α-D-fructose, , 3 The correct order of the calculated spin, only magnetic moments of complexes (A), to (D) is, (A) Ni(CO)4, (B) [Ni(H2O)6 ]Cl2, (C) Na 2[Ni(CN)4 ] (D) PdCl2(PPh3 )2, (a), (b), (c), (d), , (A) ≈ (C) < (B) ≈ (D), (C) ≈ (D) < (B) < (A), (C) < (D) < (B) < (A), (A) ≈ (C) ≈ (D) < (B), , 4 Among the reactions (a) - (d), the, reaction(s) that does/do not occur in the, blast furnace during the extraction of iron, is/are, (A) CaO + SiO2 → CaSiO3, (B) 3Fe2O3 + CO → 2Fe3 O4 + CO2
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33, , JANUARY ATTEMPT ~ 08 Jan 2020, Shift II, (C) FeO + SiO2 → FeSiO3, 1, (D) FeO → Fe + O2, 2, (a) (C) and (D), (b) (A), (c) (A) and (D), (d) (D), , maximum activity shown by Group 7-9, elements., Reason The reactants are most strongly, adsorbed on group 7-9 elements., , 5 For the following Assertion and Reason,, the correct option is, Assertion The pH of water increases with, increase in temperature., Reason The dissociation of water into H+, and OH− is an exothermic reaction., (a) Assertion is not true, but Reason is true., (b) Both assertion and Reason are true and the, Reason is the correct explanation for the, Assertion., (c) Both Assertion and Reason are false., (d) Both Assertion and Reason are true, but, the Reason is not the correct explanation, for the Assertion., , 6 An unsaturated hydrocarbon X absorbs, two hydrogen molecules on catalytic, hydrogenation, and also gives following, reaction :, +, , O, , [Ag(NH ) ], , 3, 3 2, X , , → A , , →, , Zn / H2O, , B (3-oxo-hexanedicarboxylic acid) X will be :, , (a) The Assertion is true, but the Reason is, false., (b) Both Assertion and Reason are true, but, the Reason is not the correct explanation, for the Assertion., (c) Both Assertion and Reason are true and, the Reason is the correct explanation for, the Assertion., (d) Both Assertion and Reason are false., , 10 Preparation of bakelite proceeds via, reactions, (a), (b), (c), (d), , Electrophilic addition and dehydration, Condensation and elimination, Nucleophilic addition and dehydration, Electrophilic substitution and dehydration, , 11 White phosphorus on reaction with, concentrated NaOH solution in an inert, atmosphere of CO2 gives phosphine and, compound (X). (X) on acidification with, HCl gives compound (Y ). The basicity of, compound (Y ) is, (a) 4, (c) 2, , (b) 3, (d) 1, , 12 Among (A) - (D), the complexes that can, (a), , (b), , (c), , (d), , display geometrical isomerism are, (A) [Pt(NH3 )3 Cl]+, (B) [Pt(NH3 )Cl5 ]−, (C) [Pt(NH3 )2Cl(NO2)], (D) [Pt(NH3 )4ClBr]2+, , 7 Which of the following compounds is likely, to show both Frenkel and Schottky defects, in its crystalline form?, (a) AgBr, , (b) CsCl, , (c) KBr, , (d) ZnS, , 8 The radius of the second Bohr orbit in, , terms of the Bohr radius, a 0, in Li2 + is, , (a), , 2a0, 3, , (b), , 4a0, 3, , (c), , 4a0, 9, , (d), , 2a0, 9, , 9 For the following Assertion and Reason, the correct option is, Assertion For hydrogenation reactions,, the catalytic activity increases from, Group 5 to Group 11 metals with, , (a), (b), (c), (d), , (D) and (A), (C) and (D), (A) and (B), (B) and (C), , 13 A metal (A) on heating in nitrogen gas, gives compound B. B on treatment with, H2O gives a colourless gas, which when, passed through CuSO4 solution gives a, dark blue-violet coloured solution. A and B, respectively, are, (a), (b), (c), (d), , Na and Na3 N, Mg and Mg3 N2, Mg and Mg(NO3 )2, Na and NaNO3
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34, , ONLINE, , 14 The major product [B] in the following, , JEE Main 2020 ~ Solved Papers, , (c) A = H3CO, , OCH3, , sequence of reactions is, (i) B H, , 2 6, →È [ A], CH2 C == CH CH2CH3 , , (ii) H2O 2 , O H, CH(CH3 )2, , OCH3, , Dil. H SO, , 2, 4, , , , → [B], , (a) CH3 C CH == CH CH3, , CH(CH3 )2, , HO, , (b) CH3 C == CH CH2CH3, , CH(CH3 )2, , OH, , (d) A = HO, , (c) CH3—C—CH2CH2CH3, , HO, , C, H3C, , OH, , B = HO, , ∆, , B = H3CO, , OCH3, , CH3, , (d) CH2 == C CH2CH2 CH3, , CH(CH3 )2, , OCH3, , 16 Consider the following plots of rate, , 15 Among the compounds A and B with, molecular formula C9H18O3 , A is having, higher boiling point the B. The possible, structures of A and B are, (a) A = HO, , 1, for four different, T, reactions. Which of the following orders is, correct for the activation energies of these, reactions?, , constant versus, , OH, log k, , a, c, , d, , HO, b, , B = HO, OH, , OH, (b) A = H3CO, , 1/T, , (a) Eb > Ea > Ed > Ec, (c) Eb > Ed > Ec > Ea, , (b) Ea > Ec > Ed > Eb, (d) Ec > Ea > Ed > Eb, , 17 The major product in the following, , OCH3, , reaction is, O, + H3 O, , OCH3, , CH3, , B = HO, OH, , OH OH, , O, , (a), , OH, , (b), CH3, , OH, CH3
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35, , JANUARY ATTEMPT ~ 08 Jan 2020, Shift II, OH, , Given : E ° 2 +, , . V,, = − 014, Sn |Sn, , , °, , RT, ., 2303, = 006, . V,, . , E Pb2 +|Pb = − 013, , , F, , O, , (c), , (d), CH3, , HO, , CH3, , 18 The increasing order of the atomic radii of, the following elements is, (A) C, (B) O, (C) F, (E) Br, (a), (b), (c), (d), , (D) Cl, , maximum number of atoms present in, molecule ‘C’ in one plane is ........, , 19 Hydrogen has three isotopes (A), (B) and, (C). If the number of neutron(s) in (A), (B), and (C) respectively, are (x), ( y) and (z), the, sum of (x), ( y) and (z) is, (b) 3, , (c) 2, , (d) 1, , 20 Kjeldahl’s method cannot be used to, estimate nitrogen for which of the, following compounds?, (a) C6 H5 NO2, , O, , (b) NH2 C NH2, , (c) CH3 CH2 C ≡≡ N (d) C6 H5 NH2, , Numerical Type Questions, 21 For an electrochemical cell, 2+, , Red hot, , CH Cl (1. eq. ), , Cu tube, , Anhydrous AlCl 3, , 3, A → B , , → C, , (A is a lowest molecular weight alkyne), , 24 NaClO3 is used, even in spacecrafts, to, produce O2. The daily consumption of pure, O2 by a person is 492 L at 1 atm 300 K., How much amount of NaClO3 , in grams, is, required to produce O2 for the daily, consumption of a person at 1 atm, 300 K, .......... ?, NaClO3 (s) + Fe(s) → O2 ( g) + NaCl(s), + FeO(s)R = 0082, ., L atm mol− 1K − 1, , 25 Complexes (ML5 ) of metals Ni and Fe have, , 2+, , (aq, 1M)||Pb (aq, 1M)|Pb(s), [Sn 2 + ], when this cell attains, the ratio, [Pb2 + ], equilibrium is .............. ., , Sn(s)|Sn, , when heated from 300 K to 500 K changes, its internal energy by 5000 J. The molar, heat capacity at constant volume is ............, , 23 In the following sequence of reactions the, , (a) < (b) < (c) < (d) < (e), (c) < (b) < (a) < (d) < (e), (d) < (c) < (b) < (a) < (e), (b) < (c) < (d) < (a) < (e), , (a) 4, , 22 At constant volume, 4 mol of an ideal gas, , ideal square pyramidal and trigonal, bipyramidal geometries, respectively. The, sum of the 90°, 120° and 180° L-M-L, angles in the two complexes is ............... ., , MATHEMATICS, Objective Type Questions, 1 Let A and B be two events such that the, probability that exactly one of them occurs, 2, is and the probability that A or B occurs, 5, 1, is , then the probability of both of them, 2, occur together is, (a) 0.10, (c) 0.01, , (b) 0.20, (d) 0.02, , 2 Let S be the set of all real roots of the, , equation, 3x (3x − 1) + 2 =|3x − 1| + |3x − 2|., Then S, , (a), (b), (c), (d), , is a singleton., is an empty set., contains at least four elements., contains exactly two elements., , 3 The mean and variance of 20 observations, are found to be 10 and 4, respectively. On, rechecking, it was found that an observation
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36, , JEE Main 2020 ~ Solved Papers, , ONLINE, 9 was incorrect and the correct observation, was 11. Then the correct variance is, (a) 4.01, , (b) 3.99, , (c) 3.98, , (d) 4.02, , 4 Let a = i$ − 2 $j + k$ and b = i$ − $j + k$ be two, vectors. If c is a vector such that b × c = b × a, and c ⋅ a = 0, then c ⋅ b is equal to, (a), , 1, 2, , (b) −, , 3, 2, , (c) −, , 1, 2, , (d) − 1, , 5 Let f : (1, 3) → R be a function defined by, x[x], , f (x) =, , , where [x] denotes the greatest, 1 + x2, integer ≤ x. Then the range of f is, , 2 3, 3, (a) , ∪ ,, 5 5 4, 3 4, (c) , , 5 5, , 4, , 5, , 2, (b) ,, 5, 2, (d) ,, 5, , 4, 5 , 1 3 4, ∪ ,, 2 5 5 , , 6 If α and β be the coefficients of x4 and x2, respectively in the expansion of, (x + x2 − 1 )6 + (x − x2 − 1 )6, then, (a) α + β = − 30, (c) α + β = 60, , (b) α − β = − 132, (d) α − β = 60, , (b) x + 2 y = 42, (d) x + 3 y = 58, , ∫0 t sin(10t )dt is equal to, , (a) 0, , 1, 10, , (c) −, , 1, 10, , (d) −, , 1, 5, , 9 If a line, y = mx + c is a tangent to the circle,, (x − 3)2 + y2 = 1 and it is perpendicular to a, line L1, where L1 is the tangent to the circle,, 1 1, x2 + y2 = 1 at the point , ,, ; then, 2 2, (a) c2 + 7c + 6 = 0, (c) c2 − 7c + 6 = 0, , 10 Let α =, b=, , 12 The length of the perpendicular from the, origin, on the normal to the curve,, x2 + 2xy − 3 y2 = 0 at the point (2, 2) is, (a) 2, , (b) 2 2, , (c) 4 2, , (d), , 2, , 13 Which of the following statements is a, tautology?, (a), (b), (c), (d), , ~ ( p ∧ ~ q) → p ∨ q, ~ ( p ∨ ~ q) → p ∧ q, p ∨ (~ q) → p ∧ q, ~ ( p ∨ ~ q) → p ∨ q, , 14 If I = ∫, , 2, , 1, , dx, 2x − 9x2 + 12x + 4, 3, , , then, , 1, 1, < I2 <, 8, 4, 1, 1, 2, (d), <I <, 16, 9, , (b), , 2 2, 1 0, −1, and I = , , the 10 A is, 9 4, 0 1, equal to, , 15 If A = , , (b) A − 6I, (d) A − 4I, , 16 The area (in sq. units) of the region, , x, (b), , (b) (− 1, − 1, 1), (d) (− 1, − 1, − 1), , (a) 6I − A, (c) 4I − A, , x, , x→ 0, , (a) (1, − 1, 1), (c) (1, 1, 1), , 1, 1, < I2 <, 6, 2, 1, 1, 2, (c) < I <, 9, 8, , P(10, 16) and it has vertices at (± 6, 0), then, the equation of the normal to it at P is, , 8 lim, , 4, 1, 7, plane is − , − , − . Which of the, 3, 3, 3, following points lies on this plane?, , (a), , 7 If a hyperbola passes through the point, (a) 3x + 4 y = 94, (c) 2x + 5 y = 100, , 11 The mirror image of the point (1, 2, 3) in a, , (b) c2 − 6c + 7 = 0, (d) c2 + 6c + 7 = 0, , 100, −1 + i 3, . If a = (1 + α ) ∑ α 2k and, 2, k= 0, , 100, , ∑ α3 k, then a and b are the roots of the, , k= 0, , quadratic equation, (a) x2 + 101x + 100 = 0 (b) x2 + 102x + 101 = 0, (c) x2 − 102x + 101 = 0 (d) x2 − 101x + 100 = 0, , {(x, y) ∈ R2 : x2 ≤ y ≤ 3 − 2x}, is, (a), , 31, 3, , (b), , 32, 3, , (c), , 29, 3, , (d), , 34, 3, , 17 Let S be the set of all functions, , f : [0, 1] → R, which are continuous on [0,, 1] and differentiable on (0, 1). Then for, every f in S, there exists a c ∈(0, 1),, depending on f, such that, , (a), , f (1) − f (c), = f ′ (c), 1− c, , (b) | f (c) − f (1)|< | f ′ (c)|, (c) | f (c) + f (1)|< (1 + c)| f ′ (c)|, (d) | f (c) − f (1)|< (1 − c)|(f ′ (c)|, , 18 The differential equation of the family of, curves, x2 = 4b( y + b), b ∈R, is, , (a) xy′′ = y ′, (c) x( y ′ )2 = x − 2 yy ′, , (b) x( y ′ )2 = x + 2 yy ′, (d) x( y ′ )2 = 2 yy ′ − x
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37, , JANUARY ATTEMPT ~ 08 Jan 2020, Shift II, , the x-axis at the point Q. If area (∆OPQ) = 4, sq. units, then m is equal to ..............., , 19 The system of linear equations, λx + 2 y + 2z = 5, 2λx + 3 y + 5z = 8, 4x + λy + 6z = 10 has, (a), (b), (c), (d), , 22 Let f (x) be a polynomial of degree 3 such, , no solution when λ = 2, infinitely many solutions when λ = 2, no solution when λ = 8, a unique solution when λ = − 8, , 20 If the 10th term of an A.P. is, , 1, and its 20th, 20, , 1, , then the sum of its first 200, 10, terms is, term is, , (a) 50, , 1, 4, , (b) 100, , (c) 50, , (d) 100, , that f (− 1) = 10, f (1) = − 6, f (x) has a critical, point at x = − 1 and f ′ (x) has a critical point, at x = 1. The f (x) has a local minima at x =, ............., 2 sin α, 1, 1 − cos 2β, 1, 23 If, ,, = and, =, 2, 1 + cos 2α 7, 10, π, α , β ∈ 0, , then tan(α + 2β) is equal to, 2, .............. ., , 24 The number of 4 letter words (with or, , 1, 2, , without meaning) that can be formed from, the eleven letters of the word, ‘EXAMINATION’ is .............., , Numerical Type Questions, 21 Let a line y = mx (m > 0) intersect the, , n (n + 1) (2n + 1), is equal to, 4, =1, , 7, , parabola, y = x at a point P, other than, the origin. Let the tangent to it at P meet, 2, , 25 The sum,, , ∑, n, , ..............., , Answers, Physics, 1. (d), 11. (a), 21. (30), , 2. (c), 12. (b), 22. (50), , 3., 13., 23., , (c), (c), (8), , 4. (a), 14. (c), 24. (16), , 5., 15., 25., , (d), (c), (486), , 6., 16., , (c), (c), , 7., 17., , (d), (c), , 8., 18., , (c), (c), , 9., 19., , (d), (c), , 10., 20., , (b), (d), , 10., 20., , (d), (a), , 10., 20., , (c), (d), , For Detailed Solutions, Visit : http://bit.ly/37jCFDH, Or Scan :, , Chemistry, 1. (a), 11. (d), 21. (2.15), , 2. (a), 12. (b), 22. (6.25), , 3., 13., 23., , (d), (b), (13), , 4. (a), 14. (c), 24. (2130), , 5., 15., 25., , (c), (d), (20), , 6., 16., , (b), (d), , 7., 17., , (a), (c), , 8., 18., , (b), (b), , 9., 19., , (a), (b), , For Detailed Solutions, Visit : http://bit.ly/3o3OdAY, Or Scan :, , Mathematics, 1. (a), 11. (a), 21. (0.5), , 2., 12., 22., , (a), (b), (3), , 3., 13., 23., , (b), (d), (1), , 4., (c), 14., (c), 24. (2454), , 5., (d), 15. (b), 25. (504), , 6., 16., , (b), (b), , 7., 17., , (c), (*), , 8., 18., , (a), (b), , 9., 19., , (d), (a), , For Detailed Solutions, Note (*) None of the options is correct., , Visit : http://bit.ly/35gxSAg, Or Scan :
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ONLINE QUESTION PAPER, , JEE Main 2020, (09 January, 2020), TIME 9:30-12:30 (Shift I), , MM : 300, , PHYSICS, Objective Type Questions, 1 An electric dipole of moment, , $ ) × 10−29C-m is at the origin, p = (−i$ − 3$j + 2k, (0, 0, 0). The electric field due to this, $, dipole at r = + $i + 3$j + 5k, (note that r ⋅ p = 0) is parallel to, , $), (a) (+ $i − 3$j − 2k, $, $, $), (b) (− i − 3 j + 2k, $, $, $, (c) (+ i + 3 j − 2k), , 4 A charged particle of mass m and charge q, moving under the influence of uniform, electric field E$i and a uniform magnetic, $ follows a trajectory from point P to, field Bk, Q as shown in the figure. The velocities at, P and Q are respectively, v$i and −2v$j., Then, which of the following statements, ( A, B, C , D) are the correct? (Trajectory, shown is schematic and not to scale), y, , $), (d) (− $i + 3$j − 2k, E, , 2 Consider two ideal diatomic gases A and B, at some temperature T. Molecules of the, gas A are rigid and have a mass m., Molecules of the gas B have an additional, m, vibrational mode and have a mass . The, 4, ratio of the specific heats (CVA andCVB ) of gas, A and B respectively is, (a) 5 : 9, (c) 3 : 5, , (b) 7 : 9, (d) 5 : 7, , 3 Two particles of equal mass m have, , $i + $j, ., respective initial velocities u$i and u , 2 , They collide completely inelastically. The, energy lost in the process is, , 3, mu 2, 4, 1, (c) mu 2, 3, , (a), , (b), (d), , 2, mu 2, 3, 1, mu 2, 8, , P, , B, , v, a, O, , 2a, , Q, , X, , 2v, , 1. E =, , 3 mv2, , ., 4 qa , , 2. Rate of work done by the electric field at, 3 mv3 , P is , ., 4 a , 3. Rate of work done by both the fields at Q, is zero., 4. The difference between the magnitude of, angular momentum of the particle at P, and Q is 2 mav., (a) (1), (3),(4), (c) (1), (2), (3), (4), , (b) (1), (2), (3), (d) (2), (3), (4)
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39, , JANUARY ATTEMPT ~ 09 Jan 2020, Shift I, 5 A particle moving with kinetic energy E, , 9, , has de Broglie wavelength λ. If energy ∆E, is added to its energy, the wavelength, become λ / 2. Value of ∆E is, , (a) 2E, (c) 3E, , A, , B, , (b) 4E, (d) E, , C, , 6 A vessel of depth 2h is half filled with a, liquid of refractive index 2 2 and the, upper half with another liquid of refractive, index 2. The liquids are immiscible.The, apparent depth of the inner surface of the, bottom of vessel will be, 3, h 2, 4, h, (d), 2( 2 + 1), , h, 2, h, (c), 3 2, , (b), , (a), , 7 Radiation with wavelength 6561Å falls on, a metal surface to produce photoelectrons., The electrons are made to enter a uniform, magnetic field of 3 × 10−4T. If the radius of, the largest circular path followed by the, electrons is 10 mm, the work function of, the metal is close to, (a) 0.8 eV, (c) 18, . eV, , (b) 11, . eV, (d) 16, . eV, , 8 Consider a sphere of radius R which, , carries a uniform charge density ρ. If a, R, sphere of radius is carved out of it, as, 2, |E |, shown in the figure the ratio A of, |EB|, magnitude of electric field EA and EB, respectively, at points A and B due to the, remaining portion is, , d, , O, , Three solid sphere each of mass m and, diameter d are stuck together such that, the lines connecting the centres form an, equilateral triangle of side of length d. The, ratio I 0 / I A of moment of inertia I 0 of the, system about an axis passing the centroid, and about centre of any of the spheres I A, and perpendicular to the plane of the, triangle is, (a), , 15, 13, , (b), , 13, 15, , (c), , 13, 23, , (d), , 23, 13, , 10 Water flows in a horizontal tube (see, figure). The pressure of water changes by, 700 Nm −2 between A and B, where the, area of cross-section are 40 cm 2 and, 20 cm 2, respectively. Find the rate of flow, of water through the tube., (Take, density of water = 1000 kgm −3 ), A, B, , (a) 3020 cm3 /s, (c) 2720 cm3 /s, , (b) 2420 cm3 /s, (d) 1810 cm3 /s, , 11 Three harmonic waves having equal, , frequency ν and same intensity I 0, have, π, π, and − , respectively., 4, 4, When they are superimposed,the intensity, of the resultant wave is close to, phase angles 0,, , R, 2, R, , (a) 0.2I 0, , A, , 21, 34, 17, (c), 54, , (c) 3I 0, , (d) 5.8I 0, , 12 The aperture of a telescope is 5m. The, , B, , (a), , (b) I 0, , 18, 54, 18, (d), 34, , (b), , separation between the moon and the, earth is 4 × 105 km. With light of, wavelength of 5500 Å, the minimum, separation between objects on the surface, of moon, so that they are just resolved, is, close to, (a) 600 m, (c) 60 m, , (b) 20 m, (d) 200 m
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40, , JEE Main 2020 ~ Solved Papers, , ONLINE, , (all quantities are in SI units), , 13 Which of the following is an equivalent, cyclic process corresponding to the, thermodynamic cyclic given in the figure?, where, 1 → 2 is adiabatic., , Y, B (0, 1), , (Graphs are schematic and are not to, scale), 1, , (0, 0), , p, 3, , (a), , 2, V, , (b) 2, , (b), V, , 1Ω, , V, 1, , (a) 0.4 A, (c) 2A, , V, 1, , 3, , 1, T, , T, , 14 The electric fields of two plane, electromagnetic plane waves in vacuum, are given by, E = E $j cos(ωt − kx), 0, , $ cos (ωt − ky), E2 = E 0k, , and, , 3Ω, , 20 V, , (d), V, , 2Ω, , D, , 2, , (c), , 1, , 1, 2, , C, 4Ω, , T, , 2, , B, , A, , 1, , 3, , T, , 3, , (d), , joining points B and D. The current in this, wire is, , 2, , 3, , (c) 1, , 16 In the given circuit diagram, a wire is, , 2, (a), , 3, 2, , X, , A (1, 0), , At t = 0, a particle of charge q is at origin, with a velocity v = 08, . c$j (c is the speed of, light in vacuum). The instantaneous force, experienced by the particle is, $), (a) E0 q (0.8i$ − $j + 0.4k, $, $, $), (b) E q (0.4i − 3 j + 0.8k, 0, , $), (c) E0 q(−0.8$i + $j + k, $, $, $), (d) E q (0.8i + j + 0.2k, 0, , 15 Consider a force F = − xi$ + y$j. The work, done by this force in moving a particle, from point A(1, 0) to B(0, 1) along the line, segment is, , (b) zero, (d) 4A, , 17 A long, straight wire of radius a carries a, current distributed uniformly over its, cross-section. The ratio of the magnetic, a, fields due to the wire at distance and 2a, 3, respectively, from the axis of the wire is, (a), , 3, 2, , (b) 2, , (c), , 2, 3, , (d), , 1, 2, , hc5, , where c, G, is speed of light, G universal gravitational, constant and h is the Planck’s constant., Dimension of f is that of, , 18 A quantity f is given by f =, , (a) area, (c) momentum, , (b) volume, (d) energy, , 19 If the screw on a screw gauge is given six, rotations, it moves by 3 mm on the main, scale. If there are 50 divisions on the, circular scale, the least count of the screw, gauge is, (a) 0.001 cm, (c) 0.02 cm, , (b) 0.01 cm, (d) 0.001 cm
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41, , JANUARY ATTEMPT ~ 09 Jan 2020, Shift I, 20 A body A of mass m is moving in a, , 22 The distance x covered by a particle in one, , circular orbit of radius R about a planet., m, Another body B of mass collides with A, 2, v, with a velocity which is half , the, 2, instantaneous velocity v of A. The collision, is completely inelastic. Then, the combined, body, (a) escapes from the planet’s gravitational, field, (b) starts moving in an elliptical orbit, around the planet, (c) falls vertically downward towards the, planet, (d) continues to move in a circular orbit, , Numerical Type Questions, 21 Both the diodes used in the circuit shown, are assumed to be ideal and have negligible, resistance when these are forward biased., Built in potential in each diode is 0.7V. For, the input voltages shown in the figure, the, voltage (in volts) at point A is …… ., A, Vin = 12.7 V, , dimensional motion varies with time t as, x2 = at 2 + 2bt + c. If the acceleration of the, particle depends on x as x− n , where n is an, integer, the value of n is …… ., , 23 One end of a straight uniform 1 m long bar, is pivoted on horizontal table. It is released, from rest when it makes an angle 30º from the, horizontal (see figure). Its angular speed, when its hits the table is given as n s−1,, where n is an integer. The value of n is …… ., 30º, , 24 A body of mass m = 10 kg is attached to one, end of a wire of length 0.3 m. The, maximum angular speed (in rad s−1) with, which it can be rotated about its other end, in space station is (breaking stress of wire, = 48, . × 107 Nm −2 and area of cross-section, of the wire = 10−2 cm 2) is, , 25 In a fluorescent lamp choke (a small, transformer) 100 V of reverse voltage is, produced when the choke current changes, uniformly from 0.25A to 0 in a duration of, 0.025 ms.The self-inductance of the choke, (in mH) is estimated to be …… ., , 4V, , CHEMISTRY, Objective Type Questions, 1 If the magnetic moment of a dioxygen, , 3 ‘X’ melts at low temperature and is a bad, conductor of electricity in both liquid and, solid state. X is, , species is 1.73 B.M, it may be., (a) O2 ,O2− or O+2, (c) O2 or O−2, , (b) O−2 or O+2, (d) O2 or O+2, , 2 Which of these will produce the highest, , (a) carbon tetrachloride (b) silicon carbide, (c) mercury, (d) zinc sulphide, , 4 According to the following diagram, A, reduces BO2 when the temperature is, , yield in Friedel-Crafts reaction?, NH2, (a), , (b), CONH2, OH, , (c), , (d), , ∆Gº/kJ mol–1, , Cl, –600, –800, –1000, , A+O2, , AO2, , –1200, , B+O2, , BO2, , 0, , 200 400 600 800 10001200 1400 1600, T (ºC)
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44, , JEE Main 2020 ~ Solved Papers, , ONLINE, (a), (b), (c), (d), , 23 108 g of silver (molar mass 108 g mol −1) is, , (v) < (iii) < (ii) < (iv) < (i), (iii) < (i) < (ii) < (iv) < (v), (v) < (i) < (iv) < (ii) < (iii), (iii) < (iv) < (ii) < (i) < (v), , Numerical Type Questions, 21 The hardness of a water sample, , containing 10−3 M MgSO4 expressed as, CaCO3 equivalents (in ppm) is……, (molar mass of MgSO4 is 120.37 g/mol), , 22 The molarity of HNO3 in a sample which, has density 1.4 g/mL and mass percentage, of 63% is ……… (Molecular weight of, HNO3 = 63), , deposited at cathode from AgNO3 (aq), solution by a certain quantity of electricity., The volume (in L) of oxygen gas produced, at 273 K and 1 bar pressure from water by, the same quantity of electricity is ………, , 24 The mass percentage of nitrogen in, histamine is………, , 25 How much amount of NaCl should be, added to 600 g of water (ρ = 100, . g/mL) to, decrease the freezing point of water to, −02, . ºC? …… (The freezing point depression, constant for water = 2 K kg mol −1), , MATHEMATICS, Objective Type Questions, 1 Let C be the centroid of the triangle with, , vertices (3,−1), (1, 3) and (2, 4). Let P be the, point of intersection of the lines, x + 3 y − 1 = 0 and 3x − y + 1 = 0. Then the, line passing through the points C and P, also passes through the point, , (a) (−9, − 7), (c) (7, 6), , (b) (−9, − 6), (d) (9, 7), , 1, ⋅ 416, , (a), , 1, 24, , 1, ⋅ 848, , 1, ⋅ 16128, , (b) 2, , ⋅.... to ∞ is equal to, (c), , 1, 22, , (d) 1, , 3 A spherical iron ball of 10 cm radius is, coated with a layer of ice of uniform, thickness that melts at a rate of, 50 cm3 /min. When the thickness of ice is, 5 cm, then the rate (in cm/ min.) at which, of the thickness of ice decreases, is, 5, 6π, 1, (c), 36π, , (a), , (b) 1, (d), , b+ a, b− a, , 5 The value of, , 3π , π, 3π , π, cos3 ⋅ cos + sin3 ⋅ sin is, 8, 8, 8, 8, , (a), , 1, 4, , (b), , 1, 2 2, , (c), , 1, 2, , (d), , 1, 2, , 6 The number of real roots of the equation,, , 2 The product, 1, 24, , b− c, c− a, c− a, (c), b− c, , (a), , 1, 54π, 1, (d), 18π, , (b), , 4 Let f be any function continuous on [a , b], and twice differentiable on (a , b). If for all, x ∈ (a , b), f ′ (x) > 0 and f ′′ (x) < 0, then for, f (c) − f (a ), is greater than, any c ∈ (a , b),, f (b) − f (c), , e4x + e3 x − 4e2x + ex + 1 = 0 is, , (a) 3, (c) 1, , 7 The value of ∫, , (b) 4, (d) 2, 2π, 0, , x sin 8 x, , dx is equal, sin 8 x + cos8 x, , to, (a) 2π, (c) 2 π 2, , (b) 4π, (d) π 2, , 8 If for some α and β in R, the intersection of, the following three planes, x + 4 y − 2z = 1, x + 7 y − 5z = β, x + 5 y + αz = 5, is a line in R3 , then α + β is equal to, (a) 0, (c) −10, , (b) 10, (d) 2
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45, , JANUARY ATTEMPT ~ 09 Jan 2020, Shift I, 9 If e1 and e2 are the eccentricities of the, x2, y2, ellipse,, +, = 1 and the hyperbola,, 18, 4, 2, 2, x, y, −, = 1 respectively and (e1 , e2 ) is a, 9, 4, point on the ellipse, 15x2 + 3 y2 = k, then k, is equal to, (a) 14, (c) 17, , (b) 15, (d) 16, , sin(a + 2)x + sin x, , x, , 10 If f (x) = , b, (x + 3x2 )1/ 3 − x1/ 3, , , x4/ 3, is continuous at x = 0, then a, to, (a) −2, (c) 0, , ; x<0, ; x=0, ; x>0, + 2b is equal, , 1 1 2, 11 If the matrices A = 1 3 4, B = adj A, , , 1 −1 3, |adj B|, is equal to, and C = 3 A, then, |C|, (b) 2, (d) 72, , 12 A circle touches the Y -axis at the point, (0, 4) and passes through the point (2, 0)., Which of the following lines is not a, tangent to this circle?, (a) 4x − 3 y + 17 = 0, (c) 4x + 3 y − 8 = 0, , (b) 3x + 4 y − 6 = 0, (d) 3x − 4 y − 24 = 0, , 13 Let z be a complex number such that, , 5, z−i, = 1 and|z|= . Then the value of, 2, z + 2i, |z + 3i|is, (a), (c), , (b), , 10, 15, 4, , 7, 2, , (d) 2 3, , π, π, 14 If f ′ (x) = tan (sec x + tan x), < x < , and, 2, 2, f (0) = 0, then f (1) is equal to, −1, , π+1, 4, 1, (c), 4, (a), , π+ 2, 4, π −1, (d), 4, , (b), , 5 is an integer or 5 is an irrational is, (a), (b), (c), (d), , 5 is irrational or 5 is an integer, 5 is not an integer or 5 is not irrational, 5 is an integer and 5 is irrational, 5 is not an integer and 5 is not irrational, , 16 If for all real triplets (a , b, c),, 1, , f (x) = a + bx + cx2; then ∫ f (x)dx is equal to, 0, , (b) 1, (d) −1, , (a) 16, (c) 8, , 15 Negation of the statement :, , 1, (a) 23f (1) + 2f , 2 , , 1, 1, (b) f (0) + f , 2 , 3, 1, 1, (c) f (1) + 3f , 2 , 2, 1, 1 , (d), f (0) + f (1) + 4f , 2 , 6, , 17 If the number of five digit numbers with, distinct digits and 2 at the 10th place is, 336 k, then k is equal to, (a) 8, , (b) 7, , (c) 4, , (d) 6, , 18 Let the observations xi (1 ≤ i ≤ 10) satisfy, 10, , the equations, ∑ (xi − 5) = 10 and, i =1, , 10, , ∑ (xi − 5), , = 40. If µ and λ are the mean, , 2, , i =1, , and the variance of the observations,, x1 − 3, x2 − 3,..... , x10 − 3, then the ordered, pair (µ , λ ) is equal to, (a) (6, 3), , (b) (3, 6), , 19 The integral ∫, , (c) (3, 3), , (d) (6, 6), , dx, , is equal to, (x + 4)8/ 7 (x − 3)6/ 7, (where C is a constant of integration), , x − 3, (a) − , , x + 4, x − 3, (c) , , x + 4, , −1/7, , 1/7, , +C, , +C, , (b), , 1 x − 3, , , 2 x + 4, , (d) −, , 1, 13, , 3 /7, , x − 3, , , x + 4, , +C, −13 /7, , +C, , 20 In a box, there are 20 cards, out of which, 10 are labelled as A and the remaining 10, are labelled as B. Cards are drawn at, random, one after the other and with, replacement, till a second A-card is, obtained. The probability that the second, A-card appears before the third B-card is:, (a), , 15, 16, , (b), , 9, 16, , (c), , 13, 16, , (d), , 11, 16
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46, , JEE Main 2020 ~ Solved Papers, , ONLINE, , Numerical Type Questions, 21 If the vectors p = (a + 1)i$ + aj$ + ak$,, , 23 The number of distinct solutions of the, , equation, log1/ 2|sin x|= 2 − log1/ 2|cos x|in the, interval [0, 2 π ], is, , q = ai$ + (a + 1)$j + ak$ and, r = ai$ + aj$ + (a + 1)k$ (a ∈ R) are coplanar, and 3(p . q )2 − λ|r × q|2 = 0, then the value, of λ is ........ ., , 24 If for x ≥ 0, y = y(x) is the solution of the, differential equation,, (x + 1)dy = ((x + 1)2 + y − 3)dx, y(2) = 0, then, y(3) is equal to…… ., , 22 The projection of the line segment joining, , 25 The coefficient of x4 in the expansion of, , the points (1, − 1, 3) and (2, − 4, 11) on the, line joining the points (−1, 2, 3) and, (3, − 2, 10) is……… ., , (1 + x + x2 )10 is…… ., , Answers, Physics, 1., 11., 21., , (c), (d), (12), , 2. (d), 12. (c), 22. (3), , 3., (d), 13. (b), 23. ( 15), , (b), (d), (4), , 4., 14., 24., , 5., 15., 25., , (c), (c), (10), , 6. (b), 16. (c), , 7. (b), 17. (c), , 8. (d), 18. (d), , 9. (c), 19. (a), , 10. (c), 20. (b), , For Detailed Solutions, Visit : http://bit.ly/2HeKKPg, Or Scan :, , Chemistry, 1. (b), 11. (d), 21. (100), , 2., (b), 12. (b), 22. (14.00), , 3., (a), 13. (b), 23. (5.66), , 4., (b), 14., (a), 24. (37.84), , 5., (c), 15. (d), 25. (1.76), , 6., 16., , (c), (b), , (b), (c), , 7., 17., , 8., 18., , (d), (c), , 9., 19., , (a), (a), , 10., 20., , (a), (a), , 10., 20., , (c), (d), , For Detailed Solutions, Visit : http://bit.ly/37qBKSd, Or Scan :, , Mathematics, 1., 11., 21., , (b), (c), (1), , 2., 12., 22., , (c), (c), (8), , 3., 13., 23., , (d), (b), (8), , 4., 14., 24., , (c), (a), (3), , 5. (b), 15. (d), 25. (615), , 6., 16., , (c), (d), , 7., 17., , (d), (a), , 8., 18., , (b), (c), , 9., 19., , (d), (c), , For Detailed Solutions, Visit : http://bit.ly/3lXTY1e, Or Scan :
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ONLINE QUESTION PAPER, , JEE Main 2020, (09 January, 2020), TIME 2:30-5:30 (Shift II), , MM : 300, , PHYSICS, Objective Type Questions, 1 A rod of length L has non-uniform linear, 2, , x, mass density given by ρ(x) = a + b ,, L, where a and b are constants and 0 ≤ x ≤ L., The value of x for the centre of mass of the, rod is at, , 3 2a + b , , L, 4 3a + b , 3 a + b , (c) , L, 2 2a + b , , (a), , (b), , 4 a + b , , L, 3 2a + 3b , , 3 2a + b , (d) , L, 2 3a + b , , 2 Planet A has mass M and radius R. Planet, B has half the mass and half the radius of, planet A. If the escape velocities from the, planets A and B are vA and vB respectively,, v, n, then A = . The value of n is, vB 4, (a) 1, , (b) 2, , (c) 3, , (d) 4, , 3 Two steel wires having same length are, suspended from a ceiling under the same, load. If the ratio of their energy stored per, unit volume is 1 : 4, the ratio of their, diameters is, (a), , 2 :1, , (b) 1 : 2, , (c) 2 : 1, , (d) 1 : 2, , 4 The energy required to ionise a hydrogen, like ion in its ground state is 9 Rydbergs., What is the wavelength of the radiation, emitted when the electron in this ion, jumps from the second excited state to the, ground state ?, , (a) 8.6 nm, (c) 11.4 nm, , (b) 24.2 nm, (d) 35.8 nm, , 5 For the four sets of three measured, physical quantities as given below. Which, of the following options is correct ?, , C1 = 2562, (i) A1 = 2436, . , B1 = 00724, ., ., (ii) A2 = 2444, . , B2 = 16082, . , C3 = 2402, ., (iii) A3 = 252, , C3 = 236183, . , B3 = 192812, ., ., (iv) A4 = 25, B4 = 236191, . , C 4 = 195, ., , (a) A1 + B1 + C1 < A3 + B3 + C3, < A2 + B2 + C2 < A4 + B4 + C4, (b) A4 + B4 + C4 < A1 + B1 + C1, = A2 + B2 + C2 = A3 + B3 + C3, (c) A4 + B4 + C4 < A1 + B1 + C1, = A3 + B3 + C3 < A2 + B2 + C2, (d) A1 + B1 + C1 = A2 + B2 + C2, = A3 + B3 + C3 = A4 + B4 + C4, , 6 A particle of mass m is projected with a, speed u from the ground at an angle θ =, , π, 3, , w.r.t. horizontal (X-axis). When it has, reached its maximum height, it collides, completely inelastically with another, particle of the same mass and velocity u$i., The horizontal distance covered by the, combined mass before reaching the, ground is, (a), , 3 3 u2, 3 2 u2, 5 u2, (b), (c), 8 g, 4 g, 8 g, , (d) 2 2, , u2, g
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48, , ONLINE, , 7 The current i in the network is, 5Ω, , 11 An electron of mass m and magnitude of, charge|e|initially at rest gets accelerated by, a constant electric field E. The rate of change, of de Broglie wavelength of this electron at, time t ignoring relativistic effects is, , 10 Ω, , D, 5Ω, , (a), 20 Ω, , 10 Ω, , i, , JEE Main 2020 ~ Solved Papers, , (c), , D, , h, ||E, e, t, −h, ||E, e t2, , h, (b) −, ||E, e t, ||, e Et, (d), h, , 12 A small spherical droplet of density d is, 5Ω, , 9V, , (a) 0.2A, (c) 0.6 A, , (b) 0 A, (d) 0.3 A, , 8 A wire of length L and mass per unit, , length 60, . × 10−3 kgm−1 is put under, tension of 540 N. Two consecutive, frequencies that it resonates at are :, 420 Hz and 490 Hz. Then, L in metres is, , (a) 8.1 m, , (b) 2.1 m, , (c) 5.1 m (d) 1.1 m, , 9 Two identical capacitors A and B,, charged to the same potential 5V are, connected in two different circuits as, shown below at time t =0. If the charge, on capacitors A and B at time t = CR is, QA and QB respectively, then (here e is, the base of natural logarithm), , R, , (a), (b), (c), (d), , +, +, +, +, , –, –, –, –, A, , R, , +, +, +, +, , –, –, –, –, A, , VC, QA = VC , QB =, e, VC, CV, QA =, , QB =, e, 2, CV, VC, , QB =, QA =, 2, e, QA = VC , QB = CV, , 10 Two gases-argon (atomic radius, 0.07 nm, atomic weight 40) and xenon, (atomic radius 0.1 nm, atomic weight, 140) have the same number density and, are at the same temperature. The ratio, of their respective mean free times is, closest to, (a) 4.67, , (b) 2.3, , (c) 3.67, , (d) 1.83, , floating exactly half immersed in a liquid of, density ρ and surface tension T. The radius, of the droplet is (take note that the surface, tension applies an upward force on the, droplet), (a) r =, , 3T, (2d − ρ) g, , (b) r =, , T, (d − ρ) g, , (c) r =, , T, (d + ρ) g, , (d) r =, , 2T, 3(d + ρ) g, , 13 In L-C circuit, the inductance L = 40 mH and, capacitance C = 100 µF. If a voltage, V (t ) = 10 sin(314t ) is applied to the circuit,, the current in the circuit is given as, (a) 0.52 cos 314 t, (c) 10 cos 314 t, , (b) 0.52 sin 314 t, (d) 5.2 cos 314 t, , 14 A plane electromagnetic wave is propagating, $i + $j, with its polarisation, 2, $ The correct form of the, along the direction k., magnetic field of the wave would be (here B0, is an appropriate constant), along the direction, , $ $, $ cos ωt − k i + j , (a) B0 k, , 2 , , $j − i$, , i$ + $j , (b) B0, cos ωt + k, , 2, 2 , , $i − $j, $i + $j , , , (c) B0, cos ωt − k, , 2, 2 , , $i + $j, $i + $j , , , (d) B0, cos ωt − k, , 2, 2 , , , 15 An electron gun is placed inside a long, solenoid of radius R on its axis. The solenoid, has n turns/length and carries a current I., The electron gun shoots an electron along, the radius of the solenoid with speed v. If the
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49, , JANUARY ATTEMPT ~ 09 Jan 2020, Shift II, electron does not hit the surface of the, solenoid, maximum possible value of v is, (all symbols have their standard meaning), , mω2, 3k, 2 mω2 , , , (c), 3 k , , R, , y, , eµ 0 nIR, 4m, eµ 0 nIR, (d), m, , (b), , 16 A small circular loop of conducting wire, has radius a and carries current i. It is, placed in a uniform magnetic field B, perpendicular to its plane such that when, rotated slightly about its diameter and, released, it starts performing simple, harmonic motion of time period T. If the, mass of the loop is m, then, (a) T =, (c) T =, , πm, iB, 2 πm, iB, , (b), , 19 A particle starts from the origin at t =0, , x, , 2eµ 0 nIR, m, eµ 0 nIR, (c), 2m, , 2mω2, k, mω2, (d), k, , (a), , z, , (a), , an angular velocity ω, (k >> mω 2 ), the, relative change in the length of the spring, is best given by the option, , (b) T =, (d) T =, , 2m, iB, πm, 2iB, , with an initial velocity of 30, . $i m/s and, moves in the x y-plane with a constant, acceleration (60, . $i + 40, . $j)m / s2. The, x -coordinate of the particle at the instant, when its y-coordinate is 32 m is D metres., The value of D is, (a) 50, , (b) 60, , (c) 40, , 20 A uniformly thick wheel with moment of, inertia I and radius R is free to rotate, about its centre of mass (see figure). A, massless string is wrapped over its rim, and two blocks of masses m1 and, m2 (m1 > m2 ) are attached to the ends of the, string. The system is released from rest., The angular speed of the wheel when m1, descents by a distance h is, , 17 There is a small source of light at some, depth below the surface of water, 4, (refractive index = ) in a tank of large, 3, cross-sectional surface area. Neglecting, any reflection from the bottom and, absorption by water, percentage of light, that emerges out of surface is (nearly), [Use the fact that surface area of a, spherical cap of height h and radius of, curvature R is 2πRh], (a) 34%, (c) 17%, , (b) 50%, (d) 21%, , 18 A spring mass system (mass m, spring, constant k and natural length l) rests in, equilibrium on horizontal disc. The free, end of the spring is fixed at the centre of, the disc. If the disc together with spring, mass system, rotates about it ’s axis with, , (d) 32, , m2, m1, 1, , 2(m1 + m2 ) gh 2, (a) , , 2, (m1 + m2 )R + 1, 1, , 2, , m1 + m2, (b) , gh, 2, (m1 + m2 )R + 1, 1, , 2, , m1 − m2, (c) , gh, 2, (m1 + m2 )R + 1, 1, , 2(m1 − m2 ) gh 2, (d) , , 2, (m1 + m2 )R + 1
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50, , ONLINE, , Numerical Type Questions, 21 The circuit shown below is working as a, 8 V DC regulated voltage source. When, 12 V is used as input, the power dissipated, (in mW) in each diode is; (considering both, Zener diodes are identical) ......... ., 200 Ω, 200 Ω, Vo, , Vin=12 V, , 8V, , JEE Main 2020 ~ Solved Papers, , compressed adiabatically from volume V1, V, to V2 = 1 . It is then allowed to expand, 16, isobarically to volume 2V2. If all the, processes are the quasi-static, then the, final temperature of the gas (in °K) is (to, the nearest integer) ......... ., 24 An electric field E = 4xi$ − ( y2 + 1)$j N/C, passes through the box shown in figure., The flux of the electric field through, surfaces ABCD and BCGF are marked as, φ1 and φII, respectively. The difference, between (φI − φII ) is (in N - m2/C) ...... ., z, , 22 In a meter bridge experiment, S is a, standard resistance, R is a resistance wire., It is found that balancing length is, l = 25 cm. If R is replaced by a wire of half, length and half diameter that of R of same, material, then the balancing distance l′ (in, cm) will now be .......... ., R, , S, , (0, 2, 2), , D, , B (3, 0, 2), , C, (3, 2, 2), F, x, (3, 0, 0), , E, (0, 0, 0), H, (0, 2, 0), , G, (3, 2, 0), , y, , 25 In a Young’s double slit experiment, 15, , G, , l, , A (0, 0, 2), , V, , 23 Starting at temperature 300 K, one mole, of an ideal diatomic gas (γ = 14, . ) is first, , fringes are observed on a small portion of, the screen when light of wavelength, 500 nm is used. Ten fringes are observed, on the same section of the screen when, another light source of wavelength λ is, used. Then, the value of λ is (in nm) ...... ., , CHEMISTRY, Objective Type Questions, 1 Which of the following has the shortest, C Cl bond?, (a), (b), (c), (d), , Cl CH == CH CH3, Cl CH == CH NO2, Cl CH == CH OCH3, Cl CH == CH2, , 2 Which polymer has ‘chiral’ monomer(s)?, (a) PHBV, (c) Nylon 6, 6, , (b) Buna-N, (d) Neoprene, , 3 Biochemical oxygen demand (BOD) is the, amount of oxygen required (in ppm), (a) for the photochemical breakdown of, waste present in 1 m3 volume of a water, body., (b) for sustaining life in a water body., (c) by anaerobic bacteria to breakdown, inorganic waste present in a water body., (d) by bacteria to breakdown organic waste, in a certain volume of a water sample.
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51, , JANUARY ATTEMPT ~ 09 Jan 2020, Shift II, 4 A mixture of gases O2 , H2 and CO are, , 8 In the following reaction A is, , (b), , H, A, , (a), , Time, , Pressure, , (d), , (c), , Time, , Time, , 5 The first and second ionisation enthalpies, , of a metal are 496 and 4560 kJ mol −1,, respectively. How many moles of HCl and, H2SO4, respectively, will be needed to react, completely with 1 mole of the metal, hydroxide?, , (a) 1 and 2, (c) 2 and 0.5, , (b) 1 and 1, (d) 1 and 0.5, , 6 In the figure shown below, reactant A, (represented by square) is in equilibrium, with product B (represented by circle). The, equilibrium constant is, , (a) 4, , (b) 2, , (c) 8, , (d) 1, , 7 Which of the following reactions will not, produce a racemic product?, (a) H3C, , HCl, , CH3, , O, , HCN, (b) CH3 C CH2CH3 →, HBr, , (c) CH3 CH2CH == CH2 →, CH3, , HCl, (d) CH3 C CH == CH2 →, , H, , (iii) O3, (iv) (CH3)2S, (v) NaOH (aq) + ∆, , (b), , Time, , Pressure, , (c), , O, , (i) Br2, hν, (ii) KOH (alc.), , Pressure, , (a), , Pressure, , taken in a closed vessel containing, charcoal. The graph that represents the, correct behaviour of pressure with time is, , (d), , 9 The isomer(s) of [Co(NH3 )4Cl2 ] that, has/have a Cl Co Cl angle of 90°, is/are, (a) cis and trans (b) meridional and trans, (c) cis only, (d) trans only, , 10 The number of sp2-hybrid orbitals in a, molecule of benzene is, (a) 24, (c) 18, , (b) 12, (d) 6, , 11 The true statement amongst the following is, (a) S is not a function of temperature but ∆S, is a function of temperature., (b) Both ∆ S and S are functions of, temperature., (c) Both S and ∆ S are not functions of, temperature., (d) S is a function of temperature but ∆S is, not a function of temperature., , 12 The correct order of the spin only magnetic, moments of the following complexes is, (I) [Cr(H2O)6 ]Br2, (II) Na 4 [Fe(CN)6 ], (III) Na3 [Fe(C2O4 )3 ](∆ 0 > P), (IV) (Et4N)2[CoCl4 ], (a), (b), (c), (d), , (II) ≈ (I) > (IV) > (III), (I) > (IV) > (III) > (II), (III) > (I) > (IV) > (II), (III) > (I) > (II) > (IV), , 13 The reaction of H3 N3 B3Cl3 (A) with LiBH4, in tetrahydrofuran gives inorganic, benzene (B). Further, the reaction of (A), with (C) leads to H3 N3 B3 (Me)3 . Compounds, (B) and (C) respectively, are
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52, , ONLINE, (a), (b), (c), (d), , diborane and MeMgBr, boron nitride and MeBr, borazine and MeBr, borazine and MeMgBr, , The compound [P] is, NH2, , NH2, , 14 The solubility product of Cr(OH)3 at 298 K, , (b) (18 × 10−31 )1/ 4, (d) (18 × 10−31 )1/ 2, , (b), , (a), CH3, , is 60, . × 10−31. The concentration of, hydroxide ions in a saturated solution of, Cr(OH)3 will be, (a) (2.22 × 10−31 )1/ 4, (c) (4.86 × 10−29 )1/ 4, , JEE Main 2020 ~ Solved Papers, , CH3, , CH3, (d), , (c), CH3, , 15 Among the statements (A)-(D), the correct, ones are, (A) lithium has the highest hydration, enthalpy among alkali metals., (B) lithium chloride is insoluble in pyridine., (C) lithium cannot form ethynide upon its, reaction with ethyne., (D) Both lithium and magnesium react, slowly with H2O., (a) (A) and (D) only, (b) (B) and (C) only, (c) (A), (C) and (D) only, (d) (A), (B) and (D) only, , 19 A, B and C are three biomolecules. The, results of the tests performed on them are, given below:, Molisch’s test, , Barfoed test Biuret test, , A, , Positive, , Negative, , B, , Positive, , Positive, , Negative, , C, , Negative, , Negative, , Positive, , with the lowest ionic conductance at, 298 K is, saline water used for intravenous injection, distilled water, water from a well, sea water, , (a), (b), (c), (d), , following amines is, NH2, N, , (I), , an excess of, (1) dilute hydrochloric acid and, (2) aqueous sodium hydroxide., The ratio of the volume of H2 evolved in, these two reactions is, (b) 1 : 1, (d) 1 : 2, , 18 Consider the following reactions :, (i) NaNO2/HCl, 0-5ºC, (ii) β-naphthol/NaOH, , A = Lactose, B = Glucose, C = Alanine, A = Glucose, B = Fructose, C = Albumin, A = Lactose, B = Glucose, C = Albumin, A = Lactose, B = Fructose, C = Alanine, , 20 The decreasing order of basicity of the, , 17 5 g of zinc is treated separately with, , (a) 2 : 1, (c) 1 : 4, , Negative, , A, B and C are respectively:, , 16 Amongst the following, the form of water, , (a), (b), (c), (d), , NH2, , NHCH3, , (II), NH2, , N, H, , (III), , (a), (b), (c), (d), , (IV), , (III) > (I) > (II) > (IV), (III) > (II) > (I) > (IV), (I) > (III) > (IV) > (II), (II) > (III) > (IV) > (I), , Coloured solid, , Numerical Type Questions, , [P], Br2/H2O, , C7H6NBr3, , 21 10.30 mg of O2 is dissolved into a litre of, sea water of density 1.03 g/mL. The, concentration of O2 in ppm is
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53, , JANUARY ATTEMPT ~ 09 Jan 2020, Shift II, 22 Consider the following reactions :, (i) CH 3MgBr, , 25 A cylinder containing an ideal gas (0.1 mol, , Cu, , A →, B →, +, 573K, , (ii) H 3O, , 2-methyl- 2- butene, The mass percentage of carbon in A is ......, , 23 A sample of milk splits after 60 min. at, 300 K and after 40 min. at 400 K when the, population of lactobacillus acidophilus in it, doubles. The activation energy (in kJ/mol), for this process is closest to, 2, (Given, R = 83, . J mol−1K −1, ln = 04, .,, 3, , of 1.0 dm3 ) is in thermal equilibrium with, a large volume of 0.5 molal aqueous, solution of ethylene glycol at its freezing, point. If the stoppers S1 and S2 (as shown, in the figure) are suddenly withdrawn, the, volume of the gas in litres after, equilibrium is achieved will be ........, (Given, K f (water) = 20, . K kg mol−1,, R = 008, . dm3 atm K −1mol−1), Frictionless, piston, , .), e−3 = 40, , S2, , S1, , 24 The sum of the total number of bonds, between chromium and oxygen atoms in, chromate and dichromate ions is ........., , Ideal gas, aq. ethylene glycol, , MATHEMATICS, Objective Type Questions, , 4 If 10 different balls are to be placed in 4, , 7x + 6 y − 2z = 0, , distinct boxes at random, then the, probability that two of these boxes contain, exactly 2 and 3 balls is, , 3x + 4 y + 2z = 0, , (a), , 1 The following system of linear equations, , x − 2 y − 6z = 0, has, (a) infinitely many solutions, (x, y, z ), satisfying y = 2z., (b) no solution., (c) only the trivial solution., (d) infinitely many solutions, (x, y, z ), satisfying x = 2z., , 2 If one end of a focal chord AB of the, , 1, , parabola y2 = 8x is at A , − 2 , then the, 2, , equation of the tangent to it at B is, , (a) x − 2 y + 8 = 0, (c) 2x + y − 24 = 0, , (b) x + 2 y + 8 = 0, (d) 2x − y − 24 = 0, , 3 If x = 2 sin θ − sin 2θ and y = 2 cos θ − cos 2θ,, θ ∈ [0, 2π ], then, (a) −, , 3, 4, , (b), , 3, 4, , 2, , d y, dx2, , at θ = π is, (c) −, , 3, 8, , 945, , (b), , 211, , 945, 210, , (c), , 965, 210, , (d), , 965, 211, , 5 Let a function f : [0, 5] → R be continuous,, f (1) = 3 and F be defined as:, F(x) = ∫ t 2 g(t )dt, where g(t ) = ∫ f (u )du., x, , t, , 1, , 1, , Then for the function F , the point x = 1 is, (a), (b), (c), (d), , not a critical point, a point of inflection, a point of local maxima, a point of local minima, , 6 A random variable X has the following, probability distribution, X : 1 2 3 4 5, P (X ) : K 2 2K K 2K 5K 2, Then P (X > 2) is equal to, , (d), , 3, 2, , (a), , 1, 6, , (b), , 23, 36, , (c), , 1, 36, , (d), , 7, 12
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54, , JEE Main 2020 ~ Solved Papers, , ONLINE, 16, , 1 , x, +, , if l1, cos θ x sin θ , is the least value of the term independent, π, π, of x when ≤ θ ≤ and l2 is the least value, 8, 4, of the term independent of x when, π, π, ≤ θ ≤ , then the ratio l2 : l1 is equal to, 16, 8, , 13 The length of the minor axis (along y -, , (a) 1 : 16, (c) 16 : 1, , 14 Let [t ] denote the greatest integer ≤ t and, , 7 In the expansion of , , (b) 1 : 8, (d) 8 : 1, , B − A = R − (−2, 5), A − B = [−1, 2), A ∪ B = R − (2, 5), A ∩ B = (−2, − 1), , (a), (c), , 9 Let a n be the nth term of a G.P. of positive, terms. If, , ∑ a 2n + 1, , = 200 and, , n =1, , 100, , ∑ a 2n, , = 100,, , n =1, , 200, , then, , ∑ a n is equal to, , n =1, , (a) 300, (c) 225, , 10 If ∫, , (b) 175, (d) 150, , dθ, , =, cos θ (tan 2θ + sec 2θ ), λ tan θ + 2 log e| f (θ )| + C where C is a, constant of integration, then the ordered, pair (λ , f (θ )) is equal to, 2, , (a) (1, 1 + tan θ), (c) (−1, 1 + tan θ), , (b) (1, 1 − tan θ), (d) (−1, 1 − tan θ), , 11 let a , b ∈ R, a ≠ 0 be such that the equation,, ax2 − 2bx + 5 = 0 has a repeated root α,, which is also a root of the equation,, x2 − 2bx − 10 = 0. If β is the other root of this, equation, then α 2 + β2 is equal to, (a) 26, (c) 28, , (b) 24, (d) 25, , 12 Let a − 2b + c = 1., x+ a x+2 x+ 1, If f (x) = x + b x + 3 x + 2 , then, x+ c x+4 x+3, (a) f (−50) = 501, (c) f (−50) = − 1, , 5, 6, , (a), , (b), , 1 11, 2 3, , (c), , 1 11, 1 5, (d), 3 3, 2 3, , 4 , lim x, = A . Then the function,, x , f (x) = [x2 ]sin(πx) is discontinuous, when x, is equal to, , B = { x ∈ R :|x − 2|≥ 3}; then, , 100, , x + 6 y = 8 ; then its eccentricity is, , x→ 0, , 8 If A = { x ∈ R :|x|< 2} and, (a), (b), (c), (d), , axis) of an ellipse in the standard form is, 4, . If this ellipse touches the line,, 3, , (b) f (50) = 1, (d) f (50) = − 501, , A+1, A, , 15 If x =, , (b), (d), , A + 21, A +5, , ∞, , ∞, , n =0, , n =0, , ∑ (−1)n tan2n θ and y = ∑ cos2n θ,, , π, for 0 < θ < , then, 4, (a) y(1 + x) = 1, (c) x(1 + y) = 1, , (b) y(1 − x) = 1, (d) x(1 − y) = 1, , 1, x ,, 0≤x<, , 2, 1, 1, 16 Given, f (x) = , and, , x=, 2, 2 ,, 1 − x 1 < x ≤ 1, , 2, 2, 1, , g(x) = x − , x ∈ R. Then the area (in sq., , 2, units) of the region bounded by the curves, y = f (x) and y = g(x) between the lines,, 2x = 1 and 2x = 3, is, 1, +, 2, 1, (c), −, 2, (a), , 3, 4, 3, 4, , 1, 3, +, 3, 4, 3 1, (d), −, 4 3, (b), , 17 If z be a complex number satisfying, |Re(z)| +|Im(z)| = 4, then|z|cannot be, (a), , 10, , (b), , 7, , (c), , 17, 2, , (d), , 8, , dy, xy, =, ; y(1) = 1; then a value of x, dx x2 +` y2, satisfying y(x) = e is, , 18 If, , (a), , 1, 3e, 2, , (b), , 3e, , (c), , 2e, , (d), , e, 2
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55, , JANUARY ATTEMPT ~ 09 Jan 2020, Shift II, , x+1 y−3 z +1, and, =, =, 2, 4, 3, x + 3 y + 2 z −1, k, ,, =, =, (λ ∈ R) is equal to, 2, 6, λ, 633, then k is equal to .... ., , 19 Let f and g be differentiable functions on, R such that fog is the identity function. If, for some a , b ∈ R, g′ (a ) = 5 and g(a ) = b,, then f ′ (b) is equal to, (a), , 1, 5, , (b) 5, , 2, 5, , (c), , (d) 1, , 23 If C r =, , 20 Ifp → ( p ∧ ~ q) is false, then the truth, (b) T, F, , (c) F, F, , then k is equal to... ., , (d) T, T, , 24 Let a , b and c be three vectors such that, |a| = 3 ,|b| = 5, b ⋅ c = 10 and the angle, π, between b and c is . If a is perpendicular, 3, to the vector b × c, then|a × (b × c)|is, equal to ...... ., , Numerical Type Questions, 21 If the curves, x − 6x + y + 8 = 0 and, 2, , C r and, , C 0 + 5 ⋅ C1 + 9 ⋅ C 2 + .... + (101) ⋅ C 25 = 225 ⋅ k,, , values of p and q are respectively, (a) F, T, , 25, , 2, , x2 − 8 y + y2 + 16 − k = 0, (k > 0) touch each, other at a point, then the largest value of k, is ........ ., , 22 If the distance between the plane,, , 25 The number of terms common to the two, A.P.s 3, 7, 11, …, 407 and 2, 9, 16, ...., 709, is ..... ., , 23x − 10 y − 2z + 48 = 0 and the plane, containing the lines, , Answers, Physics, 1. (a), 11. (c), 21. (40), , 2. (d), 12. (a), 22. (40), , 3., (a), 13. (a), 23. (1819), , 4., (c), 14. (c), 24. (−48), , 5., (*), 15. (c), 25. (750), , (a), (c), , 6., 16., , 7., 17., , (d), (c), , 8., 18., , (b), (d), , 9., 19., , (a), (b), , 10., 20., , (*), (d), , 10., 20., , (c), (b), , 10., 20., , (c), (d), , For Detailed Solutions, Visit : http://bit.ly/2T6a5h1, Or Scan :, , Chemistry, 1. (b), 11. (b), 21. (10), , 2., (a), 12. (b), 22. (66.67), , 3., (d), 13. (d), 23. (3.98), , 4., (c), 14., (b), 24. (12.00), , 5., 15., 25., , (d), (c), (2.18), , 6., 16., , (b), (b), , 7., 17., , (d), (b), , 8., 18., , (c), (a), , 9., 19., , (c), (c), , For Detailed Solutions, Visit : http://bit.ly/3o8a8XA, Or Scan :, , Mathematics, 1., 11., 21., , (d), (d), (36), , 2., 12., 22., , (a), (b), (3), , 3., 13., 23., , (*), (b), (51), , Note (*) None of the options is correct., , 4., 14., 24., , (b), (a), (30), , 5., 15., 25., , (d), (b), (14), , 6., 16., , (b), (d), , 7., 17., , (c), (b), , 8., 18., , (a), (b), , 9., 19., , (d), (a), , For Detailed Solutions, Visit : http://bit.ly/37fz0H8, Or Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (08 April, 2019), TIME 9:30-12:30 (Shift I), , MM : 360, , PHYSICS, 1 A steel wire having a radius of 2.0 mm,, carrying a load of 4 kg, is hanging from a, ceiling. Given that g = 3.1 π ms−2, what, will be the tensile stress that would be, developed in the wire?, , (a) 6.2 × 106 Nm−2, (c) 3.1 × 106 Nm−2, , (b) 5.2 × 106 Nm−2, (d) 4.8 × 106 Nm−2, , 2 If 1022 gas molecules each of mass, , 10−26 kg collide with a surface, (perpendicular to it) elastically per second, over an area 1 m 2 with a speed 104 m/s,, the pressure exerted by the gas molecules, will be of the order of, (a) 104 N /m2, (c) 103 N /m2, , (b) 108 N /m2, (d) 1016 N /m2, , 3 The bob of a simple pendulum has mass, 2g and a charge of 5.0 µC. It is at rest in a, uniform horizontal electric field of, intensity 2000 V/m. At equilibrium, the, angle that the pendulum makes with the, vertical is (take g = 10 m / s2), −1, , (a) tan (2.0), (c) tan −1 (5.0), , −1, , (b) tan (0.2), (d) tan −1 (0.5), , 4 A boy’s catapult is made of rubber cord, which is 42 cm long, with 6 mm diameter, of cross-section and of negligible mass., The boy keeps a stone weighing 0.02 kg, , on it and stretches the cord by 20 cm by, applying a constant force. When released, the stone flies off with a velocity of, 20 ms−1. Neglect the change in the area of, cross-section of the cord while stretched., The Young’s modulus of rubber is closest, to, , (a) 106 Nm−2, (c) 108 Nm−2, , (b) 104 Nm−2, (d) 103 Nm−2, , 5 A plane electromagnetic wave travels in, free space along the x-direction. The, electric field component of the wave at a, particular point of space and time is, E = 6Vm −1 along y-direction. Its, corresponding magnetic field component,, B would be, (a), (b), (c), (d), , 2 × 10−8 T along z - direction, 6 × 10−8 T along x - direction, 6 × 10−8 T along z - direction, 2 × 10−8 T along y - direction, , 6 Ship A is sailing towards north-east with, velocity v = 30i$ + 50$j km/h, where $i points, east and $j north. Ship B is at a distance of, 80 km east and 150 km north of Ship A, and is sailing towards west at 10 km/h. A, will be at minimum distance from B in, (a) 4.2 h, (c) 3.2 h, , (b) 2.6 h, (d) 2.2 h
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4, , JEE Main 2019 ~ Solved Paper, , ONLINE, 7 A thin strip 10 cm long is on an U-shaped, wire of negligible resistance and it is, connected to a spring of spring constant, 0.5 Nm −1 (see figure). The assembly is, kept in a uniform magnetic field of 0.1 T., If the strip is pulled from its equilibrium, position and released, the number of, oscillations it performs before its, amplitude decreases by a factor of e is N., If the mass of the strip is 50 grams, its, resistance 10 Ω and air drag negligible, N, will be close to, 10 cm, , B, , (a) 1000, , (b) 50000 (c) 5000, , (d) 10000, , 8 Four particles A, B, C and D with masses, mA = m, mB = 2m, mC = 3m and mD = 4m, are at the corners of a square. They have, accelerations of equal magnitude with, directions as shown. The acceleration of, the centre of mass of the particles, (in ms−2 ) is, a, , Y, , B, , D, , (c) zero, , (d), , a $ $, (i + j), 5, , 9 A solid conducting sphere, having a, charge Q, is surrounded by an uncharged, conducting hollow spherical shell. Let the, potential difference between the surface, of the solid sphere and that of the outer, surface of the hollow shell be V . If the, shell is now given a charge of −4 Q, the, new potential difference between the, same two surfaces is, (a) −2 V, , (b) 2 V, , (c) 4 V, , 2, ln2, , (b), , 1, ln2 (c) 2ln2, 2, , (d) ln2, , 11 A thin circular plate of mass M and, radius R has its density varying as, ρ(r ) = ρ0r with ρ0 as constant and r is the, distance from its centre. The moment of, inertia of the circular plate about an axis, perpendicular to the plate and passing, through its edge is I = aMR 2. The value, of the coefficient a is, (a), , 1, 2, , (b), , 3, 5, , (c), , 8, 5, , (d), , 12 In SI units, the dimensions of, , 3, 2, , ε0, is, µ0, , (b) AT2M −1L−1, (d) A 2T3 M −1L−2, , (a) A −1TML3, (c) AT−3 ML3/2, , (Latent heat of vaporisation of water, = 2.10 × 106 J kg−1 and latent heat of, fusion of water = 3.36 × 105 J kg−1), , a, , (b) a($i + $j), , (a), , 150 g of water at 0°C. Then, the air from, the vessel is pumped out adiabatically. A, fraction of water turns into ice and the, rest evaporates at 0°C itself. The mass of, evaporated water will be closest to, , X, , a $ $, (a), (i − j), 5, , coil is connected to, 20 H, E, a 10 ohm, resistance in, series as shown in figure. The time at, which rate of dissipation of energy, (Joule’s heat) across resistance is equal to, the rate at which magnetic energy is, stored in the inductor, is, , 13 A thermally insulated vessel contains, , a, C, , a A, , 10 W, , i, , 10 A 20 H inductor, , (d) V, , (a) 150 g (b) 20 g, , (c) 130 g, , (d) 35g, , 14 The reverse breakdown voltage of a Zener, diode is 5.6 V in the given circuit., 200 W, IZ, 9V, , 800 W, , The current I z through the Zener is, (a) 10 mA, (b) 17 mA, (c) 15 mA, (d) 7 mA
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APRIL ATTEMPT ~ 08 April 2019, Shift I, , 5, , 15 In an interference experiment, the ratio, a, 1, of amplitudes of coherent waves is 1 = ., a2 3, The ratio of maximum and minimum, intensities of fringes will be, (a) 2, (c) 4, , (b) 18, (d) 9, , 19 Two particles move at right angle to each, other. Their de-Broglie wavelengths are, λ 1 and λ 2, respectively. The particles, suffer perfectly inelastic collision. The, de-Broglie wavelength λ of the final, particle, is given by, 1, 1, 1, = 2+ 2, 2, λ, λ1 λ 2, λ1 + λ 2, (c) λ =, 2, , (b) λ = λ 1λ 2, , (a), , 16 Water from a pipe is coming at a rate of, 100 liters per minute. If the radius of the, pipe is 5 cm, the Reynolds number for the, flow is of the order of (density of water =, 1000 kg /m3 , coefficient of viscosity of, water = 1 mPa s), , (d), , 2, 1, 1, =, +, λ λ1 λ 2, , 20 A 200 Ω resistor has a certain colour, , (d) 106, , code. If one replaces the red colour by, green in the code, the new resistance will, be, , 17 Two identical beakers A and B contain, , (a) 100 Ω (b) 400 Ω (c) 300 Ω (d) 500 Ω, , (a) 103, , (b) 104, , (c) 102, , equal volumes of two different liquids at, 60°C each and left to cool down. Liquid in, A has density of 8 × 102 kg / m3 and, specific heat of 2000 J kg−1K −1 while, liquid in B has density of 103 kg m −3 and, specific heat of 4000 J kg−1K −1. Which of, the following best describes their, temperature versus time graph, schematically? (Assume the emissivity of, both the beakers to be the same), , (a), , T, , B, A, , B, , t, , t, 60°C, , (c), , (d), , T, , A and B, , A, B, , 22 The wavelength of the carrier waves in a, , (a) 2400 nm, (c) 600 nm, , (b) 1500 nm, (d) 900 nm, , 23 An upright object is placed at a distance, , t, , t, , 18 Voltage rating of a parallel plate, capacitor is 500 V. Its dielectric can, withstand a maximum electric field of, 106 V/m. The plate area is 10−4 m 2. What, is the dielectric constant, if the, capacitance is 15 pF?, −12, , (Take, ε 0 = 8.86 × 10, (a) 3.8, (c) 4.5, , GM, a, GM, (d) 1.41, a, (b) 1.16, , modern optical fibre communication, network is close to, , 60°C, , T, , a, , (a) 1.35, , T, , (b), , A, , located at the corners of a square of side, a. What should be their speed, if each of, them revolves under the influence of, other’s gravitational field in a circular, orbit circumscribing the square ?, , GM, a, GM, (c) 1.21, a, , 60°C, , 60°C, , 21 Four identical particles of mass M are, , 2, , 2, , C / N-m ), , (b) 8.5, (d) 6.2, , of 40 cm in front of a convergent lens of, focal length 20 cm. A convergent mirror, of focal length 10 cm is placed at a, distance of 60 cm on the other side of the, lens. The position and size of the final, image will be, (a) 20 cm from the convergent mirror, same, size as the object, (b) 40 cm from the convergent mirror, same, size as the object
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6, , ONLINE, (c) 40 cm from the convergent lens, twice, the size of the object, (d) 20 cm from the convergent mirror,twice, size of the object, , 24 A circular coil having N turns and radius, r carries a current I. It is held in the, XZ-plane in a magnetic field B$i. The, torque on the coil due to the magnetic, field (in N-m) is, Br 2I, (a), πN, Bπr 2I, (c), N, , (b) Bπr IN, 2, , (d) Zero, , 25 An alternating voltage, V ( t ) = 220 sin 100πt volt is applied to a, purely resistive load of 50 Ω. The time, taken for the current to rise from half of, the peak value to the peak value is, (a) 5 ms, , (b) 2.2 ms (c) 7.2 ms (d) 3.3 ms, , JEE Main 2019 ~ Solved Paper, , reflections it makes before emerging from, the other end is close to, (refractive index of fibre is 1.31 and, sin 40° = 0.64), , 40° q, 1, , (a) 55000, (c) 45000, , (a) n = 2 → n = 3, (c) n = 2 → n = 5, , 27, , A, , B, , L, , L, , rest under the influence of a force that, varies with the distance travelled by the, particle as shown in the figure. The, kinetic energy of the particle after it has, travelled 3 m is, 3, , Force, (in N), , 2, 1, , (b) n = 1 → n = 4, (d) n = 2 → n = 4, , A wire of length 2L, is made by joining, two wires A and B of same length but, different radii r and 2r and made of the, same material. It is vibrating at a, frequency such that the joint of the two, wires forms a node. If the number of, antinodes in wire A is p and that in B is, q, then the ratio p : q is, (a) 3 : 5, (c) 1 : 2, , (b) 66000, (d) 57000, , 29 A particle moves in one dimension from, , 26 Radiation coming from transitions n = 2, to n = 1 of hydrogen atoms fall on He+ ions, in n = 1 and n = 2 states. The possible, transition of helium ions as they absorb, energy from the radiation is, , d, , q2, , 1, , (a) 4 J, (c) 6.5 J, , 3, , (b) 2.5 J, (d) 5 J, , 30 For the circuit shown with R1 = 1.0 Ω,, R2 = 2.0Ω, E1 = 2 V and E2 = E3 = 4 V, the, potential difference between the points a, and b is approximately (in volt), R1, , R1, , a, , E3, , (b) 4 : 9, (d) 1 : 4, , R2, , E1, , 28 In figure, the optical fibre is l = 2 m long, and has a diameter of d = 20 µ m. If a ray, of light is incident on one end of the fibre, at angle θ1 = 40°, the number of, , 2, Distance, (in m), , R1, , E2, R1, , (a) 2.7, (c) 3.7, , b, , (b) 2.3, (d) 3.3
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APRIL ATTEMPT ~ 08 April 2019, Shift I, , 7, , CHEMISTRY, 4 The size of the iso-electronic species Cl− ,, , 1 An organic compound X showing the, , Ar and Ca 2+ is affected by, , following solubility profile is, Water, , X, , 5% HCl, , Insoluble, , 10% NaOH, , Soluble, , 10% NaHCO3, , (a), (b), (c), (d), , (a) azimuthal quantum number of valence, shell, (b) electron-electron interaction in the outer, orbitals, (c) principal quantum number of valence, shell, (d) nuclear charge, , Insoluble, , Insoluble, , o -toluidine, oleic acid, m-cresol, benzamide, , 5 In order to oxidise a mixture of one mole, of each of FeC2O4, Fe2(C2O4 )3 , FeSO4 and, Fe2(SO4 )3 in acidic medium, the number, of moles of KMnO4 required is, , 2 Adsorption of a gas follows Freundlich, adsorption isotherm. x is the mass of the, gas adsorbed on mass m of the adsorbent., x, The plot of log versus log p is shown in, m, x, is proportional to, the given graph., m, , (a) 2, , (b) 1, , (c) 3, , (d) 1.5, , 6 In the following compounds, the, decreasing order of basic strength will be, (a), (b), (c), (d), , C2H5 NH2 > NH3 > (C2H5 )2NH, (C2H5 )2NH > NH3 > C2H5 NH2, (C2H5 )2NH > C2H5 NH2 > NH3, NH3 > C2H5 NH2 > (C2H5 )2NH, , 7 The major product of the following, reaction is, x, log —, m, , OCH3, , 2, 3, , Heat, , CH==CH2, Br, , log p, , (a) p2 / 3, (c) p3, , (b) p3/ 2, (d) p2, , (a), , 3 An organic compound neither reacts with, neutral ferric chloride solution nor with, Fehling solution. It however, reacts with, Grignard reagent and gives positive, iodoform test. The compound is, , OH, , (b), Br—CHCH3, , Br—CHCH3, , Br, , (c), , (d), CH2CH2Br, , O, CH3, , (a), , Conc. HBr (excess), , O, , CH3, , (b), , H, , OH, O, , O, , OH, C2H5, , (c), O, , CH3, , CH3, , (d), , C2H5, O, , OH, , CH2CH2Br, , 8 The correct order of the spin only, magnetic moment of metal ions in the, following low spin complexes, [V(CN)6 ]4− ,, [Fe(CN)6 ]4− , [Ru(NH3 )6 ]3 + , and, [Cr(NH3 )6 ]2+ , is, (a), (b), (c), (d), , Cr 2+ > Ru3 + > Fe2+ > V 2+, V 2+ > Cr 2+ > Ru3 + > Fe2+, V 2+ > Ru3 + >Cr 2+ > Fe2+, Cr 2+ > V 2+ > Ru3 + > Fe2+
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8, , ONLINE, 9 The major product of the following, reaction is, O, , Cl, , JEE Main 2019 ~ Solved Paper, , (a) hexadentate, (c) bidentate, , (b) tetradentate, (d) tridentate, , 13 If solubility product of Zr3 (PO4 )4 is, (i) AlCl3, heat, , O+, , (ii) H2O, , O, O, , (a), Cl, , denoted by K sp and its molar solubility is, denoted by S, then which of the following, relation between S and K sp is correct?, K sp , (a) S = , , 144, , 1/ 6, , K sp , (b) S = , , 6912, , K sp , (c) S = , , 929, , 1/ 9, , K sp , (d) S = , , 216, , 1/7, , 1/7, , 14 The major product of the following, , O, CO2H, , reaction is, , Cl, , (b), , O, Br, NaBH4, , O, O, , MeOH, 25°C, , Cl, OH, Br, , (c), (a), O, O, , OH, OMe, , (b), , (d), Cl, , COOH, , 10 For silver, C p( JK −1mol−1 ) = 23 + 0.01 T. If, , OMe, , (c), , the temperature (T ) of 3 moles of silver is, raised from 300 K to 1000 K at 1 atm, pressure, the value of ∆H will be close to, (a) 62 kJ (b) 16 kJ (c) 21 kJ (d) 13 kJ, , O, , (d), , 11 Which is wrong with respect to our, responsibility as a human being to, protect our environment?, (a) Restricting the use of vehicles, (b) Avoiding the use of floodlighted, facilities, (c) Setting up compost tin in gardens, (d) Using plastic bags, , 12 The following ligand is, NEt2, N, O–, , –, , O, , 15 Diborane (B2H 6 ) reacts independently, with O2 and H 2O to produce, respectively., , (a) B2O3 and H3 BO3 (b) B2O3 and [BH4 ]−, (c) H3 BO3 and B2O3 (d) HBO2 and H3 BO3, , 16 Which one of the following equations does, not correctly represent the first law of, thermodynamics for the given processes, involving an ideal gas ? (Assume, non-expansion work is zero), (a), (b), (c), (d), , Cyclic process : q = − W, Adiabatic process : ∆U = − W, Isochoric process : ∆U = q, Isothermal process : q = − W
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APRIL ATTEMPT ~ 08 April 2019, Shift I, 17 With respect to an ore, Ellingham diagram, helps to predict the feasibility of its, (a), (b), (c), (d), , electrolysis, zone refining, vapour phase refining, thermal reduction, , 18 100 mL of a water sample contains 0.81 g, of calcium bicarbonate and 0.73 g of, magnesium bicarbonate. The hardness of, this water sample expressed in terms of, equivalents of CaCO3 is, (molar mass of calcium bicarbonate is, 162 g mol−1 and magnesium bicarbonate, is 146 g mol−1), (a) 5,000 ppm, (c) 100 ppm, , (b) 1,000 ppm, (d) 10,000 ppm, , 19 Given, that EOs 2/ H 2O = + 1.23V;, ESs, , 2−, 2−, 2O8 / SO4, , s, EBr, , E, , 2, , / Br, , s, , s, Au 3 + / Au, , = + 1.09V,, = + 1.4V, , (b) O2, (d) Br2, , 20 The IUPAC name of the following, compound is, CH3 OH, , , H3C CH CH CH 2 COOH, (a), (b), (c), (d), , 4,4 - dimethyl -3-hydroxybutanoic acid, 2-methyl-3-hydroxypentan-5-oic acid, 3- hydroxy -4- methylpentanoic acid, 4-methyl-3-hydroxypentanoic acid, , 21 Element ‘B ’ forms ccp structure and ‘A ’, occupies half of the octahedral voids,, while oxygen atoms occupy all the, tetrahedral voids. The structure of, bimetallic oxide is, (a) A2BO4, (c) A2B2O, , The rate law for the reaction is, [A](mol L−1), , [B](mol L−1), , 0.05, , 0.05, , 0.045, , 0.10, , 0.05, , 0.090, , 0.20, , 0.10, , 0.72, , (a) rate = k [ A ][B], (c) rate = k [ A ][B], , 2, , Initial rate, (mol L−1s−1 ), , (b) rate = k [ A ]2[B]2, (d) rate = k [ A ]2[B], , 23 The lanthanide ion that would show, colour is, , (a) Gd3 +, , (b) Sm3 +, , (c) La3 +, , (d) Lu3 +, , 24 Maltose on treatment with dilute HCl gives, (a), (b), (c), (d), , D-glucose and D-fructose, D-fructose, D-galactose, D-glucose, , 25 The vapour pressures of pure liquids A, , = 2.05V;, , The strongest oxidising agent is, , (a) Au3 +, (c) S 2O82−, , 9, , (b) AB2O4, (d) A4B2O, , 22 For the reaction, 2 A + B → C, the values, of initial rate at different reactant, concentrations are given in the table, below., , and B are 400 and 600 mmHg, respectively, at 298 K. On mixing the two liquids, the, sum of their initial volumes is equal to, the volume of the final mixture. The mole, fraction of liquid B is 0.5 in the mixture., The vapour pressure of the final solution,, the mole fractions of components A and B, in vapour phase, respectively are, (a) 450 mmHg, 0.4, 0.6 (b) 500 mmHg, 0.5, 0.5, (c) 450 mmHg, 0.5,0.5 (d) 500 mmHg, 0.4,0.6, , 26 Which of the following amines can be, prepared by Gabriel phthalimide reaction?, (a) n - butylamine, (c) t-butylamine, , (b) triethylamine, (d) neo -pentylamine, , 27 The quantum number of four electrons, are given below:, 1, 2, 1, II. n = 3, l = 2, ml = 1, ms = +, 2, 1, III. n = 4, l = 1, ml = 0, ms = +, 2, 1, IV. n = 3, l = 1, ml = 1, ms = −, 2, I. n = 4, l = 2, ml = − 2, ms = −, , The correct order of their increasing, energies will be, (a) IV < III < II < I, (c) IV < II < III < I, , (b) I < II < III < IV, (d) I < III < II < IV
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10, , ONLINE, , 28 Coupling of benzene diazonium chloride, with 1-naphthol in alkaline medium will, give, OH, , (a), , (b), , OH, , N, , N, , N, , Reason (R) Ozone holes increase the, amount of UV radiation reaching the, earth., , of alkali metal ions is, , (d), , N, , CFCs in the upper stratosphere., , 30 The correct order of hydration enthalpies, , OH, , (c), , 29 Assertion (A) Ozone is destroyed by, , (a) Assertion and Reason are incorrect., (b) Assertion and Reason are both correct, and the Reason is the correct, explanation for the Assertion., (c) Assertion and Reason are correct, but, the Reason is not the explanation for the, Assertion., (d) Assertion is false, but the Reason is, correct., , N, , N, , JEE Main 2019 ~ Solved Paper, , N, N, , (a), (b), (c), (d), , Li+ > Na + > K + > Cs + > Rb+, Na + > Li+ > K + > Rb+ > Cs +, Na + > Li+ > K + > Cs + > Rb+, Li+ > Na + > K + > Rb+ > Cs +, , OH, , MATHEMATICS, 1 The shortest distance between the line, y = x and the curve y 2 = x − 2 is, , (c), , 2 lim, , 7, 4 2, , x→ 0, , you are born in India, then you are a, citizen of India’’, is, , 7, (b), 8, 11, (d), 4 2, , (a) 2, , sin2 x, 2 − 1 + cos x, , (a) If you are not a citizen of India, then you, are not born in India., (b) If you are a citizen of India, then you, are born in India., (c) If you are born in India, then you are not, a citizen of India., (d) If you are not born in India, then you, are not a citizen of India., , equals, (b) 2, (d) 4, , (a) 4 2, (c) 2 2, , 3 The greatest value of c ∈ R for which the, system of linear equations, , has a non-trivial solution, is, (b), , 1, 2, , (c) 2, , 5 All possible numbers are formed using, the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all, at a time. The number of such numbers, in which the odd digits occupy even, places is, , x −cy − cz = 0, cx − y + cz = 0,, cx + cy − z = 0, (a) −1, , 4 The contrapositive of the statement ‘‘If, , (d) 0, , (a) 180, (c) 160, , (b) 175, (d) 162
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APRIL ATTEMPT ~ 08 April 2019, Shift I, cos α − sin α, ,(α ∈ R ) such that, sin α cos α , 0 −1, =, . Then, a value of α is, 1 0 , , 6 Let A = , A32, , π, 32, π, (c), 64, , (d), , π, 16, , 3, 5, , 7 If cos(α + β ) = , sin(α − β) =, 0 < α ,β <, 63, 52, 21, (c), 16, , 5, and, 13, , 63, 16, 33, (d), 52, , (b), , 8 The sum of the coefficients of all even, degree terms is x in the expansion of, ( x + x3 − 1 )6 + ( x − x3 − 1 )6, ( x > 1) is, equal to, (a) 29, (c) 26, , 9, , ∫, , (b) 32, (d) 24, , 5x, 2 dx is equal to, x, sin, 2, , sin, , (where, C is a constant of integration ), (a), (b), (c), (d), , 2x + sin x + 2 sin 2x + C, x + 2 sin x + 2 sin 2x + C, x + 2 sin x + sin 2x + C, 2x + sin x + sin 2x + C, , 10 The mean and variance of seven, observations are 8 and 16, respectively. If, 5 of the observations are 2, 4, 10, 12, 14,, then the product of the remaining two, observations is, (a) 45, (c) 48, , (b) 49, (d) 40, , 11 The equation of a plane containing the, line of intersection of the planes, 2x − y − 4 = 0 and y + 2z − 4 = 0 and, passing through the point (1, 1, 0) is, (a) x − 3 y − 2z = − 2, (c) x − y − z = 0, , $ on the vector, vector 2$i + 3$j + k, perpendicular to the plane containing the, $ and i$ + 2$j + 3k, $ , is, vectors i$ + $j + k, 3, 2, , (c) 3 6, , π, , then tan( 2α ) is equal to, 4, , (a), , 12 The magnitude of the projection of the, , (a), , (b) 0, , (a), , 11, , (b) 2x − z = 2, (d) x + 3 y + z = 4, , (b), , 6, , (d), , 3, 2, , 13 The sum of the squares of the lengths of, the chords intercepted on the circle,, x 2 + y 2 = 16, by the lines, x + y = n, n ∈ N ,, where N is the set of all natural, numbers, is, (a) 320, (c) 160, , (b) 105, (d) 210, , 14 Let A and B be two non-null events such, that A ⊂ B. Then, which of the following, statements is always correct., (a), (b), (c), (d), , P ( A /B) = P (B) − P ( A ), P ( A/B) ≥ P ( A ), P ( A/B) ≤ P ( A ), P ( A/B) = 1, , 15 If α and β are the roots of the equation, x 2 − 2x + 2 = 0, then the least value of n, α, for which , β, (a) 2, (c) 4, , n, , = 1 is, (b) 5, (d) 3, , 16 The area (in sq units) of the region, A = {( x , y ) ∈ R × R|0 ≤ x ≤ 3,, 0 ≤ y ≤ 4, y ≤ x 2 + 3x } is, 53, 6, 59, (c), 6, , (a), , (b) 8, (d), , 26, 3, , 17 If S1 and S 2 are respectively the sets of, local minimum and local maximum, points of the function,, f ( x ) = 9x 4 + 12x3 − 36x 2 + 25, x ∈ R, then, (a), (b), (c), (d), , S1 = { −2} ; S 2 = {0,1}, S1 = { −2, 0} ; S 2 = {1}, S1 = { −2, 1} ; S 2 = {0}, S1 = { −1} ; S 2 = {0, 2}
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12, , JEE Main 2019 ~ Solved Paper, , ONLINE, 3, 5, , 1, 3, , 25 A point on the straight line, 3x + 5 y = 15, , 18 If α = cos−1 , β = tan−1 , where, , which is equidistant from the coordinate, axes will lie only in, , π, 0 < α , β < , then α − β is equal to, 2, , 9 , (a) tan , , 5 10 , 9, (c) tan −1 , 14, −1 , , 9 , (b) cos , , 5 10 , 9 , (d) sin −1 , , 5 10 , −1 , , 2⋅ 20C0 + 5⋅ 20 C1 + 8⋅ 20 C2 + 11⋅ 20 C3, + .... + 62 ⋅20 C20 is equal to, (b) 225, (d) 224, , 20 The sum of the solutions of the equation, | x − 2| + x ( x − 4) + 2 = 0 ( x > 0) is, equal to, (a) 9, , (b) 12, , (c) 4, , (d) 10, , 21 If the tangents on the ellipse 4x 2 + y 2 = 8, at the points (1, 2) and ( a , b) are, perpendicular to each other, then a 2 is, equal to, (a), , 128, 17, , (b), , 64, 17, , (c), , 4, 17, , (d), , 2, 17, , 22 Let y = y( x ) be the solution of the, differential equation,, dy, ( x 2 + 1)2, + 2x( x 2 + 1) y = 1 such that, dx, π, , then the value of, y( 0) = 0. If a y(1) =, 32, ‘a’ is, 1, (a), 4, , 1, (b), 2, , (c) 1, , 1, (d), 16, , 23 The sum of all natural numbers ‘n’ such, that 100 < n < 200 and HCF (91, n)>1 is, (a) 3203, (c) 3221, , (b) 3303, (d) 3121, , 24 The length of the perpendicular from the, point ( 2, − 1, 4) on the straight line,, x+3 y− 2 z, = is, =, 10, 1, −7, (a), (b), (c), (d), , greater than 3 but less than 4, less than 2, greater than 2 but less than 3, greater than 4, , IV quadrant, I quadrant, I and II quadrants, I, II and IV quadrants, , 26 Let O( 0, 0) and A( 0, 1) be two fixed points,, then the locus of a point P such that the, perimeter of ∆AOP is 4, is, , 19 The sum of the series, , (a) 226, (c) 223, , (a), (b), (c), (d), , (a), (b), (c), (d), , 8x2 − 9 y2 + 9 y = 18, 9x2 − 8 y2 + 8 y = 16, 9x2 + 8 y2 − 8 y = 16, 8x2 + 9 y2 − 9 y = 18, , 27 If, 2, , , 3 cos x + sin x , π, 2 y = cot−1 , , x ∈ 0, , 2, cos x − 3 sin x , , dy, is equal to, then, dx, , π, −x, 6, π, (c), −x, 3, , π, 6, π, (d) 2x −, 3, (b) x −, , (a), , 2x , 1 − x, , ,|x|< 1, then f , 1 + x, 1 + x2 , , 28 If f ( x ) = loge , is equal to, (a) 2 f (x), (c) ( f (x))2, , (b) 2 f (x2), (d) −2 f (x), , 29 Let f : [0, 2] → R be a twice differentiable, function such that f ′ ′ ( x ) > 0, for all, x ∈( 0, 2). If φ( x ) = f ( x ) + f ( 2 − x ) , then φ is, (a) increasing on (0, 1) and decreasing on, (1, 2), (b) decreasing on (0, 2), (c) decreasing on (0, 1) and increasing on, (1, 2), (d) increasing on (0, 2), , 2 − x cos x, and g( x ) = loge x, ( x > 0), 2 + x cos x, then the value of the integral, π/ 4, ∫ g( f ( x ))dx is, , 30 If f ( x ) =, , −π/ 4, , (a) log e 3, (c) log e 2, , (b) log e e, (d) log e 1
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APRIL ATTEMPT ~ 08 April 2019, Shift I, , Answers, Physics, 1., 11., 21., , (c), (*), (b), , 2., 12., 22., , (*), (d), (b), , 3., 13., 23., , (d), (b), (*), , 4., 14., 24., , (a), (a), (b), , 5., 15., 25., , (a), (c), (d), , 6., 16., 26., , (b), (b), (d), , 7., 17., 27., , (c), (b), (c), , 8., 18., 28., , (a), (b), (d), , 9., 19., 29., , (d), (a), (c), , 10., 20., 30., , (c), (d), (d), , (a), (b), (a), , 3., 13., 23., , (d), (b), (b), , 4., 14., 24., , (d), (d), (d), , 5., 15., 25., , (a), (a), (d), , 6., 16., 26., , (c), (b), (a), , 7., 17., 27., , (b), (d), (c), , 8., 18., 28., , (b), (d), (c), , 9., 19., 29., , (d), (c), (c), , 10., 20., 30., , (a), (c), (d), , 3., 13., 23., , (b), (d), (d), , 4., 14., 24., , (a), (b), (a), , 5., 15., 25., , (a), (c), (c), , 6., 16., 26., , (c), (c), (c), , 7., 17., 27., , (b), (c), (b), , 8., 18., 28., , (d), (d), (a), , 9., 19., 29., , (c), (b), (c), , 10., 20., 30., , (c), (d), (d), , Chemistry, 1., 11., 21., , (c), (d), (b), , 2., 12., 22., , Mathematics, 1., 11., 21., , (c), (c), (d), , 2., 12., 22., , (a), (d), (d), , Note (*) None of the options is correct., , For Detailed Solutions Visit : https://bit.ly/2DTTdTu Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (08 April, 2019), TIME 2:30-5 :30 (Shift II), , MM : 360, , PHYSICS, R3, , 1 In a simple pendulum, experiment for, determination of acceleration due to, gravity ( g), time taken for 20 oscillations is, measured by using a watch of 1 second, least count. The mean value of time taken, comes out to be 30 s. The length of, pendulum is measured by using a meter, scale of least count 1 mm and the value, obtained 55.0 cm. The percentage error in, the determination of g is close to, (a) 0.7%, (c) 3.5%, , (b) 6.8%, (d) 0.2%, , 2 A nucleus A, with a finite de-Broglie, wavelength λ A , undergoes spontaneous, fission into two nuclei B and C of equal, mass. B flies in the same directions as, that of A, while C flies in the opposite, direction with a velocity equal to half of, that of B. The de-Broglie wavelengths λ B, and λ C of B and C respectively, (a) 2λ A , λ A, (c) λ A , 2λ A, , λA, , λA, 2, λ, (d) λ A , A, 2, , (b), , 3 In the figure shown, what is the current, (in ampere) drawn from the battery? You, are given :, R1 = 15 Ω, R2 = 10 Ω, R3 = 20 Ω, R4 = 5 Ω,, R5 = 25 Ω, R6 = 30 Ω, E = 15 V, , R1, +, E, –, , R2, , R6, , (a) 13/24 (b) 7/18, , R4, , R5, , (c) 20/3, , (d) 9/32, , 4 Two magnetic dipoles X and Y are placed, at a separation d, with their axes, perpendicular to each other. The dipole, moment of Y is twice that of X. A particle, of charge q is passing through their, mid-point P, at angle θ = 45° with the, horizontal line, as shown in figure. What, would be the, d, magnitude of, S, θ, force on the, S, N, P, particle at that, N, X, ( M), instant? (d is, Y, (2 M), much larger than, the dimensions of the dipole), µ M, (a) 0 , × qv, 4π d 3, , 2, (c), , (b) 0, , µ M, µ , × qv (d) 0 , 2 0 , 4π d 3, 4π , , 2, , 2M, d, , 2, , 3, , × qv
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APRIL ATTEMPT ~ 08 April 2019, Shift II, 5 A rocket has to be launched from earth in, such a way that it never returns. If E is, the minimum energy delivered by the, rocket launcher, what should be the, minimum energy that the launcher, should have, if the same rocket is to be, launched from the surface of the moon?, Assume that the density of the earth and, the moon are equal and that the earth’s, volume is 64 times the volume of the moon., (a), , E, 64, , (b), , E, 16, , (c), , E, 32, , (d), , E, 4, , 6 The electric field in a region is given by, , E = ( Ax + B)$i, where E is in NC−1 and x is, in metres. The values of constants are, A = 20 SI unit and B = 10 SI unit. If the, potential at x = 1 is V1 and that at x = − 5, is V 2, then V1 − V 2 is, , (a) − 48 V (b) − 520 V(c) 180 V, , (d) 320 V, , 7 Let| A1| = 3,| A2| = 5 and| A1 + A2| = 5. The, value of ( 2 A1 + 3 A 2 ) ⋅ ( 3 A1 − 2 A 2 ) is, (a) −106.5, (c) −99.5, , (b) −112 . 5, (d) −118 . 5, , 8 The temperature, at which the root mean, square velocity of hydrogen molecules, equals their escape velocity from the, earth, is closest to :, [Boltzmann constant kB = 1.38 × 10−23 J/K,, Avogadro number N A = 6.02 × 1026/kg,, Radius of earth = 6.4 × 106 m,, Gravitational acceleration on earth, = 10 ms −2], (a) 104 K, (c) 3 × 105 K, , (b) 650 K, (d) 800 K, , 9 Two very long, straight and insulated, wires are kept at 90° angle from each, other in xy-plane as shown in the figure., y, I, , d, , P, d, , I, , x, , 15, These wires carry currents of equal, magnitude I, whose directions are shown, in the figure. The net magnetic field at, point P will be, (a) zero, (c) −, , +µ 0I, (z$ ), πd, µ I, $), (d) 0 (x$ + y, 2 πd, (b), , µ 0I, $), (x$ + y, 2 πd, , 10 An electric dipole is formed by two equal, and opposite charges q with separation d., The charges have same mass m. It is kept, in a uniform electric field E. If it is, slightly rotated from its equilibrium, orientation, then its angular frequency, ω is, (a), , 2qE, qE, (b) 2, (c), md, md, , qE, md, , (d), , qE, 2md, , 11 A cell of internal resistance r drives, current through an external resistance R., The power delivered by the cell to the, external resistance will be maximum, when, (a) R = 2r, (c) R = 0.001 r, , (b) R = r, (d) R = 1000 r, , 12 A body of mass m1 moving with an, unknown velocity of v1$i, undergoes a, collinear collision with a body of mass m2, moving with a velocity v2$i. After collision,, m1 and m2 move with velocities of v3 $i and, v i$ , respectively., 4, , If m2 = 0.5m1 and v3 = 0.5 v1, then v1 is, (a) v4 + v2, (c) v4 −, , v2, 2, , v2, 4, (d) v4 − v2, (b) v4 −, , 13 A circuit connected to an AC source of, emf e = e0 sin(100t ) with t in seconds,, π, gives a phase difference of between the, 4, emf e and current i. Which of the, following circuits will exhibit this?, (a), (b), (c), (d), , RC circuit with R = 1 kΩ and C = 1 µF, RL circuit with R = 1 kΩ and L = 1 mH, RC circuit with R = 1 kΩ and C = 10 µF, RL circuit with R = 1 kΩ and L = 10 mH
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16, , ONLINE, , 14 In the circuit shown, a four-wire, , 17 The ratio of mass densities of nuclei of, , potentiometer is made of a 400 cm long, wire, which extends between A and B., The resistance per unit length of the, potentiometer wire is r = 0.01 Ω/cm. If an, ideal voltmeter is connected as shown, with jockey J at 50 cm from end A, the, expected reading of the voltmeter will be, 1.5 V, 1.5 V,, 0.5 Ω 0.5 Ω, , V, J, 50 cm, , A, , JEE Main 2019 ~ Solved Paper, , 40, , Ca and 16O is close to, , (a) 5, , (b) 2, , (c) 0.1, , (d) 1, , 18 A rectangular solid box of length 0.3 m is, held horizontally, with one of its sides on, the edge of a platform of height 5 m., When released, it slips off the table in a, very short time τ = 0.01 s, remaining, essentially horizontal. The angle by, which it would rotate when it hits the, ground will be (in radians) close to, l, , h, , 1Ω, B, , 100 cm, , (a) 0.20 V (b) 0.75 V (c) 0.25 V (d) 0.50 V, , 15 A solid sphere and solid cylinder of, identical radii approach an incline with, the same linear velocity (see figure). Both, roll without slipping all throughout. The, two climb maximum heights hsph and hcyl, hsph, on the incline. The ratio, is given by, hcyl, , (a) 0.02, (c) 0.5, , (b) 0.3, (d) 0.28, , 19 In a line of sight radio communication, a, distance of about 50 km is kept between, the transmitting and receiving antennas., If the height of the receiving antenna is, 70 m, then the minimum height of the, transmitting antenna should be, (Radius of the earth = 6.4 × 106 m), (a) 20 m, (c) 40 m, , (a), , 2, 5, , (b), , 14, 15, , (c) 1, , (d), , 4, 5, , 16 The given diagram shows four processes,, i.e. isochoric, isobaric, isothermal and, adiabatic. The correct assignment of the, processes, in the same order is given by, , (b) 32 m, (d) 51 m, , 20 A positive point charge is released from, rest at a distance r0 from a positive line, charge with uniform density. The speed, ( v ) of the point charge, as a function of, instantaneous distance r from line, charge, is proportional to, , a, p, r0, , b, d, , c, V, , (a) d a b c, (c) d a c b, , (b) a d b c, (d) a d c b, , +, , r, r0, , r, (a) v ∝ , r0 , , (b) v ∝ e, , r, (c) v ∝ ln , r0 , , r, (d) v ∝ ln , r0
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APRIL ATTEMPT ~ 08 April 2019, Shift II, 21 A particle starts from origin O from rest, and moves with a uniform acceleration, along the positive X-axis. Identify all, figures that correctly represent the, motion qualitatively., (a = acceleration, v = velocity,, x = displacement, t = time), , 17, 25 A uniform rectangular thin sheet ABCD, of mass M has length a and breadth b, as, shown in the figure. If the shaded portion, HBGO is cut-off, the coordinates of the, centre of mass of the remaining portion, will be, (0, b), A, , a b, 2 2, , (B) v, , (A) a, , E, , O, , O, , t, , O, , (a), (b), (c), (d), , C, (a, 0), , F, , (D) x, , t, , O, , t, , (A), (A), (B), (C), (B), (C), (A), (B), (D), , telescope objective having a diameter of, 200 cm, if it has to detect light of, wavelength 500 nm coming from a star., , (a) 610 × 10−9 rad, (c) 457.5 × 10−9 rad, , (b) 305 × 10−9 rad, (d) 152.5 × 10−9 rad, , 23 If surface tension (S ), moment of inertia, ( I ) and Planck’s constant ( h ), were to be, taken as the fundamental units, the, dimensional formula for linear, momentum would be, (a) S1/ 2I1/ 2h −1, (c) S1/ 2I1/ 2h 0, , 2a 2b, (a) , , , 3 3, 3a 3b, (c) , , , 4 4, , 5a, (b) , 12, 5a, (d) , 3, , 5b, , 12 , 5b, , , 3, , ,, , 26 A convex lens (of focal length 20 cm) and, , 22 Calculate the limit of resolution of a, , (b) S3/ 2I1/ 2h 0, (d) S1/ 2I3/ 2h −1, , 24 A damped harmonic oscillator has a, frequency of 5 oscillations per second., The amplitude drops to half its value for, every 10 oscillations. The time it will take, 1, of the original amplitude, to drop to, 1000, is close to, (a) 20 s, (c) 100 s, , G, , O, , t, D, (0, 0), , (C) x, , (a , b ), B, , H, , (b) 50 s, (d) 10 s, , a concave mirror, having their principal, axes along the same lines, are kept 80 cm, apart from each other. The concave, mirror is to the right of the convex lens., When an object is kept at a distance of, 30 cm to the left of the convex lens, its, image remains at the same position even, if the concave mirror is removed. The, maximum distance of the object for which, this concave mirror, by itself would, produce a virtual image would be, (a) 25 cm, (c) 10 cm, , (b) 20 cm, (d) 30 cm, , 27 The magnetic field of an electromagnetic, wave is given by, B = 1.6 × 10−6 cos( 2 × 107 z + 6 × 1015 t ), ( 2$i + $j) Wbm −2, The associated electric field will be, (a) E = 4.8 × 102 cos(2 × 107 z − 6 × 1015 t ), (−2$j + i$ ) Vm−1, (b) E = 4.8 × 102 cos(2 × 107 z − 6 × 1015 t ), (2$j + i$ ) Vm−1
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18, , ONLINE, , JEE Main 2019 ~ Solved Paper, , (c) E = 4.8 × 102 cos(2 × 107 z + 6 × 1015 t ), (i$ − 2$j) Vm−1, , RB, , (d) E = 4.8 × 102 cos(2 × 107 z + 6 × 1015 t ), (− i$ + 2$j)Vm−1, , RC, VCC, , VB, , 28 A parallel plate capacitor has 1µF, capacitance. One of its two plates is given, + 2µC charge and the other plate + 4µC, charge. The potential difference, developed across the capacitor is, (a) 1 V, (c) 2 V, , (b) 5 V, (d) 3 V, , (a) 40 µA, (c) 100 µA, , (b) 10 µA, (d) 7 µA, , 30 Young’s moduli of two wires A and B are, , 29 A common emitter amplifier circuit, built, using an n - p - n transistor, is shown in, the figure. Its DC current gain is 250,, RC = 1 kΩ and VCC = 10 V. What is the, minimum base current for VCE to reach, saturation?, , in the ratio 7 : 4. Wire A is 2 m long and, has radius R. Wire B is 1.5 m long and, has radius 2 mm. If the two wires stretch, by the same length for a given load, then, the value of R is close to, (a) 1.3 mm, (c) 1.9 mm, , (b) 1.5 mm, (d) 1.7 mm, , CHEMISTRY, 1 Calculate the standard cell potential, (in V) of the cell in which following, reaction takes place, Fe2+ ( aq ) + Ag+ ( aq ) → Fe3 + ( aq ) + Ag( s), , the central atom, is, (a) [ICl2]− (b) [BrF2]− (c) [ICl4 ]− (d) [IF6 ]−, , 5 Consider the bcc unit cells of the solids 1, and 2 with the position of atoms as shown, below. The radius of atom B is twice that, of atom A. The unit cell edge length is, 50% more is solid 2 than in 1. What is the, approximate packing efficiency in solid 2?, , Given that,, E ° Ag + / Ag = x V, , E ° Fe 2+ / Fe = y V, , E ° Fe3 + / Fe = z V, (a) x + 2 y − 3z, (c) x + y − z, , 4 The ion that has sp3 d 2 hybridisation for, , (b) x − y, (d) x − z, , A, A, , (a), (b), (c), (d), , trans-[Pt(Cl)2(NH3 )2], cis-[Pd(Cl)2(NH3 )2], cis-[Pt(Cl)2(NH3 )2], trans-[Pd(Cl)2(NH3 )2], , 3 The statement that is incorrect about the, , A, , B, , A, A, , A, , A, , A, , (b) 90%, , A, , A, A, Solid 2, , Solid 1, , (a) 65%, , A, A, , A, , A, , 2 The compound that inhibits the growth, of tumors is, , A, , A, , (c) 75%, , (d) 45%, , 6 Which of the following compounds will, , interstitial compounds is, , show the maximum ‘enol’ content?, , (a), (b), (c), (d), , (a), (b), (c), (d), , they are very hard, they have metallic conductivity, they have high melting points, they are chemically reactive, , CH3COCH3, CH3COCH2COCH3, CH3COCH2COOC2H5, CH3COCH2CONH2
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APRIL ATTEMPT ~ 08 April 2019, Shift II, 7 The major product of the following, , 11 For the solution of the gases w, x , y and z, , reaction is, , (b), (a), , O, , O, , x w, (0, 0) Mole fraction, of water, , (d), , (c), , 8 The major product in the following, reaction is, NH2, N, , N, , N, H, , (c), +CH3I, , Base, , N, , NH2, , NH2, +, NCH3, , N, (a), N, H, , N, , N, , N, , N, , (c), N, H, , N, , N, N, H, , N, +, N, CH3, , 9 5 moles of an ideal gas at 100 K are, allowed to undergo reversible, compression till its temperature becomes, 200 K. If CV = 28 JK −1 mol −1, calculate, ∆U and ∆pV for this process., ( R = 8.0 JK −1mol−1), (a), (b), (c), (d), , ∆U, ∆U, ∆U, ∆U, , w, , x, w, , xw, , (0, 0) Mole fraction, of water, , (X = Cl, Br, I) is, (b) CaX 2 (c) MgX 2 (d) BeX 2, , 13 0.27 g of a long chain fatty acid was, , NH2, (d), , (d), , (0, 0) Mole fraction, of water, , (a) SrX 2, , N, , CH3, NHCH3, , y, x, , (0, 0) Mole fraction, of water, z, y, , z, y, , z, , 12 The covalent alkaline earth metal halide, , N, (b), , N, , (b), , z, y, , Partial pressure, , O, , O, (a), , Partial pressure, , (2) Conc. H2 SO4 /∆, , Cl, , Partial pressure, , in water at 298 K, the Henry’s law, constants ( K H ) are 0.5, 2, 35 and 40 K, bar, respectively. The correct plot for the, given data is, , (1) t-BuOK, , Partial pressure, , O, , 19, , = 2.8 kJ; ∆ ( pV ) = 0.8 kJ, = 14 J; ∆ ( pV ) = 0.8 J, = 14 kJ; ∆ ( pV ) = 4 kJ, = 14 kJ; ∆ ( pV ) = 18 kJ, , 10 Which one of the following alkenes when, treated with HCl yields majorly an, anti Markownikov product?, (a) Cl CH == CH2, (b) H2N CH == CH2, (c) CH3 O CH == CH2 (d) F3C CH == CH2, , dissolved in 100 cm3 of hexane. 10 mL of, this solution was added dropwise to the, surface of water in a round watch glass., Hexane evaporates and a monolayer is, formed. The distance from edge to centre, of the watch glass is 10 cm. What is the, height of the monolayer?, [Density of fatty acid = 0.9 g cm −3 ; π = 3], (a) 10−6 m, (c) 10−8 m, , (b) 10−4 m, (d) 10−2 m, , 14 The percentage composition of carbon by, mole in methane is, (a) 75%, , (b) 20%, , (c) 25%, , (d) 80%, , 15 The maximum prescribed concentration, of copper in drinking water is, (a) 5 ppm, (c) 0.05 ppm, , (b) 0.5 ppm, (d) 3 ppm, , 16 For the following reactions, equilibrium, constants are given :, S( s) + O2( g), SO2( g); K 1 = 1052, , 2S( s) + 3O ( g) - 2SO ( g); K, 2, , 3, , 2, , = 10129
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20, , ONLINE, The equilibrium constant for the reaction,, 2SO( g) + O2( g), (a) 10, , 25, , - 2SO (g) is, 3, , 77, , (b) 10, , 154, , (c) 10, , 181, , (d) 10, , 17 The strength of 11.2 volume solution of, H 2O2 is [Given that molar mass of, H = 1 g mol −1 and O = 16 g mol −1], (a) 1.7%, (c) 13.6%, , JEE Main 2019 ~ Solved Paper, , 21 The calculated spin only magnetic, moments (BM) of the anionic and cationic, species of [Fe(H 2O)6 ]2 and [Fe(CN)6 ],, respectively, are, (a) 0 and 4.9, (c) 0 and 5.92, , 22 The major product obtained in the, , (b) 34%, (d) 3.4%, , following reaction is, NH2, , 18 If p is the momentum of the fastest, electron ejected from a metal surface, after the irradiation of light having, wavelength λ, then for 1.5 p momentum, of the photoelectron, the wavelength of, the light should be, , 4, λ, 9, , (b), , 3, λ, 4, , (c), , 2, λ, 3, , (d), , CN, , 19 The correct statement about ICl5 and ICl−4 is, (a) ICl5 is square pyramidal and ICl−4 is, tetrahedral, (b) ICl5 is square pyramidal and ICl−4 is, square planar, (c) Both are isostructural, (d) ICl5 is trigonal bipyramidal and ICl−4 is, tetrahedral, , 20 The major product of the following, reaction is, , H, NCH3, (b), , (a), , CN, , O, H, NCHCl2, , (c), , OH, H, NCH3, , (d), CN, , OH, , H 2N, , OH, , 23 The structure of nylon-6 is, O H, || |, (a) , [ (CH2)6 C N , ]n, O, H, ||, |, (b) , [ C (CH2)5 N , ]n, O H, || |, (c) , [ (CH2)4 C N , ]n, , CH3, (1) Cl2/hν, (2) H2O,∆, , O, H, ||, |, (d) , [ C(CH2)6 N , ]n, , Cl, CHCl2, , O, , H, NCH3, , CN, , 1, λ, 2, , (i) CHCl3/KOH, (ii) Pd/C/H2, , (Assume kinetic energy of ejected, photoelectron to be very high in, comparison to work function), (a), , (b) 2.84 and 5.92, (d) 4.9 and 0, , CO2H, , 24 Fructose and glucose can be, distinguished by, , (a), , (b), , Cl, , Cl, , CH2 OH, , CHO, , (a) Fehling’s test, (b) Barfoed’s test, (c) Benedict’s test, (d) Seliwanoff’s test, , 25 Polysubstitutiion is a major drawback in, (c), , (d), , Cl, , Cl, , (a), (b), (c), (d), , Friedel-Craft’s alkylation, Reimer-Tiemann reaction, Friedel-Craft’s acylation, Acetylation of aniline
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APRIL ATTEMPT ~ 08 April 2019, Shift II, , k2, , k1, , 26 For a reaction scheme, A → B → C, if, the rate of formation of B is set to be zero, then the concentration of B is given by, (a) k1k2[ A ], k , (b) 1 [ A ], k2, , 21, 29 Among the following molecules/ions,, 2−, 2−, C2−, 2 , N 2 , O2 , O2, , Which one is diamagnetic and has the, shortest bond length?, (a) C2−, 2, , (b) O2, , (d) N2−, 2, , 30 The major product obtained in the, following reaction is, , (c) (k1 − k2)[ A ], (d) (k1 + k2)[ A ], , CH3, , atomic number 119 would be, (a) unh, (c) uun, , O, NaOH, ∆, , OHC, , 27 The IUPAC symbol for the element with, , CH3, , (b) uue, (d) une, , H 3C, , (a) H, , (b) H, O, , 28 The Mond process is used for the, (a), (b), (c), (d), , (c) O2−, 2, , O, , CH3, CH3, , purification of Ni, extraction of Mo, purification of Zr and Ti, extraction of Zn, , (c), , CH2, CH3, , (d), O, , O, , MATHEMATICS, 1 If the system of linear equations, x − 2 y + kz = 1 , 2x + y + z = 2 ,, 3x − y − kz = 3, has a solution ( x , y , z ), z ≠ 0, then ( x , y ), lies on the straight line whose equation is, (a) 3x − 4 y − 4 = 0, (c) 4x − 3 y − 4 = 0, 20, , 2 The sum, , ∑k, , k=1, , 11, 219, 3, (c) 2 − 17, 2, , 1, 2k, , (b) 3x − 4 y − 1 = 0, (d) 4x − 3 y − 1 = 0, , x+5, , 5, , (a) 5, , ∫, , g (t )dt, , (b), , (b) (2 + 2, (d) [2, 3), , 3/ 4, , ∫, , g (t )dt, , 5, , ∫ g(t )dt, , 5, , x+5, , 5, , (d), , ∫ g(t )dt, , x+5, , 5 If the lengths of the sides of a triangle are, , 1 1 1 , A = 2 b c . If det( A) ∈ [2, 16], then c, , , 2, 2, 4 b c , lies in the interval, ], , 0, , (c) 2, , 3 Let the numbers 2, b, c be in an AP and, , (a) [3, 2 + 2, (c) [4, 6], , x, , ∫ f ( t)dt equals, x+5, , (b) 1 −, , 3/ 4, , 0, , even function. If f ( x + 5) = g ( x ), then, , is equal to, 11, 220, 21, (d) 2 − 20, 2, , (a) 2 −, , x, , 4 Let f ( x ) = ∫ g ( t )dt, where g is a non-zero, , , 4), , in AP and the greatest angle is double the, smallest, then a ratio of lengths of the, sides of this triangle is, (a) 3 : 4 : 5, (b) 4 : 5 : 6, (c) 5 : 9 : 13, (d) 5 : 6 : 7
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22, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 6 If ∫, , dx, , = xf ( x )(1 +, , x3 (1 + x 6 )2/ 3, , 1, x 6 )3, , +C, , where, C is a constant of integration, then, the function f ( x ) is equal to, (a) −, , 1, 6x3, , (b) −, , 1, 2x3, , (c) −, , 1, 2 x2, , (d), , 3, x2, , 7 Which one of the following statements is, not a tautology?, (a), (b), (c), (d), , ( p ∧ q) → (~ p) ∨ q, ( p ∧ q) → p, p → ( p ∨ q), ( p ∨ q) → ( p ∨ (~ q)), , f ( f ( f ( x ))) + ( f ( x ))2 at x = 1 is, (b) 9, , (c) 15, , x2 log e| y| = − 2(x − 1), x log e| y|= x − 1, x log e| y| = 2(x − 1), x log e| y| = − 2(x − 1), , 13 Let f : [−1, 3] → R be defined as, |x| + [x ], −1 ≤ x < 1, , f ( x ) = x +|x|, 1 ≤ x < 2, x + [x ], 2 ≤ x ≤ 3 ,, , where, [t ] denotes the greatest integer, less than or equal to t. Then, f is, discontinuous at, , 8 If f(1) = 1, f ′ (1) = 3, then the derivative of, (a) 12, , (a), (b), (c), (d), , (a) four or more points (b) only two points, (c) only three points (d) only one point, , 14 The height of a right circular cylinder of, (d) 33, , 9 If three distinct numbers a , b and c are in, GP and the equations ax 2 + 2bx + c = 0, and dx 2 + 2ex + f = 0 have a common root,, then which one of the following, statements is correct?, (a) d , e and f are in GP, d e, f, (b), , and are in AP, a b, c, (c) d , e and f are in AP, d e, f, (d), , and are in GP, a b, c, , maximum volume inscribed in a sphere of, radius 3 is, (a), , 6, , (b) 2 3, , (c), , 3, , (d), , 2, 3, 3, , 3 i, + ( i = −1 ), then, 2, 2, 5, (1 + iz + z + iz 8 )9 is equal to, , 15 If z =, , (b) (−1 + 2i )9, (d) 0, , (a) 1, (c) −1, , 16 A student scores the following marks in, , toss a fair coin so that the probability of, observing atleast one head is atleast 90% is, , five tests 45, 54, 41, 57, 43. His score is, not known for the sixth test. If the mean, score is 48 in the six tests, then the, standard deviation of the marks in six, tests is, , (a) 2, , (a), , 10 The minimum number of times one has to, , (b) 3, , (c) 5, , (d) 4, , 11 Suppose that the points ( h , k), (1, 2) and, ( −3, 4) lie on the line L1. If a line L2, passing through the points ( h , k) and, (4, 3) is perpendicular to L1, then k/ h, equals, (a) −, , 1, 7, , (b), , 1, 3, , (c) 3, , (d) 0, , 12 Given that the slope of the tangent to a, curve y = y( x ) at any point ( x , y ) is, , 2y, , . If, x2, the curve passes through the centre of the, circle x 2 + y 2 − 2x − 2 y = 0, then its, equation is, , 10, 3, , (b), , 10, 3, , (c), , 100, 3, , (d), , 100, 3, , 17 The number of integral values of m for, which the equation, (1 + m 2 )x 2 − 2(1 + 3m )x + (1 + 8m ) = 0, has, no real root is, (a) 3, (c) 1, , (b) infinitely many, (d) 2, , 18 In an ellipse, with centre at the origin, if, the difference of the lengths of major axis, and minor axis is 10 and one of the foci is, at ( 0, 5 3 ), then the length of its latus, rectum is, (a) 5, , (b) 10, , (c) 8, , (d) 6
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APRIL ATTEMPT ~ 08 April 2019, Shift II, $ and b = i$ − $j + k, $ , for, 19 Let a = 3i$ + 2$j + xk, some real x. Then|a × b| = r is possible if, 3, (a) 0 < r ≤, 2, 3, 3, (c) 3, < r <5, 2, 2, , 3, 3, (b), < r ≤3, 2, 2, 3, (d) r ≥ 5, 2, , 20 Let f : R → R be a differentiable function, satisfying f ′ ( 3) + f ′ ( 2) = 0. Then, 1, , 1 + f ( 3 + x ) − f ( 3) x, lim , is equal to, x → 0 1 + f ( 2 − x ) − f ( 2), (a) e, (c) e2, , (b) e−1, (d) 1, , 21 The vector equation of the plane through, the line of intersection of the planes, x + y + z = 1 and 2x + 3 y + 4z = 5, which is, perpendicular to the plane x − y + z = 0 is, , $ ) − 2 = 0 (b) r × (i$ + k, $)+ 2 =0, (a) r ⋅ ($i − k, $, $, $, $, (c) r × (i − k) + 2 = 0 (d) r ⋅ (i − k) + 2 = 0, , 22 If the fourth term in the binomial, 6, , 1 , 1, , 1+ log10 x , 12, expansion of x, + x is equal, , , , , to 200, and x > 1, then the value of x is, (a) 100, (c) 10, , (b) 104, (d) 103, , 23 The tangent to the parabola y 2 = 4x at the, point where it intersects the circle, x 2 + y 2 = 5 in the first quadrant, passes, through the point, , 1 3, (a) , , 4 4, 1 4, (c) − , , 3 3, , 3 7, (b) , , 4 4, 1 1, (d) − , , 4 2, , 24 If the eccentricity of the standard, hyperbola passing through the point ( 4, 6), is 2, then the equation of the tangent to, the hyperbola at ( 4, 6) is, (a), (b), (c), (d), , 3x − 2 y = 0, x − 2y + 8 = 0, 2x − y − 2 = 0, 2x − 3 y + 10 = 0, , 23, 25 Let S (α ) = {( x , y ) : y 2 ≤ x, 0 ≤ x ≤ α} and, A(α ) is area of the region S(α ). If for λ,, 0 < λ < 4, A( λ ) : A( 4) = 2 : 5, then λ equals, 1, , 1, , 4 3, (a) 2 , 25, , 2 3, (b) 4 , 5, , 1, , 1, , 4 3, (c) 4 , 25, , 2 3, (d) 2 , 5, , 26 Let f ( x ) = a x ( a > 0) be written as, f ( x ) = f1( x ) + f2( x ), where f1( x ) is an even, function and f2( x ) is an odd function., Then f1( x + y ) + f1( x − y ) equals, (a), (b), (c), (d), , 2 f1 (x + y) ⋅ f2(x − y), 2 f1 (x + y) ⋅ f1 (x − y), 2 f1 (x) ⋅ f2( y), 2 f1 (x) ⋅ f1 ( y), , 27 The number of four-digit numbers strictly, greater than 4321 that can be formed, using the digits 0, 1, 2, 3, 4, 5 (repetition, of digits is allowed) is, (a) 306, (c) 360, , (b) 310, (d) 288, , 28 Two vertical poles of heights, 20 m and, 80 m stand apart on a horizontal plane., The height (in m) of the point of, intersection of the lines joining the top of, each pole to the foot of the other, from, this horizontal plane is, (a) 15, , (b) 16, , (c) 12, , (d) 18, , 29 If a point R( 4, y , z ) lies on the line, segment joining the points P( 2, − 3, 4) and, Q( 8, 0, 10), then the distance of R from the, origin is, (a) 2 21, (c) 2 14, , (b) 53, (d) 6, , 30 The tangent and the normal lines at the, point ( 3 , 1) to the circle x 2 + y 2 = 4 and, the X-axis form a triangle. The area of, this triangle (in square units) is, 1, 3, 2, (c), 3, (a), , 4, 3, 1, (d), 3, (b)
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24, , ONLINE, , JEE Main 2019 ~ Solved Paper, , Answers, Physics, 1., 11., 21., , (b), (b), (d), , 2., 12., 22., , (b), (d), (b), , 3., 13., 23., , (d), (c), (c), , 4., 14., 24., , (b), (c), (a), , 5., 15., 25., , (b), (b), (b), , 6., 16., 26., , (c), (a), (c), , 7., 17., 27., , (d), (d), (c), , 8., 18., 28., , (a), (c), (a), , 9., 19., 29., , (a), (b), (a), , 10., 20., 30., , (a), (d), (d), , (c), (d), (d), , 3., 13., 23., , (d), (a), (b), , 4., 14., 24., , (c), (b), (d), , 5., 15., 25., , (b), (d), (a), , 6., 16., 26., , (b), (a), (b), , 7., 17., 27., , (d), (d), (b), , 8., 18., 28., , (*), (a), (a), , 9., 19., 29., , (c), (b), (a), , 10., 20., 30., , (d), (d), (c), , 3., 13., 23., , (c), (c), (b), , 4., 14., 24., , (d), (b), (c), , 5., 15., 25., , (b), (c), (c), , 6., 16., 26., , (b), (b), (d), , 7., 17., 27., , (d), (b), (b), , 8., 18., 28., , (d), (a), (b), , 9., 19., 29., , (b), (d), (c), , 10., 20., 30., , (d), (d), (c), , Chemistry, 1., 11., 21., , (a), (a), (a), , 2., 12., 22., , Mathematics, 1., 11., 21., , (c), (c), (d), , 2., 12., 22., , (a), (c), (c), , Note (*) None of the option is correct., , For Detailed Solutions Visit : https://bit.ly/2Lwc2Ch Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (09 April, 2019), TIME 9:30-12:30 (Shift I), , MM : 360, , PHYSICS, 1 A stationary horizontal disc is free to, rotate about its axis. When a torque is, applied on it, its kinetic energy as a, function of θ, where θ is the angle by, which it has rotated, is given as kθ 2. If its, moment of inertia is I, then the angular, acceleration of the disc is, k, θ, 2I, k, (c), θ, 4I, , k, θ, I, 2k, (d), θ, I, , period T . The bob of the pendulum is, completely immersed in a non-viscous, 1, liquid. The density of the liquid is th of, 16, the material of the bob. If the bob is, inside liquid all the time, its period of, oscillation in this liquid is, , (b), , (a), , (a) 2T, , speed of the molecules is 200 m/s at, 127° C. At 2 atm pressure and at 227° C,, the rms speed of the molecules will be, (a) 100 5 m/s, (c) 100 m/s, , (b) 80 m/s, (d) 80 5 m/s, , square ABCD as shown in the figure. The, effective resistance between E and C is, [E is mid-point of arm CD], , D, , 3, (b) R, 4, , B, , E, , C, , (c) R, , (d), , shown in the figure, D, –q, , +q, , Q, , d, , 3 A wire of resistance R is bent to form a, , A, , 1, 1, 1, 1, (b) 2T, (c) 4T, (d) 4T, 10, 14, 14, 15, , 5 A system of three charges are placed as, , 2 For a given gas at 1 atm pressure, rms, , 7, (a), R, 64, , 4 A simple pendulum oscillating in air has, , 1, R, 16, , If D >> d, the potential energy of the system, is best given by, 1 q2 2qQd , (a), +, −, , 4πε 0 d, D2 , 1 q2 qQd , (b), +, +, , 4πε 0 d, D2 , 1 q2 qQd , (c), −, −, , 4πε 0 d, 2D 2 , 1 q2 qQd , (d), −, −, , 4πε 0 d, D2
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26, , ONLINE, , 6 A body of mass 2 kg makes an elastic, collision with a second body at rest and, continues to move in the original, direction but with one-fourth of its, original speed. What is the mass of the, second body ?, (a) 1.5 kg, (c) 1.8 kg, , (b) 1.2 kg, (d) 1.0 kg, , 7 A concave mirror for face viewing has, focal length of 0.4 m. The distance at, which you hold the mirror from your face, in order to see your image upright with a, magnification of 5 is, (a) 0.16 m, (c) 0.32 m, , (b) 1.60 m, (d) 0.24 m, , 8 The stream of a river is flowing with a, speed of 2 km/h. A swimmer can swim at, a speed of 4 km/h. What should be the, direction of the swimmer with respect to, the flow of the river to cross the river, straight ?, (a) 60°, (c) 90°, , (b) 120°, (d) 150°, , 9 A string is clamped at both the ends and, it is vibrating in its 4th harmonic. The, equation of the stationary wave is, Y = 0.3 sin( 0157, ., x ) cos( 200πt ). The length, of the string is (All quantities are in SI, units), (a) 60 m, (c) 80 m, , (b) 40 m, (d) 20 m, , 10 A moving coil galvanometer has, resistance 50 Ω and it indicates full, deflection at 4 mA current. A voltmeter is, made using this galvanometer and a 5 kΩ, resistance. The maximum voltage, that, can be measured using this voltmeter,, will be close to, (a) 40 V, (c) 15 V, , 12 In the density measurement of a cube,, the mass and edge length are measured, as (10.00 ± 010, . ) kg and ( 010, . ± 0.01) m,, respectively. The error in the, measurement of density is, , 13 The total number of turns and, cross-section area in a solenoid is fixed., However, its length L is varied by, adjusting the separation between, windings. The inductance of solenoid will, be proportional to, (b) L2, , (a) 1 / L, , (b) 2.16 × 10−6 J, (d) 3.75 × 10−6 J, , (c) L, , (d) 1 / L2, , 14 The following bodies are made to roll up, (without slipping) the same inclined, plane from a horizontal plane : (i) a ring, of radius R, (ii) a solid cylinder of radius, R/ 2 and (iii) a solid sphere of radius R/ 4., If in each case, the speed of the centre of, mass at the bottom of the incline is same,, the ratio of the maximum height they, climb is, (a) 10 : 15 : 7, (c) 14 : 15 : 20, , (b) 4 : 3 : 2, (d) 2 : 3 : 4, , 15 If M is the mass of water that rises in a, capillary tube of radius r, then mass of, water which will rise in a capillary tube, of radius 2r is, (a) 2M, , (b) 4M, , (c), , M, 2, , (d) M, , 16 Following figure shows two processes A, and B for a gas. If ∆QA and ∆QB are the, amount of heat absorbed by the system in, two cases, and ∆U A and ∆U B are changes, in internal energies respectively, then, f, , p, , A, , (b) 10 V, (d) 20 V, , charged to 5 µC. If the plates are pulled, apart to reduce the capacitance to 2 µF,, how much work is done?, , (b) 0.10 kg/m3, (d) 0.31 kg/m3, , (a) 0.01 kg/m3, (c) 0.07 kg/m3, , B, , 11 A capacitor with capacitance 5 µF is, , (a) 6.25 × 10−6 J, (c) 2.55 × 10−6 J, , JEE Main 2019 ~ Solved Paper, , i, V, , (a), (b), (c), (d), , ∆QA > ∆QB ,, ∆QA < ∆QB ,, ∆QA > ∆QB ,, ∆QA = ∆QB ;, , ∆U A > ∆U B, ∆U A < ∆U B, ∆U A = ∆U B, ∆U A = ∆U B
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APRIL ATTEMPT ~ 09 April 2019, Shift I, , 27, , 17 Determine the charge on the capacitor in, the following circuit, 6Ω, 72V, , v0 sinω 0t as carrier wave. The correct, amplitude modulated (AM) signal is, , 2Ω, 4Ω, , 10µF, , 10Ω, , (a) 2 µC, (c) 10 µC, , (b) 200 µC, (d) 60 µC, , is placed on a horizontal surface such, 1, that its th part is hanging below the, n, edge of the surface. To lift the hanging, part of the cable upto the surface, the, work done should be, 2MgL, MgL, (b) nMgL (c), n2, n2, , (d), , MgL, 2n 2, , 19 The electric field of light wave is given as, E = 10−3, , 2 πx, , − 2π × 6 × 1014 t x$ NC−1., cos , 5 × 10−7, , , This light falls on a metal plate of work, function 2eV. The stopping potential of, the photoelectrons is, 12375, Given, E (in eV) =, λ( in A° ), (a) 0.48 V, (c) 2.0 V, , 20 A ball is thrown vertically up (taken as, + Z-axis) from the ground. The correct, momentum-height (p-h) diagram is, , (a), , p, h, , O, , (b), , translational and vibrational motions. If, the rms velocity of HCl molecules in its, gaseous phase is v, m is its mass and kB is, Boltzmann constant, then its temperature, will be, mv 2, 3kB, mv 2, (c), 5kB, , mv 2, 7kB, mv 2, (d), 6kB, , (a), , (b), , 23 The pressure wave, , p = 0.01 sin[1000t − 3x ]Nm −2, corresponds, to the sound produced by a vibrating, blade on a day when atmospheric, temperature is 0° C. On some other day, when temperature is T , the speed of sound, produced by the same blade and at the, same frequency is found to be, 336 ms −1. Approximate value of T is, , (a) 15°C, (c) 12° C, , (b) 0.72 V, (d) 2.48 V, , p, , (a) (v0 sin ω 0t + A cos ωt, (b) (v0 + A ) cos ωt sin ω 0t, (c) v0 sin[ω 0 (1 + 0.01 A sin ωt )t ], A, A, (d) v0 sin ω 0t + sin(ω 0 − ω )t + sin(ω 0 + ω )t, 2, 2, , 22 An HCl molecule has rotational,, , 18 A uniform cable of mass M and length L, , (a), , 21 A signal A cosωt is transmitted using, , h, , O, , (b) 11°C, (d) 4° C, , 24 The figure shows a Young’s double slit, experimental setup. It is observed that, when a thin transparent sheet of, thickness t and refractive index µ is put, in front of one of the slits, the central, maximum gets shifted by a distance equal, to n fringe widths. If the wavelength of, light used is λ, t will be, , Screen, , a, , p, , p, (c), , O, , h, , (d), , O, , h, , 2nDλ, (a), a ( µ − 1), Dλ, (c), a ( µ − 1), , D, , 2 Dλ, a ( µ − 1), nDλ, (d), a ( µ − 1), , (b)
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28, , ONLINE, , 25 A rectangular coil (dimension 5 cm × 2.5 cm), with 100 turns, carrying a current of 3A, in the clockwise direction, is kept centred, at the origin and in the X-Z plane. A, magnetic field of 1 T is applied along, X-axis. If the coil is tilted through 45°, about Z-axis, then the torque on the coil is, (a) 0.27 N-m, (c) 0.42 N-m, , (b) 0.38 N-m, (d) 0.55 N-m, , 26 A rigid square loop of side a and carrying, current I 2 is lying on a horizontal surface, near a long current I1 carrying wire in, the same plane as shown in figure. The, net force on the loop due to the wire will, be, I1, , I2, a, , JEE Main 2019 ~ Solved Paper, , 28 An n-p-n transistor is used in common, emitter configuration as an amplifier, with 1 kΩ load resistance. Signal voltage, of 10 mV is applied across the, base-emitter. This produces a 3 mA, change in the collector current and 15 µA, change in the base current of the, amplifier. The input resistance and, voltage gain are, (a) 0.67 kΩ, 200, (b) 0.33 kΩ, 1.5, (c) 0.67 kΩ, 300, (d) 0.33 kΩ, 300, , 29 A solid sphere of mass M and radius a is, surrounded by a uniform concentric, spherical shell of thickness 2a and 2M., The gravitational field at distance 3a, from the centre will be, GM, 9a 2, GM, (c), 3a 2, (a), , a, , µ 0I1I 2, 2π, µ 0I1I 2, (b) attractive and equal to, 3π, (c) zero, µ II, (d) repulsive and equal to 0 1 2, 4π, (a) repulsive and equal to, , 30 The magnetic field of a plane, , 27 Taking the wavelength of first Balmer, line in hydrogen spectrum (n = 3 to n = 2), as 660 nm, the wavelength of the 2nd, Balmer line (n = 4 to n = 2) will be, (a) 889.2 nm, (c) 642.7 nm, , 2GM, 9a 2, 2GM, (d), 3a 2, (b), , (b) 388.9 nm, (d) 488.9 nm, , electromagnetic wave is given by, B = B0 [cos( kz − ωt )]$i + B1 cos( kz + ωt )$j, where, B0 = 3 × 10−5 T and B1 = 2 × 10−6 T., The rms value of the force experienced by, a stationary charge Q = 10−4 C at z = 0 is, closest to, (a) 0.1 N, (c) 0.6 N, , (b) 3 × 10−2 N, (d) 0.9 N, , CHEMISTRY, 1 The increasing order of reactivity of the, following compounds towards aromatic, electrophilic substitution reaction is, Cl, , OMe, , Me, , CN, , 2 The standard Gibbs energy for the given, cell reaction in kJ mol−1 at 298 K is, , Zn( s) + Cu2+ ( aq ) → Zn2+ ( aq ) + Cu( s),, E° = 2V at 298 K, (Faraday’s constant, F = 96000 C mol−1), , A, , B, , (a) A < B < C < D, (c) D < A < C < B, , C, , D, , (b) B < C < A < D, (d) D < B < A < C, , (a), (b), (c), (d), , 384, 192, −384, −192
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APRIL ATTEMPT ~ 09 April 2019, Shift I, , 29, CH3, , 3 The major product of the following, reaction is, , (d), , (c), 1. PBr3, , OH, , n, , n, , 2. KOH (alc.), , O, , (b), , (a), , OH, , OH, , OH, , 7 Among the following the set of, HO, , parameters that represents path, functions, is, , O, , (c), , (d), O, , O, , 4 Which of the following statement is not, true about sucrose?, (a) It is also named as invert sugar., (b) The glycosidic linkage is present between, C1 of α-glucose and C1 of β-fructose, (c) It is a non-reducing sugar, (d) On hydrolysis, it produces glucose and, fructose, , 5 For a reaction,, N 2( g) + 3H 2( g) → 2NH3 ( g), identify, dihydrogen (H 2 ) as a limiting reagent in, the following reaction mixtures., (a), (b), (c), (d), , 56 g of N2 + 10 g of H2, 35 g of N2 + 8 g of H2, 14 g of N2 + 4 g of H2, 28 g of N2 + 6 g of H2, , (A) q + W, (C) W, (a) (A) and (D), (c) (B), (C) and (D), , (B) q, (D) H − TS, (b) (A), (B) and (C), (d) (B) and (C), , 8 The degenerate orbitals of [Cr(H 2O)6 ]3 +, are, (a) dz 2 and dxz, (c) dx 2 − y 2 and dxy, , (b) dxz and dyz, (d) dyz and dz 2, , 9 The aerosol is a kind of colloid in which, (a) gas is dispersed in liquid, (b) gas is dispersed in solid, (c) liquid is dispersed in water, (d) solid is dispersed in gas, , 10 C60 an allotrope of carbon contains, (a), (b), (c), (d), , 16 hexagons and 16 pentagons, 20 hexagons and 12 pentagons, 12 hexagons and 20 pentagons, 18 hexagons and 14 pentagons, , 11 The major product of the following, , 6 The major product of the following, , reaction is, , reaction is, , 4, , →, CH3CH == CHCO2CH3 LiAlH, , 1. KOH (alc.), , Cl, , (a) CH3CH == CHCH 2OH, , 2. Free radical, polymerisation, , (b) CH3CH 2CH 2CH 2OH, , Cl, CH3, (a), , (c) CH3CH 2CH 2CO2CH3, , (b), n, , (d) CH3CH 2CH 2CHO, n, , 12 The ore that contains the metal in the, form of fluoride is, , Cl, Cl, , (a) magnetite, (c) malachite, , (b) sphalerite, (d) cryolite
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30, , JEE Main 2019 ~ Solved Paper, , ONLINE, , NH2, , 13 The number of water molecule(s) not, coordinated to copper ion directly in, CuSO4 ⋅ 5H 2O, is, (a) 2, , (b) 3, , (c) 1, , (d) 4, , 14 Aniline dissolved in dil. HCl is reacted, with sodium nitrite at 0° C. This solution, was added dropwise to a solution, containing equimolar mixture of aniline, and phenol in dil. HCl. The structure of, the major product is, , OH, (b), , (a), , OH, , NH2, (c), , (d), , 19 Consider the van der Waals’ constants,, a and b, for the following gases., Gas, 6, , −2, , a/(atm dm mol ), , (a), , N, , N, , NH2, , b/(10, (b), , N, , N, , (c), , N, , N, , (d), , N, , N, , −2, , 3, , −1, , dm mol ), , Ar, , Ne, , Kr, , Xe, , 1.3, , 0.2, , 5.1, , 4.1, , 3.2, , 1.7, , 1.0, , 5.0, , Which gas is expected to have the highest, critical temperature ?, , O, , OH, , (a) Kr, , (b) Xe, , (c) Ar, , (d) Ne, , 20 The major product of the following, NH, , reaction is, , 15 The osmotic pressure of a dilute solution, of an ionic compound XY in water is four, times that of a solution of 0.01 M BaCl2, in water. Assuming complete dissociation, of the given ionic compounds in water,, the concentration of XY (in mol L−1) in, solution is, −2, , (a) 4 × 10, (c) 4 × 10−4, , −4, , (b) 16 × 10, (d) 6 × 10−2, , 16 For any given series of spectral lines of, atomic hydrogen, let ∆ν = νmax − νmin be, the difference in maximum and minimum, frequencies in cm −1. The ratio, ∆ νLyman / ∆ νBalmer is, (a) 27 : 5, , (b) 5 : 4, , (c) 9 : 4, , (d) 4 : 1, , 17 The element having greatest difference, between its first and second ionisation, energy, is, (a) Ca, , (b) Sc, , (c) Ba, , (d) K, , 18 The organic compound that gives, following qualitative analysis is, Test, (i) Dil. HCl, (ii) NaOH solution, (iii) Br2 /water, , Inference, Insoluble, Soluble, Decolourisation, , ( l equiv.), DCl, , , →, CH3C ≡≡ CH (i), (ii) DI, , (a) CH3CD(Cl)CHD(I), (b) CH3CD2CH(Cl)(I), (c) CH3CD(I)CHD(Cl), (d) CH3C(I)(Cl)CHD2, , 21 Magnesium powder burns in air to give, (a), (b), (c), (d), , MgO and Mg3 N2, Mg (NO3 )2 and Mg3 N2, MgO only, MgO and Mg (NO3 )2, , 22 Liquid M and liquid N form an ideal, solution. The vapour pressures of pure, liquids M and N are 450 and 700 mmHg,, respectively, at the same temperature., Then correct statement is, x M = mole fraction of M in solution;, xN = mole fraction of N in solution;, y M = mole fraction of M in vapour phase;, yN = mole fraction of N in vapour phase, (a), , xM, y, > M, xN, yN, , (b), , xM, y, = M, xN, yN, , (c), , xM, y, < M, xN, yN, , (d) (xM − yM ) < (xN − yN )
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APRIL ATTEMPT ~ 09 April 2019, Shift I, , 31, , 23 The correct IUPAC name of the following, compound is, , 27 The major product of the following, reaction is, CH2CH3, , NO2, , (i) Alkaline KMnO4, (ii) H3 O+, , Cl, , (a), (b), (c), (d), , CH2CHO, , COOH, , CH3, , 2-methyl-5-nitro-1-chlorobenzene, 3-chloro-1-methyl-1-nitrobenzene, 2-chloro-1-methyl 1-4-nitrobenzene, 5-chloro-4-methyl 1-1-nitrobenzene, , (a), , (b), COCH3, , CH2COOH, , 24 Excessive release of CO2 into the, atmosphere results in, (a), (b), (c), (d), , (c), , formation of smog, depletion of ozone, polar vortex, global warming, , 28 Among the following, the molecule, expected to be stabilised by anion, formation is C2 , O2 , NO, F2., , 25 The one that will show optical activity is, , (a) C2, (c) NO, , (en = ethane-1, 2-diamine), A, , A, , A, (a), , B, A, , B, , of nitrogen in NO,NO2 , NO2 and N 2O3 is, , M, , (a) NO2 < NO < N2O3 < N2O, (b) N2O < NO < N2O3 < NO2, (c) O2 < N2O3 < NO < N2O, , B, , B, , B, , A, , A, , A, , (d) N2O < N2O3 < NO < NO2, , A, (c), , M, , en (d) en, , M, , en, , B, , 30 Match the catalysts Column I with, products Column II., , B, , A, , Column I, (Catalyst), , 26 The given plots represent the variation of, the concentration of a reaction R with, time for two different reactions (i) and, (ii). The respective orders of the reactions, are, (i), , (ii), , In [R], , [R], , time, , (a) 1, 1, , (b) F2, (d) O2, , 29 The correct order of the oxidation states, , B, , B, (b), , M, , (d), , (b) 0, 2, , time, , (c) 0, 1, , (d) 1, 0, , Column II, (Product), , (A), , V2O5, , (i), , Polyethlyene, , (B), , TiCl 4 / Al(Me) 3, , (ii), , Ethanal, , (C), , PbCl 2, , (iii) H2SO 4, , (D), , Iron oxide, , (iv), , (a), (b), (c), (d), , NH3, , (A)-(ii), (B)-(iii), (C)-(i), (D)-(iv), (A)-(iv), (B)-(iii), (C)-(ii), (D)-(i), (A)-(iii), (B)-(i), (C)-(ii), (D)-(iv), (A)-(iii), (B)-(iv), (C)-(i), (D)-(ii)
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32, , JEE Main 2019 ~ Solved Paper, , ONLINE, , MATHEMATICS, 1 Slope of a line passing through P (2, 3), and intersecting the line, x + y = 7 at a, distance of 4 units from P, is, 1−, 1+, 1−, (c), 1+, (a), , 5, 5, 7, 7, , 7 −1, 7+1, 5 −1, 5+1, , (b), (d), , 8 If the function f : R − { 1, − 1} → A defined, , four, having local extreme points at, x = − 1, 0, 1, then the set, S = { x ∈ R : f ( x ) = f ( 0)} contains exactly, four rational numbers, two irrational and two rational numbers, four irrational numbers, two irrational and one rational number, , 3 Four persons can hit a target correctly, 1 1 1, 1, , , and, 2 3 4, 8, respectively. If all hit at the target, independently, then the probability that, the target would be hit, is, with probabilities, , (a), , 1, 192, , (b), , 25, 32, , (c), , 7, 32, , (d), , 25, 192, , 10, , 4 Let, , ∑ f ( a + k) = 16( 210 − 1), where the, , k=1, , function f satisfies f ( x + y ) = f ( x ) f ( y ) for, all natural numbers x , y and f(1) = 2., Then, the natural number ‘a’ is, (a) 2, , (b) 4, , (c) 3, , (d) 16, , x−1 y+1 z − 2, meets the, =, =, 2, 3, 4, plane, x + 2 y + 3z = 15 at a point P, then, the distance of P from the origin is, , 5 If the line, , (a) 7 / 2, (c) 5 / 2, , (b) 9 / 2, (d) 2 5, , 6 If the line y = mx + 7 3 is normal to the, hyperbola, , x2 y2, −, = 1, then a value of m, 24 18, , is, 3, 5, 2, (c), 5, (a), , 15, 2, 5, (d), 2, (b), , intersects the coordinate axes at distinct, points P and Q, then the locus of the, mid-point of PQ is, (a) x2 + y2 − 2x2y2 = 0 (b) x2 + y2 − 2xy = 0, (c) x2 + y2 − 4x2y2 = 0 (d) x2 + y2 − 16x2y2 = 0, , 2 If f ( x ) is a non-zero polynomial of degree, , (a), (b), (c), (d), , 7 If a tangent to the circle x 2 + y 2 = 1, , by f ( x ) =, , x2, 1 − x2, , , is surjective, then A is, , equal to, (a) R − { −1}, (c) R − [−1, 0), , (b) [0, ∞ ), (d) R − (−1, 0), , 9 The value of ∫, , π/ 2, , 0, , π −1, (a), 2, , (b), , sin3 x, dx is, sin x + cos x, , π −2, π −1, (c), 8, 4, , (d), , π −2, 4, , 10 If one end of a focal chord of the parabola,, y 2 = 16x is at (1, 4), then the length of, this focal chord is, (a) 22, , (b) 25, , (c) 24, , (d) 20, , 11 The solution of the differential equation, x, , dy, + 2 y = x 2( x ≠ 0) with y(1) = 1, is, dx, , 3, x2, +, 4 4 x2, 3, 1, (c) y = x2 + 2, 4, 4x, (a) y =, , 1, x3, + 2, 5, 5x, 4, 1, (d) y = x3 + 2, 5, 5x, (b) y =, , 12 All the points in the set, , , α + i, : α ∈ R ( i = −1 ) lie on a, S=, , α − i, (a), (b), (c), (d), , circle whose radius is 2., straight line whose slope is −1., circle whose radius is 1., straight line whose slope is 1., , π π, 6 3, , 13 If the function f defined on , by, 2 cos x − 1, , x≠, , f ( x ) = cot x − 1, , k,, x=, , then k is equal to, (a), , 1, 2, , (b) 2, , (c) 1, , π, 4 is continuous,, π, 4, (d), , 1, 2
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APRIL ATTEMPT ~ 09 April 2019, Shift I, 14 Let S = { θ ∈ [−2π , 2π ] : 2 cos2 θ + 3 sin θ = 0},, then the sum of the elements of S is, (b) π, 13π, (d), 6, , (a) 2π, 5π, (c), 3, , 15 If the tangent to the curve, y = x3 + ax − b, at the point (1, − 5) is perpendicular to the, line, − x + y + 4 = 0, then which one of the, following points lies on the curve ?, (a) (−2, 2), (c) (−2, 1), , (b) (2, − 2), (d) (2, − 1), , 16 If the standard deviation of the numbers, , −1, 0, 1, k is 5 where k > 0, then k is equal, to, , (a) 2, , 10, 3, , (b) 2 6, , (c) 4, , 5, 3, , (d), , 6, , 17 Let p, q ∈ R. If 2 − 3 is a root of the, quadratic equation, x 2 + px + q = 0, then, (a), (b), (c), (d), , q2 − 4 p − 16 = 0, p2 − 4q − 12 = 0, p2 − 4q + 12 = 0, q2 + 4 p + 14 = 0, , set of all values of x, at which the, function, g( x ) = f ( f ( x )) is not, differentiable, is, (a), (b), (c), (d), , {5, 10, 15, 20}, {5, 10, 15}, {10}, {10, 15}, , 21 Let S be the set of all values of x for, which the tangent to the curve, y = f ( x ) = x3 − x 2 − 2x at ( x , y ) is parallel, to the line segment joining the points, (1, f (1)) and ( −1, f ( −1)), then S is equal to, , 1, (a) , − 1, 3, , , 1 , (c) − , 1, 3 , , 1 , (b) , 1, 3 , , 1, (d) − , − 1, , 3, , 22 For any two statements p and q, the, negation of the expression p ∨ (~ p ∧ q ) is, (a) ~ p ∧ ~ q, (c) p ∧ q, , (b) ~ p ∨ ~ q, (d) p ↔ q, 6, , ( 0, − 1, 0) and ( 0, 0, 1) and making an angle, π, with the plane y − z + 5 = 0, also passes, 4, through the point, (a) ( 2 , 1, 4), , log x , 2, expansion of + x 8 ( x > 0) is, , x, 20 × 87 , then the value of x is, , (a) 8−2, (c) 8, , (b) 83, (d) 82, , 24 The value of, cos2 10° − cos 10° cos 50° + cos2 50° is, 3, (1 + cos 20° ), 2, (c) 3 / 2, , (a), , (b) (− 2 , 1, − 4), (c) (− 2 , − 1, − 4), (d) ( 2 , − 1, 4), , 3, + cos 20°, 4, (d) 3 / 4, (b), , 25 Let α and β be the roots of the equation, , 19 If, , 1 1 1 2 1 3 1 n − 1 1 78, ,, =, 0 1 . 0 1 . 0 1 ... 0, 1 0 1 , , , , , 1 n, then the inverse of , is, 0 1 , 0, 1, 0, 1, , 20 Let f ( x ) = 15 − x − 10 ; x ∈ R. Then, the, , 23 If the fourth term in the binomial, , 18 A plane passing through the points, , 1, (a) , 12, 1, (c) , 13, , 33, , 1 −13, (b) , , 0 1 , 1 −12, (d) , , 0 1 , , x 2 + x + 1 = 0. Then, for y ≠ 0 in R,, y+1, α, α, y+β, β, (a), (b), (c), (d), , 1, y( y − 1), y ( y2 − 3 ), y3 − 1, y3, 2, , β, 1, y+α, , is equal to
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34, , ONLINE, , number of ways the committee is formed, with atleast 3 females, then, , 26 The area (in sq units) of the region, A = {( x , y ) : x 2 ≤ y ≤ x + 2} is, 13, 6, 31, (c), 6, , (a) m = n = 68, (c) m = n = 78, , 9, 2, 10, (d), 3, , (a), , (b), , 27 The integral ∫ sec, , 2/ 3, , x cosec, , JEE Main 2019 ~ Solved Paper, , (b) m + n = 68, (d) n = m − 8, , 29 Let the sum of the first n terms of a, 4/ 3, , x dx is equal, , to (here C is a constant of integration), (a) 3 tan −1/3 x + C, (b) −3 tan −1/3 x + C, (c) −3 cot−1/3 x + C, 3, (d) − tan −4 /3 x + C, 4, , non-constant AP a1 , a2 , a3 .....be, n( n − 7), A, where A is a constant., 50n +, 2, If d is the common difference of this AP,, then the ordered pair ( d , a50 ) is equal to, (a) (A, 50 + 46A), (c) (50, 50 + 46A), , r, , (b) (50, 50 + 45A), (d) (A, 50 + 45A), , r, $ If, 30 Let α = 3$i + $j and β = 2$i − $j + 3k., , 28 A committee of 11 members is to be, formed from 8 males and 5 females. If m, is the number of ways the committee is, formed with at least 6 males and n is the, , r, r, r r, r, r, β = β1 − β 2, where β1 is parallel to α and β 2, r, r, r, is perpendicular to α, then β1 × β 2 is equal to, 1 $, $), (3i − 9$j + 5k, 2, $, (c) −3$i + 9$j + 5k, (a), , 1, $), (−3$i + 9$j + 5k, 2, $), (d) 3$i − 9$j − 5k, (b), , Answers, Physics, 1. (d), 11. (d), 21. (d), , 2. (a), 12. (*), 22. (b), , 3. (a), 13. (a), 23. (d), , 4. (d), 14. (c), 24. (*), , 5. (d), 15. (a), 25. (a), , 6. (b), 16. (c), 26. (d), , 7. (c), 17. (b), 27. (d), , 8. (b), 18. (d), 28. (c), , 9. (c), 19. (a), 29. (c), , 10. (d), 20. (d), 30. (c), , 3. (c), 13. (c), 23. (c), , 4. (b), 14. (a), 24. (d), , 5. (a), 15. (d), 25. (c), , 6. (b), 16. (c), 26. (d), , 7. (d), 17. (d), 27. (a), , 8. (b), 18. (b), 28. (a), , 9. (d), 19. (a), 29. (b), , 10. (b), 20. (d), 30. (c), , 3. (b), 13. (a), 23. (d), , 4. (c), 14. (a), 24. (d), , 5. (b), 15. (b), 25. (d), , 6. (c), 16. (b), 26. (b), , 7. (c), 17. (b), 27. (b), , 8. (c), 18. (a), 28. (c), , 9. (c), 19. (b), 29. (a), , 10. (b), 20. (b), 30. (b), , Chemistry, 1. (c), 11. (a), 21. (a), , 2. (c), 12. (d), 22. (a), , Mathematics, 1. (c), 11. (a), 21. (c), , 2. (d), 12. (c), 22. (a), , Note (*) None of the option is correct., , For Detailed Solutions Visit : https://bit.ly/2DUlzNc Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (09 April, 2019), TIME 2:30-5:30 (Shift II), , MM : 360, , PHYSICS, 1 A thin convex lens L (refractive index, = 1.5) is placed on a plane mirror M., When a pin is placed at A, such that, OA = 18 cm, its real inverted image is, formed at A itself, as shown in figure., When a liquid of refractive index µ l is put, between the lens and the mirror, the pin, has to be moved to A′, such that OA′ = 27, cm, to get its inverted real image atA′, itself. The value of µ l will be, A′, A, , L, M, , (a), , 3, , O, , (b), , 2, , (c), , 4, 3, , (d), , 3, 2, , 2 A massless spring (k = 800 N/m),, attached with a mass (500 g) is, completely immersed in 1 kg of water., The spring is stretched by 2 cm and, released, so that it starts vibrating. What, would be the order of magnitude of the, change in the temperature of water when, the vibrations stop completely? (Assume, that the water container and spring, , receive negligible heat and specific heat, of mass = 400 J/kg K, specific heat of, water = 4184 J/kg K), (a) 10−4 K, (c) 10−1 K, , (b) 10−3 K, (d) 10−5 K, , 3 Two materials having coefficients of, thermal conductivity ‘3K ’ and ‘K ’ and, thickness ‘d’ and ‘3d’ respectively, are, joined to form a slab as shown in the, figure. The temperatures of the outer, surfaces are ‘θ 2’ and ‘θ1’ respectively,, (θ 2 > θ1 ). The temperature at the interface, is, θ +θ, (a) 2 1, 2, θ1 5θ 2, (c), +, 6, 6, , d 3d, θ2 3K K, , θ1, , 2θ, θ, (b) 1 + 2, 3, 3, θ1 9θ 2, (d), +, 10 10, , 4 A test particle is moving in a circular, orbit in the gravitational field produced, K, by mass density ρ(r ) = 2 . Identify the, r, correct relation between the radius R of, the particle’s orbit and its period T, T2, T, is a constant (b) 2 is a constant, 3, R, R, T, is a constant, (c) TR is a constant (d), R, (a)
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36, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 5 A convex lens of focal length 20 cm, produces images of the same, magnification 2 when an object is kept at, two distances x1 and x2 ( x1 > x2 ) from the, lens. The ratio of x1 and x2 is, (a) 5 : 3, , (b) 2 : 1, , (c) 4 : 3, , (d) 3 : 1, , 6 A wedge of mass M = 4 m lies on a, frictionless plane. A particle of mass m, aproaches the wedge with speed v. There, is no friction between the particle and the, plane or between the particle and the, wedge. The maximum height climbed by, the particle on the wedge is given by, (a), , 2 v2, 7g, , v2, g, , (b), , (c), , 2 v2, 5g, , (d), , v2, 2g, , 7 The parallel combination of two air filled, parallel plate capacitors of capacitance C, and nC is connected to a battery of, voltage, V . When the capacitors are fully, charged, the battery is removed and after, that a dielectric material of dielectric, constant K is placed between the two, plates of the first capacitor. The new, potential difference of the combined, system is, (a), , (n + 1)V, (K + n ), , (b), , nV, K+n, , (c) V, , (d), , V, K+n, , 2, , 8 The area of a square is 5.29 cm . The, area of 7 such squares taking into, account the significant figures is, (a) 37.030 cm 2, (c) 37.03 cm 2, , (b) 37.0 cm 2, (d) 37 cm 2, , 9 The logic gate equivalent to the given, logic circuit is, , Y, , (b) 0.5 ohm, (d) 0.02 ohm, , 11 The position vector of particle changes, with time according to the relation, r( t ) = 15t 2$i + ( 4 − 20t 2 )$j. What is the, magnitude of the acceleration (in ms−2 ), at t = 1?, (a) 50, , (b) 100, , (c) 25, , (d) 40, , 12 A particle P is formed due to a, completely inelastic collision of particles x, and y having de-Broglie wavelengths λ x, and λ y , respectively. If x and y were, moving in opposite directions, then the, de-Broglie wavelength of P is, (a) λ x − λ y, (c), , (b), , λ xλ y, , λx λy, , λx − λy, , (d) λ x + λ y, , λx + λy, , 13 A moving coil galvanometer has a coil, with 175 turns and area 1 cm 2. It uses, a torsion band of torsion constant, 10−6 N-m/rad. The coil is placed in a, magnetic field B parallel to its plane. The, coil deflects by 1º for a current of 1 mA., The value of B (in Tesla) is approximately, (a) 10−3, , (b) 10−4, , (c) 10−1, , (d) 10−2, , 14 Four point charges − q , + q , + q and −q, are placed on Y -axis at y = −2d, y = − d,, y = + d and y = +2d, respectively. The, magnitude of the electric field E at a, point on the X-axis at x = D, with D >> d,, will behave as, 1, D, 1, (c) E ∝ 2, D, (a) E ∝, , A, , 1, D3, 1, (d) E ∝ 4, D, (b) E ∝, , 15 The physical sizes of the transmitter and, , B, , (a) NOR, , (a) 0.2 ohm, (c) 0.002 ohm, , (b) NAND (c) OR, , (d) AND, , 10 The resistance of a galvanometer is, 50 ohm and the maximum current which, can be passed through it is 0.002 A. What, resistance must be connected to it in, order to convert it into an ammeter of, range 0-0.5 A?, , receiver antenna in a communication, system are, (a) proportional to carrier frequency, (b) inversely proportional to modulation, frequency, (c) independent of both carrier and, modulation frequency, (d) inversely proportional to carrier frequency
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APRIL ATTEMPT ~ 09 April 2019, Shift II, 16 Diameter of the objective lens of a, telescope is 250 cm. For light of, wavelength 600 nm coming from a, distant object, the limit of resolution of, the telescope is close to, (a) 3.0 × 10−7 rad, (c) 1.5 × 10−7 rad, , (b) 2.0 × 10−7 rad, (d) 4.5 × 10−7 rad, , 17 Two cars A and B are moving away from, each other in opposite directions. Both, the cars are moving with a speed of 20 ms −1, with respect to the ground. If an observer, in car A detects a frequency 2000 Hz of, the sound coming from car B, what is the, natural frequency of the sound source in, car B ?, −1, , (speed of sound in air = 340 ms ), (a) 2060 Hz, (c) 2300 Hz, , (b) 2250 Hz, (d) 2150 Hz, , 18 The position of a particle as a function of, time t, is given by, x( t ) = at + bt 2 − ct3, where a , b and c are constants. When the, particle attains zero acceleration, then its, velocity will be, (a) a +, , b2, b2, b2, b2, (b) a +, (c) a +, (d) a +, 2c, 4c, 3c, c, , 19 In a conductor, if the number of, conduction electrons per unit volume is, 8.5 × 1028 m −3 and mean free time is 25 fs, (femto second), it’s approximate, resistivity is (Take, me = 91, . × 10−31 kg), −7, , (a) 10 Ω-m, (c) 10−6 Ω-m, , −5, , (b) 10 Ω-m, (d) 10−8 Ω-m, , 20 The specific heats, C p and CV of a gas of, diatomic molecules, A are given (in units, of J mol −1 K −1) by 29 and 22, respectively., Another gas of diatomic molecules B, has, the corresponding values 30 and 21. If, they are treated as ideal gases, then, (a) A has a vibrational mode but B has none, (b) Both A and B have a vibrational mode, each, (c) A has one vibrational mode and B has two, (d) A is rigid but B has a vibrational mode, , 37, 21 50 W/m 2 energy density of sunlight is, normally incident on the surface of a, solar panel. Some part of incident energy, (25%) is reflected from the surface and, the rest is absorbed. The force exerted on, 1 m 2 surface area will be close to, (c = 3 × 108 m/s), (a) 20 × 10−8 N, (c) 15 × 10−8 N, , (b) 35 × 10−8 N, (d) 10 × 10−8 N, , 22 A string 2.0 m long and fixed at its ends, is driven by a 240 Hz vibrator. The string, vibrates in its third harmonic mode. The, speed of the wave and its fundamental, frequency is, (a) 180 m/s, 80 Hz, (c) 320 m/s, 120 Hz, , (b) 320 m/s, 80 Hz, (d) 180 m/s, 120 Hz, , 23 A thin smooth rod of length L and mass, M is rotating freely with angular speed, ω 0 about an axis perpendicular to the rod, and passing through its centre. Two, beads of mass m and negligible size are at, the centre of the rod initially. The beads, are free to slide along the rod. The, angular speed of the system, when the, beads reach the opposite ends of the rod,, will be, M ω0, M + 3m, M ω0, (c), M + 2m, , M ω0, M +m, M ω0, (d), M +6m, (b), , (a), , 24 A particle of mass m is moving with, speed 2v and collides with a mass 2m, moving with speed v in the same, direction. After collision, the first mass is, stopped completely while the second one, splits into two particles each of mass m,, which move at angle 45º with respect to, the original direction., The speed of each of the moving particle, will be, (a), , 2v, , (b), , v, 2, , (c), , v, (2 2 ), , (d) 2 2 v, , 25 A metal wire of resistance 3 Ω is, elongated to make a uniform wire of, double its previous length. This new wire, is now bent and the ends joined to make a
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38, , ONLINE, circle. If two points on this circle make an, angle 60º at the centre, the equivalent, resistance between these two points will, be, (a), , 7, Ω, 2, , (b), , 5, Ω, 2, , (c), , 12, Ω, 5, , (d), , 5, Ω, 3, , 26 A very long solenoid of radius R is, , carrying current I ( t ) = kte− αt ( k > 0), as a, function of time ( t ≥ 0). Counter clockwise, current is taken to be positive. A circular, conducting coil of radius 2R is placed in, the equatorial plane of the solenoid and, concentric with the solenoid. The current, induced in the outer coil is correctly, depicted, as a function of time, by, I, , I, (a) t=0, , (b) t=0, , t, , I, , t, I, , (c) t=0, , t, , 27 A He+ ion is in its first excited state. Its, ionisation energy is, (a) 54.40 eV, (c) 48.36 eV, , 28 A wooden block floating in a bucket of, 4, of its volume submerged., 5, When certain amount of an oil is poured, into the bucket, it is found that the block, is just under the oil surface with half of its, volume under water and half in oil. The, density of oil relative to that of water is, , water has, , (a) 0.6, (c) 0.7, , (b) 0.8, (d) 0.5, , 29 Two coils P and Q are separated by some, distance. When a current of 3 A flows, through coil P, a magnetic flux of 10−3 Wb, passes through Q. No current is passed, through Q. When no current passes, through P and a current of 2 A passes, through Q, the flux through P is, (a) 6.67 × 10−3 Wb, (c) 3.67 × 10−3 Wb, , (b) 6.67 × 10−4 Wb, (d) 3.67 × 10−4 Wb, , 30 Moment of inertia of a body about a, , (d) t=0, , t, , JEE Main 2019 ~ Solved Paper, , given axis is 1.5 kg m 2. Initially, the body, is at rest. In order to produce a rotational, kinetic energy of 1200 J, the angular, acceleration of 20 rad/s 2 must be applied, about the axis for a duration of, (a) 5 s, (c) 3 s, , (b) 13.60 eV, (d) 6.04 eV, , (b) 2 s, (d) 2.5 s, , CHEMISTRY, 1 In an acid-base titration, 0.1 M HCl, solution was added to the NaOH solution, of unknown strength. Which of the, following correctly shows the change of, pH of the titration mixture in this, experiment?, , pH, , (a) (D), pH, , pH, , pH, , V(mL), , V(mL), , (C), , (D), , (b) (A), , (c) (B), , (d) (C), , 2 Among the following species, the, diamagnetic molecule is, , V(mL), , V(mL), , (A), , (B), , (a) CO, (c) NO, ., , (b) B2, (d) O2
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APRIL ATTEMPT ~ 09 April 2019, Shift II, 3 The amorphous form of silica is, (a) tridymite, (c) cristobalite, , (b) kieselguhr, (d) quartz, , 4 HF has highest boiling point among, hydrogen halides, because it has, (a), (b), (c), (d), , lowest ionic character, strongest van der Waals’ interactions, strongest hydrogen bonding, lowest dissociation enthalpy, , 39, (b) Propanal as substrate and methanol in, stoichiometric amount, (c) Acetone as substrate and methanol in, stoichiometric amount, (d) Propanal as substrate and methanol in, excess, , 9 Consider the given plot of enthalpy of the, following reaction between A and B., A + B → C+D, Identify the incorrect statement., , 5 The structures of beryllium chloride in, the solid state and vapour phase,, respectively are, (a), (b), (c), (d), , dimeric and dimeric, chain and chain, dimeric and chain, chain and dimeric, , 20, Enthalpy 15, (kJ mol–1)10, , D, , 5, , A +B, , I. Valence bond theory cannot explain the, color exhibited by transition metal, complexes., II. Valence bond theory can predict, quantitatively the magnetic properties, of transition metal complexes., III. Valence bond theory cannot distinguish, ligands as weak and strong field ones., (a) II and III only, (b) I, II and III, (c) I and II only, (d) I and III only, , (a) D is kinetically stable product., (b) Formation of A and B from C has highest, enthalpy of activation., (c) C is the thermodynamically stable, product., (d) Activation enthalpy to form C is 5 kJ, mol −1 less than that to form D., , 10 The major products A and B for the, following reactions are, respectively, O, I, , 7 Assertion For the extraction of iron,, haematite ore is used., , (a) Only the reason is correct., (b) Both the assertion and reason are, correct explanation for the assertion., (c) Both the assertion and reason are, correct and the reason is the correct, explanation for the assertion., (d) Only the assertion is correct., , 8 In the following reaction,, , KCN, DMSO, , [A], , H2/Pd, , CN, , CH2NH2, ;, , (a), , HO, , CN, , HO, , CH2, , I, , NH2, H, , ;, , (b), , O, , O, CN, , CH2NH2, ;, , (c), HCl, , Carbonyl compound + MeOH, acetal, Rate of the reaction is the highest for:, , -, , (a) Acetone as substrate and methanol in, excess, , HO, , HO, , CN, I, , (d), , [B], , OH, , O, , Reason Heamatite is a carbonate ore of, iron., , C, , Reaction, coordinate, , 6 The correct statements among I to III are :, , ;, , CH2, , NH2, I
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40, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 11 Which one of the following about an, electron occupying the 1s-orbital in a, hydrogen atom is incorrect? (The Bohr, radius is represented by a0), (a) The electron can be found at a distance, 2a 0 from the nucleus., (b) The magnitude of the potential energy is, double that of its kinetic energy on an, average., (c) The probability density of finding the, electron is maximum at the nucleus., (d) The total energy of the electron is, maximum when it is at a distance a 0, from the nucleus., , 18 The layer of atmosphere between 10 km, to 50 km above the sea level is called as, (a) stratosphere, (c) thermosphere, , 19 Increasing order of reactivity of the, following compounds for SN 1 substitution, is, CH3, CH3, , (b) C6H5COCl, (d) (COCl)2, , 13 The one that is not a carbonate ore is, (a) siderite, (c) malachite, , (b) calamine, (d) bauxite, , 14 Molal depression constant for a solvent is, −1, , 4.0 K kg mol . The depression in the, freezing point of the solvent for 0.03 mol, kg −1 solution of K 2SO4 is, (Assume complete dissociation of the, electrolyte), (a) 0.18 K, (c) 0.12 K, , (b) 0.36 K, (d) 0.24 K, , 15 What would be the molality of 20%, (mass/mass) aqueous solution of KI?, (Molar mass of KI = 166 g mol −1), (a) 1.48, , (b) 1.51, , (c) 1.35, , (d) 1.08, , 16 The correct statements among I to III, regarding group 13 element oxides are:, I. Boron trioxide is acidic., II. Oxides of aluminium and gallium are, amphoteric., III. Oxides of indium and thallium are basic., (a) I, II and III, (b) I and III only, (c) I and II only, (d) II and III only, , CH2, , Cl, , H3C, , (A ), , Cl, (B), , Cl, H3CO, , 12 Hinsberg’s reagent is, (a) SOCl2, (c) C6H5SO2Cl, , (b) mesosphere, (d) troposphere, , (a), (b), (c), (d), , Cl, , (C), , (D), , (A) < (B) < (D) < (C), (B) < (C) < (D) < (A), (B) < (A) < (D) < (C), (B) < (C) < (A) < (D), , 20 Noradrenaline is a/an, (a) antidepressant (c) antihistamine, (c) neurotransmitter (d) antacid, , 21 Which of the following compounds is a, constituent of the polymer, O, , —, [ HN — C — NH — CH 2—, ]n ?, (a), (b), (c), (d), , N -methyl urea, Methylamine, Ammonia, Formaldehyde, , 22 A solution of Ni(NO3 )2 is electrolysed, between platinum electrodes using, 0.1 Faraday electricity. How many mole, of Ni will be deposited at the cathode?, (a) 0.20, (c) 0.15, , (b) 0.10, (d) 0.05, , 23 Which of the following potential energy, (PE) diagrams represents the SN 1, reaction?, , 17 During compression of a spring the work, done is 10 kJ and 2 kJ escaped to the, surroundings as heat. The change in, internal energy, ∆U (in kJ) is, (a) 8, , (b) −12, , (c) 12, , (d) −8, , (a) PE, , Progress of reaction, , (b) PE, , Progress of reaction
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APRIL ATTEMPT ~ 09 April 2019, Shift II, , (c), , (d), , PE, , PE, , Progress of reaction, , Progress of reaction, , 24 The maximum number of possible, oxidation states of actinoides are shown by, (a), (b), (c), (d), , berkelium, (Bk) and californium (Cf), nobelium (No) and lawrencium (Lr), actinium (Ac) and thorium (Th), neptunium (Np) and plutonium (Pu), , 25 The peptide that gives positive ceric, ammonium nitrate and carbylamine, tests is, (a) Lys-Asp, (c) Gln-Asp, , (b) Ser-Lys, (d) Asp-Gln, , 26 p-hydroxybenzophenone upon reaction, with bromine in carbon tetrachloride, gives, O, Br, , (a), HO, O, Br, , 41, Here, b is the van der Waals’ constant., Which gas will exhibit steepest increase, in the plot of Z (compression factor) vs p?, (a) Xe, (c) Kr, , (b) Ar, (d) Ne, , 28 The maximum possible denticities of a, ligand given below towards a common, transition and inner-transition metal ion,, respectively, are, σooc, cooσ, N, N, N, σooc, cooσ, σ, coo, (a) 8 and 8, (c) 6 and 6, , (b) 8 and 6, (d) 6 and 8, , 29 10 mL of 1 mM surfactant solution forms, a monolayer covering 0.24 cm 2 on a polar, substrate. If the polar head is, approximated as a cube, what is its edge, length?, (a), (b), (c), (d), , 2.0 pm, 0.1 nm, 1.0 pm, 2.0 nm, , 30 The major product of the following, , (b), , reaction is, HO, , OH, , O, Br, , CH2OH, , (c), , CO2Et, , HO, Br, , CHCl3, , O, , O, , O, , (a), , (b), , (d), , CO2Et, , HO, , COOH, OH, , OH, , 27 At a given temperature T , gases Ne, Ar,, Xe and Kr are found to deviate from ideal, gas behaviour. Their equation of state is, RT, at T ., given as, p =, V −b, , H2SO4(cat.), , (c), , OEt, O, , (d), O, O
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42, , ONLINE, , JEE Main 2019 ~ Solved Paper, , MATHEMATICS, 1 Let z ∈ C be such that|z|< 1. If, , (a) 2 + 1, (c) 2 2 + 1, , 5 + 3z, , then, ω=, 5(1 − z ), (a) 4 Im(ω ) > 5, (c) 5 Im (ω ) < 1, , (b) 5 Re (ω ) > 1, (d) 5 Re(ω ) > 4, , π, with $i,, 3, π, $ then a value, with $j and θ ∈( 0, π ) with k,, 4, of θ is, , 2 If a unit vector a makes angles, , 5π, 6, 5π, (c), 12, , π, 4, 2π, (d), 3, , (a), , is, , (b), , (a) T, T, F, (c) F, F, F, , (b) T, F, F, (d) F, T, T, , 10 If the two lines x + ( a − 1) y = 1 and, 2x + a 2 y = 1, ( a ∈ R − { 0, 1}) are, perpendicular, then the distance of their, point of intersection from the origin is, 2, 5, 2, (c), 5, , 2, 5, 2, (d), 5, , (a), , (b) 205 5, 17, (d), 5, , 5 A water tank has the shape of an, inverted right circular cone, whose, 1, semi-vertical angle is tan−1 . Water is, 2, poured into it at a constant rate of, 5 cu m/min. Then, the rate (in m/min) at, which the level of water is rising at the, instant when the depth of water in the, tank is 10 m is, 1, (c), 15π, , 53, 3, (d) 18, , (a) 30, , values of p, q , r are respectively, , line of intersection of the planes,, x + y + z − 6 = 0 and 2x + 3 y + z + 5 = 0, and it is perpendicular to the XY -plane., Then, the distance of the point (0, 0, 256), from P is equal to, , 1, (b), 5π, , (b) 84, (d) 56, , 9 If p ⇒ ( q ∨ r ) is false, then the truth, , 4 Let P be the plane, which contains the, , 2, (a), π, , (a) 72, (c) 98, , (c) 16, , 1, 32, 1, (d), 18, , (b), , (a) 63 5, 11, (c), 5, , diameter lying along the line 3 y = x + 7. If, the two adjacent vertices of the rectangle, are (–8, 5) and (6, 5), then the area of the, rectangle (in sq units) is, , , , y2, A = ( x , y ) :, ≤ x ≤ y + 4 is, 2, , , , 3 The value of sin 10º sin 30º sin 50º sin 70º, 1, 36, 1, (c), 16, , 7 A rectangle is inscribed in a circle with a, , 8 The area (in sq units) of the region, , (b), , (a), , (b) 2 − 1, (d) 2 2 − 1, , 1, (d), 10π, , 6 If the tangent to the parabola y 2 = x at a, point (α , β ), (β > 0) is also a tangent to the, ellipse, x 2 + 2 y 2 = 1, then α is equal to, , (b), , 11 If some three consecutive coefficients in, the binomial expansion of ( x + 1)n in, powers of x are in the ratio 2 : 15 : 70,, then the average of these three, coefficients is, (a) 964, , (b) 227, , (c) 232, , (d) 625, , 12 If f : R → R is a differentiable function, and, f( 2) = 6, then, (a) 12 f′ (2), (c) 24 f′ (2), , lim, x→ 2, , f (x ), , ∫, , 6, , 2t dt, is, ( x − 2), , (b) 0, (d) 2 f′ (2)
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APRIL ATTEMPT ~ 09 April 2019, Shift II, 13 The mean and the median of the, , 19 Some identical balls are arranged in rows, , following ten numbers in increasing order, 10, 22, 26, 29, 34, x, 42, 67, 70, y, y, are 42 and 35 respectively, then is, x, equal to, (a), , 7, 3, , (b), , 7, 2, , (c), , 8, 3, , (d), , 9, 4, , 14 The sum of the series, 1 + 2 × 3 + 3 × 5 + 4 × 7 +... upto 11th term, is, (a) 915, (c) 916, , (b) 946, (d) 945, , 15 If m is chosen in the quadratic equation, ( m 2 + 1)x 2 − 3x + ( m 2 + 1)2 = 0 such that, the sum of its roots is greatest, then the, absolute difference of the cubes of its, roots is, (a) 10 5, (c) 8 3, , (b) 8 5, (d) 4 3, , 16 The vertices B and C of a ∆ABC lie on the, , x+ 2 y−1 z, =, = such that BC = 5, 3, 0, 4, units. Then, the area (in sq units) of this, triangle, given that the point A(1, − 1, 2) is, , line,, , (a) 34, (c) 5 17, , (b) 2 34, (d) 6, , x, dy, , − y sin x = 6x, 0 < x < and, , 2, dx, π, , = 0, then y is equal to, 6, , 17 If cos x, π, y , 3, , π2, 2 3, π2, (c) −, 4 3, (a), , π2, 2 3, π2, (d) −, 2, , (b) −, , 18 Two poles standing on a horizontal, ground are of heights 5 m and 10 m,, respectively. The line joining their tops, makes an angle of 15º with the ground., Then, the distance (in m) between the, poles, is, (a) 5( 3 + 1), (c) 10( 3 − 1), , 5, (2 + 3 ), 2, (d) 5(2 + 3 ), , (b), , 43, , to form an equilateral triangle. The first, row consists of one ball, the second row, consists of two balls and so on. If 99 more, identical balls are added to the total, number of balls used in forming the, equilateral triangle, then all these balls, can be arranged in a square whose each, side contains exactly 2 balls less than the, number of balls each side of the triangle, contains. Then, the number of balls used, to form the equilateral triangle is, (a) 262, (c) 225, , (b) 190, (d) 157, , 20 If ∫ esec x, , (sec x tan x f ( x ) + (sec x tan x + sec2 x )), , dx = esec x f ( x ) + C, then a possible choice of, f ( x ) is, (a) x sec x + tan x +, , 1, 2, , 1, 2, 1, (c) sec x + x tan x −, 2, 1, (d) sec x − tan x −, 2, (b) sec x + tan x +, , 21 Two newspapers A and B are published, in a city. It is known that 25% of the city, population reads A and 20% reads B, while 8% reads both A and B. Further,, 30% of those who read A but not B look, into advertisements and 40% of those, who read B but not A also look into, advertisements, while 50% of those who, read both A and B look into, advertisements. Then, the percentage of, the population who look into, advertisements is, (a) 13.5, , (b) 13, , (c) 12.8, , (d) 13.9, , 22 The area (in sq units) of the smaller of, the two circles that touch the parabola,, y 2 = 4x at the point (1, 2) and the X-axis is, (a) 8π(3 − 2 2 ), (c) 8π (2 − 2 ), , (b) 4π (3 + 2 ), (d) 4π (2 − 2 )
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44, 23 If the sum and product of the first three, , 27 The value of the integral, 1, , terms in an AP are 33 and 1155, respectively,, then a value of its 11th term is, (a) 25, , (b) –36, , (c) –25, , ∫ x cot, , π 1, − log e 2, 4 2, π, (c), − log e 2, 4, , the greatest integer function, then, lim f (x) exists but lim f (x) does not exist, , x→ 4 +, , x→ 4 −, , x 2 + y 2 = 4 and x 2 + y 2 + 6x + 8 y − 24 = 0, also passes through the point, , x→ 4 +, , (a) (6, − 2), (c) (−6, 4), , not equal, (d) lim f (x) exists but lim f (x) does not exist, x→ 4 −, , x→ 4 +, , 25 The domain of the definition of the, function f ( x ) =, , 1, 4− x, , 2, , a|π − x|+1, x ≤ 5, is, b|x − π|+3, x > 5, , continuous at x = 5, then the value of, a − b is, , + log10( x3 − x ) is, , −2, π +5, 2, (c), π −5, , (c) −, , 1, 4, , (d), , 0 2y 1 , A = 2x y −1 , ( x , y ∈ R , x ≠ y ) for which, , , 2x − y 1 , AT A = 3I3 is, , 3, 4, , (a) 2, , (b) 4, , (c) 3, , (d) 6, , Answers, , Physics, (c), (a), (a), , (b), , 30 The total number of matrices, , x + ky − 2z = 0 and 2x − y + z = 0 has a, non-trivial solution ( x , y , z ), then, x y z, + + + k is equal to, y z x, 1, 2, , 2, π +5, 2, (d), 5−π, , (a), , 26 If the system of equations 2x + 3 y − z = 0,, , (b), , (b) (4, − 2), (d) (−4, 6), , 29 If the function f ( x ) = , , (a) (−1, 0) ∪ (1, 2) ∪ (3, ∞ ), (b) (−2, − 1) ∪ (−1, 0) ∪ (2, ∞ ), (c) (−1, 0) ∪ (1, 2) ∪ (2, ∞ ), (d) (1, 2) ∪ (2, ∞ ), , (a) −4, , π 1, − log e 2, 2 2, π, (d), − log e 2, 2, (b), , 28 The common tangent to the circles, , (b) f is continuous at x = 4, (c) Both lim f (x) and lim f (x) exist but are, x→ 4 −, , (1 − x 2 + x 4 )dx is, , (a), , x, , (a), , −1, , 0, , (d) –35, , 24 If f ( x ) = [x ] − , x ∈ R where [x ] denotes, 4, , 1., 11., 21., , JEE Main 2019 ~ Solved Paper, , ONLINE, , 2., 12., 22., , (d), (b), (b), , 3., 13., 23., , (d), (a), (d), , 4., 14., 24., , (d), (d), (d), , 5., 15., 25., , (d), (d), (d), , 6., 16., 26., , (c), (a), (d), , 7., 17., 27., , (a), (b), (b), , 8., 18., 28., , (c), (c), (a), , 9., 19., 29., , (c), (d), (b), , 10., 20., 30., , (a), (a), (b), , (a), (c), (d), , 3., 13., 23., , (b), (d), (b), , 4., 14., 24., , (c), (b), (d), , 5., 15., 25., , (d), (b), (b), , 6., 16., 26., , (d), (a), (b), , 7., 17., 27., , (d), (a), (a), , 8., 18., 28., , (d), (a), (d), , 9., 19., 29., , (d), (c), (a), , 10., 20., 30., , (c), (c), (d), , 3., 13., 23., , (c), (a), (c), , 4., 14., 24., , (c), (b), (b), , 5., 15., 25., , (b), (b), (c), , 6., 16., 26., , (a), (a), (b), , 7., 17., 27., , (b), (b), (a), , 8., 18., 28., , (d), (d), (a), , 9., 19., 29., , (b), (b), (d), , 10., 20., 30., , (d), (b), (b), , Chemistry, 1., 11., 21., , (b), (d), (d), , 2., 12., 22., , Mathematics, 1., 11., 21., , (b), (c), (d), , 2., 12., 22., , (d), (a), (a), , For Detailed Solutions Visit : https://bit.ly/2Hchu9r Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (10 April, 2019), TIME 9:30-12:30 (Shift I), , MM : 360, , PHYSICS, 1 A uniformly charged ring of radius 3a, and total charge q is placed in xy-plane, centred at origin. A point charge q is, moving towards the ring along the Z-axis, and has speed v at z = 4a. The minimum, value of v such that it crosses the origin is, (a), (c), , 2 1 q2 , , , m 5 4πε 0a , , 1/ 2, , 2 1, q2 , , , m 15 4πε 0a , , (b), 1/ 2, , (d), , 2 4, q2 , , , m 15 4πε 0a , , 1/ 2, , 2 2, q2 , , , m 15 4πε 0a , , 1/ 2, , (V ) graph for series and parallel, combination of two given capacitors. The, capacitances are, A, , 500, , B, , B, , I2, x, d, , I2 , I2 , (a) x = , d and x = , d, I1 + I 2, I1 − I 2, I1 , I2 , (b) x = , d and x = , d, I1 − I 2, I1 + I 2, I1 , I2 , (c) x = , d and x = , d, I1 + I 2, I1 − I 2, I1d, (d) x = ±, (I1 − I 2), , 4 A message signal of frequency 100 MHz, , 80, 10 V, , (a) 60 µF and 40 µF, (c) 20 µF and 30 µF, , C, , A, , I1, , 2 Figure shows charge ( q ) versus voltage, , q(µC), , wire C carrying a current I is to be kept, parallel to them at a distance x from A, such that the net force acting on it is, zero. The possible values of x are, , V(volt), , (b) 50 µF and 30 µF, (d) 40 µF and 10µF, , 3 Two wires A and B are carrying currents, I1 and I 2 as shown in the figure. The, separation between them is d. A third, , and peak voltage 100 V is used to execute, amplitude modulation on a carrier wave, of frequency 300 GHz and peak voltage, 400 V. The modulation index and, difference between the two side band, frequencies are, (a) 0.25 ; 1 × 108 Hz, (c) 0.25 ; 2 × 108 Hz, , (b) 4 ; 1 × 108 Hz, (d) 4 ; 2 × 108 Hz
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46, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 5 Two coaxial discs, having moments of, I, inertia I1 and 1 are rotating with, 2, respective angular velocities ω1 and, , (d) 60, , 7 The displacement of a damped, harmonic oscillator is given by, x( t ) = e− 0.1t cos (10 πt + φ )., Here, t is in seconds., The time taken for its amplitude of, vibration to drop to half of its initial, value is close to, (a) 27 s, , (b) 13 s, , (c) 4 s, , (d) 7 s, , 8 The ratio of surface tensions of mercury, and water is given to be 7.5 while the, ratio of their densities is 13.6. Their, contact angles with glass are close to, 135° and 0°, respectively. It is observed, that mercury gets depressed by an, amount h in a capillary tube of radius, r1, while water rises by the same, amount h in a capillary tube of radius, r2. The ratio (r1 / r2 ), is then close to, (a) 3/5, (c) 2/5, , 60°, , b, , O, , Vacuum, Glass, B, , 2 3, (a), + 2b, a, (c) 2a + 2b, , 2b, 3, 2b, (d) 2a +, 3, (b) 2a +, , 10 n moles of an ideal gas with constant, , common emitter amplifier, with a power, gain of 60 dB. The input circuit, resistance is 100 Ω and the output load, resistance is 10 kΩ. The common, emitter current gain β is, (b) 6 × 102 (c) 104, , a, , 30°, , I ω2, (b) − 1 1, 12, I1ω12, (d), 6, , 6 An n-p-n transistor operates as a, , (a) 102, , A, , ω1, ,, 2, , about their common axis. They are, brought in contact with each other and, thereafter they rotate with a common, angular velocity. If E f and Ei are the, final and initial total energies, then, ( E f − Ei ) is, I ω2, (a) − 1 1, 24, 3, (c) I1ω12, 8, , The optical path length of light ray from A, to B is, , (b) 2/3, (d) 4/5, , 9 A ray of light AO in vacuum is incident, on a glass slab at angle 60° and, refracted at angle 30° along OB as, shown in the figure., , volume heat capacity CV undergo an, isobaric expansion by certain volume. The, ratio of the work done in the process, to the, heat supplied is, 4nR, CV + nR, nR, (c), CV − nR, , 4nR, CV − nR, nR, (d), CV + nR, (b), , (a), , 11 A thin disc of mass M and radius R has, mass per unit area σ(r) = kr 2, where r is the, distance from its centre. Its moment of, inertia about an axis going through its, centre of mass and perpendicular to its, plane is, MR2, 2, MR2, (c), 3, , MR2, 6, 2MR2, (d), 3, (b), , (a), , 12 A particle of mass m is moving along a, trajectory given by, x = x0 + a cosω1t and y = y0 + b sinω 2t., The torque acting on the particle about the, origin at t = 0 is, (a) zero, $, (b) m (− x0b + y0a ) ω12 k, $, (c) − m (x0bω 22 − y0aω12) k, 2 $, (d) + my a ω k, 0, , 1, , 13 A proton, an electron and a helium nucleus,, have the same energy. They are in circular, orbits in a plane due to magnetic field, perpendicular to the plane.
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APRIL ATTEMPT ~ 10 April 2019, Shift I, Let rp, re and rHe be their respective radii,, then, (a) re < rp = rHe, (c) re < rp < rHe, , (b) re > rp = rHe, (d) re > rp > rHe, , 14 Two radioactive materials A and B have, decay constants 10 λ and λ, respectively., If initially they have the same number of, nuclei, then the ratio of the number of, nuclei of A to that of B will be 1/e after a, time, (a), , 1, 11 λ, , 11, 10 λ, , (b), , (c), , 1, 9λ, , 1, 10 λ, , (d), , 15 A 25 × 10−3 m3 volume cylinder is filled, with 1 mole of O2 gas at room, temperature (300 K). The molecular, diameter of O2 and its root mean square, speed are found to be 0.3 nm and, 200 m/s, respectively. What is the, average collision rate (per second) for an, O2 molecule?, (a) ~ 1010, (c) ~ 1011, , (b) ~ 1012, (d) ~ 1013, , 47, 18 A moving coil galvanometer allows a full, , scale current of 10−4 A. A series resistance, of 2 MΩ is required to convert the above, galvanometer into a voltmeter of range, 0-5 V. Therefore, the value of shunt, resistance required to convert the above, galvanometer into an ammeter of range, 0.10 mA is, , (a) 100 Ω, (c) 200 Ω, , (b) 500 Ω, (d) 10 Ω, , 19 A current of 5 A passes through a copper, , conductor (resistivity = 1.7 × 10−8 Ω-m) of, radius of cross-section 5 mm. Find the, mobility of the charges, if their drift, velocity is 11, . × 10−3 m/s., , (a) 1.5 m2 / V-s, (c) 1.0 m2 / V-s, , 20 In a meter bridge experiment, the circuit, diagram and the corresponding, observation table are shown in figure, X, , R, Resistance, box, , 16 In an experiment, the resistance of a, material is plotted as a function of, temperature (in some range). As shown in, the figure, it is a straight line., , G, , Unknown, resistance, , l, K, , E, , InR(T), , 1/T2, , One may conclude that, −T 2/T02, , (a) R(T ) = R0e, , −T02/T 2, , (c) R(T ) = R0e, , T 2/T02, , (b) R(T ) = R0e, R, (d) R(T ) = 02, T, , 17 In a photoelectric effect experiment, the, threshold wavelength of light is 380 nm., If the wavelength of incident light is, 260 nm, the maximum kinetic energy of, emitted electrons will be, 1237, Given, E (in eV) =, λ( in nm), (a) 15.1 eV, (c) 1.5 eV, , (b) 1.3 m2 / V-s, (d) 1.8 m2 / V-s, , (b) 3.0 eV, (d) 4.5 eV, , S. No., , R (Ω), , l (cm), , 1., , 1000, , 60, , 2., , 100, , 13, , 3., , 10, , 1.5, , 4., , 1, , 1.0, , Which of the readings is inconsistent?, (a) 3, (c) 1, , (b) 2, (d) 4, , 21 A ball is thrown upward with an initial, velocity v0 from the surface of the earth., The motion of the ball is affected by a, drag force equal to mγv 2 (where, m is, mass of the ball, v is its instantaneous, velocity and γ is a constant). Time taken, by the ball to rise to its zenith is
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48, , ONLINE, , (a), , 2γ , 1, tan −1 , v0, 2γg, g, , , (b), , γ , 1, tan −1 , v0, γg, g , , (c), , γ , 1, sin −1 , v0, γg, g , , (d), , , 1, ln 1 +, γg, , , detect sound to be of frequencies 480 Hz, and 530 Hz. Their respective speeds are, in ms−1,, (Take, speed of sound = 300 m/s), (a) 12, 16, (c) 16, 14, , (b) 12, 18, (d) 8, 18, , 25 The electric field of a plane, , γ , v0, g , , electromagnetic wave is given by, E = E i$ cos ( kz ) cos (ωt ), 0, , 22 One plano-convex and one plano-concave, lens of same radius of curvature R but of, different materials are joined side by side, as shown in the figure. If the refractive, index of the material of 1 is µ 1 and that of, 2 is µ 2, then the focal length of the, combination is, 1, , JEE Main 2019 ~ Solved Paper, , µ2, , The corresponding magnetic field B is, then given by, E0, c, E, (b) B = 0, c, E0, (c) B =, c, E0, (d) B =, c, , (a) B =, , $j sin (kz ) sin (ωt ), $j sin (kz ) cos (ωt ), $ sin (kz ) cos (ωt ), k, $j cos (kz ) sin (ωt ), , 26 A transformer consisting of 300 turns in, µ1, , 2R, µ1 − µ 2, R, (c), 2(µ1 − µ 2), (a), , 2, , R, 2 − (µ1 − µ 2), R, (d), µ1 − µ 2, , (b), , 23 Given below in the left column are, different modes of communication using, the kinds of waves given in the right, column., A., , Optical fibre, communication, , P., , Ultrasound, , B., , Radar, , Q., , Infrared light, , C., , Sonar, , R., , Microwaves, , D., , Mobile phones, , S., , Radio waves, , the primary and 150 turns in the, secondary gives output power of 2.2 kW. If, the current in the secondary coil is 10 A,, then the input voltage and current in the, primary coil are, (a) 440 V and 5 A, (c) 220 V and 10 A, , 27 Two particles of masses M and 2M,, moving as shown, with speeds of 10 m/s, and 5 m/s, collide elastically at the origin., After the collision, they move along the, indicated directions with speed v1 and v2, are nearly, M, , From the options given below, find the, most appropriate match between entries, in the left and the right column., (a), (b), (c), (d), , A-Q, B-S, C-R, D-P, A-S, B-Q, C-R, D-P, A-Q, B-S, C-P, D-R, A-R, B-P, C-S, D-Q, , 24 A stationary source emits sound waves of, frequency 500 Hz. Two observers moving, along a line passing through the source, , (b) 220 V and 20 A, (d) 440 V and 20 A, , 2M, 10 m/s, , v1, , 30°, , 30°, , 45°, , 45°, , 5m/s, 2M, , (a), (b), (c), (d), , 6.5 m/s and 3.2 m/s, 3.2 m/s and 6.3 m/s, 3.2 m/s and 12.6 m/s, 6.5 m/s and 6.3 m/s, , v2, M
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APRIL ATTEMPT ~ 10 April 2019, Shift I, 28 The value of acceleration due to gravity, , at earth’s surface is 9.8 ms−2. The altitude, above its surface at which the, acceleration due to gravity decreases to, 4.9 ms−2, is close to (Take, radius of earth, = 6.4 × 106 m ), , (a) 9.0 × 106 m, (c) 6.4 × 106 m, , 49, 30 In the given circuit, an ideal voltmeter, connected across the 10 Ω resistance, reads 2 V. The internal resistance r, of, each cell is, 15 Ω, 2Ω, , (b) 2.6 × 106 m, (d) 1.6 × 106 m, , 10 Ω, , 29 A cylinder with fixed capacity of 67.2 L, contains helium gas at STP. The amount, of heat needed to raise the temperature of, the gas by 20°C is, [Take, R = 8.31 J mol−1K −1], (a) 700 J (b) 748 J (c) 374 J, , (d) 350 J, , 1.5 V, 1.5 V,, rΩ rΩ, , (a) 1.5 Ω, (c) 1 Ω, , (b) 0.5 Ω, (d) 0 Ω, , CHEMISTRY, 1 Match the refining methods Column I, with metals Column II., Column I, (Refining Methods), , are, CHO, , Column II, (Metals), , I. Liquation, , (A) Zr, , II. Zone refining, , (B) Ni, , III. Mond process, , (C) Sn, , IV. van Arkel method, , (D) Ga, , (a), (b), (c), (d), , 3 Major products of the following reaction, , I- (C) ; II-(D); III-(B) ; IV-(A), I- (B) ; II-(C); III-(D) ; IV-(A), I- (C) ; II-(A); III-(B) ; IV-(D), I- (B) ; II-(D); III-(A) ; IV-(C), , + HCHO, , (i) 50% NaOH, (ii) H3O+, , (a) CH3OH and HCO2H, COOH, (b) CH3OH and, CH2OH, (c) HCOOH and, , 2 Consider the statements S1 and S 2 :, S1 : Conductivity always increases with, decrease in the concentration of, electrolyte., S2 : Molar conductivity always increases, with decrease in the concentration of, electrolyte., The correct option among the following is, (a), (b), (c), (d), , S1 is correct and S2 is wrong, S1 is wrong and S2 is correct, Both S1 and S2 are wrong, Both S1 and S2 are correct, , CH2OH, (d), , COOH, and, , 4 The regions of the atmosphere, where, clouds form and where we live,, respectively, are, (a) stratosphere and stratosphere, (b) troposphere and troposphere, (c) troposphere and stratosphere, (d) stratosphere and troposphere
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50, , ONLINE, , 5 A gas undergoes physical adsorption on a, surface and follows the given Freundlich, x, adsorption isotherm equation, = Kp0.5, m, Adsorption of the gas increases with, (a), (b), (c), (d), , increase in p and increase in T, increase in p and decrease in T, decrease in p and decrease in T, decrease in p and increase in T, , 6 Three complexes,, [CoCl(NH3 )5 ]2+ (I), [Co(NH3 )5 H 2O]3 + (II), and [Co(NH3 )6 ]3 + (III), absorb light in the visible region. The, correct order of the wavelength of light, absorbed by them is, (a) II > I > III, (c) III > I > II, , (b) I > II > III, (d) III > II > I, , 7 At 300 K and 1 atmospheric pressure,, 10 mL of a hydrocarbon required 55 mL, of O2 for complete combustion and 40 mL, of CO2 is formed. The formula of the, hydrocarbon is, (a) C4H7Cl, (c) C4H10, , (b) C4H6, (d) C4H8, , 8 The isoelectronic set of ions is, (a), (b), (c), (d), , F− , Li+ , Na + and Mg 2+, N3 − , Li+ , Mg 2+ and O2−, Li+ , Na + , O2− and F−, N3 − , O2− , F− and Na +, , JEE Main 2019 ~ Solved Paper, , OH, , (c) CH3 CH CH == CH2, O, , (d), O, , H, , CH3CHCH2CH2NH2, , 11 Consider the hydrated ions of, , Ti2+ , V 2+ , Ti3 + and Sc3 + . The correct order, of their spin-only magnetic moment is, (a), (b), (c), (d), , Sc3 + < Ti3 + < Ti2+ < V 2+, Sc3 + < Ti3 + < V 2+ < Ti2+, Ti3 + < Ti2+ < Sc3 + < V 2+, V 2+ < Ti2+ < Ti3 + < Sc3 +, , 12 Consider the following statements., I. The pH of a mixture containing 400 mL, of 0.1 M H2SO4 and 400 mL of 0.1 M, NaOH will be approximately 1.3., II. Ionic product of water is temperature, dependent., III. A monobasic acid with K a = 10−5 has a, pH = 5. The degree of dissociation of this, acid is 50%., IV. The Le-Chatelier’s principle is not, applicable to common-ion effect., The correct statements are, (a) I, II and IV, (b) II and III, (c) I and II, (d) I, II and III, , 13 The oxoacid of sulphur that does not, contain bond between sulphur atoms is, , 9 The principle of column chromatography is, (a) differential absorption of the substances, on the solid phase, (b) differential adsorption of the substances, on the solid phase, (c) gravitational force, (d) capillary action, , 10 The major product of the following, reaction is, OH, , Ethyl formate (1 equiv.), CH3 CH CH 2CH 2NH 2 →, Triethylamine, , OH, , (a) CH3 CHCH2CH2NHCHO, (b) CH3CH == CH CH2NH2, , (a) H2S 2O3, (c) H2S 2O7, , (b) H2S 2O4, (d) H2S 4O6, , 14 At room temperature, a dilute solution of, urea is prepared by dissolving 0.60 g of, urea in 360 g of water. If the vapour, pressure of pure water at this, temperature is 35 mm Hg, lowering of, vapour pressure will be, , (Molar mass of urea = 60 g mol −1), (a) 0.027 mmHg, (b) 0.031 mmHg, (c) 0.017 mmHg, (d) 0.028 mmHg, , 15 The alloy used in the construction of, aircrafts is, (a) Mg-Zn, (c) Mg-Sn, , (b) Mg-Mn, (d) Mg-Al
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APRIL ATTEMPT ~ 10 April 2019, Shift I, , 51, , 16 The graph between|ψ|2 and r (radial, , 22 Consider the following table., , distance) is shown below. This represents, , 2, , |Ψ|, , 17 Increasing rate of SN 1 reaction in the, following compounds is, I, , I, MeO, (B), I, , (C), , I, , (D), H 3C, , (a), (b), (c), (d), , H3CO, , (A) < (B) < (C) < (D), (B) < (A) < (C) < (D), (A) < (B) < (D) < (C), (B) < (A) < (D) < (C), , temperature if, ∆H > 0 and ∆S < 0, ∆H < 0 and ∆S > 0, ∆H < 0 and ∆S < 0, ∆H > 0 and ∆S > 0, , 19 During the change of O2 to O−2 , the, incoming electron goes to the orbital., (a) π2 px, (c) π2 py, , (b) π 2 px, (d) σ * 2 pz, *, , 20 The synonym for water gas when used in, the production of methanol is, (a) natural gas, (c) syn gas, , A, , 642.32, , 0.05196, , B, , 155.21, , 0.04136, , C, , 431.91, , 0.05196, , D, , 155.21, , 0.4382, , 23 Which of the following is a condensation, polymer?, (a) Nylon-6, 6, (c) Teflon, , (b) Neoprene, (d) Buna - S, , 24 The major product of the following, , 18 A process will be spontaneous at all, (a), (b), (c), (d), , b/(dm 3 mol −1 ), , (a) gas C will occupy lesser volume than gas, A; gas B will be lesser compressible than, gas D, (b) gas C will occupy more volume than gas, A; gas B will be more compressible than, gas D, (c) gas C will occupy more volume than gas, A; gas B will be lesser compressible than, gas D, (d) gas C will occupy more volume than gas, A; gas B will be lesser compressible than, gas D, , (b) 2p-orbital, (d) 2s-orbital, , (A), , a/(k Pa dm 6mol −1), , a and b are van der Waals’ constants. The, correct statement about the gases is, , r, , (a) 1s-orbital, (c) 3s-orbital, , Gas, , (b) laughing gas, (d) fuel gas, , 21 Amylopectin is composed of, (a) β-D-glucose, C1-C4 and C2-C6 linkages, (b) α-D-glucose, C1-C4 and C2-C6 linkages, (c) β-D-glucose, C1-C4 and C1-C6 linkages, (d) α-D-glucose, C1-C4 and C1 -C6linkages, , reaction is, CH3, , CH OH, CH3 C C HCH3 3→, , H Br, CH3, , (a) CH3 C == CHCH3, CH3, , (b) CH3 C CH == CH 2, , H, CH3, , (c) CH3 C CH 2 CH3, , OCH3, CH3, , (d) CH3 C CHCH3, , , H OCH3
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52, , JEE Main 2019 ~ Solved Paper, , ONLINE, , OH, , 25 A bacterial infection in an internal wound, grows as N ′ ( t ) = N0 exp ( t ), where the, time t is in hours. A dose of antibiotic,, taken orally, needs 1 hour to reach the, wound. Once it reaches there, the, bacterial population goes down as, dN, N, = − 5N 2. What will be the plot of 0, dt, N, vs t after 1 hour ?, , (a), , N0, N, , (b), , N0, (c), N, , (c), , (d), , NC, , I, , I, , from N-ethylphthalimide on treatment, with, (a) NaBH4, (c) H2O, , N, (d) 0, N, t(h), , OH, , I, , 28 Ethylamine (C2H5NH 2 ) can be obtained, t(h), , t(h), , NC, OH, , OH, , NC, , NC, , N0, N, , I, (b), , (a), , (b) NH2NH2, (d) CaH2, , 29 The correct order of catenation is, (a) C > Sn > Si ≈ Ge (b) Si > Sn > C > Ge, (c) C > Si > Ge ≈ Sn (d) Ge > Sn > Si > C, , t(h), , 26 The species that can have a trans-isomer, is (en = ethane -1, 2-diamine, ox = oxalate), (a) [Pt(en)Cl2], , (b) [Cr(en)2(ox)], , (c) [Pt(en)2Cl2]2+, , (d) [Zn(en)Cl2], , +, , 30 The increasing order of the reactivity of, the following compounds towards, electrophilic aromatic substitution, reaction is, , 27 The major product of the following, , Cl, , CH3, , COCH3, , (I), , (II), , (III), , reaction is, O, HI (excess), ∆, , (a) III < I < II, (c) III < II < I, , O, , NC, , (b) II < I < III, (d) I < III < II, , MATHEMATICS, 1 If for some x ∈ R, the frequency, distribution of the marks obtained by 20, students in a test is, Marks, , 2, , Frequency (x + 1) 2, , 3, , 5, , 7, , 2x − 5, , x 2 − 3x, , x, , Then, the mean of the marks is, (a) 3.0, (c) 2.5, , (b) 2.8, (d) 3.2, , 2 If Q( 0, − 1, − 3) is the image of the point P, in the plane 3x − y + 4z = 2 and R is the, point ( 3, − 1, − 2) , then the area (in sq, units) of ∆PQR is, , (a), (c), , 91, 2, 91, 4, , (b) 2 13, (d), , 65, 2, , 3 If the circles x 2 + y 2 + 5Kx + 2 y + K = 0, and 2 ( x 2 + y 2 ) + 2Kx + 3 y −1 = 0, ( K ∈ R ),, intersect at the points P and Q, then the, line 4x + 5 y − K = 0 passes through P and, Q, for, (a) no values of K, (b) exactly one value of K, (c) exactly two values of K, (d) infinitely many values of K
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APRIL ATTEMPT ~ 10 April 2019, Shift I, 4 Let f ( x ) = ex − x and g( x ) = x 2 − x, ∀ x ∈ R., Then, the set of all x ∈ R, where the, function h( x ) = ( fog) ( x ) is increasing, is, −1 1 , , (b) −1,, ∪, , ∞, 2 2 , , −1 , (d), , 0 ∪ [1, ∞ ), 2, , , 1, (a) 0,, ∪ [1, ∞ ), 2 , (c) [0, ∞ ), , 5 If ∫, , dx, , ( x − 2x + 10), , , f(x), x − 1, = A tan−1 , + C,, + 2, , , 3, , x − 2x + 10, 2, , 2, , where, C is a constant of integration, then, 1, and f (x) = 9 (x − 1), 27, 1, (b) A =, and f (x) = 3 (x − 1), 81, 1, (c) A =, and f (x) = 3 (x − 1), 54, 1, (d) A =, and f (x) = 9 (x − 1)2, 54, (a) A =, , 6 If a directrix of a hyperbola centred at the, origin and passing through the point, ( 4, − 2 3 ) is 5x = 4 5 and its eccentricity, is e, then, (a), (b), (c), (d), , 4e4 − 12e2 − 27 = 0, 4e4 − 24e2 + 27 = 0, 4e4 + 8e2 − 35 = 0, 4e4 − 24e2 + 35 = 0, , 2, , +, , y2, 2, , (a) 8 3, (c) 5, , be formed using the digits 0, 1, 2,5, 7 and, 9 which are divisible by 11 and no digit is, repeated, is, (a) 60, (c) 48, , (b) 72, (d) 36, , 10 If a1 , a2 , a3 , ... , an are in AP and, a1 + a4 + a7 + ... + a16 = 114 , then, a1 + a6 + a11 + a16 is equal to, (a) 64, , (b) 76, , (c) 98, , (d) 38, , 11 ABC is a triangular park with, AB = AC = 100 m. A vertical tower is, situated at the mid-point of BC. If the, angles of elevation of the top of the tower, at A and B are cot−1 ( 3 2 ) and, cosec−1( 2 2 ) respectively, then the height, of the tower (in m) is, (a) 25, , (b) 20, 100, (d), 3 3, , (c) 10 5, , ( n + 1)1/ 3, , 12 lim , n→∞, , , , n, , 4/ 3, , 4 4/3, (2), 3, 3, 3, (c), (2)4/3 −, 4, 4, (a), , −9, = 1 at the point 3, ,, 2, a, b, then the length of the latusrectum of the, ellipse is, x2, , 9 The number of 6 digits numbers that can, , +, , ( n + 2)1/ 3, n, , 4/ 3, , + ..... +, , ( 2n )1/ 3 , , n 4/ 3 , , is equal to, , 7 If the line x − 2 y = 12 is tangent to the, ellipse, , 53, , (b) 9, (d) 12 2, , 8 If α and β are the roots of the quadratic, equation, x 2 + x sin θ − 2 sin θ = 0,, α12 + β12, π, is, θ ∈ 0, , then −12, 2, (α, + β −12 )(α − β )24, equal to, (a), , 212, (sin θ + 8)12, , (b), , 26, (sin θ + 8)12, , (c), , 212, (sin θ − 4)12, , (d), , 212, (sin θ − 8)6, , 3 4/3 4, (2) −, 4, 3, 4 3/ 4, (d) (2), 3, , (b), , 13 The region represented by|x − y|≤ 2 and, |x + y|≤ 2 is bounded by a, (a) rhombus of side length 2 units, (b) rhombus of area 8 2 sq units, (c) square of side length 2 2 units, (d) square of area 16 sq units, , 14 If a > 0 and z =, , (1 + i )2, , has magnitude, a−i, , 2, , then z is equal to, 5, 1 3, − i, 5 5, 1 3, (c) − + i, 5 5, (a), , 1 3, − i, 5 5, 3 1, (d) − − i, 5 5, (b) −
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54, , ONLINE, , 15 If the length of the perpendicular from, the point (β, 0, β ) (β ≠ 0) to the line,, x y−1 z +1, is, =, =, −1, 1, 0, , 3, , then β is equal to, 2, , (a) 2, (c) − 1, , (b) − 2, (d) 1, , 16 If ∆1 = − sin θ, , −x, 1 and, cos θ, 1, x, x, sin 2θ cos 2θ, , x ≠ 0, then, −x, 1, ∆ 2 = − sin 2θ, cos 2θ, 1, x, π, for all θ ∈ 0, , 2, , (c) ∆1 + ∆ 2 = − 2x3, (d) ∆1 − ∆ 2 = x(cos 2θ − cos 4θ ), , 17 Let f ( x ) = x 2 , x ∈ R. For any A ⊆ R, define, g( A) = { x ∈ R : f ( x ) ∈ A}. If S = [0, 4], then, which one of the following statements is, not true?, , x→1, , (b) g ( f (S )) ≠ S, (d) f(g(S)) ≠ f (S ), , x4 − 1, x3 − k3, , then k is, = lim 2, x − 1 x → k x − k2, , 4, 3, 3, (c), 2, , (b), , sin 2 x − 2 sin x + 5, , satisfy the equation, (a) 2|sin x| = 3 sin y, (b) sin x = |sin y|, (c) sin x = 2 sin y, (d) 2 sin x = sin y, , (a), (c), , 1, 15, 1, 30, , 1, 2 15, 1, (d), 6 10, (b), , 22 Which one of the following Boolean, ( p ∨ q) ∨ ( p ∨ ~ q), ( p ∧ q) ∨ ( p ∧ ~ q), ( p ∨ q) ∧ ( p ∨ ~ q), ( p ∨ q) ∧ (~ p ∨ ~ q), , 23 Let f : R → R be differentiable at c ∈ R, and f ( c) = 0. If g( x ) =| f ( x )|, then at x = c,, g is, (a), (b), (c), (d), , not differentiable, differentiable if f ′ (c) ≠ 0, not differentiable if f ′ (c) = 0, differentiable if f ′ (c) = 0, , 24 If the coefficients of x 2 and x3 are both, , ⋅, , 1, 4sin, , 2, , (b) (− 21, 714), (d) (− 54, 315), , (a) (28, 315), (c) (28, 861), , 19 All the pairs ( x , y ) that satisfy the, inequality 2, , the vertices of a triangle and M be the, mid-point of AC. If G divides BM in the, ratio 2 : 1, then cos ( ∠GOA) (O being the, origin) is equal to, , zero, in the expansion of the expression, (1 + ax + bx 2 ) (1 − 3x )15 in powers of x,, then the ordered pair ( a , b) is equal to, , 3, 8, 8, (d), 3, , (a), , (b) 2 2, (d) 3, , (a) 3 2, (c) 2, , (a), (b), (c), (d), , (b) ∆1 − ∆ 2 = − 2x3, , 18 If lim, , (1, 1). If the circle also passes through the, point (1, − 3), then its radius is, , expressions is a tautology ?, , (a) ∆1 + ∆ 2 = − 2(x + x − 1), 3, , (a) f ( g (S )) = S, (c) g ( f (S )) = g (S ), , 20 The line x = y touches a circle at the point, , 21 Let A( 3, 0, −1), B ( 2, 10, 6) and C(1, 2, 1) be, , sin θ cos θ, , x, , JEE Main 2019 ~ Solved Paper, , ≤ 1 also, , 25 The sum of series, , 3 × 13, , y, , +, , 7 × (13 + 23 + 33 ), , 12 + 22 + 32, term, is, , (a) 680, (c) 660, , 2, , 1, , +, , 5 × (13 + 23 ), 12 + 22, , + .......... + upto 10th, , (b) 600, (d) 620
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APRIL ATTEMPT ~ 10 April 2019, Shift I, 26 Assume that each born child is equally, likely to be a boy or a girl. If two families, have two children each, then the, conditional probability that all children, are girls given that at least two are girls;, is, 1, (a), 17, , 1, (b), 12, , 1, (c), 10, , 1, (d), 11, , 27 If the system of linear equations, x+ y+z=5, x + 2 y + 2z = 6, x + 3 y + λz = µ, (λ , µ ∈ R), has infinitely, many solutions, then the value of λ + µ is, (a) 7, , (b) 12, , (c) 10, , (d) 9, , sin ( p + 1) x + sin x, ,x< 0, , x, , 28 If f ( x ) = , x=0, q,, 2, , x> 0, x+x − x, ,, , 3/ 2, , x, , 55, 1, 3, (a) − , − , 2, 2, , 1 3, (b) − , , 2 2, , 5 1, (c) , , 2 2, , 3 1, (d) − , , 2 2, , 29 If y = y( x ) is the solution of the, differential equation, dy, π π, = (tan x − y ) sec2 x, x ∈ − , , such, 2 2, dx, π, that y ( 0) = 0, then y − is equal to, 4, 1, −2, e, 1, (c) 2 +, e, , (b), , (a), , 1, −e, 2, , (d) e − 2, 2π, , 30 The value of, , ∫ [sin 2x (1 + cos 3x )] dx,, 0, , where [t ] denotes the greatest integer, function, is, , is continuous at x = 0 , then the ordered, pair ( p, q ) is equal to, , (a) − π, (c) − 2π, , (b) 2π, (d) π, , Answers, Physics, 1. (d), 11. (d), 21. (b), , 2. (d), 12. (d), 22. (d), , 3. (d), 13. (c), 23. (c), , 4. (c), 14. (c), 24. (b), , 5. (a), 15. (*), 25. (a), , 6. (a), 16. (c), 26. (a), , 7. (d), 17. (c), 27. (d), , 8. (c), 18. (*), 28. (b), , 9. (c), 19. (c), 29. (b), , 10. (d), 20. (d), 30. (b), , 3. (c), 13. (c), 23. (a), , 4. (b), 14. (c), 24. (c), , 5. (b), 15. (d), 25. (a), , 6. (b), 16. (d), 26. (d), , 7. (b), 17. (b), 27. (c), , 8. (d), 18. (b), 28. (b), , 9. (b), 19. (b), 29. (c), , 10. (a), 20. (c), 30. (a), , 3. (a), 13. (c), 23. (d), , 4. (a), 14. (b), 24. (a), , 5. (c), 15. (c), 25. (c), , 6. (d), 16. (c), 26. (d), , 7. (b), 17. (c), 27. (c), , 8. (a), 18. (d), 28. (d), , 9. (a), 19. (b), 29. (d), , 10. (b), 20. (b), 30. (a), , Chemistry, 1. (a), 11. (a), 21. (d), , 2. (b), 12. (d), 22. (b), , Mathematics, 1. (b), 11. (b), 21. (a), , 2. (a), 12. (c), 22. (a), , Note (*) None of the option is correct., , For Detailed Solutions Visit : https://bit.ly/2H6iTNu Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (10 April, 2019), TIME 2:30-5:30 (Shift II), , MM : 360, , PHYSICS, 1 A plane is inclined at an angle α = 30º, with respect to the horizontal. A particle, is projected with a speed u = 2 ms− 1, from, the base of the plane, making an angle, θ = 15º with respect to the plane as shown, in the figure. The distance from the base,, at which the particle hits the plane is, close to, [Take, g = 10 ms− 2], , A, B, , (a) 12 N, (c) 8 N, , (b) 16 N, (d) 40 N, , 3 The time dependence of the position of a, particle of mass m = 2 is given by, r( t ) = 2t$i − 3t 2$j. Its angular momentum,, with respect to the origin, at time t = 2 is, , $, (a) 36 k, u, , (a) 26 cm, (c) 18 cm, , $ − $i ), (b) − 34 (k, (d) 48 (i$ + $j), , $, (c) − 48 k, , °, 15, θ=, α=30°, , F, , 4 A spaceship orbits around a planet at a, (b) 20 cm, (d) 14 cm, , 2 Two blocks A and B of masses mA = 1 kg, and mB = 3 kg are kept on the table as, shown in figure. The coefficient of friction, between A and B is 0.2 and between B, and the surface of the table is also 0.2., The maximum force F that can be applied, on B horizontally, so that the block A does, not slide over the block B is, [Take, g = 10 m / s2], , height of 20 km from its surface., Assuming that only gravitational field of, the planet acts on the spaceship, what, will be the number of complete, revolutions made by the spaceship in, 24 hours around the planet?, [Take, mass of planet = 8 × 1022 kg,, radius of planet = 2 × 106 m,, gravitational constant, G = 6.67 × 10− 11 N - m 2 / kg2], (a) 11, , (b) 17, , (c) 13, , (d) 9
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APRIL ATTEMPT ~ 10 April 2019, Shift II, 5 In free space, a particle A of charge 1 µC, is held fixed at a point P. Another, particle B of the same charge and mass, 4 µg is kept at a distance of 1 mm from P., If B is released, then its velocity at a, distance of 9 mm from P is, , 1, 2 − 2, 9, Take, 4πε = 9 × 10 N - m C , , , 0, (a) 1.5 × 102 m /s, (c) 1.0 m/s, , (b) 3.0 × 104 m /s, (d) 2.0 × 103 m /s, , 6 A submarine experience a pressure of, 5.05 × 106 Pa at a depth of d1 in a sea., When it goes further to a depth of d2, it, experiences a pressure of 8.08 × 106 Pa,, then d2 − d1 is approximately (density of, water = 103 kg / m3 and acceleration due, to gravity = 10 ms− 2), (a) 500 m, (c) 600 m, , divided into two unequal parts. The first, 7M, part has a mass of, and is converted, 8, into a uniform disc of radius 2R. The, second part is converted into a uniform, solid sphere. Let I1 be the moment of, inertia of the disc about its axis and I 2 be, the moment of inertia of the new sphere, about its axis., The ratio I1 / I 2 is given by, (a) 285, , (b) 185, , (c) 65, , (d) 140, , 11 The correct figure that shows, schematically, the wave pattern produced, by superposition of two waves of, frequencies 9Hz and 11 Hz, is, y, , (a) 0, , completely absorbing surface with an, energy flux of 25 W cm − 2. If the surface, has an area of 25 cm 2, the momentum, transferred to the surface in 40 min time, duration will be, , (a) 3.5 × 10− 6 N -s, (c) 1.4 × 10− 6 N -s, , (b) 6.3 × 10− 4 N -s, (d) 5.0 × 10− 3 N -s, , 8 A square loop is carrying a steady current, I and the magnitude of its magnetic, dipole moment is m. If this square loop is, changed to a circular loop and it carries, the same current, the magnitude of the, magnetic dipole moment of circular loop, (in A-m) will be, 4m, π, , 10 A solid sphere of mass M and radius R is, , (b) 400 m, (d) 300 m, , 7 Light is incident normally on a, , (a), , 57, , (b), , 3m, π, , (c), , 2m, π, , (d), , m, π, , y, , t(s), 1, , 2, , (b) 0, y, , t(s), 1, , 2, , (c) 0, , y, , t(s), 1, , 2, , 9 A 2 mW laser operates at a wavelength of, 500 nm. The number of photons that will, be emitted per second is, [Given, Planck’s constant, h = 6.6 × 10− 34 Js, speed of light, c = 3.0 × 108 m / s], (a) 1 × 1016, (c) 1.5 × 1016, , (b) 5 × 1015, (d) 2 × 1016, , (d) 0, , t(s), 1, , 2, , 12 A source of sound S is moving with a, velocity of 50 m/s towards a stationary, observer. The observer measures the
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58, , ONLINE, , JEE Main 2019 ~ Solved Paper, A, , frequency of the source as 1000 Hz. What, will be the apparent frequency of the, source when it is moving away from the, observer after crossing him? (Take,, velocity of sound in air is 350 m/s), (a) 807 Hz, (c) 750 Hz, , 1 cm, , (b) 1143 Hz, (d) 857 Hz, , 13 A cubical block of side 0.5 m floats on, water with 30% of its volume under, water. What is the maximum weight that, can be put on the block without fully, submerging it under water?, [Take, density of water = 103 kg / m3 ], (a) 30.1 kg, (c) 87.5 kg, , (b) 46.3 kg, (d) 65.4 kg, , 14 In the formula X = 5YZ , X and Z have, dimensions of capacitance and magnetic, field, respectively. What are the, dimensions of Y in SI units?, (b) [M − 2L0 T− 4A − 2], (d) [M − 2L− 2 T6A3 ], , 15 In a Young’s double slit experiment, the, ratio of the slit’s width is 4 : 1. The ratio of, the intensity of maxima to minima, close, to the central fringe on the screen, will be, (a) 4 : 1, (c) 9 : 1, , (b) 25 : 9, (d) ( 3 + 1)4 : 16, , 16 The graph shows how the magnification, m produced by a thin lens varies with, image distance v. What is the focal length, of the lens used?, m, , ρ, 2π, ρ, (c), 2π, , 1 1, + , a b, 1 1, − , a b, , ρ, 4π, ρ, (d), 4π, (b), , 1 1, − , a b, 1 1, + , a b, , 19 A bullet of mass 20 g has an initial speed, , of 1 ms− 1, just before it starts penetrating, a mud wall of thickness 20 cm. If the wall, offers a mean resistance of 2.5 × 10− 2N,, the speed of the bullet after emerging, from the other side of the wall is close to, , (a) 0.3 ms − 1, (c) 0.1 ms − 1, , (b) 0.4 ms − 1, (d) 0.7 ms − 1, , 20 The magnitude of the magnetic field at, the centre of an equilateral triangular, loop of side 1 m which is carrying a, current of 10 A is, [Take, µ 0 = 4π × 10− 7 NA − 2], (b) 1 µT, , (c) 3 µT, , (d) 18 µT, , 21 In an experiment, brass and steel wires of, , a, 2, , bc, a, , spheres of radii a and b ( b > a ) is filled, with a medium of resistivity ρ. The, resistance between the two spheres will be, , (a) 9 µT, , c, , (a), , (b) 2.0 × 10− 5 N -m, (d) 7.9 × 10− 6 N -m, , 18 Space between two concentric conducting, , (a), , 2, , (a) [M − 1L− 2 T4A 2], (c) [M − 3 L− 2 T8A 4 ], , B, , (a) 4.0 × 10− 6 N -m, (c) 1.6 × 10− 5 N -m, , (b), , b, ac, , v, , b, , 2, , (c), , a, c, , (d), , b, c, , 17 A metal coin of mass 5g and radius 1 cm is, fixed to a thin stick AB of negligible mass, as shown in the figure. The system is, initially at rest. The constant torque, that, will make the system rotate about AB at, 25 rotations per second in 5s, is close to, , length 1 m each with areas of, cross-section 1 mm 2 are used. The wires, are connected in series and one end of the, combined wire is connected to a rigid, support and other end is subjected to, elongation. The stress requires to produce, a net elongation of 0.2 mm is, [Take, the Young’s modulus for steel and, brass are respectively 120 × 109 N / m 2 and, 60 × 109 N / m 2], (a) 1.2 × 106 N /m2, (c) 1.8 × 106 N /m2, , (b) 0.2 × 106 N /m2, (d) 4.0 × 106 N /m2
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APRIL ATTEMPT ~ 10 April 2019, Shift II, 22 A coil of self inductance 10 mH and, , 59, 25 When heat Q is supplied to a diatomic, , resistance 01, . Ω is connected through a, switch to a battery of internal resistance, 0.9 Ω. After the switch is closed, the time, taken for the current to attain 80% of the, saturation value is [Take, ln 5 = 1.6], , gas of rigid molecules, at constant, volume, its temperature increases by ∆T ., The heat required to produce the same, change in temperature, at a constant, pressure is, , (a) 0.002 s, (c) 0.103 s, , 2, Q, 3, 3, (c) Q, 2, , (b) 0.324 s, (d) 0.016 s, , (a), , 23 The figure represents a voltage regulator, circuit using a Zener diode. The breakdown, voltage of the Zener diode is 6 V and the, load resistance is RL = 4 kΩ. The series, resistance of the circuit is Ri = 1 kΩ. If the, battery voltage V B varies from 8V to 16V,, what are the minimum and maximum, values of the current through Zener diode?, Ri, , (b) 1 mA, 8.5 mA, (d) 0.5 mA, 6 mA, , 24 A simple pendulum of length L is placed, between the plates of a parallel plate, capacitor having electric field E, as shown, in figure. Its bob has mass m and charge, q. The time period of the pendulum is, given by, +, +, +, +, +, +, +, +, +, +, +, , –, –, L –, –, –, m –, –, q, –, –, –, –, , L, qE , g2 + , , m, L, qE , , , g +, , m, , 2, , (b) 2π, , downwards with an initial speed of, 1.0 ms− 1. The cross-sectional area of the, tap is 10− 4 m 2. Assume that the pressure, is constant throughout the stream of, water and that the flow is streamlined., The cross-sectional area of the stream,, 0.15 m below the tap would be, [Take, g = 10 ms− 2], (b) 1 × 10− 5 m2, (d) 5 × 10− 5 m2, , 28 In Li++ , electron in first Bohr orbit is, , L, g2 −, , (d) 2π, , 1 p0V 0, 4 R, 5 p0V 0, (d), 4 R, (b), , 27 Water from a tap emerges vertically, , (a) 2 × 10− 5 m2, (c) 5 × 10− 4m2, , E, , (c) 2π, , a process, where pressure and volume, 2, , 1 V , obey the relation p = p0 1 − 0 ., 2V , , , Here, p0 and V 0 are constants. Calculate, the change in the temperature of the, gas, if its volume changes from V 0 to 2V 0., 1 p0V 0, 2 R, 3 p0V 0, (c), 4 R, , RL, , (a) 1.5 mA, 8.5 mA, (c) 0.5 mA, 8.5 mA, , (a) 2π, , 26 One mole of an ideal gas passes through, , (a), , √B, , 5, Q, 3, 7, (d) Q, 5, (b), , q2E 2, m2, , L, qE , , , g −, , m, , excited to a level by a radiation of, wavelength λ. When the ion gets, de-excited to the ground state in all, possible ways (including intermediate, emissions), a total of six spectral lines, are observed. What is the value of λ?, [Take, h = 6.63 × 10− 34 Js;, c = 3 × 108 ms− 1], (a) 9.4 nm, (c) 10.8 nm, , (b) 12.3 nm, (d) 11.4 nm
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60, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 29 The elastic limit of brass is 379 MPa., What should be the minimum diameter of, a brass rod, if it is to support a 400 N, load without exceeding its elastic limit?, (a), (b), (c), (d), , 0.90 mm, 1.00 mm, 1.16 mm, 1.36 mm, , 30 Two radioactive substances A and B have, decay constants 5 λ and λ, respectively., Att = 0, a sample has the same number of, the two nuclei. The time taken for the, ratio of the number of nuclei to become, 2, 1, will be, e, (a) 2 / λ, , (b) 1 / 2 λ (c) 1 / 4 λ, , (d) 1 / λ, , CHEMISTRY, NH2, , 1 The correct statement is, (a) zone refining process is used for the, refining of titanium., (b) zincite is a carbonate ore., (c) sodium cyanide cannot be used in the, metallurgy of silver., (d) aniline is a froth stabiliser., , 2 For the reaction of H 2 with I2, the rate, , constant is 2.5 × 10− 4 dm3 mol− 1s− 1 at, 327ºC and 1.0 dm3 mol− 1 s− 1 at 527ºC. The, activation energy for the reaction, in, kJ mol− 1 is (R = 8.314 JK − 1 mol− 1), , (a) 59, (c) 150, , (b) 72, (d) 166, , 3 In chromatography, which of the, , NH2, , (c), , O, , (d), Ph, , O, , Ph, , 5 The correct option among the following is, (a) colloidal medicines are more effective,, because they have small surface area., (b) brownian motion in colloidal solution is, faster if the viscosity of the solution is, very high., (c) addition of alum to water makes it unfit, for drinking., (d) colloidal particles in lyophobic sols can, be precipitated by electrophoresis., , 6 The highest possible oxidation states of, , following statements is incorrect for R f ?, , uranium and plutonium, respectively, are, , (a) Rf value depends on the type of, chromatography, (b) Higher Rf value means higher, adsorption, (c) Rf value is dependent on the mobile, phase, (d) The value of Rf can not be more than one, , (a) 7 and 6, (c) 6 and 4, , between molar conductivity (Λ m ) versus, C is correct?, Cl, , (a) Λm, , KC, l, , (b) Λm, , CH3, , Ph, , NaOCl, , (i) SOCl2, , X, , (ii) Aniline, , Y, √C, , O, , √C, l, KC, , O, Ph, , N, , (b), , Ph, , (c) Λm, , (d) Λm, , Na, , l, KC, Cl, , O, , HN, , Na, , (a), , Cl, Na, l, KC, , reaction is, , 7 Which one of the following graphs, , Na, , 4 The major product Y in the following, , (b) 6 and 7, (d) 4 and 6, , √C, , √C, , Cl
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APRIL ATTEMPT ~ 10 April 2019, Shift II, 8 Points I, II and III in the following plot, respectively correspond to (V mp : most, probable velocity), , 61, (a), (b), (c), (d), , baking soda and soda ash, washing soda and soda ash, baking soda and dead burnt plaster, washing soda and dead burnt plaster, , Distribution function f( v), , 12 Air pollution that occurs in sunlight is, (a), (b), (c), (d), , acid rain, oxidising smog, fog, reducing smog, , 13 The incorrect statement is, I, , II, , III, , Speed, v, , (a) vmp of H2(300 K ); vmp of N2(300 K); vmp of, O2(400 K), (b) vmp of O2(400 K ); vmp of N2(300 K); vmp of, H2(300 K), (c) vmp of N2(300 K); vmp of O2(400 K ); vmp of, H2(300 K), (d) vmp of N2(300 K); vmp of H2(300 K); vmp of, O2(400 K), , 9 The major product Y in the following, reaction is, Cl, , EtONa, Heat, , X, , HBr, , Y, , Br, (a) Br, , (b), , (c), , (d), , HO, , Br, , (a) the gemstone, ruby, has Cr3 + ions, occupying the octahedral sites of beryl, (b) the color of [CoCl(NH3 )5 ]2 + is violet as it, absorbs the yellow light, (c) the spin only magnetic moments of, Fe(H2O)6 ]2 + and [Cr(H2O)6 ]2 + are nearly, similar, (d) the spin only magnetic moment of, [Ni(NH3 )4 (H2O)2]2 + is 2.83 BM, , 14 For the reaction,, 2SO2( g) + O2( g) → 2SO3 ( g),, ∆H = − 57.2 kJ mol− 1 and K c = 1.7 × 1016., Which of the following statement is, incorrect?, (a) The equilibrium constant decreases as, the temperature increases, (b) The addition of inert gas at constant, volume will not affect the equilibrium, constant, (c) The equilibrium will shift in forward, direction as the pressure increases, (d) The equilibrium constant is large, suggestive of reaction going to, completion and so no catalyst is required, , 15 The ratio of the shortest wavelength of, , enthalpies is, , two spectral series of hydrogen spectrum, is found to be about 9. The spectral series, are, , (a), (b), (c), (d), , (a), (b), (c), (d), , 10 The correct order of the first ionisation, Mn < Ti < Zn < Ni, Ti < Mn < Zn < Ni, Zn < Ni < Mn < Ti, Ti < Mn < Ni < Zn, , 11 A hydrated solid X on heating initially, gives a monohydrated compound Y ., Y upon heating above 373 K leads to an, anhydrous white powder Z. X and Z,, respectively, are, , Lyman and Paschen, Brackett and Pfund, Paschen and Pfund, Balmer and Brackett, , 16 Number of stereo-centers present in, linear and cyclic structures of glucose are, respectively, (a) 4 and 5, (c) 5 and 4, , (b) 4 and 4, (d) 5 and 5
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62, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 17 Compound A(C9 H10O) shows positive, , 22 The number of pentagons in C60 and, , iodoform test. Oxidation of A with, KMnO4 / KOH gives acid B(C8H 6O4 )., Anhydride of B is used for the, preparation of phenolphthalein., Compound A is, , trigons (triangles) in white phosphorus,, respectively, are, (a) 20 and 3, (c) 20 and 4, , 23 The increasing order of nucleophilicity of, , O, CH2, , C, , (a), , the following nucleophiles is, H, , CH3, (b), , CH3, O, , CH3, CH3, , CH3, (c), , CH3, , (d), O, , O, , 18 1 g of a non-volatile, non-electrolyte, solute is dissolved in 100 g of two, different solvents A and B, whose, ebullisocopic constants are in the ratio of, 1 : 5. The ratio of the elevation in their, ∆Tb( A), boiling points,, , is, ∆Tb( B), (a) 5 : 1, (c) 1 : 5, , (b) 10 : 1, (d) 1 : 0.2, , 19 The pH of a 0.02 M NH 4Cl solution will be, [Given K b(NH 4OH) = 10−5, and log 2 = 0.301], , (a) 4.65, (c) 5.35, , (b) 2.65, (d) 4.35, , 20 The difference between ∆H and ∆U, , ( ∆H − ∆U ), when the combustion of one, mole of heptane (l) is carried out at a, temperature T, is equal to, (a) − 4 RT, (c) 4 RT, , (b) 3 RT, (d) − 3 RT, , 21 Which of the following is not a correct, method of the preparation of benzylamine, from cyanobenzene?, (a), (b), (c), (d), , (b) 12 and 4, (d) 12 and 3, , H2 / Ni, (i) HCl / H2O (ii) NaBH4, (i) LiAlH4 (ii) H3 O+, (i) SnCl2 + HCl(gas) (ii) NaBH4, , (1) CH3CO¨2, , (2) H2O, , (3), , CH3SO3¨, , (4) O H, , (a), (b), (c), (d), , (1) < (4) < (3) < (2), (2) < (3) < (1) < (4), (4) < (1) < (3) < (2), (2) < (3) < (4) < (1), , ¨, , 24 Which of these factors does not govern, the stability of a conformation in acyclic, compounds?, (a), (b), (c), (d), , Electrostatic forces of interaction, Torsional strain, Angle strain, Steric interactions, , 25 The correct match between Item-I and, Item-II is, Item-I, A. High density, polythene, , Item-II, I., , Peroxide catalyst, , B. Polyacrylonitrile II. Condensation at high, temperature and, pressure, C. Novolac, , III. Ziegler-Natta catalyst, , D. Nylon-6, , IV. Acid or base catalyst, , Codes, A B C D, (a) III I IV II, (c) II IV I III, , A, (b) IV, (d) III, , B, II, I, , C, I, II, , D, III, IV, , 26 The minimum amount of O2( g) consumed, per gram of reactant is for the reaction, (Given atomic mass : Fe = 56, O = 16,, Mg = 24, P = 31, C = 12, H = 1), (a) C3 H8 ( g ) + 5O2( g ) → 3CO2( g ) + 4H2O(l), (b) P4 (s) + 5O2( g ) → P4O10 (s), (c) 4Fe(s) + 3O2( g ) → 2Fe2O3 (s), (d) 2Mg (s) + O2( g ) → 2MgO(s)
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APRIL ATTEMPT ~ 10 April 2019, Shift II, 27 The correct statements among (a) to (d) are:, 1. Saline hydrides produce H2 gas when, reacted with H2O., 2. Reaction of LiAlH4 with BF3 leads to, B2H6., 3. PH3 and CH4 are electron rich and, electron precise hydrides, respectively., 4. HF and CH4 are called as molecular, hydrides., (a) (1), (2), (3) and (4), (b) (1), (2) and (3) only, (c) (3) and (4) only, (d) (1), (3) and (4) only, , 28 The major product obtained in the given, reaction is, CH3, , O, , CH2, , CH2, , CH, , AlCl3, , CH3, , Product, , (b) H3C, , CH, , O, CH2, , (c) H3C, , CH3, , CH, , O, , CH3, , (d) H3C, , CH2, , O, , CH, , CH2, , CH2, , 29 The noble gas that does not occur in the, atmosphere is, (a) Ra, (c) He, , (b) Kr, (d) Ne, , 30 The crystal field stabilisation energy, (CFSE) of [Fe(H 2O)6 ]Cl2 and K 2 [NiCl4 ],, respectively, are, , Cl, CH3, (a) CH3, , 63, , (a), (b), (c), (d), , O, , − 0.4 ∆ o and − 1.2 ∆ t, − 0.4 ∆ o and − 0.8 ∆ t, − 2.4 ∆ o and − 1.2 ∆ t, − 0.6 ∆ o and − 0.8 ∆ t, , MATHEMATICS, 1 The integral ∫, , π /3, , π /6, , sec 2/ 3 x cosec4/ 3 x dx is, , equal to, (a) 35/ 6 − 32/ 3, (c) 35/3 − 31/3, , (b) 37/ 6 − 35/ 6, (d) 34/3 − 31/3, , 2 The sum of series, 13 + 23 13 + 23 + 33, +, + ..., 1+ 2, 1+ 2+ 3, 13 + 23 + 33 + K + 153 1, +, − (1 + 2 + 3 + K + 15), 1 + 2 + 3 + K + 15, 2, is equal to, 1+, , (a) 620, (c) 1240, , (b) 660, (d) 1860, , 3 The area (in sq units) of the region, bounded by the curves y = 2x and, y =| x + 1|, in the first quadrant is, , 3, 2, 1, (c), 2, , (a), , (b) log e 2 +, (d), , 3, 2, , 3, 1, −, 2 log e 2, , 4 If 5x + 9 = 0 is the directrix of the, hyperbola 16x 2 − 9 y 2 = 144, then its, corresponding focus is, 5 , (a) − , 0, 3 , 5 , (c) , 0, 3 , , (b) (− 5, 0), (d) (5, 0), , 5 The locus of the centres of the circles,, which touch the circle, x 2 + y 2 = 1, externally, also touch the Y-axis and lie, in the first quadrant, is, (a) y = 1 + 2x, x ≥ 0 (b) y = 1 + 4x, x ≥ 0, (c) x = 1 + 2 y, y ≥ 0 (d) x = 1 + 4 y, y ≥ 0, , 6 The tangent and normal to the ellipse, 3x 2 + 5 y 2 = 32 at the point P( 2, 2) meets, the X-axis at Q and R, respectively. Then,, the area (in sq units) of the ∆PQR is, (a), , 16, 3, , (b), , 14, 3, , (c), , 34, 15, , (d), , 68, 15
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64, , ONLINE, , 7 If the tangent to the curve y =, , x, , ,, x −3, x ∈ R, ( x ≠ ± 3 ), at a point (α , β ) ≠ ( 0, 0) on, it is parallel to the line 2x + 6 y − 11 = 0,, then, 2, , (a) |6α + 2β | = 19, (b) |6α + 2β | = 9, (c) |2α + 6β | = 19, (d) |2α + 6β | = 11, x→1, , x − ax + b, = 5, then a + b is equal, x−1, , to, (a) − 4, (c) − 7, , (b) 1, (d) 5, , 9 Suppose that 20 pillars of the same, height have been erected along the, boundary of a circular stadium. If the top, of each pillar has been connected by, beams with the top of all its non-adjacent, pillars, then the total number of beams is, (a) 180, (c) 170, , (b) 210, (d) 190, , 10 Let λ be a real number for which the, system of linear equations, x + y + z = 6, 4x + λy − λz = λ − 2 and, 3x + 2 y − 4z = − 5, has infinitely many solutions. Then λ is a, root of the quadratic equation, (a) λ − 3λ − 4 = 0, (c) λ2 − λ − 6 = 0, 2, , (b) λ + 3λ − 4 = 0, (d) λ2 + λ − 6 = 0, 2, , 11 The angles A, B and C of a ∆ABC are in, AP and a : b = 1 : 3. If c = 4 cm, then the, area (in sq cm) of this triangle is, (a), , 2, 3, , (c) 2 3, , (b) 4 3, (d), , 4, 3, , 12 The distance of the point having position, $ from the straight line, vector − i$ + 2$j + 6k, passing through the point ( 2, 3, − 4) and, $ is, parallel to the vector, 6$i + 3$j − 4k, (a) 2 13, (c) 6, , 13 If cos− 1 x − cos− 1, , y, = α, where − 1 ≤ x ≤ 1,, 2, , y, , then for all x , y,, 2, 4x 2 − 4xy cosα + y 2 is equal to, − 2 ≤ y ≤ 2, x ≤, , (a) 2 sin 2 α, (c) 4 sin 2 α, , (b) 4 cos 2 α + 2x2y2, (d) 4 sin 2 α − 2x2y2, , 14 If both the mean and the standard, , 2, , 8 If lim, , JEE Main 2019 ~ Solved Paper, , (b) 4 3, (d) 7, , deviation of 50 observations x1 , x2 , K , x50, are equal to 16, then the mean of ( x1 − 4)2,, ( x2 − 4)2 , K , ( x50 − 4)2 is, (a) 480, (c) 380, , (b) 400, (d) 525, , 15 If the plane 2x − y + 2z + 3 = 0 has the, 1, 2, and units from the planes, 3, 3, 4x − 2 y + 4z + λ = 0 and, 2x − y + 2z + µ = 0, respectively, then the, maximum value of λ + µ is equal to, distances, , (a) 13, , (b) 15, , (c) 5, , (d) 9, , 16 The sum of the real roots of the equation, x, 2, −3, , −6, −1, − 3x x − 3 = 0, is equal to, x+2, , 2x, , (a) 0, , (b) − 4, , (c) 6, , (d) 1, , 17 Lines are drawn parallel to the line, 3, from the, 5, origin. Then which one of the following, points lies on any of these lines?, 4x − 3 y + 2 = 0, at a distance, , 2, 1, (a) − , − , 4, 3, 1, 1, , , (c) , − , 4, 3, , 1 2, (b) − , , 4 3, 1 1, (d) , , 4 3, , 18 A perpendicular is drawn from a point on, x−1 y+1 z, = to the plane, =, 2, 1, −1, x + y + z = 3 such that the foot of the, perpendicular Q also lies on the plane, x − y + z = 3. Then, the coordinates of Q, are, the line, , (a) (− 1, 0, 4), (c) (2, 0, 1), , (b) (4, 0, − 1), (d) (1, 0, 2)
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APRIL ATTEMPT ~ 10 April 2019, Shift II, 19 Let f ( x ) = loge (sin x ), ( 0 < x < π ) and, , 25 The negation of the boolean expression, , g( x ) = sin− 1( e− x ), ( x ≥ 0). If α is a positive, real number such that a = ( fog)′ (α ) and, b = ( fog)(α ), then, , (a), (b), (c), (d), , aα 2 − bα − a = 0, aα 2 − bα − a = 1, aα 2 + bα − a = − 2α 2, aα 2 + bα + a = 0, , (a), , 1, 2, , 2, , (b) 2, 2, , (c), , 2, , (d), , 1, 2, , 2, , 21 If ∫ x5 e− x dx = g ( x )e− x + C, where C is a, constant of integration, then g( − 1) is, equal to, , (a) − 1, 1, (c) −, 2, , 5, (d) −, 2, , (b), , 2, 3, , (c), , 3, 2, , (d), , 6, 5, , 23 If z and w are two complex numbers such, π, that| zw| = 1 and arg( z ) − arg( w) = ,, 2, then, , (a) zw = − i, (c) zw = i, , 1−i, 2, −1 + i, (d) zw =, 2, , (b) zw =, , 24 A spherical iron ball of radius 10 cm is, coated with a layer of ice of uniform, thickness that melts at a rate of, 50 cm3 /min. When the thickness of the ice, is 5 cm, then the rate at which the thickness, (in cm/min) of the ice decreases, is, 1, 9π, 1, (c), 36 π, , (a), , 1, 18 π, 5, (d), 6π, , (b) 6, (d) 5, , 27 The smallest natural number n, such that, the coefficient of x in the expansion of, n, 2 1, n, x + 3 is C23 , is, , x , (a) 35, (c) 58, , (b) 23, (d) 38, , 28 The number of real roots of the equation, (a) 1, (c) 4, , Then, the common difference of this AP,, which maximises the product a1 , a4 , a5 , is, 8, 5, , (a) 8, (c) 7, , 5 +| 2x − 1| = 2x ( 2x − 2) is, , (b) 1, , 22 Let a1 , a2 , a3 ,K be an AP with a6 = 2., , (a), , (b) ~ s ∧ ~ r, (d) r, , must be tossed so that the probability of, getting atleast one head is more than, 99% is, , curves x + y = 1 and y = 4 2x, then| c|, is equal to, 2, , ~ s ∨ (~ r ∧ s) is equivalent to, , (a) s ∧ r, (c) s ∨ r, , 26 Minimum number of times a fair coin, , 20 If the line ax + y = c, touches both the, 2, , 65, , (b) 3, (d) 2, , 29 Let y = y( x ) be the solution of the, differential equation,, dy, π π, + y tan x = 2x + x 2 tan x, x ∈ − , ,, 2 2, dx, such that y( 0) = 1. Then, , π, π, (a) y ′ − y ′ − = π − 2, 4, 4, π, , π, (b) y ′ + y ′ − = − 2, 4, 4, 2, π, π π, (c) y + y − =, +2, 4, 4, 2, π, π, (d) y − y − = 2, 4, 4, , 30 Let a , b and c be in GP with common ratio, 1, r, where a ≠ 0 and 0 < r ≤ . If, 2, 3a, 7b and 15c are the first three terms of, an AP, then the 4th term of this AP is, (a) 5a, , (b), , (c) a, , 2, a, 3, 7, (d) a, 3, (b)
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66, , ONLINE, , JEE Main 2019 ~ Solved Paper, , Answers, Physics, 1. (b), 11. (a), 21. (*), , 2. (b), 12. (c), 22. (d), , 3. (c), 13. (c), 23. (c), , 4. (a), 14. (c), 24. (a), , 5. (d), 15. (c), 25. (d), , 6. (d), 16. (d), 26. (d), , 7. (d), 17. (b), 27. (d), , 8. (a), 18. (b), 28. (c), , 9. (b), 19. (d), 29. (c), , 10. (d), 20. (d), 30. (b), , 3. (b), 13. (a), 23. (b), , 4. (b), 14. (d), 24. (c), , 5. (d), 15. (a), 25. (a), , 6. (b), 16. (a), 26. (b), , 7. (c), 17. (c), 27. (a), , 8. (c), 18. (c), 28. (c), , 9. (b), 19. (c), 29. (a), , 10. (d), 20. (a), 30. (b), , 3. (d), 13. (c), 23. (a), , 4. (b), 14. (b), 24. (b), , 5. (a), 15. (a), 25. (a), , 6. (d), 16. (a), 26. (c), , 7. (a), 17. (b), 27. (d), , 8. (c), 18. (c), 28. (a), , 9. (c), 19. (b), 29. (a), , 10. (c), 20. (c), 30. (c), , Chemistry, 1. (d), 11. (b), 21. (b), , 2. (d), 12. (b), 22. (b), , Mathematics, 1. (b), 11. (c), 21. (d), , 2. (a), 12. (d), 22. (a), , Note (*) None of the option is correct., , For Detailed Solutions Visit : http://tinyurl.com/yyfybsoy Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (12 April, 2019), TIME 9:30-12:30 (Shift I), , MM : 360, , PHYSICS, 1 A shell is fired from a fixed artillery gun, , In this case,, , with an initial speed u such that it hits, the target on the ground at a distance R, from it. If t1 and t2 are the values of the, time taken by it to hit the target in two, possible ways, the product t1t2 is, R, 4g, R, (c), 2g, (a), , R, g, 2R, (d), g, , p, , (b), , 2 The trajectory of a projectile near the, surface of the earth is given as, y = 2x − 9x 2., If it were launched at an angle θ 0 with, speed v0, then (Take, g = 10 ms −2), 5, 1, (a) θ 0 = sin −1 and v0 = ms −1, 5, 3, 3, −1 2 , (b) θ 0 = cos and v0 = ms −1, 5, 5, 5, −1 1 , (c) θ 0 = cos and v0 = ms −1, 5, 3, 2, 3, , , (d) θ 0 = sin −1 and v0 = ms −1, 5, 5, , 3 Shown in the figure is a shell made of a, conductor. It has inner radius a and outer, radius b and carries charge Q. At its, centre is a dipole p as shown., , (a) surface charge density on the inner, Q, , 2, surface is uniform and equal to, 4 πa 2, (b) electric field outside the shell is the same, as that of a point charge at the centre of, the shell, (c) surface charge density on the outer, surface depends on p, (d) surface charge density on the inner, surface of the shell is zero everywhere, , 4 When M1 gram of ice at −10°C (specific, , heat = 0.5 cal g −1°C −1) is added to, M 2 gram of water at 50°C, finally no ice, is left and the water is at 0°C. The value, of latent heat of ice, in cal g −1 is, , 50M 2, −5, M1, 50M 2, (c), M1, , (a), , 50M1, − 50, M2, 5M 2, (d), −5, M1, (b)
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68, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 5 The truth table for the circuit given in the, , 3.0, , figure is, 2.0, Y, , A, B, , A B Y, , V0, , 1.0, , A B Y, , 0, , 0, , 1, , 1, , 1, , 1, , 0, (b) 0, , 0, , (a) 0, , 1, , 0, , 1, , 0, , 1, , 1, , 0, , 0, , 1 1 1, A B Y, 0 0 1, (c) 0 1 1, 1 0 0, 1 1 0, , 1 1 0, A B Y, 0 0 0, (d) 0 1 0, 1 0 1, 1 1 1, , 6 A circular disc of radius b has a hole of, radius a at its centre (see figure). If the, mass per unit area of the disc varies as, σ0, , then the radius of gyration of the, r , disc about its axis passing through the, centre is, , 2, , 4, , 6, 8, ν(1014Hz), , (a) 1.82 eV, (c) 1.95 eV, , (b) 1.66 eV, (d) 2.12 eV, , 8 A uniform rod of length l is being rotated, in a horizontal plane with a constant, angular speed about an axis passing, through one of its ends. If the tension, generated in the rod due to rotation is, T ( x ) at a distance x from the axis, then, which of the following graphs depicts it, most closely?, T(x), , T(x), , (a), , (b), l, , b, , x, , l, , T(x), , x, , T(x), , (c), , a, , 10, , (d), l, , x, l, , x, , 9 To verify Ohm’s law, a student connects, (a), , a + b + ab, 2, , (b), , a+b, 2, , (c), , a 2 + b2 + ab, 3, , (d), , a+b, 3, , 2, , 2, , the voltmeter across the battery as shown, in the figure. The measured voltage is, plotted as a function of the current and, the following graph is obtained, V, , 7 The stopping potential V 0 (in volt) as a, function of frequency ( ν ) for a sodium, emitter, is shown in the figure. The work, function of sodium, from the data plotted, in the figure, will be, (Take, Planck’s constant ( h ) = 6.63 × 10−34, J-s, electron charge, e = 1.6 × 10−19 C], , Internal, resistance, Ammeter, , R
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APRIL ATTEMPT ~ 12 April 2019, Shift I, V, , 69, 13 At 40°C, a brass wire of 1 mm radius is, , 1.5V, , hung from the ceiling. A small mass M is, hung from the free end of the wire. When, the wire is cooled down from 40°C to, 20°C, it regains its original length of 0.2, m. The value of M is close to, , V0, , I, , 1000 mA, , If V 0 is almost zero, then identify the, correct statement., (a) The emf of the battery is 1.5 V and its, internal resistance is 1.5 Ω, (b) The value of the resistance R is 1.5 Ω, (c) The potential difference across the, battery is 1.5 V when it sends a current, of 1000 mA, (d) The emf of the battery is 1.5 V and the, value of R is 1.5 Ω, , 10 A thin ring of 10 cm radius carries a, uniformly distributed charge. The ring, rotates at a constant angular speed of, 40π rad s −1 about its axis, perpendicular, to its plane. If the magnetic field at its, centre is 3.8 × 10−9 T, then the charge, carried by the ring is close to, (µ 0 = 4π × 10−7 N/A 2)., (a) 2 × 10−6 C, (c) 4 × 10−5 C, , (b) 3 × 10−5 C, (d) 7 × 10−6 C, , [Coefficient of linear expansion and, Young’s modulus of brass are 10−5 /°C and, 1011 N/m 2 respectively, g = 10 ms −2], (a) 9 kg, (c) 1.5 kg, , 14 A galvanometer of resistance 100 Ω has, 50 divisions on its scale and has, sensitivity of 20 µA/division. It is to be, converted to a voltmeter with three, ranges of 0-2 V, 0-10 V and 0-20 V. The, appropriate circuit to do so is, G, , $ + 3$j, − 4k, (b) s$ =, 5, $, 4$j − 3k, (d) s$ =, 5, , 30 times per minute at a place, where the, dip is 45° and 40 times per minute, where, the dip is 30°. If B1 and B2 are, respectively, the total magnetic field due, to the earth at the two places, then the, B, ratio 1 is best given by, B2, (b) 0.7, , R3, R1 = 2000 Ω, R2 = 8000 Ω, 10 V, , G, R1, , R2, , R3, , R2, , 10 V, R3, , (b), 2V, G, , R1, , R3 = 10000 Ω, 20 V, , R1 = 1900 Ω, R2 = 9900 Ω, R3 = 19900 Ω, 20 V, R1 = 1900 Ω, R2 = 8000 Ω, , (c), 2V, , G, , R1, , 10 V, , R2, , R3, , (d), 20 V, , 10 V, , R3 = 10000 Ω, 20 V, , R1 = 19900 Ω, R2 = 9900 Ω, R3 = 1900 Ω, 2V, , 15 A progressive wave travelling along the, , 12 A magnetic compass needle oscillates, , (a) 1.8, , R2, , 2V, , by the electric field, , 3$i − 4$j, (a) s$ =, 5, $, − 3$j + 4k, , (c) s$ = , 5, , , , R1, , (a), , 11 An electromagnetic wave is represented, $ sin[ωt + ( 6 y − 8z )]. Taking unit, E = E0 n, vectors in x , y and z- directions to be, $ the direction of propagation s$ , is, $i, $j, k,, , (b) 0.5 kg, (d) 0.9 kg, , (c) 3.6, , (d) 2.2, , positive x-direction is represented by, y( x , t ) = A sin ( kx − ωt + φ ). Its snapshot at, t = 0 is given in the figure., y, A, x
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70, , ONLINE, For this wave, the phase φ is, , π, (a) −, 2, , (b) π, , π, (d), 2, , (c) 0, , (a) 2.5 × 104 , 2.5 × 106 (b) 5 × 104 , 5 × 106, (c) 5 × 104 , 5 × 105, (d) 5 × 104 , 2.5 × 106, , 20 Which of the following combinations has, , 16 The value of numerical aperture of the, , the dimension of electrical resistance, (ε 0 is the permittivity of vacuum and µ 0 is, the permeability of vacuum)?, , objective lens of a microscope is 1.25. If, light of wavelength 5000Å is used, the, minimum separation between two points,, to be seen as distinct, will be, (a) 0.24 µm, (c) 0.12 µm, , (c), , origin. The potential and electric field due, to this dipole on the Y-axis at a distance d, are, respectively [Take, V = 0 at infinity], p, , (a), , ,, , p, 4πε 0d3, , 4πε 0d, p, (c) 0,, 4πε 0d3, 2, , (a), , (b) 0.38 µm, (d) 0.48 µm, , $ is kept at the, 17 A point dipole p = − p0 x, , µ0, ε0, ε0, µ0, , µ0, ε0, ε, (d) 0, µ0, (b), , 21 A sample of an ideal gas is taken through, the cyclic process abca as shown in the, figure. The change in the internal energy, of the gas along the path ca is −180 J. The, gas absorbs 250 J of heat along the path, ab and 60 J along the path bc. The work, done by the gas along the path abc is, , −p, 4πε 0d3, p, −p, (d), ,, 4πε 0d 2 4πε 0d3, (b) 0,, , 18 The resistive network shown below is, , c, , p, , connected to a DC source of 16 V. The, power consumed by the network is 4 W., The value of R is, 4R, , JEE Main 2019 ~ Solved Paper, , a, , b, , 6R, R, , V, , R, , 4R, , (a) 120 J, (c) 100 J, , 12 R, , (b) 130 J, (d) 140 J, , 22 The figure shows a square loop L of side, 5 cm which is connected to a network of, resistances. The whole setup is moving, towards right with a constant speed of, 1 cm s −1. At some instant, a part of L is in, a uniform magnetic field of 1 T,, perpendicular to the plane of the loop., If the resistance of L is 1.7 Ω, the current, in the loop at that instant will be close to, , E = 16 V, , (a) 6 Ω, , (b) 8 Ω, , (c) 1 Ω, , (d) 16 Ω, , 19 The transfer characteristic curve of a, transistor, having input and output, resistance 100 Ω and 100 kΩ respectively,, is shown in the figure. The voltage and, power gain, are respectively, , v=1 cm/s, , (400, 20), , L, 1Ω, , (300, 15), Ic, (mA), , A, , B, , 1Ω, , (200, 10), 5 cm, , (100, 5), Ib (µA), , (a) 60 µA, (c) 150 µA, , (b) 170 µA, (d) 115 µA, , B, , 2Ω, , 3Ω, D, , C, 2Ω
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APRIL ATTEMPT ~ 12 April 2019, Shift I, , 71, , 23 Two identical parallel plate capacitors of, capacitance C each, have plates of area A,, separated by a distance d. The space, between the plates of the two capacitors,, is filled with three dielectrics of equal, thickness and dielectric constants K 1 , K 2, and K 3 ., The first capacitor is filled as shown in, Fig. I, and the second one is filled as, shown in Fig. II. If these two modified, capacitors are charged by the same, potential V , the ratio of the energy stored, in the two, would be (E1 refers to, capacitor (I) and E2 to capacitor (II)) :, K1, K2, , K1, , K2, , K3, , K3, (I), , (II), , E, K1 K 2K 3, (a) 1 =, E2 (K1 + K 2 + K 3 )(K 2K 3 + K 3K1 + K1 K 2 ), , (b), , (K1 + K 2 + K 3 )(K 2K 3 + K 3K1 + K1 K 2 ), E1, =, E2, K1 K 2K 3, , (c), , 9 K1 K 2K 3, E1, =, E2 (K1 + K 2 + K 3 )(K 2K 3 + K 3K1 + K1 K 2 ), , (d), , (K1 + K 2 + K 3 )(K 2K 3 + K 3K1 + K1 K 2 ), E1, =, E2, 9 K1 K 2K 3, , 24 A person of mass M is sitting on a swing, to length L and swinging with an angular, amplitude θ 0. If the person stands up, when the swing passes through its lowest, point, the work done by him, assuming, that his centre of mass moves by a, distance l( l << L ), is close to, (a) Mgl (1 − θ 20 ), (c) Mgl, , [Take, R = 8.3 J/mol-K], (a) 19.7 J/mol-K, (c) 17.4 J/mol-K, , (b) 15.7 J/mol-K, (d) 21.6 J/mol-K, , 26 A submarine A travelling at 18 km/h is, being chased along the line of its velocity, by another submarine B travelling at, 27 km/h. B sends a sonar signal of 500 Hz, to detect A and receives a reflected sound, of frequency ν. The value of ν is close to, (Speed of sound in water = 1500 ms −1), (a) 504 Hz, (c) 499 Hz, , (b) 507 Hz, (d) 502 Hz, , 27 A man (mass = 50 kg) and his son (mass, , = 20 kg) are standing on a frictionless, surface facing each other. The man, pushes his son, so that he starts moving, at a speed of 0.70 ms −1 with respect to the, man. The speed of the man with respect, to the surface is, , (a) 0.28 ms −1, (c) 0.47 ms −1, , (b) 0.20 ms −1, (d) 0.14 ms −1, , 28 A concave mirror has radius of curvature, of 40 cm. It is at the bottom of a glass, that has water filled up to 5 cm, (see figure)., If a small particle is floating on the, surface of water, its image as seen, from, directly above the glass, is at a distance d, from the surface of water. The value of d, is close to, [Refractive index of water = 1.33], Particle, , (b) Mgl (1 + θ 20 ), , θ2 , (d) Mgl 1 + 0 , 2, , , 5 cm, , 25 Two moles of helium gas is mixed with, three moles of hydrogen molecules (taken, to be rigid). What is the molar specific, heat of mixture at constant volume?, , (a) 6.7 cm, (c) 8.8 cm, , (b) 13.4 cm, (d) 11.7 cm
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72, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 29 An excited He+ ion emits two photons in, succession, with wavelengths 108.5 nm, and 30.4 nm, in making a transition to, ground state. The quantum number n, corresponding to its initial excited state is, [for photon of wavelength λ, energy, 1240 eV, ], E=, λ ( in nm), (a) n = 4, (c) n = 7, , (b) n = 5, (d) n = 6, , 30 In a double slit experiment, when a thin, film of thickness t having refractive index, µ is introduced in front of one of the slits,, the maximum at the centre of the fringe, pattern shifts by one fringe width. The, value of t is (λ is the wavelength of the, light used), 2λ, (µ − 1), λ, (c), (µ − 1), , λ, 2(µ − 1), λ, (d), (2µ − 1), , (a), , (b), , CHEMISTRY, 1 An example of a disproportionation, , CHO, , (c) OHC, , reaction is, , (a) 2MnO−4 + 10 I− + 16H+ → 2Mn 2+, +5I2 + 8H2O, (b) 2NaBr + Cl2 → 2NaCl + Br2, (c) 2KMnO4 → K 2MnO4 + MnO2 + O2, (d) 2CuBr → CuBr2 + Cu, , 2 The mole fraction of a solvent in aqueous, solution of a solute is 0.8. The molality, (in mol kg −1) of the aqueous solution is, (a) 13.88 × 10, (c) 13.88, , −1, , −2, , (b) 13.88 × 10, (d) 13.88 × 10−3, , OtBu, , (d) OHC, CHO, , 6 The metal that gives hydrogen gas upon, treatment with both acid as well as base is, (a) magnesium, (c) zinc, , 7 The major product of the following, reaction is, , 3 An ideal gas is allowed to expand from, , HO, , 1 L to 10 L against a constant external, pressure of 1 bar. The work done in kJ is, (a) − 9.0, , (b) + 10.0 (c) − 0.9, , (b) mercury, (d) iron, , (i) CrO3, (ii) SOCl2/∆, (iii) ∆, , HO, , (d) − 2.0, , O, , 4 Which of the following is a thermosetting, polymer?, (a) Bakelite, (c) Nylon-6, , (b) Buna-N, (d) PVC, , O, , (b), , (a), , 5 The major product(s) obtained in the, , HO, , HO, , following reaction is/are, , O, , (i) KOtBu, (ii) O3/Me2S, , (a) OHC, , (d), , O, , (c), , Br, , CHO and OHC CHO, , Cl, , Cl, , 8 Glucose and galactose are having identical, (b) OHC, CHO, , configuration in all the positions except, position., (a) C-3, , (b) C-4, , (c) C-2, , (d) C-5
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APRIL ATTEMPT ~ 12 April 2019, Shift I, 9 The major product of the following, addition reaction is, Cl 2/ H 2O, , H3C CH == CH 2 →, (a) CH3 CH CH2, , , Cl, OH, , 73, 14 In the following reaction; xA → yB, d [B], d [ A], + 0.3010, = log10 , log10 −, , dt, dt , , , A and B respectively can be, (a), (b), (c), (d), , (b) CH3 CH C H2, , , OH Cl, O, (c) H3C, , n-butane and iso-butane, C2H2 and C6H6, C2H4 and C4H8, N2O4 and NO2, , 15 The increasing order of the pK b of the, following compound is, , O, , F, S, , (d) H3C, , (A), , CH3, , N, , 10 Given,, Co3 + + e− → Co2+ ; E ° = + 1.81 V, Pb4+ + 2e− → Pb2+ ; E ° = + 1.67 V, , H, , CH3O, , Oxidising power of the species will, increase in the order, (a), (b), (c), (d), , Ce4+, Bi3 +, Co3 +, Co3 +, , < Pb4+ < Bi3 + < Co3 +, < Ce4+ < Pb4+ < Co3 +, < Ce4+ < Bi3 + < Pb4+, < Pb4+ < Ce4+ < Bi3 +, , (B), , N, , N, , H, , H, , O2N, , S, , (C), , H3C, , N, , N, , H, , H, S, , (D), , 11 Which of the following statement is not, true about RNA?, (a) It controls the synthesis of protein, (b) It has always double stranded α-helix, structure, (c) It usually does not replicate, (d) It is present in the nucleus of the cell, , (a), (b), (c), (d), , N, , N, , H, , H, , (A) < (C) < (D) < (B), (C) < (A) < (D) < (B), (B) < (D) < (A) < (C), (B) < (D) < (C) < (A), , 16 The electrons are more likely to be found, , 12 The group number, number of valence, , a, , electrons and valency of an element with, atomic number 15, respectively, are, (a) 16, 5 and 2, (c) 16, 6 and 3, , H, S, , Ce4+ + e− → Ce3 + ; E ° = + 1.61 V, Bi3 + + 3e− → Bi; E ° = + 0.20 V, , N, , Ψ (x), b, , (b) 15, 5 and 3, (d) 15, 6 and 2, , c, , 13 The basic structural unit of feldspar,, zeolites, mica and asbestos is, (a) (SiO3 )2−, , (d), , (b) SiO2, , R, , ( Si O ), (R = Me), n, , R, , x, , –x, , (c) (SiO4 )4−, (a), (b), (c), (d), , in the region a and c, in the region a and b, only in the region a, only in the region c
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74, , ONLINE, , 17 The correct sequence of thermal stability, of the following carbonates is, (a), (b), (c), (d), , JEE Main 2019 ~ Solved Paper, , 21 An organic compound A is oxidised with, Na 2O2 followed by boiling with HNO3 . The, resultant solution is then treated with, ammonium molybdate to yield a yellow, precipitate., , BaCO3 < CaCO3 < SrCO3 < MgCO3, MgCO3 < CaCO3 < SrCO3 < BaCO3, MgCO3 < SrCO3 < CaCO3 < BaCO3, BaCO3 < SrCO3 < CaCO3 < MgCO3, , 18 The complex ion that will lose its crystal, field stabilisation energy upon oxidation of, its metal to +3 state is, , Based on above observation, the element, present in the given compound is, (a) nitrogen, (c) fluorine, , (b) phosphorus, (d) sulphur, , 22 The correct set of species responsible for, the photochemical smog is, , (Phen =, , (a), (b), (c), (d), , N, N, Ignore pairing energy, , (a), (b), (c), (d), , [Co(phen)3 ]2+, [Ni(phen)3 ]2+, [Zn(phen)3 ]2+, [Fe(phen)3 ]2+, , 23 Peptisation is a, , 19 But-2-ene on reaction with alkaline, KMnO4 at elevated temperature followed, by acidification will give, (a) CH3 CH CH CH3, , , OH, OH, , is, , 20 Complete removal of both the axial ligands, (along the z-axis) from an octahedral, complex leads to which of the following, splitting patterns? (relative orbital, energies not on scale)., , (c) E, , dx2 – y2, , dz2, , dxy, , dx2 – y2, , dz2, , (b) E, , dxz, dyz, , dxz, dyz, , dxy, , dx2 – y2, , dx2 – y2, , dz2, , (d) E, , (a) process of bringing colloidal molecule, into solution, (b) process of converting precipitate into, colloidal solution, (c) process of converting a colloidal solution, into precipitate, (d) process of converting soluble particles to, form colloidal solution, , 24 The correct statement among the following, , (b) one molecule of CH3CHO and one, molecule of CH3COOH, (c) 2 molecules of CH3COOH, (d) 2 molecules of CH3CHO, , (a) E, , N2, NO2 and hydrocarbons, CO2, NO2, SO2 and hydrocarbons, NO, NO2, O3 and hydrocarbons, N2, O2, O3 and hydrocarbons, , dz2, , dxy, , dyz, dxz, , dxz, dyz, , dxy, , (a) (SiH3 )3 N is planar and less basic than, (CH3 )3 N., (b) (SiH3 )3 N is pyramidal and more basic, than (CH3 )3 N., (c) (SiH3 )3 N is pyramidal and less basic, than (CH3 )3 N., (d) (SiH3 )3 N is planar and more basic than, (CH3 )3 N., , 25 Enthalpy of sublimation of iodine is, , 24 cal g −1 at 200°C. If specific heat of I2( s), and I2(vap.) are 0.055 and 0.031 cal g −1 K −1, respectively, then enthalpy of sublimation, of iodine at 250°C in cal g −1 is, , (a) 2.85, (c) 22.8, , (b) 5.7, (d) 11.4, , 26 An element has a face-centred cubic (fcc), structure with a cell edge of a. The, distance between the centres of two, nearest tetrahedral voids in the lattice is
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APRIL ATTEMPT ~ 12 April 2019, Shift I, (a), , OH, and formic acid, , (c), , 27 What is the molar solubility of Al(OH)3 in, 0.2 M NaOH solution? Given that,, solubility product of Al(OH)3 = 2.4 × 10−24, , (a) 3 × 10−19, (c) 3 × 10−22, , (b) 12 × 10−21, (d) 12 × 10−23, , 28 The major products of the following, reaction are, , (1) CHCl3/aq. NaOH, (2) HCHO, NaOH (conc.), (3) H3O+, , Cl, , 29 5 moles of AB2 weight 125 × 10−3 kg and, , 10 moles of A2B2 weight 300 × 10−3 kg. The, molar mass of A( M A ) and molar mass of, B ( M B ) in kg mol −1 are, M A = 10 × 10−3 and MB = 5 × 10−3, M A = 50 × 10−3 and MB = 25 × 10−3, M A = 25 × 10−3 and MB = 50 × 10−3, M A = 5 × 10−3 and MB = 10 × 10−3, , 30 The idea of froth floatation method came, , Cl, OH, , OH, , COOH, , COOH, and methanol, , OH, and formic, acid, , (d), , OH, , (a), (b), (c), (d), , OH, , (a), , OH, , OH, , (b) a, 3, (d) a, 2, , 2a, , a, (c), 2, , 75, , and methanol, , (b), , OH, , Cl, , from a person X and this method is, related to the process Y of ores. X and Y ,, respectively, are, (a), (b), (c), (d), , fisher woman and concentration, washer woman and concentration, fisher man and reduction, washer man and reduction, , MATHEMATICS, 1 If A is a symmetric matrix and B is a, skew-symmetric matrix such that, 2 3 , A+ B= , , then AB is equal to, 5 −1, , −4 −2 , (a) , , −1 4 , 4 −2, (c) , , 1 −4, , 4, (b) , −1, −4, (d) , 1, , −2 , −4, 2, 4, , dy d 2 y , ,, , dx dx 2 , , 2 If e y + xy = e, the ordered pair , at x = 0 is equal to, , 1, 1, (a) , − 2, e, e, 1 1 , (c) , 2, e e , , 1 1, (b) − , 2, e e, 1, 1, (d) − , − 2, e, e, , 3 If the angle of intersection at a point, where the two circles with radii 5 cm and, 12 cm intersect is 90°, then the length (in, cm) of their common chord is, , (a), , 13, 5, , (b), , 120, 13, , (c), , 60, 13, , (d), , 13, 2, , 4 If the area (in sq units) of the region, {( x , y ): y 2 ≤ 4x , x + y ≤ 1, x ≥ 0, y ≥ 0} is, a 2 + b, then a − b is equal to, 10, 3, 8, (c), 3, , (a), , (b) 6, (d) −, , 2, 3, , 5 For x ∈ R, let [x ] denote the greatest, integer ≤ x, then the sum of the series, 1 1, 2 , 1 1, − 3 + − 3 − 100 + − 3 − 100 +, 99 , 1, is, … + − −, 3 100, (a) − 153 (b) − 133 (c) − 131, , (d) − 135
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76, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 6 The number of ways of choosing 10 objects, out of 31 objects of which 10 are identical, and the remaining 21 are distinct, is, (a) 220 − 1, (c) 220, , (b) 221, (d) 220 + 1, , 7 The integral ∫, , 2x3 − 1, , dx is equal to, x4 + x, (here C is a constant of integration), , |x + 1|, 1, +C, log e, 2, x2, (x3 + 1)2, 1, (b) log e, +C, 2, |x3|, x3 + 1, (c) log e, +C, x, 3, , (a), , |x + 1|, +C, x2, , 9 Let f : R → R be a continuously, differentiable function such that f( 2) = 6, f (x ), 1, and f ′ ( 2) =, . If ∫, 4t3 dt = ( x − 2)g( x ),, 6, 48, then lim g ( x ) is equal to, x→2, , (c) 12, , (d) 36, , (b) − 126, (d) 126, , 11 If there of the six vertices of a regular, hexagon are chosen at random, then the, probability that the triangle formed with, these chosen vertices is equilateral is, 1, 10, , (b), , 1, 5, , (c), , 3, 10, , (d), , 12 Consider the differential equation,, , (b) 121, , (c) 1, , (d) 137, , 15 The number of solutions of the equation, 5π 5π , is, 1 + sin4 x = cos2 3x , x ∈ −, ,, 2 2 , (a) 3, , (b) 5, , (c) 7, , (d) 4, , 16 The equation|z − i| =|z − 1|, i = −1,, represents, 1, 2, (b) the line passing through the origin with, slope 1, (c) a circle of radius 1, (d) the line passing through the origin with, slope − 1, (a) a circle of radius, , p → (~ q ∨ r ) is false (F), then the truth, values of the statements p, q and r are, respectively, , (1 + x )(1 − x )10(1 + x + x 2 )9 is, , (a), , $), (b) 4 (2$i − 2$j − k, $), (d) 4 (− 2$i − 2$j + k, , 17 If the truth value of the statement, , 10 The coefficient of x18 in the product, (a) 84, (c) − 84, , two vectors. If a vector perpendicular to, both the vectors a + b and a − b has the, magnitude 12, then one such vector is, , (a) 17, , second and third quadrants only, first, second and fourth quadrants, first, third and fourth quadrants, third and fourth quadrants only, , (b) 24, , $ and b = i$ + 2$j − 2k, $ be, 13 Let a = 3$i + 2$j + 2k, , distribution with mean 8 and variance 4., k, If P ( X ≤ 2) = 16 , then k is equal to, 2, , y = sin x sin( x + 2) − sin2( x + 1) represents, a straight line lying in, , (a) 18, , 3, 1, −, 2, e, 3, (d) − e, 2, (b), , 14 Let a random variable X have a binomial, , 8 The equation, , (a), (b), (c), (d), , 5, 1, +, 2, e, 1, 1, (c) +, 2, e, (a), , $), (a) 4 (2$i + 2$j + k, $), (c) 4 (2$i + 2$j − k, , 3, , (d) log e, , when x = 1, then the value of x for which, y = 2, is, , 3, 20, , 1, , y 2dx + x − dy = 0. If value of y is 1, , y, , (a) T, T and F, (c) T, F and T, , (b) T, F and F, (d) F, T and T, , π /2, , cot x, dx = m( π + n ), then, cot x + cosec x, m ⋅ n is equal to, , 18 If ∫, , 0, , (a) −, , 1, 2, , (b) 1, , (c), , 1, 2, , (d) −1
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APRIL ATTEMPT ~ 12 April 2019, Shift I, , , , 3, 2, , 19 For x ∈ 0, , let f ( x ) = x , g( x ) = tan x, and h( x ) =, , 1 − x2, 1 + x2, , . If φ( x ) = (( hof )og)( x ),, , π, then φ is equal to, 3, π, 12, 7π, (c) tan, 12, , (a) − 260, (c) − 320, , 12, −1 3, − sin is equal, 13, 5, , 20 The value of sin−1 , , π, 56, − sin −1 , 65, 2, −1 33, (d) π − cos , 65, , 63, (a) π − sin −1 , 65, π, −1 9 , (c), − cos , 65, 2, , (b), , 21 A 2 m ladder leans against a vertical wall., If the top of the ladder begins to slide, down the wall at the rate 25 cm/s, then the, rate (in cm/s) at which the bottom of the, ladder slides away from the wall on the, horizontal ground when the top of the, ladder is 1 m above the ground is, (a) 25 3, , (b), , 25, 3, , (c), , 25, 3, , (d) 25, , 22 If α and β are the roots of the equation, 375x 2 − 25x − 2 = 0, then, lim, , n→∞, , (a), , n, , n, , r =1, , r =1, , ∑ α r + nlim, ∑ β r is equal to, →∞, , 21, 346, , (b), , 29, 358, , (c), , 1, 12, , (d), , 7, 116, , 23 If the normal to the ellipse 3x + 4 y = 12, 2, , 2, , at a point P on it is parallel to the line,, 2x + y = 4 and the tangent to the ellipse at, P passes through Q( 4, 4) then PQ is equal, to, 5 5, 2, 221, (c), 2, (a), , (b), (d), , (a) (4, 3 2 ), (c) (3, 3 3 ), , (b) (4, 3 3 ), (d) (5, 3 6 ), , of an AP. If S 4 = 16 and S 6 = − 48, then S10, is equal to, , 11π, 12, 5π, (d) tan, 12, , to, , maximum value of f in the interval [0, 3], when k = m, then the ordered pair ( m , M ), is equal to, , 25 Let S n denote the sum of the first n terms, , (b) tan, , (a) tan, , 77, , 61, 2, 157, 2, , 24 If m is the minimum value of k for which, the function f ( x ) = x kx − x 2 is increasing, in the interval [0, 3] and M is the, , (b) − 410, (d) − 380, , 26 If the data x1 , x2 , … , x10 is such that the, mean of first four of these is 11, the mean, of the remaining six is 16 and the sum of, squares of all of these is 2000, then the, standard deviation of this data is, (a) 2 2, , (b) 2, , (c) 4, , (d), , 2, , 27 Let P be the point of intersection of the, common tangents to the parabola y 2 = 12x, and the hyperbola 8x 2 − y 2 = 8. If S and S ′, denotes the foci of the hyperbola where S, lies on the positive X-axis then P divides, SS ′ in a ratio, (a) 13 : 11, (c) 5 : 4, , (b) 14 : 13, (d) 2 : 1, , 5 2α, 28 If B = 0 2, , α 3, , 1, 1 is the inverse of a 3 × 3, , −1, matrix A, then the sum of all values of α, for which det ( A) + 1 = 0, is, (b) −1, (d) 2, , (a) 0, (c) 1, , 29 If the volume of parallelopiped formed by, $ and λ$i + k, $ is, $ , $j + λk, the vectors $i + λ$j + k, minimum, then λ is equal to, (a) −, (c), , 1, 3, , 3, , 1, 3, (d) − 3, (b), , x− 2 y+1 z −1, intersects, =, =, 3, 2, −1, the plane 2x + 3 y − z + 13 = 0 at a point P, and the plane 3x + y + 4z = 16 at a point, Q, then PQ is equal to, , 30 If the line, , (a) 14, (c) 2 7, , (b) 14, (d) 2 14
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78, , ONLINE, , JEE Main 2019 ~ Solved Paper, , Answers, Physics, 1., 11., 21., , (d), (c), (b), , 2., 12., 22., , (c), (b), (b), , 3., 13., 23., , (b), (a), (d), , 4., 14., 24., , (a), (c), (b), , 5., 15., 25., , (c), (b), (c), , 6., 16., 26., , (c), (a), (d), , 7., 17., 27., , (b), (b), (b), , 8., 18., 28., , (b), (b), (c), , 9., 19., 29., , (a), (d), (b), , 10., 20., 30., , (b), (a), (c), , (c), (b), (c), , 3., 13., 23., , (c), (c), (b), , 4., 14., 24., , (a), (c), (d), , 5., 15., 25., , (a), (c), (c), , 6., 16., 26., , (c), (a), (c), , 7., 17., 27., , (b), (b), (c), , 8., 18., 28., , (b), (d), (d), , 9., 19., 29., , (b), (c), (d), , 10., 20., 30., , (b), (a), (b), , 3., 13., 23., , (b), (b), (a), , 4., 14., 24., , (b), (d), (b), , 5., 15., 25., , (b), (b), (c), , 6., 16., 26., , (c), (b), (b), , 7., 17., 27., , (c), (a), (c), , 8., 18., 28., , (d), (d), (c), , 9., 19., 29., , (a), (b), (b), , 10., 20., 30., , (a), (b), (d), , Chemistry, 1., 11., 21., , (d), (b), (b), , 2., 12., 22., , Mathematics, 1., 11., 21., , (b), (a), (b), , 2., 12., 22., , (b), (b), (c), , For Detailed Solutions Visit : https://bit.ly/2VkT7il Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (12 April, 2019), TIME 2:30-5:30 (Shift II), , MM : 360, , PHYSICS, Y, , 1 Two particles are projected from the same, point with the same speed u such that, they have the same range R, but different, maximum heights h1 and h2. Which of the, following is correct?, (a) R2 = 4 h1h2, (c) R2 = 2 h1h2, , (b) R2 = 16 h1h2, (d) R2 = h1h2, , m3=150 g, , 50 g = m1, 0, , 2 In an amplitude modulator circuit, the, carrier wave is given by, C( t ) = 4 sin( 20000 πt ) while modulating, signal is given by, m( t ) = 2 sin( 2000 πt )., The values of modulation index and lower, side band frequency are, (a) 0.5 and 10 kHz, (c) 0.3 and 9 kHz, , (b) 0.4 and 10 kHz, (d) 0.5 and 9 kHz, , 3 Two sources of sound S1 and S 2 produce, sound waves of same frequency 660 Hz., A listener is moving from source S1, towards S 2 with a constant speed u m/s, and he hears 10 beats/s. The velocity of, sound is 330 m/s. Then, u equal to, (a) 5.5 m/s, (c) 2.5 m/s, , (b) 15.0 m/s, (d) 10.0 m/s, , 4 Three particles of masses 50 g, 100 g and, 150 g are placed at the vertices of an, equilateral triangle of side 1 m (as shown, in the figure). The ( x , y ) coordinates of the, centre of mass will be, , m2=100 g, X, 0.5 m 1.0 m, , 60°, , 3, 5 , (a) , m,, m, 12 , 4, , 7, 3 , (b) , m,, m, 8 , 12, , 7, 3 , (c) , m,, m, 4 , 12, , 3, 7 , (d) , m,, m, 12 , 8, , 5 A Carnot engine has an efficiency of 1/6., When the temperature of the sink is, reduced by 62°C, its efficiency is doubled., The temperatures of the source and the, sink are respectively,, (a) 62°C, 124°C, (c) 124°C, 62°C, , (b) 99°C, 37°C, (d) 37°C, 99°C, , 6 A spring whose unstretched length is l, has a force constant k. The spring is cut, into two pieces of unstretched lengths l1, and l2 where, l1 = nl2 and n is an integer., The ratio k1 / k2 of the corresponding force, constants k1 and k2 will be, (a) n, , (b), , 1, n2, , (c), , 1, n, , (d) n 2
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80, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 7 A transparent cube of side d, made of a, material of refractive index µ 2, is, immersed in a liquid of refractive index, µ 1(µ 1 < µ 2 ). A ray is incident on the face, AB at an angle θ (shown in the figure)., Total internal reflection takes place at, point E on the face BC., B, , E, , C, , distance from the centre. Two charges A, and B, of − Q each, are placed on, diametrically opposite points, at equal, distance a, from the centre. If A and B do, not experience any force, then, (a) a = 8−1/ 4 R, (c) a = 2−1/ 4 R, , 3R, 21/ 4, (d) a = R / 3, , (b) a =, , 12 Consider an electron in a hydrogen atom,, q, , revolving in its second excited state, (having radius 4.65 Å). The de-Broglie, wavelength of this electron is, , m2, , m1, A, , (a) 3.5 Å, (c) 12.9 Å, , D, , Then, θ must satisfy, (a) θ < sin, , −1, , (c) θ < sin −1, , µ1, µ2, , (b) θ > sin, , −1, , µ 22, −1, µ12, , µ 22, µ, − 1 (d) θ > sin −1 1, 2, µ2, µ1, , 8 A tuning fork of frequency 480 Hz is used, in an experiment for measuring speed of, sound ( v ) in air by resonance tube, method. Resonance is observed to occur at, two successive lengths of the air column, l1 = 30 cm and l2 = 70 cm., Then, v is equal to, , (a) 332 ms −1, (c) 338 ms −1, , (b) 384 ms −1, (d) 379 ms −1, , 9 The electron in a hydrogen atom first, jumps from the third excited state to the, second excited state and subsequently to, the first excited state. The ratio of the, respective wavelengths λ 1 / λ 2 of the, photons emitted in this process is, (a) 20/7, (c) 7/5, , (b) 27/5, (d) 9/7, , 10 A diatomic gas with rigid molecules does, 10 J of work when expanded at constant, pressure. What would be the heat energy, absorbed by the gas, in this process?, (a) 25 J, (c) 30 J, , (b) 35 J, (d) 40 J, , 11 Let a total charge 2Q be distributed in a, sphere of radius R, with the charge, density given by ρ(r ) = kr, where r is the, , (b) 6.6 Å, (d) 9.7 Å, , 13 A solid sphere of radius R acquires a, terminal velocity v1 when falling (due to, gravity) through a viscous fluid having a, coefficient of viscosity η. The sphere is, broken into 27 identical solid spheres. If, each of these spheres acquires a terminal, velocity, v2 when falling through the, same fluid, the ratio ( v1 / v2 ) equals, (a) 9, (c) 1/9, , (b) 1/27, (d) 27, , 14 A smooth wire of length, , w, , 2πr is bent into a circle, and kept in a vertical, A, plane. A bead can slide, r, smoothly on the wire., O, When the circle is rotating, with angular speed ω, r/2, P, about the vertical diameter, B, AB, as shown in figure, the, bead is at rest with respect to the circular, ring at position P as shown. Then, the, value of ω 2 is equal to, 3g, 2r, (c) ( g 3 ) / r, (a), , (b) 2 g / (r 3 ), (d) 2 g / r, , 15 A particle is moving with speed v = b x, along positive X-axis. Calculate the speed, of the particle at time t = τ (assume that, the particle is at origin at t = 0)., (a), , b2τ, 4, , (c) b2τ, , b2τ, 2, b2τ, (d), 2, , (b)
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APRIL ATTEMPT ~ 12 April 2019, Shift II, 16 The ratio of the weights of a body on the, earth’s surface, so that on the surface of a, planet is 9 : 4. The mass of the planet is, 1, th of that of the earth. If R is the radius, 9, of the earth, what is the radius of the, planet? (Take, the planets to have the, same mass density), R, 3, R, (c), 9, (a), , R, 4, R, (d), 2, (b), , 17 A system of three polarisers P1 , P2 , P3 is, set up such that the pass axis of P3 is, crossed with respect to that of P1. The, pass axis of P2 is inclined at 60° to the, pass axis of P3 . When a beam of, unpolarised light of intensityI 0 is incident, on P1, the intensity of light transmitted, by the three polarisers is I. The ratio, ( I 0 / I ) equals (nearly), (a) 5.33, (c) 10.67, , 81, 21 Half lives of two radioactive nuclei A and, B are 10 minutes and 20 minutes,, respectively. If initially a sample has, equal number of nuclei, then after, 60 minutes, the ratio of decayed numbers, of nuclei A and B will be, (a) 3 : 8, , (b) 1 : 8, , (c) 8 : 1, , (d) 9 : 8, , 22 An electron moving along the X-axis with, an initial energy of 100 eV, enters a, region of magnetic field, $ at S (see figure). The, B = (1.5 × 10−3 T ) k, field extends between x = 0 and x = 2 cm., The electron is detected at the point Q on, a screen placed 8 cm away from the point, S. The distance d between P and Q (on, the screen) is, (Take, electron’s charge = 1.6 × 10−19 C,, mass of electron = 91, . × 10−31 kg), Q, , (b) 16.00, (d) 1.80, , d, , 18 A uniform cylindrical rod of length L and, radius r, is made from a material whose, Young’s modulus of elasticity equals Y ., When this rod is heated by temperature, T and simultaneously subjected to a net, longitudinal compressional force F, its, length remains unchanged. The, coefficient of volume expansion of the, material of the rod, is (nearly) equal to, (a) 9F / (πr 2YT ), (c) 3F / (πr 2YT ), , (b) 6F / (πr 2YT ), (d) F / (3πr 2YT ), , P, , S, , 2 cm, 8 cm, , (a) 11.65 cm, (c) 1.22 cm, , 23 In the given circuit, the charge on 4 µF, capacitor will be, 1 mF, , 19 The number density of molecules of a gas, , 4 mF, , depends on their distance r from the, 4, origin as, n(r ) = n 0e− ar .Then, the total, number of molecules is proportional to, , (a) n0α −3/ 4, (c) n0α 1/ 4, , 5 mF, , (b) n0 α 1/ 2, (d) n0α −3, , 3 mF, , 20 A small speaker delivers 2 W of audio, output. At what distance from the, speaker will one detect 120 dB intensity, sound? [Take, reference intensity of, sound as 10−12 W/m 2], (a) 40 cm, (c) 10 cm, , (b) 20 cm, (d) 30 cm, , (b) 12.87 cm, (d) 2.25 cm, , 10 V, , (a) 5.4 µC, (c) 13.4 µC, , (b) 9.6 µC, (d) 24 µC, , 24 One kilogram of water at 20°C is heated, in an electric kettle whose heating, element has a mean (temperature
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82, , ONLINE, averaged) resistance of 20 Ω. The rms, voltage in the mains is 200 V. Ignoring, heat loss from the kettle, time taken for, water to evaporate fully, is close to, , 27 A plane electromagnetic wave having a, frequency ν = 23.9 GHz propagates along, the positive z -direction in free space. The, peak value of the electric field is 60 V/m., Which among the following is the, acceptable magnetic field component in, the electromagnetic wave?, , [Specific heat of water = 4200 J/(kg°C),, Latent heat of water = 2260 kJ/kg], (a) 16 min, (c) 3 min, , (b) 22 min, (d) 10 min, , (a) B = 2 × 107 sin (0.5 × 103 z + 1.5 × 1011 t ) $i, , 25 A moving coil galvanometer, having a, resistance G, produces full scale, deflection when a current I g flows, through it. This galvanometer can be, converted into (i) an ammeter of range 0, to I 0( I 0 > I g ) by connecting a shunt, resistance RA to it and (ii) into a, voltmeter of range 0 to V (V = GI 0 ) by, connecting a series resistance RV to it., Then,, , I0 − Ig , , (a) RARV = G 2, Ig , , Ig , RA , , and, = , RV (I 0 − I g ), (b) RARV = G 2 and, , RA I g , , =, RV I 0 − I g , , JEE Main 2019 ~ Solved Paper, , (b) B = 2 × 10–7 sin (0.5 × 103 z − 1.5 × 1011 t ) i$, $, (c) B = 60 sin (0.5 × 103 x + 1.5 × 1011 t )k, (d) B = 2 × 10–7 sin (1.5 × 102x + 0.5 × 1011 t ) $j, , 28 Consider the L-R circuit shown in the, , figure. If the switch S is closed at t = 0,, then the amount of charge that passes, through the battery between t = 0 and, L, t = is, R, R, , E, , S, , i, , 2, , 2, , I − Ig , Ig , R, and A = 0, , (c) RARV = G , R, −, I, I, Ig , 0, g, V, , L, , 2.7 EL, R2, 7.3 EL, (c), R2, , EL, 2.7 R2, EL, (d), 7.3 R2, , (a), , 2, , 2, , (b), , 29 Figure shows a DC voltage regulator, (d) RARV = G 2 and, , Ig, , RA, =, RV, (I 0 − I g ), , 26 Find the magnetic field at point P due to, a straight line segment AB of length 6 cm, carrying a current of 5 A (See figure)., (Take, µ 0 = 4π × 10−7 N - A −2 ), , circuit, with a Zener diode of breakdown, voltage = 6 V. If the unregulated input, voltage varies between 10 V to 16 V, then, what is the maximum Zener current?, Is, Rs=2kΩ, IL, , P, , RL=4kΩ, , m, , 5c, , 5c, , m, , IZ, , A, , B, 6 cm, , −5, , (a) 2.0 × 10 T, (c) 3.0 × 10−5 T, , (b) 1.5 × 10−5 T, (d) 2.5 × 10−5 T, , (a) 2.5 mA, (c) 7.5 mA, , (b) 1.5 mA, (d) 3.5 mA, , 30 A block of mass 5 kg is (i) pushed in case, (A) and (ii) pulled in case (B), by a force, F = 20 N, making an angle of 30° with the
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APRIL ATTEMPT ~ 12 April 2019, Shift II, horizontal, as shown in the figures. The, coefficient of friction between the block,, the floor is µ = 0.2. The difference between, the accelerations of the block, in case (B), and case (A) will be (Take, g = 10 ms−2), , 83, F=20 N, , 30°, 30°, , F=20 N, (A), , (B), , (b) 3.2 ms −2, (d) 0 ms −2, , (a) 0.4 ms −2, (c) 0.8 ms −2, , CHEMISTRY, 1 Thermal decomposition of a Mn, compound (X) at 513 K results in, compound (Y ), MnO2 and a gaseous, product. MnO2 reacts with NaCl and, concentrated H 2SO4 to give a pungent gas, Z. X, Y and Z, respectively, are, (a) K3 MnO4 , K 2MnO4 and Cl2, (b) K 2MnO4 , KMnO4 and SO2, (c) KMnO4 , K 2MnO4 and Cl2, (d) K 2MnO4 , KMnO4 and Cl2, , 2 NO2 required for a reaction is produced, by the decomposition of N 2O5 in CCl4 as, per the equation,, 2N 2O5 ( g) → 4NO2( g) + O2( g), The initial concentration of N 2O5 is, 3.00 mol L−1 and it is 2.75 mol L −1 after, 30 minutes. The rate of formation of NO2 is, , (a) 4.167 × 10−3 mol L −1 min −1, (b) 1.667 × 10−2 mol L −1 min −1, (c) 8.333 × 10−3 mol L −1 min −1, (d) 2.083 × 10−3 mol L −1 min −1, , 3 The pair that has similar atomic radii is, (a) Mn and Re, (c) Sc and Ni, , (b) Ti and Hf, (d) Mo and W, , 4 The incorrect statement is, (a) lithium is the strongest reducing agent, among the alkali metals., (b) lithium is least reactive with water, among the alkali metals., (c) LiNO3 decomposes on heating to give, LiNO2 and O2., (d) LiCl crystallise from aqueous solution as, LiCl ⋅2H2O., , 5 The C C bond length is maximum in, (a) graphite, (c) C60, , (b) C70, (d) diamond, , 6 A solution is prepared by dissolving 0.6 g, of urea (molar mass = 60 g mol −1) and, 1.8 g of glucose (molar mass = 180 g, mol −1) in 100 mL of water at 27°C. The, osmotic pressure of the solution is, , ( R = 0.08206 L atm K −1 mol −1), (a) 8.2 atm, (c) 4.92 atm, , (b) 2.46 atm, (d) 1.64 atm, , 7 In comparison to boron, berylium has, (a) lesser nuclear charge and lesser first, ionisation enthalpy, (b) greater nuclear charge and lesser first, ionisation enthalpy, (c) greater nuclear charge and greater first, ionisation enthalpy, (d) lesser nuclear charge and greater first, ionisation enthalpy, , 8 The decreasing order of electrical, conductivity of the following aqueous, solution is, 0.1 M formic acid (A),, 0.1 M acetic acid (B),, 0.1 M benzoic acid (C)., (a) A > C > B, (b) C > B > A, (c) A > B > C, (d) C > A > B, , 9 What will be the major product when, m-cresol is reacted with propargyl, bromide (HC ≡≡ C CH 2Br) in presence of, K 2CO3 in acetone?, OH, , O, , (a), , (b), CH3, , CH3
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84, , ONLINE, OH, , OH, , (c), , JEE Main 2019 ~ Solved Paper, , 14 The IUPAC name for the following, compound is, , (d), , CH3, CH, , H3 C, , CH3, , CH3, , 10 The molar solubility of Cd (OH )2 is, , 1.84 × 10−5 m in water. The expected, solubility of Cd(OH)2 in a buffer solution, of pH = 12 is, (a) 1.84 × 10, , −9, , 2.49, (b), × 10−9 M, 1.84, (d) 2.49 × 10−10 M, , M, , (c) 6.23 × 10−11 M, , 11 Benzene diazonium chloride on reaction, with aniline in the presence of dilute, hydrochloric acid gives, (a), , (b), , —N==N —, , (d), , —N==N—NH—, , H, H, , —NH2, , (a) leaching of bauxite using concentrated, NaOH solution gives sodium aluminate, and sodium silicate., (b) the hall-heroult process is used for the, production of aluminium and iron., (c) pig iron is obtained from cast iron., (d) the blistered appearance of copper, during the metallurgical process is due, to the evolution of CO2., , 13 The primary pollutant that leads to, (a) acrolein, (b) nitrogen oxides, (c) ozone, (d) sulphur dioxide, , sample is due to compound X. Boiling, this sample converts X to compound Y . X, and Y , respectively, are, , ethane, H ′ C C H ′′ dihedral angle is, , 12 The correct statement is, , photochemical smog is, , 15 The temporary hardness of a water, , 16 In the following skew conformation of, , H2N, —N==N—, , (a) 3-methyl-4-(3-methylprop-1-enyl)-1-heptyne, (b) 3, 5-dimethyl-4-propylhept-6-en-1-yne, (c) 3-methyl-4-(1-methylprop-2-ynyl)-1-heptene, (d) 3, 5-dimethyl-4-propylhept-1-en-6-yne, , (a) Mg(HCO3 )2 and Mg(OH)2, (b) Ca(HCO3 )2 and Ca(OH)2, (c) Mg(HCO3 )2 and MgCO3, (d) Ca(HCO3 )2 and CaO, , —NH2, , (c), , CH3, CH2, , H′ 29°, H, , H′′ H, , (a) 58°, (c) 151°, , (b) 149°, (d) 120°, , 17 Among the following, the energy of, 2s-orbital is lowest in, (a) K, (c) Li, , (b) H, (d) Na, , 18 Which one of the following is likely to, give a precipitate with AgNO3 solution?, , (a) CH2 == CH Cl, (c) CHCl3, , (b) CCl4, (d) (CH3 )3 CCl, , 19 25 g of an unknown hydrocarbon upon, burning produces 88 g of CO2 and 9 g of, H 2O. This unknown hydrocarbon contains, (a) 20 g of carbon and 5 g of hydrogen, (b) 22 g of carbon and 3 g of hydrogen, (c) 24 g of carbon and 1 g of hydrogen, (d) 18 g of carbon and 7 g of hydrogen
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APRIL ATTEMPT ~ 12 April 2019, Shift II, 20 Heating of 2-chloro-1-phenyl butane with, EtOK/EtOH gives X as the major, product. Reaction of X with, Hg(OAc)2 / H 2O followed by NaBH 4 gives, Y as the major product. Y is, OH, , (a) Ph, , (b) Ph, OH, OH, , (c) Ph, , (d) Ph, , 21 The compound used in the treatment of, lead poisoning is, (a) D-penicillamine, (c) cis-platin, , (b) desferrioxime-B, (d) EDTA, , 22 Which of the given statements is, incorrect about glycogen?, (a) It is straight chain polymer similar to, amylose, (b) Only α-linkages are present in the molecule, (c) It is present in animal cells, (d) It is present in some yeast and fungi, , 23 Consider the following reactions,, Ag2O, ∆, , A, , ppt, , Hg2+/H+, , B, , NaBH4, , C, , ZnCl2, Conc. HCl, , Turbidity, within, 5 minutes, , A is, , Assertion (A) Vinyl halides do not, undergo nucleophilic substitution easily., Reason (R) Even though the, intermediate carbocation is stabilised by, loosely held π-electrons, the cleavage is, difficult because of strong bonding., (a) Both (A) and (R) are wrong statements., (b) Both (A) and (R) are correct statements, and (R) is correct explanation of (A)., (c) Both (A) and (R) are correct statements, but (R) is not the correct explanation of, (A)., (d) (A) is a correct statement but (R) is a, wrong statement., , 26 The ratio of number of atoms present in a, simple cubic, body centered cubic and, face centered cubic structure are,, respectively., (a) 8 : 1 : 6, (c) 4 : 2 : 1, , (b) 1 : 2 : 4, (d) 4 : 2 : 3, , 27 In which one of the following equilibria,, K p ≠ K c?, 2CO( g ), (a) 2C(s) + O2( g ), H2( g ) + I2( g ), (b) 2HI( g ), (c) NO2( g ) + SO2( g ), NO( g ) + SO3 ( g ), (d) 2NO( g ), N2( g ) + O2( g ), , c, c c, c, , 28 The coordination numbers of Co and Al in, [CoCl(en)2 ]Cl and K3 [Al(C2O4 )3 ],, respectively, are, (en = ethane-1, 2-diamine), (a) 5 and 3, (c) 6 and 6, , (a) CH ≡≡ CH, (b) CH3 C ≡≡ C CH3, (c) CH3 C ≡≡ CH, (d) CH2 == CH2, , (b) 3 and 3, (d) 5 and 6, , 29 The incorrect match in the following is, , 24 The correct name of the following, , (a) ∆G ° < 0, K > 1, (c) ∆G ° > 0, K < 1, , (b) ∆G ° = 0, K = 1, (d) ∆G ° < 0, K < 1, , 30 Among the following, the incorrect, , polymer is, CH3 CH3, n, , (a) polyisobutane, (c) polyisoprene, , 85, , (b) polytert-butylene, (d) polyisobutylene, , 25 An Assertion and a Reason are given, below. Choose the correct answer from, the following options., , statement about colloids is, (a) They can scatter light, (b) They are larger than small molecules, and have high molar mass, (c) The osmotic pressure of a colloidal, solution is of higher order than the true, solution at the same concentration, (d) The range of diameters of colloidal, particles is between 1 and 1000 nm
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86, , ONLINE, , JEE Main 2019 ~ Solved Paper, , MATHEMATICS, sin x − cos x , ,, sin x + cos x , x, , π, with respect to , where x ∈ 0, is, 2 , , 2, , 1 The derivative of tan−1 , , 2, 3, , (a) 1, , (b), , 1, (c), 2, , (d) 2, , 201 1, , 5 5, , 54 4, (c), , 5 5, , 49, , (b), , 316 4, , 25 5, , 48, , 164 1, (d), , 25 5, , 48, , 3 A value of α such that, α +1, , ∫, , α, , dx, 9, = loge is, 8, ( x + α ) ( x + α + 1), , (a) − 2, (c) −, , 1, 2, , (b), , (b) 15 (5 − 3 ), (d) 15 (1 + 3 ), , equation, cos 2x + α sin x = 2α − 7 has a, solution. Then, S is equal to, , test, a candidate is given fifty problems to, solve. If the probability that the, 4, candidate can solve any problem is ,, 5, then the probability that he is unable to, solve less than two problem is, (a), , (a) 15 (3 + 3 ), (c) 15 (3 − 3 ), , 6 Let S be the set of all α ∈ R such that the, , 2 For an initial screening of an admission, , 49, , of elevation of the top of the tower from B, be 30°, then the distance (in m) of the foot, of the tower from the point A is, , 1, 2, , (d) 2, , 4 Let α ∈( 0, π / 2) be fixed. If the integral, tan x + tan α, , ∫ tan x − tan α dx = A( x ) cos 2α + B ( x ), sin 2α + C, where C is a constant of, integration, then the functions A( x ) and, B ( x ) are respectively, (a) x + α and log e|sin(x + α )|, (b) x − α and log e|sin(x − α )|, (c) x − α and log e|cos (x − α )|, (d) x + α and log e|sin(x − α )|, , 5 The angle of elevation of the top of a, vertical tower standing on a horizontal, plane is observed to be 45° from a point A, on the plane. Let B be the point 30 m, vertically above the point A. If the angle, , (a) R, (c) [3, 7], , (b) [1, 4], (d) [2, 6], , 7 A plane which bisects the angle between, the two given planes 2x − y + 2z − 4 = 0, and x + 2 y + 2z − 2 = 0, passes through, the point, (a) (1, − 4, 1), (c) (2, 4, 1), , 8 lim, , x→0, , (b) (1, 4, − 1), (d) (2, − 4, 1), , x + 2 sin x, x + 2 sin x + 1 − sin2 x − x + 1, 2, , (a) 6, (c) 3, , is, , (b) 2, (d) 1, , 9 A group of students comprises of 5 boys, and n girls. If the number of ways, in, which a team of 3 students can randomly, be selected from this group such that, there is at least one boy and at least one, girl in each team, is 1750, then n is equal, to, (a) 28, (c) 25, , (b) 27, (d) 24, , 10 An ellipse, with foci at (0, 2) and ( 0, − 2), and minor axis of length 4, passes, through which of the following points?, (a) ( 2 , 2), (c) (2, 2 2 ), , (b) (2, 2 ), (d) (1, 2 2 ), , 11 The boolean expression ~ ( p ⇒ (~ q )) is, equivalent to, (a) p ∧ q, (c) p ∨ q, , (b) q ⇒ ~ p, (d) (~ p) ⇒ q, , 12 A circle touching the X-axis at (3, 0) and, making a intercept of length 8 on the, Y -axis passes through the point, (a) (3, 10), (c) (2, 3), , (b) (3, 5), (d) (1, 5)
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APRIL ATTEMPT ~ 12 April 2019, Shift II, C1 + ( 22 ) 20C2 + ( 32 ) 20C3 + ....., + ( 202 )20C20 = A( 2β ) , then the ordered, pair ( A, β) is equal to, , 13 If, , 20, , (a) (420, 19), (c) (380, 18), , (b) (420, 18), (d) (380, 19), , 14 A value of θ ∈( 0, π / 3), for which, sin2 θ, 1 + cos2 θ, 4 cos 6θ, 2, cos θ, 1 + sin2 θ, 4 cos 6θ = 0, is, 1 + 4 cos 6θ, cos2 θ, sin2 θ, (a), , π, 9, , (b), , π, 18, , (c), , 7π, 24, , (d), , 7π, 36, , 15 The equation of a common tangent to the, curves, y 2 = 16x and xy = − 4, is, (a) x − y + 4 = 0, (c) x − 2 y + 16 = 0, , (b) x + y + 4 = 0, (d) 2x − y + 2 = 0, , 16 Let z ∈ C with Im ( z ) = 10 and it satisfies, 2z − n, = 2i − 1 for some natural number, 2z + n, n, then, , (a), (b), (c), (d), , n = 20 and Re(z ) = − 10, n = 40 and Re(z ) = 10, n = 40 and Re(z ) = − 10, n = 20 and Re(z ) = 10, , 17 A triangle has a vertex at (1, 2) and the, mid-points of the two sides through it are, ( −1, 1) and ( 2, 3). Then, the centroid of this, triangle is, 7, (a) 1, , 3, 1 , (c) , 1, 3 , , 1 , (b) , 2, 3 , 1 5, (d) , , 3 3, , 18 If a1 , a2 , a3 , ... are in AP such that, , 87, π 2π , θ ∈ , and has a unique solution if, 2 3 , 7π , θ ∈π,, ., , 6, (b) has a unique solution if, π 2π , 7π , θ ∈ , ∪ π,, , 2 3 , , 6, π 2π , (c) has a unique solution if θ ∈ , , 2 3 , and have infinitely many solutions if, 7π , θ ∈π,, , , 6, (d) have infinitely many solutions if, π 2π 7π , θ ∈ , ∪ π,, , 2 3 , 6, , 20 A straight line L at a distance of 4 units, from the origin makes positive intercepts, on the coordinate axes and the, perpendicular from the origin to this line, makes an angle of 60° with the line, x + y = 0. Then, an equation of the line L is, , (a) x + 3 y = 8, (b) ( 3 + 1) x + ( 3 − 1) y = 8 2, (c) 3x + y = 8, (d) ( 3 − 1)x + ( 3 + 1) y = 8 2, , 21 Let f ( x ) = 5 −|x − 2| and g( x ) =|x + 1,, |, x ∈ R. If f ( x ) attains maximum value at α, and g( x ) attains minimum value of β, then, ( x − 1)( x 2 − 5x + 6), is equal to, lim, x → − αβ, x 2 − 6x + 8, (a) 1/2, (c) − 1 / 2, , (b) − 3 / 2, (d) 3/2, , 22 Let α ∈ R and the three vectors, , a1 + a7 + a16 = 40, then the sum of the, first 15 terms of this AP is, , $ , b = 2i$ + $j − αk, $, a = αi$ + $j + 3k, $ . Then, the set, and c = αi$ − 2$j + 3k, , (a) 200, (c) 120, , S = { α : a, b and c are coplanar}, , (b) 280, (d) 150, , 19 If [x ] denotes the greatest integer ≤ x ,, then the system of liner equations, [sin θ ]x + [− cos θ ] y = 0, [cot θ ]x + y = 0, (a) have infinitely many solutions if, , (a) is singleton, (b) is empty, (c) contains exactly two positive numbers, (d) contains exactly two numbers only one of, which is positive
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88, , JEE Main 2019 ~ Solved Paper, , ONLINE, , (b) If ( A − B) ⊆ C, then A ⊆ C, (c) (C ∪ A ) ∩ (C ∪ B) = C, (d) If ( A − C ) ⊆ B, then A ⊆ B, , 23 A person throws two fair dice. He wins, ` 15 for throwing a doublet (same, numbers on the two dice), wins ` 12 when, , the throw results in the sum of 9, and, loses ` 6 for any other outcome on the, throw. Then, the expected gain/loss (in `), of the person is, (a), , 1, 1, 1, gain (b) loss (c) loss, 2, 4, 2, , 27 The general solution of the differential, equation ( y 2 − x3 )dx − xydy = 0 ( x ≠ 0) is, (where, C is a constant of integration), (a) y2 − 2x2 + Cx3 = 0 (b) y2 + 2x3 + Cx2 = 0, (c) y2 + 2x2 + Cx3 = 0 (d) y2 − 2x3 + Cx2 = 0, , (d) 2 gain, , 24 The tangents to the curve y = ( x − 2)2 − 1, , 28 If the area (in sq units) bounded by the, parabola y 2 = 4λx and the line y = λx,, 1, λ > 0, is , then λ is equal to, 9, , at its points of intersection with the line, x − y = 3, intersect at the point, 5, , (b) − , − 1, 2, , 5 , (d) − , 1, 2 , , 5 , (a) , 1, 2 , , 5, (c) , − 1, , 2, , (a) 2 6, , (c) αγ, , (d) 4 3, , from the point (2, 1, 4) to the plane, containing the lines, $), r = ( $i + $j) + λ( i$ + 2$j − k, , of a non-constant GP such that the, equations αx 2 + 2βx + γ = 0 and, x 2 + x − 1 = 0 have a common root, then,, α(β + γ) is equal to, (b) αβ, , (c) 24, , 29 The length of the perpendicular drawn, , 25 If α , β and γ are three consecutive terms, , (a) 0, , (b) 48, , $ ) is, and r = ( $i + $j) + µ ( − i$ + $j − 2k, (a) 3, , (b), , 1, 3, , (d), , (c) 3, , 1, 3, , 30 The term independent of x in the, , (d) βγ, , 6, 1, 3, x8 2, expansion of , −, . 2x − 2 is, x , 60 81 , equal to, , 26 Let A, B and C be sets such that, φ ≠ A ∩ B ⊆ C. Then, which of the, following statements is not true?, , (a) − 72, , (a) B ∩ C ≠ φ, , (c) − 36, , (b) 36, , (d) − 108, , Answers, Physics, 1., 11., 21., , (b), (a), (d), , 2., 12., 22., , (d), (d), (*), , 3., 13., 23., , (c), (a), (d), , 4., 14., 24., , (c), (b), (b), , 5., 15., 25., , (b), (b), (b), , 6., 16., 26., , (c), (d), (b), , 7., 17., 27., , (c), (c), (b), , 8., 18., 28., , (b), (c), (b), , 9., 19., 29., , (a), (a), (d), , 10., 20., 30., , (b), (a), (c), , (b), (a), (a), , 3., 13., 23., , (d), (b), (c), , 4., 14., 24., , (c), (d), (d), , 5., 15., 25., , (d), (a), (c), , 6., 16., 26., , (c), (b), (b), , 7., 17., 27., , (d), (a), (a), , 8., 18., 28., , (a), (d), (d), , 9., 19., 29., , (a), (c), (d), , 10., 20., 30., , (d), (c), (c), , 3., 13., 23., , (a), (b), (c), , 4., 14., 24., , (b), (a), (c), , 5., 15., 25., , (a), (a), (d), , 6., 16., 26., , (d), (c), (d), , 7., 17., 27., , (d), (b), (b), , 8., 18., 28., , (b), (a), (c), , 9., 19., 29., , (c), (a), (c), , 10., 20., 30., , (a), (d), (c), , Chemistry, 1., 11., 21., , (c), (c), (d), , 2., 12., 22., , Mathematics, 1., 11., 21., , (d), (a), (a), , 2., 12., 22., , (c), (a), (b), , For Detailed Solutions Visit : https://bit.ly/2vIznG8 Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (09 January, 2019), TIME 9:30-12:30 (Shift I), , MM : 360, , PHYSICS, 1 A bar magnet is demagnetised by, inserting it inside a solenoid of length, 0.2 m, 100 turns and carrying a current of, 5.2 A. The coercivity of the bar magnet is, (a) 1200 A/m, (c) 2600A/m, , (b) 285 A/m, (d) 520A/m, , 2 A rod of length L at room temperature, and uniform area of cross-section A, is, made of a metal having coefficient of, linear expansion α / °C. It is observed that, an external compressive force F, is, applied on each of its ends, prevents any, change in the length of the rod, when its, temperature rises by ∆T K. Young’s, modulus, Y for this metal is, F, 2 Aα ∆T, F, (b), Aα (∆T − 273), 2F, (c), Aα∆T, F, (d), Aα∆T, (a), , 3 Three charges +Q , q , + Q are placed, d, and d from, 2, the origin on the X-axis. If the net force, , respectively at distance 0,, , experienced by +Q placed at x = 0 is zero,, then value of q is, , +Q, 2, −Q, (c), 2, , +Q, 4, −Q, (d), 4, , (a), , (b), , m, are connected at, 2, the two ends of a massless rigid rod of, length l. The rod is suspended by a thin, wire of torsional constant k at the centre, of mass of the rod-mass system (see, figure). Because of torsional constant k,, the restoring torque is τ = kθ for angular, displacement θ. If the rod is rotated by θ 0, and released, the tension in it when it, passes through its mean position will be, , 4 Two masses m and, , l, m, m/2, , 2kθ 20, l, 3kθ 20, (c), l, , (a), , kθ 20, l, kθ 20, (d), 2l, (b)
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4, , JEE Main 2019 ~ Solved Paper, , ONLINE, 5 An infinitely long current-carrying wire, , 9 A copper wire is stretched to make it 0.5%, , and a small current-carrying loop are in, the plane of the paper as shown. The, radius of the loop is a and distance of its, centre from the wire is d( d >> a ). If the, loop applies a force F on the wire, then, , longer. The percentage change in its, electrical resistance, if its volume remains, unchanged is, (a) 2.0%, (c) 0.5%, , (b) 1.0%, (d) 2.5%, , 10 A gas can be taken from A to B via two, different processes ACB and ADB., p, , C, , B, , A, , D, , d, , a 2, (a) F ∝ 3 , d , a, (c) F ∝ , d, , (b) F = 0, a, (d) F ∝ , d, , 2, , 6 A plane electromagnetic wave of, frequency 50 MHz travels in free space, along the positive x - direction. At a, particular point in space and time,, E = 6.3 $j V/m. The, r corresponding, magnetic field B, at that point will be, $ T, (a) 18.9 × 108 k, −8 $, (c) 18.9 × 10 k T, , $ T, (b) 6.3 × 10−8 k, −8 $, (d) 2.1 × 10 k T, , 7 Drift speed of electrons, when 1.5 A of, current flows in a copper wire of, cross-section 5 mm 2 is v. If the electron, density in copper is 9 × 1028 / m3 , the, value of v in mm/s is close to (Take,, charge of electron to be = 1.6 × 10−19 C), (a) 0.02, (c) 2, , (b) 0.2, (d) 3, , 8 Mobility of electrons in a semiconductor, is defined as the ratio of their drift, velocity to the applied electric field. If, for an n - type semiconductor, the, density of electrons is 1019m −3 and their, mobility is 1.6 m 2 (V-s), then the, resistivity of the semiconductor (since,, it is an n-type semiconductor, contribution of holes is ignored) is close, to, (a) 2 Ω-m, (c) 0.4 Ω-m, , (b) 0.2 Ω-m, (d) 4 Ω-m, , V, , When path ACB is used 60 J of heat flows, into the system and 30 J of work is done by, the system. If path ADB is used work done, by the system is 10 J the heat flow into the, system in path ADB is, (a) 80 J, (c) 100 J, , (b) 40 J, (d) 20 J, , 11 Two coherent sources produce waves of, different intensities which interfere. After, interference, the ratio of the maximum, intensity to the minimum intensity is 16., The intensity of the waves are in the ratio, (a) 16 : 9, (c) 25 : 9, , (b) 5 : 3, (d) 4 : 1, , 12 A particle is moving with a velocity, v = k( yi$ + x$j), where k is a constant., The general equation for its path is, (a) y = x2 + constant (b) y2 = x + constant, (c) xy = constant, (d) y2 = x2 + constant, , 13 Temperature difference of 120°C is, maintained between two ends of a uniform, rod AB of length 2L. Another bent rod PQ,, 3L, of same cross-section as AB and length, 2, is connected across AB, (see figure). In steady state, temperature, difference between P and Q will be close to, L, 4, A, , (a) 45°, (c) 75°C, , P, , L, , Q, , (b) 35°C, (d) 60°C, , B
Page 524 : JANUARY ATTEMPT ~ 9 Jan 2019, Shift I, 14 Surface of certain metal is first, , 17 Consider a tank made of glass (refractive, , illuminated with light of wavelength, λ 1 = 350 n-m and then by light of, wavelength λ 2 = 540 n-m. It is found that, the maximum speed of the photoelectrons, in the two cases differ by a factor of 2., The work function of the metal (in eV) is, close to, 1240, (energy of photon =, eV), λ (in n - m ), (a) 5.6, (c) 1.8, , 5, , index is 1.5) with a thick bottom. It is, filled with a liquid of refractive index µ. A, student finds that, irrespective of what, the incident angle i (see figure) is for a, beam of light entering the liquid, the, light reflected from the liquid glass, interface is never completely polarised., For this to happen, the minimum value, of µ is, i, , (b) 2.5, (d) 1.4, , 15 A parallel plate capacitor is made of two, square plates of side ‘a’ separated by a, distance d (d<<a). The lower triangular, portions is filled with a dielectric of, dielectric constant k, as shown in the, figure. Capacitance of this capacitor is, , n =1.5, , 3, 5, 4, (c), 3, (a), , d, K, , 5, 3, 5, (d), 3, (b), , 18 A convex lens is put 10 cm from a light, a, , (a), , Kε 0 a 2, ln K, d, , (b), , Kε 0 a 2, ln K, d (K − 1), , (c), , Kε 0 a 2, 2d (K + 1), , (d), , 1 . Kε 0 a 2, 2, d, , 16 A current loop, having two circular arcs, joined by two radial lines as shown in the, figure. It carries a current of 10 A. The, magnetic field at point O will be close to, O, , m, , °, m, , θ=45, , 3c, , 3c, , (a), (b), (c), (d), , 0, 1.1 cm away from the lens, 0.55 cm away from the lens, 0.55 cm towards the lens, , 19 A sample of radioactive material A, that, , R, , m, , 2c, , 2c, , m, , Q, , P, , S, i=10 A, , (a) 1 .0 × 10−5 T, (c) 1 . 5 × 10−7 T, , source and it makes a sharp image on a, screen, kept 10 cm from the lens. Now, a, glass block (refractive index is 1.5) of, 1.5 cm thickness is placed in contact with, the light source., To get the sharp image again, the screen is, shifted by a distance d. Then, d is, , (b) 1 . 0 × 10−7 T, (d) 1 . 5 × 10−5 T, , has an activity of 10 mCi (1 Ci = 3.7 × 1010, decays/s) has twice the number of nuclei, as another sample of a different, radioactive material B which has an, activity of 20 mCi. The correct choices for, half-lives of A and B would, then be, respectively, (a), (b), (c), (d), , 20 days and 10 days, 5 days and 10 days, 10 days and 40 days, 20 days and 5 days
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6, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 20 A block of mass 10 kg is kept on a rough, inclined plane as shown in the figure. A, force of 3 N is applied on the block. The, coefficient of static friction between the, plane and the block is 0.6. What should, be the minimum value of force F, such, that the block does not move downward ?, (Take, g = 10ms−2), F, , 10, 3N, , kg, , 23 Three blocks A, B and C are lying on a, smooth horizontal surface as shown in, the figure. A and B have equal masses m, while C has mass M. Block A is given an, initial speed v towards B due to which it, collides with B perfectly inelastically. The, combined mass collides with C, also, 5, perfectly inelastically th of the initial, 6, kinetic energy is lost in whole process., M, What is value of ?, m, , 45°, , (a) 32 N, (c) 23 N, , (b) 25 N, (d) 18 N, , A, , B, , C, , m, , m, , M, , (a) 4, (c) 3, , 21 A heavy ball of mass M is suspended, , (b) 2, (d) 5, , 24 A resistance is shown in the figure. Its, , from the ceiling of a car by a light string, of mass m( m << M ). When the car is at, rest, the speed of transverse waves in the, string is 60 ms−1. When the car has, acceleration a, the wave speed increases, to 60.5 ms−1. The value of a, in terms of, gravitational acceleration g is closest to, , value and tolerance are given respectively, by, , g, (a), 20, g, (c), 30, , (a) 270 Ω, 5%, (c) 27 k Ω, 10%, , g, (b), 5, g, (d), 10, , Red, , Violet, , (b) 27 k Ω, 20%, (d) 270 k Ω, 10%, , closed, then the value of current i will be, 20 V i1, , uniform mass density is suspended with a, string as shown in figure. If AB = BC and, the angle is made by AB with downward, vertical is θ, then, , A, , i2 10 V, , C, 2Ω, , 4Ω, , i, , B, , 2Ω, S, , A, , V=0, , z, , θ, , (a) 4A, (c) 2A, , 90°, , x, , (b) 3A, (d) 5A, , 26 For a uniformly charged ring of radius R,, the electric field on its axis has the, largest magnitude at a distance h from its, centre. Then, value of h is, , C, , 2, (a) tan θ =, 3, 1, (c) tan θ =, 2, , Silver, , 25 When the switch S in the circuit shown is, , 22 An L-shaped object made of thin rods of, , B, , Orange, , 1, 2 3, 1, (d) tan θ =, 3, , (b) tan θ =, , (a), , R, 2, , (c) R, , (b) R 2, (d), , R, 5
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JANUARY ATTEMPT ~ 9 Jan 2019, Shift I, 27 A conducting circular loop is made of a, , thin wire has area 3.5 × 10−3 m 2 and, resistance 10 Ω. It is placed, perpendicular to a time dependent, magnetic field B ( t ) = ( 0.4T ) sin( 0.5 π t )., The field is uniform in space. Then the, net charge flowing through the loop, during t = 0 s and t = 10 ms is close to, , (a) 6 mC, (c) 7 mC, , (b) 21 mC, (d) 14 mC, , 28 A mixture of 2 moles of helium gas, (atomic mass = 4u) and 1 mole of argon, gas (atomic mass = 40u) is kept at 300 K, in a container. The ratio of their rms, speeds, vrms (helium) , is close to, , vrms (argon) , (a) 0.32, (c) 3.16, , 7, orbit is L about the centre of the sun , its, areal velocity is, 4L, m, L, (c), 2m, (a), , 2L, m, L, (d), m, (b), , 30 A block of mass m lying on a smooth, horizontal surface is attached to a spring, (of negligible mass) of spring constant k., The other end of the spring is fixed as, shown in the figure. The block is initially, at rest in its equilibrium position. If now, the block is pulled with a constant force, F, the maximum speed of the block is, , m, , (b) 2.24, (d) 0.45, , πF, mk, 2F, (c), mk, (a), , 29 If the angular momentum of a planet of, mass m, moving around sun in a circular, , F, , F, mk, F, (d), π mk, , (b), , CHEMISTRY, 1 The alkaline earth metal nitrate that does, not crystallise with water molecules, is, (a) Ca(NO3 )2, (c) Ba(NO3 )2, , (b) Sr(NO3 )2, (d) Mg(NO3 )2, , 2 0.5 moles of gas A and x moles of gas B, exert a pressure of 200 Pa in a container, of volume 10m3 at 1000 K. Given R is the, gas constant in JK −1 mol−1, x is, 2R, 4−R, 4+R, (c), 2R, (a), , 4 −R, 2R, 2R, (d), 4+ R, (b), , 3 According to molecular orbital theory,, which of the following is true with respect, to Li+2 and Li−2 ?, (a) Both are unstable, (b) Li+2 is unstable and Li−2 is stable, (c) Both are stable, (d) Li+2 is stable and Li−2 is unstable, , 4 The major product of following reaction is, R C ≡≡ N, (a) RCHO, (c) RCOOH, , (i) AIH( i - Bu) 2, , → ?, (ii) H 2O, , (b) RCONH2, (d) RCH2NH2, , 5 The correct decreasing order for acid, strength is, (a) FCH2COOH > NCCH2COOH, > NO2CH2COOH > ClCH2COOH, (b) CNCH2COOH > O2NCH2COOH, > FCH2COOH > ClCH2COOH, (c) NO2CH2COOH > NCCH2COOH, > FCH2COOH > ClCH2COOH, (d) NO2CH2COOH > FCH2COOH, > CNCH2COOH > ClCH2COOH, , 6 The one that is extensively used as a, piezoelectric material is, (a) quartz, (b) tridymite, (c) amorphous silica (d) mica
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8, , JEE Main 2019 ~ Solved Paper, , ONLINE, 7 The ore that contains both iron and, , 12 Arrange the following amines in the, , copper is, , decreasing order of basicity:, , (a) malachite, (c) dolomite, , (b) azurite, (d) copper pyrites, , N, (I), , 8 For emission line of atomic hydrogen from, n i = 8 to n f = n, the plot of wave number ( ν ), 1, against 2 will be (The Rydberg, n , constant, RH is in wave number unit), (a), (b), (c), (d), , H, (II), , H, (III), , (b) III > II > I, (d) III > I > II, , and increase down a group in the periodic, table, respectively are, , oxidation state. In contrast, thallium, exists in +1 and +3 oxidation states. This, is due to, lattice effect, lanthanoid contraction, inert pair effect, diagonal relationship, , (a) electronegativity and atomic radius, (b) electronegativity and electron gain, enthalpy, (c) electron gain enthalpy and, electronegativity, (d) atomic radius and electronegativity, , 14 Adsorption of a gas follows Freundlich, , 10 A water sample has ppm level, concentration of the following metals:, Fe = 0.2; Mn = 5.0 ; Cu = 3.0; Zn = 5.0. The, metal that makes the water sample, unsuitable for drinking is, (a) Cu, (c) Mn, , N, , 13 In general, the properties that decrease, , non linear, linear with slope −RH, linear with slope RH, linear with intercept −RH, , 9 Aluminium is usually found in +3, , (a), (b), (c), (d), , (a) I > II > III, (c) I > III > II, , N, , adsorption isotherm. In the given plot,x is, the mass of the gas adsorbed on mass m, x, of the adsorbent at pressure p ⋅, is, m, proportional to, , x, log m, , (b) Fe, (d) Zn, , 2 unit, 4 unit, , 11 Major product of the following reaction is, log p, , Cl, NH2, , Cl, + H2N, , Cl, (a), , O, n, , O, , Cl, NH2 (b), , N, H, , n, , Cl, , O, NH2, , (d), n, NH2, O, , O, , N, H, , (b) 7.6, (d) 22.8, , 16 The isotopes of hydrogen are, , n, , HN, , recharged using electricity of, 0.05 Faraday. The amount of PbSO4, electrolysed in g during the process is, (Molar mass of PbSO4 = 303g mol−1), (a) 11.4, (c) 15.2, , Cl, , (c), , (b) p1/ 4, (d) p, , 15 The anodic half-cell of lead-acid battery is, , O, , HN, Ol, , (a) p, (c) p1/ 2, , (i) Et3N, (ii) Free radical, polymerisation, , O, , O, , 2, , NH2, O, , (a), (b), (c), (d), , deuterium and tritium only, protium and deuterium only, protium, deuterium and tritium, tritium and protium only
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JANUARY ATTEMPT ~ 9 Jan 2019, Shift I, 17 A solution of sodium sulphate contains, , 9, 21 The compounds A and B in the following, , 92 g of Na + ions per kilogram of water., The molality of Na + ions in that solution, in mol kg−1 is, , reaction are, respectively, , (a) 16, (c) 132, , (a), (b), (c), (d), , (b) 4, (d) 8, , 18 The major product of the following, reaction is, , Br, , OEt, OEt, , OEt, , OEt, , Br, , OEt, (d), , 19 Two complexes [Cr(H 2O)6 ]Cl3 (A) and, [Cr(NH3 )6 ]Cl3 (B) are violet and yellow, coloured, respectively. The incorrect, statement regarding them is, (a) ∆ o value for (A) is less than that of (B), (b) both absorb energies corresponding to, their complementary colours, (c) ∆ o values of (A) and (B) are calculated, from the energies of violet and yellow, light, respectively, (d) both are paramagnetic with three, unpaired electrons, , reaction is, , O, (a), , regarding Henry’s law is not correct?, (a) Different gases have different K H, (Henry’s law constant) values at the, same temperature, (b) Higher the value of K H at a given, pressure, higher is the solubility of the, gas in the liquids, (c) The value of K H increases with increase, of temperature and K H is function of the, nature of the gas, (d) The partial pressure of the gas in vapour, phase is proportional to the mole fraction, of the gas in the solution, , 24 The correct match between Item - I and, Item - II is, , (ii) CrO3/H+, (iii) H2SO4/∆, , O, , Item I (Drug), , Item II (Test), , A., , Chloroxylenol, , P., , Carbylamine, test, , B., , Norethindrone, , Q., , Sodium, hydrogen, carbonate test, , C., , Sulphapyridine, , R., , Ferric chloride, test, , D., , Penicillin, , S., , Bayer’s test, , (b), , Br, O, (c), , (i) KOH (aq.), , (b) 5.0, (d) 5.2, , 23 Which one of the following statements, , 20 The major product of the following, , Br, , B, , A = Benzyl alcohol, B = Benzyl isocyanide, A = Benzyl alcohol, B = Benzyl cyanide, A = Benzyl chloride, B = Benzyl isocyanide, A = Benzyl chloride, B = Benzyl cyanide, , (a) 9.3, (c) 9.0, , (b), , Br, , AgCN, , to 30 mL of 0.2 M NH 4OH solution. The, pH of the resultant mixture is [pK b of, NH 4OH = 4.7], , (ii) EtOH, , (c), , A, , 22 20 mL of 0.1 M H 2SO4 solution is added, , (i) Br2, , (a), , HCHO+HCl, , HO, O, (d), , HO, Br, , (a), (b), (c), (d), , A→ R ; B→ P ; C→ S ; D→ Q, A→ R ; B→ S ; C→ P ; D→ Q, A→ Q ; B→ P ; C→ S ; D→ R, A→ Q ; B→ S ; C→ P ; D→ R
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10, , JEE Main 2019 ~ Solved Paper, , ONLINE, |W|, , 25 Correct statements among (I) to (IV), , T2, , |W|, , regarding silicones are:, I. They are polymers with hydrophobic, character., II. They are biocompatible., III. In general, they have high thermal, stability and low dielectric strength., IV. Usually, they are resistant to oxidation, and used as greases., (a) I and II only, (b) I, II, III only, (c) I, II, III and IV, (d) I, II and IV only, , 26 The highest value of the calculated spin, only magnetic moment (in BM) among all, the transition metal complexes is, (a) 5.92, (c) 6.93, , (b) 3.87, (d) 4.90, , expansion of an ideal gas in a closed, system at two different temperatures T1, and T2 (T1 < T2 ). The correct graphical, depiction of the dependence of work done, (W) on the final volume (V) is, T2, , |W|, T1, , T2, , (b), O, , ln V, , O, , (d), O, , O, , ln V, , ln V, , 28 The following results were obtained, during kinetic studies of the reaction;, 2A + B → Products, Experiment, , Initial rate of, reaction, (in mol L−1 min −1 ), , [A], [B], (in mol L−1) (in mol L−1 ), , I., , 0.10, , 0.20, , 6.93 × 10−3, , II., , 0.10, , 0.25, , 6.93 × 10−3, , III., , 0.20, , 0.30, , 1386, ., × 10−2, , (a) 5, (c) 100, , (b) 10, (d) 1, , 29 Which amongst the following is the, strongest acid?, (b) CHI3, (d) CH(CN)3, , (a) CHBr3, (c) CHCl3, , 30 The increasing order of pK a of the, T1, , (a), , T1, , T1, (c), , The time (in minutes) required to, consume half of A is, , 27 Consider the reversible isothermal, , |W|, , T2, , ln V, , following amino acids in aqueous solution, is Gly, Asp, Lys, Arg, (a), (b), (c), (d), , Asp < Gly < Arg < Lys, Arg < Lys < Gly < Asp, Gly < Asp < Arg < Lys, Asp < Gly < Lys < Arg, , MATHEMATICS, π, 3, 2, −1 3 , + cos = x > , then, 3x , 4x 2 , 4, x is equal to, , 1 If cos−1 , , (a), (b), (c), (d), , 145, 10, 146, 12, 145, 12, 145, 11, , π, , 2 The value of ∫ |cos x|3 dx is, 0, , (a), , 2, 3, , (c) 0, , (b) −, (d), , 4, 3, , 4, 3, , 3 For x 2 ≠ nπ + 1, n ∈ N (the set of natural, numbers), the integral, , ∫x, , 2 sin( x 2 − 1) − sin 2( x 2 − 1), 2 sin( x 2 − 1) + sin 2( x 2 − 1), , dx is equal
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JANUARY ATTEMPT ~ 9 Jan 2019, Shift I, to (where C is a constant of integration ), 1, (a) log e|sec(x2 − 1)| + C, 2, x2 − 1 , (b) log e sec , +C, 2 , 1, (c) log e sec2(x2 − 1) + C, 2, x2 − 1 , 1, (d) log e sec2 , +C, 2, 2 , , 4 If y = y( x ) is the solution of the, dy, + 2 y = x2, dx, 1, satisfying y(1) = 1, then y is equal to, 2, differential equation, x, , 13, (a), 16, 49, (c), 16, , 1, (b), 4, 7, (d), 64, , 5 The equation of the line passing through, (−4, 3, 1), parallel to the plane, x + 2 y − z − 5 = 0 and intersecting the line, x +1 y − 3 z − 2, is, =, =, 2, −1, −3, , x+4, =, 3, x+4, (b), =, −1, x+4, (c), =, 1, x −4, (d), =, 2, (a), , y−3 z −1, =, −1, 1, y−3 z −1, =, 1, 1, y−3 z −1, =, 1, 3, y+3 z+1, =, 1, 4, , 6 Let f: R → R be a function defined as, 5,, a + bx ,, f(x) = , b + 5x ,, 30,, Then, f is, (a), (b), (c), (d), , if, x≤1, if 1 < x < 3, if 3 ≤ x < 5, if, x≥ 5, , continuous if a = − 5 and b = 10, continuous if a = 5 and b = 5, continuous if a = 0 and b = 5, not continuous for any values of a and b, , 11, positive X-axis, then which of the, following points does not lie on it?, (a) (4, −4), (c) (8, 6), , (b) (6, 4 2), (d) (5, 2 6), , 8 Consider the set of all lines, , px + qy + r = 0 such that 3 p + 2q + 4 r = 0., Which one of the following statements is, true?, , (a) Each line passes through the origin., (b) The lines are concurrent at the point, 3 1, , , 4 2, (c) The lines are all parallel, (d) The lines are not concurrent, , 9 Let α and β be two roots of the equation, x 2 + 2x + 2 = 0, then α15 + β15 is equal to, (a) 256, (c) −256, , (b) 512, (d) −512, , 10 If the fractional part of the number, is, , 2403, 15, , k, , then k is equal to, 15, , (a) 14, (c) 4, , (b) 6, (d) 8, , 11 5 students of a class have an average, height 150 cm and variance 18 cm 2. A, new student, whose height is 156 cm,, joined them. The variance (in cm 2) of the, height of these six students is, (a) 16, (c) 20, , (b) 22, (d) 18, , 12 If a , b and c be three distinct real, numbers in GP and a + b + c = xb, then x, cannot be, (a) 4, (c) −2, , (b) 2, (d) −3, , 13 The plane through the intersection of the, planes x + y + z = 1 and 2x + 3 y − z + 4 = 0, and parallel to Y -axis also passes through, the point, (a) (3, 3, −1), (c) (3, 2, 1), , (b) (−3, 1, 1), (d) (−3, 0, −1), , 7 Axis of a parabola lies along X-axis. If its, , 14 The maximum volume (in cu.m) of the, , vertex and focus are at distances 2 and 4, respectively from the origin, on the, , right circular cone having slant height, 3m is
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12, , JEE Main 2019 ~ Solved Paper, , ONLINE, 4, π, 3, (c) 3 3π, , (b) 2 3π, , (a), , (d) 6π, , cos θ − sin θ, , then the matrix, cos θ , , 15 If A = , sin θ, , A−50 when θ =, 1, , (a) 2, − 3, 2, 3, , (c) 2, − 1, 2, , π, , is equal to, 12, , 3, 2 , , 1 , 2 , 1 , 2 , , 3, 2 , , , , (b) , , , , , (d) , , , , 3, 2, 1, 2, 1, 2, 3, 2, , 16 For x ∈ R − { 0, 1}, let f1( x ) =, , 1, − , 2, , 3, 2 , 3, −, 2 , , 1 , 2 , , 1, , f2( x ) = 1 − x, x, , 1, and f3 ( x ) =, be three given functions., 1−x, If a function, J (x) satisfies, ( f2 ° J ° f1 )( x ) = f3 ( x ), then J ( x ) is equal to, (a) f2(x), , (b) f3 (x), 1, (d) f3 (x), x, , (c) f1 (x), , number of different teams consisting of 2, girls and 3 boys that can be formed from, this class, if there are two specific boys A, and B, who refuse to be the members of, the same team, is, (b) 500, (d) 300, , 18 If θ denotes the acute angle between the, curves, y = 10 − x and y = 2 + x at a, point of their intersection, then|tan θ| is, equal to, 2, , 7, 17, 4, (c), 9, (a), , π π, 4 2, , 20 For any θ ∈ , , the expression, 3 (sin θ − cos θ )4 + 6 (sin θ + cos θ )2 + 4 sin6 θ, equals, (a), (b), (c), (d), , 13 − 4 cos 4 θ + 2 sin 2 θ cos 2 θ, 13 − 4 cos 2 θ + 6 cos 4 θ, 13 − 4 cos 2 θ + 6 sin 2 θ cos 2 θ, 13 − 4 cos 6 θ, , 21 If the Boolean expression, ( p ⊕ q ) ∧ (~ p ⋅ q ) is equivalent to p ∧ q,, where ⊕, ⋅ ∈{ ∧,∨}, then the ordered, pair(⊕, ⋅) is, (a) (∧, ∨), (c) (∨, ∧), , (b) (∧, ∧), (d) (∨, ∨), , 22 Equation of a common tangent to the, circle, x 2 + y 2 − 6x = 0 and the parabola,, y 2 = 4x, is, , 17 Consider a class of 5 girls and 7 boys. The, , (a) 350, (c) 200, , (a) a , b, c are in AP, 1, 1, 1, (b), =, +, a, b, c, (c) a , b , c are in AP, 1, 1, 1, (d), =, +, b, a, c, , 2, , 8, 15, 8, (d), 17, (b), , 3 y = 3x + 1, 3y = x + 3, , (a), (c), , (b) 2 3 y = 12x + 1, (d) 2 3 y = − x − 12, , , , π 3 + 2i sin θ, , π :, 2 1 − 2i sin θ, , , is purely imaginary, , Then, the sum of the elements in A is, , 23 Let A = θ ∈ −, , (a), , 3π, 4, , (c) π, , 5π, 6, 2π, (d), 3, (b), , $ and c be a vector, 24 Let a = $i − $j, b = i$ + $j + k, such that a × c + b = 0 and a ⋅ c = 4, then, |c|2 is equal to, , 19 Three circles of radii a , b, c( a < b < c) touch, , (a) 8, , each other externally. If they have X-axis, as a common tangent, then, , (c) 9, , 19, 2, 17, (d), 2, (b)
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JANUARY ATTEMPT ~ 9 Jan 2019, Shift I, , 13, π, 2, , 25 The system of linear equations, , 28 Let 0 < θ < . If the eccentricity of the, , x+ y+ z =2, 2x + 3 y + 2z = 5, 2x + 3 y + (a 2 − 1)z = a + 1, (a), (b), (c), (d), , 3, (a) (1, ], 2, , parabola y = x 2 − 1, the tangent at the, point (2, 3) to it and the Y -axis is, , 27 lim, , (b), , 56, 3, , (c), , 32, 3, , (d), , T =, , 14, 3, , (b) does not exist, , (d) (2, 3], 30, , ∑ ai and, , i =1, , 15, , ∑ a( 2i − 1) . If a5 = 27 and S − 2T = 75,, , then a10 is equal to, (a) 42, , y4, , (a) exists and equals, , 3, (c) ( ,2], 2, , (b) (3,∞), , i =1, , 1 + 1 + y4 − 2, , y→ 0, , −, , 29 Let a1 , a2 , ..... a30 be an AP, S =, , 26 The area (in sq units) bounded by the, , 8, 3, , y2, , = 1 is greater, cos2 θ sin2 θ, than 2, then the length of its latus rectum, lies in the interval, , has infinitely many solutions for a = 4, is inconsistent when a = 4, has a unique solution for|a| = 3, is inconsistent when|a| = 3, , (a), , x2, , hyperbola, , (b) 57, , (c) 52, , (d) 47, , 30 Two cards are drawn successively with, , 1, 4 2, , (c) exists and equals, , 1, 2 2, , (d) exists and equals, , 1, 2 2 ( 2 + 1), , replacement from a well shuffled deck of, 52 cards. Let X denote the random, variable of number of aces obtained in the, two drawn cards. Then,, P ( X = 1) + P ( X = 2) equals, (a), , 25, 169, , (b), , 52, 169, , (c), , 49, 169, , (d), , 24, 169, , Answers, Physics, 1., 11., 21., , (c), (c), (b), , 2., 12., 22., , (d), (d), (d), , 3., 13., 23., , (d), (a), (a), , 4., 14., 24., , (b), (c), (c), , 5., 15., 25., , (d), (b), (d), , 6., 16., 26., , (d), (a), (a), , 7., 17., 27., , (a), (a), (d), , 8., 18., 28., , (c), (c), (c), , 9., 19., 29., , (b), (d), (c), , 10., 20., 30., , (b), (a), (b), , (b), (d), (a), , 3., 13., 23., , (d), (a), (b), , 4., 14., 24., , (a), (c), (b), , 5., 15., 25., , (c), (b), (d), , 6., 16., 26., , (a), (c), (a), , 7., 17., 27., , (d), (b), (c), , 8., 18., 28., , (c), (d), (b), , 9., 19., 29., , (c), (c), (d), , 10., 20., 30., , (c), (a), (d), , 3., 13., 23., , (b), (c), (d), , 4., 14., 24., , (c), (b), (b), , 5., 15., 25., , (a), (c), (d), , 6., 16., 26., , (d), (b), (a), , 7., 17., 27., , (c), (d), (a), , 8., 18., 28., , (b), (b), (b), , 9., 19., 29., , (c), (b), (c), , 10., 20., 30., , (d), (d), (a), , Chemistry, 1., 11., 21., , (c), (d), (c), , 2., 12., 22., , Mathematics, 1., 11., 21., , (c), (c), (a), , 2., 12., 22., , (d), (b), (c), , For Detailed Solutions Visit : https://bit.ly/307bQwo Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (09 January, 2019), TIME 2:30-5:30 (Shift II), , MM : 360, , PHYSICS, 1 In form of G (universal gravitational, constant), h (Planck constant) and c (speed, of light), the time period will be, proportional to, (a), , Gh, 5, , (b), , hc5, G, , (d), , Gh, , c, (c), , c3, Gh, , c3, , 2 A parallel plate capacitor with square, plates is filled with four dielectrics of, dielectric constants K1 , K 2 , K3 , K 4, arranged as shown in the figure. The, effective dielectric constant K will be:, K1, , K2, , L/2, , K3, , K4, , L/2, , d/2, , d/2, , 3 A series AC circuit containing an inductor, , (20 mH), a capacitor (120 µF) and a, resistor (60 Ω ) is driven by an AC source of, 24 V/50 Hz. The energy dissipated in the, circuit in 60 s is, , (a) 3.39 × 103 J, (b) 5.65 × 102 J, (c) 2.26 × 103 J, (d) 517, . × 102 J, , 4 In the given circuit, the internal resistance, of the 18 V cell is negligible. If R1 = 400 Ω,, R3 = 100 Ω and R4 = 500 Ω and the reading, of an ideal voltmeter across R4 is 5 V, then, the value of R2, will be, R3, R1, , (a), (b), (c), (d), , (K1 + K 2 ) (K3 + K 4 ), K =, 2 (K1 + K 2 + K3 + K 4 ), (K + K 2 ) (K3 + K 4 ), K = 1, K1 + K 2 + K3 + K 4, (K1 + K3 ) (K 2 + K 4 ), K =, K1 + K 2 + K3 + K 4, (K1 + K 4 ) (K 2 + K3 ), K =, 2 (K1 + K 2 + K3 + K 4 ), , R4, R2, , 18 V, , (a) 550 Ω, (c) 300 Ω, , (b) 230 Ω, (d) 450 Ω, , 5 In a car race on a straight path, car A, takes a time t less than car B at the finish, and passes finishing point with a speed ‘v’, more than that of car B. Both the cars, start from rest and travel with constant
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15, , JANUARY ATTEMPT ~ 9 Jan 2019, Shift II, acceleration a1 and a 2 respectively. Then, ‘v’ is equal to, (a), , 2a1 a2, t, a1 + a2, , (b) 2a1 a2 t, (d), , (c) a1 a2 t, , height ‘h’ above earth surface (where,, radius of earth = 64, . × 103 km) is E1 and, kinetic energy required for the satellite to, be in a circular orbit at this height is E 2., The value of h for which E1 and E 2 are, equal is, (b) 1.28 × 104 km, (d) 1.6 × 103 km, , 7 At 0.3V and 0.7 V, the diodes Ge and Si, become conductor respectively. In given, figure, if ends of diode Ge overturned, the, change in potential V0 will be, Ge, V0, Si, , 12 V, , 5 kΩ, , (a) 0.2 V, , (b) 0.6V, , (c) 0.4 V, , (d) 0.8V, , 8. A particle having the same charge as of, electron moves in a circular path of radius, 0.5 cm under the influence of a magnetic, field of 0.5 T. If an electric field of 100 V/m, makes it to move in a straight path, then, the mass of the particle is (Take, charge of, electron = 16, . × 10−19 C), (a) 1.6 × 10−19 kg, −31, , (c) 9.1 × 10, , kg, , (a) 70 N, (c) 100 N, , (b) 200 N, (d) 140 N, , 10 A 15 g mass of nitrogen gas is enclosed in a, , a1 + a2, t, 2, , 6 The energy required to take a satellite to a, , (a) 3.2 × 103 km, (c) 6.4 × 103 km, , (Take, g = 10 ms−2), , (b) 1.6 × 10−27 kg, (d) 2.0 × 10−24 kg, , 9. A mass of 10 kg is suspended vertically by a, rope from the roof. When a horizontal force, is applied on the mass, the rope deviated at, an angle of 45° at the roof point. If the, suspended mass is at equilibrium, the, magnitude of the force applied is, , vessel at a temperature 27°C. Amount of, heat transferred to the gas, so that rms, velocity of molecules is doubled is about, (Take, R = 83, . J / K - mole), (a) 10 kJ, (c) 14 kJ, , (b) 0.9 kJ, (d) 6 kJ, , 11 A power transmission line feeds input, power at 2300 V to a step-down, transformer with its primary windings, having 4000 turns. The output power is, delivered at 230 V by the transformer. If, the current in the primary of the, transformer is 5A and its efficiency is 90%,, the output current would be, (a) 45 A, (c) 25 A, , (b) 50 A, (d) 35 A, , 12 A rod of mass ‘M’ and length ‘2L’ is, suspended at its middle by a wire. It, exhibits torsional oscillations. If two, masses each of ‘m’ are attached at distance, ‘L/2’ from its centre on both sides, it, reduces the oscillation frequency by 20%., The value of ratio m/M is close to, (a) 0.57, (c) 0.77, , (b) 0.37, (d) 0.17, , 13 Two Carnot engines A and B are operated, in series. The first one, A receives heat at, T1 (= 600 K) and rejects to a reservoir at, temperature T2. The second engine B, receives heat rejected by the first engine, and in turn rejects to a heat reservoir at, T3 ( = 400 K). Calculate the temperature T2, if the work outputs of the two engines are, equal., (a) 600 K, (c) 400 K, , (b) 500 K, (d) 300 K, , 14 A musician produce the sound of second, harmonics from open end flute of 50 cm., The other person moves toward the, musician with speed 10 km/h from the, second end of room. If the speed of sound
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16, , JEE Main 2019 ~ Solved Paper, , ONLINE, 330 m/s, the frequency heard by running, person will be, (a) 666 Hz, (c) 753 Hz, , (b) 500 Hz, (d) 333 Hz, , 15 The plane mirrors (M1 and M 2) are, inclined to each other such that a ray of, light incident on mirror M1 and parallel to, the mirror M 2 is reflected from mirror M 2, parallel to the mirror M1. The angle, between the two mirror is, (a) 45°, (c) 90°, , (b) 75°, (d) 60°, , 16 In free space, the energy of, electromagnetic wave in electric field is U E, and in magnetic field is U B . Then, , (a)UE = UB, (c)UE < UB, , (b)UE > UB, U, (d)UE = B, 2, , 17 Charge is distributed within a sphere of, radius R with a volume charge density, − 2r, A, ρ (r ) = 2 e a , where A and a are, r, constants. If Q is the total charge of this, charge distribution, the radius R is, , , , , 1, (a) a log , , Q, , 1−, , 2 πaA , a, Q , (c) log 1 −, , , 2, 2 πaA , , Q , (b) a log 1 −, , , 2 πaA , , , , , a, 1, (d) log , , Q, 2, , 1−, , 2 πaA , , 18 In a Young’s double slit experiment, the, slits are placed 0.320 mm apart. Light of, wavelength λ = 500 n-m is incident on the, slits. The total number of bright fringes that, are observed in the angular range, − 30° ≤ θ ≤ 30° is, (a) 320, (c) 640, , (b) 321, (d) 641, , 19 In communication system, only one, percent frequency of signal of wavelength, 800 nm can be used as bandwidth. How, many channal of 6MHz bandwidth can be, broadcast this?, (c = 3 × 108 m / s, h = 6.6 × 10−34 J - s), (a) 3.75 × 106, (b) 3.86 × 106, 5, (c) 6.25 × 10, (d) 4.87 × 105, , 20 In given time t = 0, Activity of two, radioactive substances A and B are equal., R, After time t, the ratio of their activities B, RA, decreases according to e−3 t . If the half life, of A is In 2, the half-life of B will be, , (a) 4 ln 2, (c), , ln 2, 2, , (b), , ln 2, 4, , (d) 2 ln 2, , 21 In three dimensional system, the position, coordinates of a particle (in motion) are, given below, x = a cos ωt, y = a sin ωt, z = aωt, The velocity of particle will be, (a) 2 aω, (c) aω, , (b) 2 aω, (d) 3 aω, , 22 A force acts on a 2 kg object, so that its, position is given as a function of time as, x = 3t 2 + 5. What is the work done by this, force in first 5 seconds?, (a) 850 J, (c) 950 J, , (b) 900 J, (d) 875 J, , 23 A particle is executing simple harmonic, motion (SHM) of amplitude A, along the, X-axis, about x = 0. when its potential, energy (PE) equals kinetic energy (KE),, the position of the particle will be, (a) A, (c), , A, 2 2, , A, 2, A, (d), 2, (b), , 24 The magnetic field associated with a light, wave is given at the origin, by B = B0, [sin (314, . × 107 ) ct + sin (628, . × 107 )ct ]., , If this light falls on a silver plate having a, work function of 4.7 eV, what will be the, maximum kinetic energy of the, photoelectrons?, (Take, c = 3 × 108 ms−1 and, h = 66, . × 10−34 J-s), (a) 7.72 eV, (b) 6.82 eV, (c) 8.52 eV, (d) 12.5 eV
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17, , JANUARY ATTEMPT ~ 9 Jan 2019, Shift II, 25 Two point charges q1 ( 10 µC) and, q2 (− 25 µC) are placed on the x-axis at, x = 1 m and x = 4 m, respectively. The, electric field (in V/m) at a point y = 3 m on, Y -axis is, , , 1, = 9 × 109 N - m2C−2, Take,, 4πε 0, , , (a) (63 $i − 27$j) × 102 (b) (81 $i − 81$j) × 102, (c) (−81 $i + 81$j) × 102 (d) (−63 $i + 27$j) × 102, , 26 The top of a water tank is open to air and, its water level is maintained. It is giving, out 0.74 m3 water per minute through a, circular opening of 2 cm radius is its wall., The depth of the centre of the opening, from the level of water in the tank is, close to, (a) 4.8 m, (c) 2.9 m, , (b) 6.0 m, (d) 9.6 m, , 27 One of the two identical conducting wires, of length L is bent in the form of a circular, loop and the other one into a circular coil, of N identical turns. If the same current is, passed in both, the ratio of the magnetic, field at the centre of the loop (BL ) to that, B, at the centre of the coil (BC ), i.e. L will be, BC, 1, (a), N, 1, (c), N2, , G O Y, , Golden, , (a) 5.3 MΩ ± 5%, (c) 6.4 MΩ ± 5%, , (b) 64 kΩ ± 10%, (d) 530 kΩ ± 5%, , 29 The pitch and the number of divisions, on, the circular scale for a given screw gauge, are 0.5 mm and 100, respectively. When, the screw gauge is fully tightened, without any object, the zero of its circular, scale lies 3 divisions below the mean line., The readings of the main scale and the, circular scale for a thin sheet are 5.5 mm, and 48 respectively, the thickness of this, sheet is, (a) 5.950 mm, (c) 5.755 mm, , (b) 5.725 mm, (d) 5.740 mm, , 30 A rod of length 50 cm is pivoted at one end., It is raised such that if makes an angle of, 30° from the horizontal as shown and, released from rest. Its angular speed when, it passes through the horizontal (in rad s−1), will be (Take, g = 10 ms−2 ), , 30º, , (b) N, (a), , (d) N 2, , 28 A carbon resistance has a following color, , (c), , 30, 2, 20, 3, , (b) 30, (d), , 30, 2, , code. What is the value of the resistance?, , CHEMISTRY, 1 The products formed in the reaction of cumene with O2 followed by treatment with dil. HCl are, CH3, (a), , (c), , and CH3—OH, , and, , H 3C, , CH3, , (d), , CH3, , H 3C, , OH, , OH, , OH, (b), , and, , and, , H 3C, , CH3
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18, , JEE Main 2019 ~ Solved Paper, , ONLINE, 2 Which of the salt-solution is most effective, for coagulation of arsenious sulphide?, (a) BaCl 2, , (b)AlCl3, , (c) Na3 PO4 (d)NaCl, , 3 In which of the following processes, the, bond order has increased and, paramagnetic character has changed to, diamagnetic?, (a) O2 → O+2, (c) O2 → O22−, , (b) N2 → N+2, (d) NO → NO+, , (a) At 800°C, Cu can be used for the, extraction of Zn from ZnO, (b) At 1400°C, Al can be used for the, extraction of Zn from ZnO, (c) At 500°C, coke can be used for the, extraction of Zn from ZnO, (d) Coke cannot be used for the extraction of, Cu from Cu 2O, , 7 What is reason of temporary hardness of, , 4 The major product of the following reaction, is, , water?, (a) Na 2SO 4, (c) NaCl, , 8 Which of the following compounds is not, , C, , aromatic?, , (i) Br2/hν, , NH2, , (ii) KOH (dil.), , CH2CH3, , (a), , (b), , N, H, , NH, , (a), , (b) CaCl 2, (d) Ca(HCO3 ) 2, , (b), , NH, , CH3, , (c), , (d), N, , CH3, , 9 The tests performed on compound X and, their inferences are :, , NH, , (c), , NH, , (d), , Test, , 5 The correct match between item-I and, Item-II is, A. Benzaldehyde P. Dynamic phase, B. Alumina, Q. Adsorbent, C. Acetonitrile, R. Adsorbate, (a) (A) → (R) ; (B) → (Q); (C) → (P), (b) (A) → (P); (B) → (R); (C) → (Q), (c) (A) → (Q); (B) → (P); (C) → (R), (d) (A) → (Q); (B) → (R); (C) → (P), , Inference, , (a) 2, 4- DNP, test, , Coloured precipitate, , (b) Iodoform, test, , Yellow precipitate, , (c), , No dye formation, , Azo-dye, test, , Compound ‘X’ is, H3C, , 6 The correct statement regarding the given, , N, , CH3, , H 3C, CHO, , (a), , N, , CH3, COCH3, , (b), , Ellingham diagram is, →, +O 2, 4Cu, , O, 2Cu 2, , NH2 OH, (c), , NH2, CH3, , (d), , ∆Gº (kJ/mol), , –300, , 2C, –600, , O2, 2Zn+, , nO, → 2Z, , +O, , l+O 2, 4 /3 A, , –1050, , →2, , 2, , CO, , O3, 3 Al 2, , → 2/, , 500ºC 800ºC, Temperature (ºC), , 2000ºC, , 10 Good reducing nature of H3 PO2 is, attributed to the presence of, (a) two P H bonds, (b) one P H bond, (c) two P OH bonds, (d) one P OH bond, , CHO
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19, , JANUARY ATTEMPT ~ 9 Jan 2019, Shift II, 11 The major product of the following reaction, is, HO, CH3, O, , +, , OH, , OH, , 17 The major product obtained in the, , CH3, , (a), , (∆ e g H ) of oxygen is − 141 kJ / mol, its, second electron gain enthalpy is, , (a) a positive value, (b) a more negative value than the first, (c) almost the same as that of the first, (d) negative, but less negative than the first, , AlCl3, ∆, , H 3C, , 16 When the first electron gain enthalpy, , following reaction is, , (b), , OH, OH, , NH2, , OH, , CH3, , CH3, (c), , (CH3CO)2O/pyridine (1 eqv.), room temperature, , COCH3, OH, , (d), , (a), , 12 The complex that has highest crystal field, , NH2, , OH, (b), , splitting energy (∆ ), is, , OCOCH3, , (b) [Co(NH3 )5 (H2O)]Cl3, (d) K2[CoCl 4 ], , (a) [Co(NH3 )5 Cl] Cl 2, (c) K3 [Co(CN)6 ], , 13 The condition for methemoglobinemia by, (b) > 50 ppm chloride, (d) > 100 ppm sulphate, , 14 Consider the following reversible chemical, reactions,, , 6 AB ( g), , (c), , NHCOCH3, , (d), , NH2, , 18 For the reaction, 2A + B → products, , drinking water is, (a) > 50 ppm nitrate, (c) > 50 ppm lead, , A2 ( g) + B2 ( g), , NHCOCH3, , K1, , -2 AB ( g), , K2, , -3A, , 2, , ( g) + 3B2 ( g), , …(i), …(ii), , The relation between K1 and K 2 is, , (a) K 2 = K13, , (b) K1 K 2 = 3, 1, (d) K1 K 2 =, 3, , (c) K 2 = K1 − 3, , 15 The increasing basicity order of the, following compounds is, (A) CH3 CH2NH2, , CH2CH3, , (B) CH3 CH2NH, , CH3, , (C) H3 C N CH3, , CH3, , (D) Ph N H, , (a) (D) < (C) < (B) < (A), (b) (A) < (B) < (C) < (D), (c) (A) < (B) < (D) < (C), (d) (D) < (C) < (A) < (B), , When concentration of both (A and B), becomes double, then rate of reaction, increases from 0.3 mol L −1 s −1 to, 2.4 mol L −1 s −1., When concentration of only A is doubled,, the rate of reaction increases from, 0.3 mol L −1 s −1 to 0.6 mol L −1 s −1., Which of the following is true?, (a) The whole reaction is of 4th order, (b) The order of reaction w.r.t. B is one, (c) The order of reaction w.r.t. B is 2, (d) The order of reaction w.r.t. A is 2, , 19 The entropy change associated with the, conversion of 1 kg of ice at 273 K to water, vapours at 383 K is, (Specific heat of water liquid and, water vapour are 4.2 kJK −1kg −1 and, 20, . kJK −1 kg −1; heat of liquid fusion and, vapourisation of water are 334 kJ kg −1 and, 2491 kJkg −1 respectively).(log 273 = 2436, ., ,, log 373 = 2572, ., , log 383 = 2583, ., ), (a) 9.26 kJ kg −1 K−1, (c) 7.90 kJ kg −1 K−1, , (b) 8.49 kJ kg −1 K−1, (d) 2.64 kJ kg −1 K−1
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20, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 20 The transition element having least, enthalpy of atomisation is, (a) Zn, , (b) V, , (c) Fe, , (d) Cu, , 21 For the following reaction, the mass of, water produced from 445 g of C57 H110O6 is :, 2C57 H110O6 (s) + 163O2 ( g) → 114CO2 ( g), + 110 H2O (l), (a) 490 g, , (b) 495 g, , (c) 445 g, , (d) 890 g, , 22 The metal that forms nitride by reacting, directly with N2 of air, is, (a) Rb, , (b) K, , (c) Cs, , (d) Li, , 23 The correct sequence of amino acids, present in the tripeptide given below is, Me, , Me, H, N, , H2N, , OH, , (a) Thr - Ser - Leu, (c) Val - Ser - Thr, , Me, , OH, , N, H, , C, , OH, , (b) Leu - Ser - Thr, (d) Thr - Ser - Val, , 24 A solution contain 62 g of ethylene glycol, in 250 g of water is cooled upto –10º C. If, K f for water is 1.86 K kg mol −1, then, amount of water (in g) separated as ice is, (a) 32, (c) 64, , (b) 48, (d) 16, , 25 The major product formed in the following, reaction is, , H, , O, (a), , Dil. NaOH, , +, , OH, H 3C, , OH, , cell is 2V at 300 K, the equilibrium, constant (K) for the reaction,, Zn (s) + Cu 2+ (aq), , 2+, , (aq) + Cu (s), , (R = 8 JK −1mol−1 , F = 96000 C mol−1 ), (a) e−160, (c) e−80, , (b) e160, (d) e320, , 27 Which of the following combination of, statements is true regarding the, interpretation of the atomic orbitals?, I. An electron in an orbital of high angular, momentum stays away from the nucleus, than an electron in the orbital of lower, angular momentum., II. For a given value of the principal, quantum number, the size of the orbit is, inversely proportional to the azimuthal, quantum number., III. According to wave mechanics, the, ground state angular momentum is, h, equal to, ., 2π, IV. The plot of ψ vs r for various azimuthal, quantum numbers, shows peak shifting, towards higher r value., (a) I, III, (c) I, II, , (b) II, III, (d) I, IV, , 28 The pH of rain water, is approximately, (b) 6.5, (d) 7.0, , 29 At 100°C, copper (Cu) has FCC unit cell, structure with cell edge length of x Å. What, is the approximate density of Cu (in g cm −3 ), at this temperature?, [Atomic mass of Cu = 6355, . u], (a), , O, , (c), (b) H3C, , - Zn, , at 300 K is approximately, , (a) 7.5, (c) 5.6, , CH3, H 3C, , 26 If the standard electrode potential for a, , 211, x3, 105, x3, , (b), (d), , 205, x3, 422, x3, , 30 Homoleptic octahedral complexes of a, OH, , O, H, , (c) H3C, O, (d) H, , OH, H 3C, , metal ion ‘M3 + ’ with three monodentate, ligands L1 , L2 and L3 absorb wavelengths, in the region of green, blue and red, respectively. The increasing order of the, ligand strength is, , (a) L1 < L2 < L3, (c) L3 < L1 < L2, , (b) L2 < L1 < L3, (d) L3 < L2 < L1
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MATHEMATICS, 1 Let the equations of two sides of a triangle, , be 3x − 2 y + 6 = 0 and 4x + 5 y − 20 = 0. If the, orthocentre of this triangle is at (1, 1) then, the equation of its third side is, , (a) 122 y − 26x − 1675 = 0, (b) 26x − 122 y − 1675 = 0, (c) 122 y + 26x + 1675 = 0, (d) 26x + 61y + 1675 = 0, , x2 + x + 1 = 0, If z = 3 + 6iz081 − 3iz093 , then, arg z is equal to, π, 4, , π, 6, π, (d), 3, , (b), , (c) 0, , 7 The area of the region, , A = {(x, y); 0 ≤ y ≤ x| x| + 1 and − 1 ≤ x ≤ 1} in, sq. units, is, 1, 3, , x y z, = = and perpendicular to, 2 3 4, the plane containing the straight lines, x y z, x y z, = = and = = is, 3 4 2, 4 2 3, straight line, , −t, , (a) invertible only when t = π, (b) invertible for every t ∈ R, (c) not invertible for any t ∈ R, π, (d) invertible only when t =, 2, , (a) 5x + 2 y − 4z = 0, (c) 3x + 2 y − 3z = 0, , (b) x + 2 y − 2z = 0, (d) x − 2 y + z = 0, , $ , b = b i$ + b $j + 2 k, $, 9 Let a = $i + $j + 2 k, 1, 2, , 4 A pot contain 5 red and 2 green balls. At, random a ball is drawn from this pot. If a, drawn ball is green then put a red ball in, the pot and if a drawn ball is red, then put, a green ball in the pot, while drawn ball is, not replace in the pot. Now we draw, another ball randomnly, the probability of, second ball to be red is, 26, 49, 32, (d), 49, , (b), , $ be three vectors such, and c = 5 $i + $j + 2 k, that the projection vector of b on a is a. If, a + b is perpendicular to c, then|b |is, equal to, (a) 6, (c) 22, , (b) 4, (d) 32, , 10 If x = sin −1 (sin 10) and y = cos−1 (cos 10),, then y − x is equal to, (a) 0, (c) 7π, , (b) 10, (d) π, , 11 Let a , b and c be the 7th, 11th and 13th, , 5 Let f be a differentiable function from R to R, 3, , such that | f (x) − f ( y)| ≤ 2|x − y|2 , for all, , terms respectively of a non-constant AP. If, these are also the three consecutive terms, a, of a GP, then is equal to, c, (a) 2, , 1, , x, y ∈ R. If f (0) = 1, then ∫ f 2 (x) dx is equal to, 0, , 4, 3, 2, (d), 3, (b), , 8 The equation of the plane containing the, , , , − e sin t + e cos t then A is, , −2e− t cos t, , −t, , (a) ab′+ bc′+1 = 0, (b) bb′+ cc′+1 = 0, (c) aa ′+ c + c′ = 0, (d) cc′+ a + a ′ = 0, , (c), , e− t sin t, , 27, 49, 21, (c), 49, , 6 If lines x = ay + b, z = cy + d and x = a′ z + b′,, , (a) 2, , et, e− t cos t, t, −t, 3 If A = e −e cos t − e− t sin t, et, 2e− t sin t, , , (a), , (c) 1, , 1, 2, (d) 0, (b), , y = c′ z + d′ are perpendicular, then, , 2 Let z0 be a root of the quadratic equation,, , (a), , (a) 2, , (c) 4, , 7, 13, 1, (d), 2, (b)
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22, , ONLINE, , JEE Main 2019 ~ Solved Paper, , 12 Let A = { x ∈ R : x is not a positive integer}., , 18 For each x ∈ R, let [x] be the greatest, , 2x, Define a function f : A → R as f (x) =, ,, x−1, then f is, , integer less than or equal to x. Then,, x([x] + |x|) sin [x], is equal to, lim, |x|, x → 0−, , (a) injective but not surjective, (b) not injective, (c) surjective but not injective, (d) neither injective nor surjective, , (a) 0, (c) − sin 1, , 13 In a group of data, there are n, n, , observations, x, x2 , .... , xn . If Σ (xi + 1)2 = 9n, i =1, , n, , and Σ (xi − 1)2 = 5n, the standard, i =1, , (b) 7, (d) 5, , π, 2, for which sin x − sin 2x + sin 3x = 0, is, , 14 If 0 ≤ x < , then the number of values of x, (a) 2, (c) 1, , (b) 3, (d) 4, , 15 If the system of linear equations, x − 4 y + 7z = g, 3 y − 5z = h, − 2x + 5 y − 9z = k, is consistent, then, , (b) 10, (d) 14, , xy-plane, each having one vertex at the, origin and the other two vertices lie on, coordinate axes with integral coordinates., If each triangle in S has area 50 sq. units,, then the number of elements in the set S is, (a) 36, (c) 18, , (b) 32, (d) 9, , 21 The logical statement, [~ (~ p ∨ q) ∨ ( p ∧ r )] ∧ (~ q ∧ r ), is equivalent to, (b) ( p ∧ ~ q) ∨ r, (d) (~ p ∧ ~ q) ∧ r, , and (x − 4)2 + ( y − 7)2 = 36 intersect at two, distinct points, then, , parabola, y2 = 4x. Let C be chosen on the, arc AOB of the parabola, where O is the, origin, such that the area of ∆ACB is, maximum. Then, the area (in sq. units) of, ∆ACB, is, (b) 32, (d) 30, , 1, 2, , 17 The number of all possible positive, , integral values of α for which the roots of, the quadratic equation, 6x2 − 11x + α = 0, are rational numbers is, , (a) 5, (c) 4, , (a) 12, (c) 15, , 22 If the circles x2 + y2 −16x − 20 y + 164 = r 2, , 16 Let A (4, − 4) and B(9, 6) be points on the, , 1, 4, 3, (c) 31, 4, , 3, , 1 − t6 , is, , 1−t, , (a) ~ p ∨ r, (c) ( p ∧ r ) ∧ ~ q, , (a) 2 g + h + k = 0, (b) g + 2h + k = 0, (c) g + h + k = 0, (d) g + h + 2k = 0, , (a) 31, , 19 The coefficient of t 4 in the expansion of, , 20 Let S be the set of all triangles in the, , deviation of the data is, (a) 2, (c) 5, , (b) sin 1, (d) 1, , (b) 2, (d) 3, , (a) 0 < r < 1, (c) 1 < r < 11, , (b) r > 11, (d) r = 11, , 23 If both the roots of the quadratic equation, x2 − mx + 4 = 0 are real and distinct and, they lie in the interval [1, 5] then m lies in, the interval, (a) (4, 5), (c) (5, 6), , (b) (−5, − 4), (d) (3, 4), , 24 The number of natural numbers less than, 7,000 which can be formed by using the, digits 0, 1, 3, 7, 9 (repitition of digits, allowed) is equal to, (a) 374, (c) 372, , (b) 375, (d) 250
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23, , JANUARY ATTEMPT ~ 9 Jan 2019, Shift II, tan θ, 1, , (k > 0), then the, dθ =1 −, 2, 2k sec θ, value of k is, , 25 If ∫, , π /3, , (b), , (c) 2, , 5x8 + 7x6, , 26 If f (x) = ∫, , (a) 7510, (c) 7830, , dx, (x ≥ 0), and, , (x2 + 1 + 2x7 )2, f (0) = 0, then the value of f (1) is, , (a) −, , 9 (12 + 22 + 32 ) 12 (12 + 22 + 32 + 42 ), +, 7, 9, 2, 2, 2, 15 (1 + 2 + ... + 5 ), +, + ...up to 15 terms is, 11, , 1+6+, , 1, 2, (d) 4, , (a) 1, , (c), , 28 The sum of the following series, , 0, , 1, 2, , (b) −, , 1, 4, , (d), , 29 If x = 3 tan t and y = 3 sec t, then the value, , 1, 4, , of, , d2 y, dx2, , π, at t = , is, 4, , 1, 6, 1, (c), 3 2, , 1, 2, , 1, 6 2, 3, (d), 2 2, (b), , (a), , 27 Let f : [0, 1] → R be such that, f (xy) = f (x). f ( y), for all x, y ∈ [0, 1] and, f (0) ≠ 0. If y = y (x) satisfies the differential, dy, equation,, = f (x) with y(0) = 1, then, dx, 3, 1, y + y is equal to, 4, 4, (a) 5, (c) 2, , (b) 7820, (d) 7520, , 30 A hyperbola has its centre at the origin,, passes through the point (4, 2) and has, transverse axis of length 4 along the, X-axis. Then the eccentricity of the, hyperbola is, (a) 2, , (b) 3, (d) 4, , (c), , (b), , 3, 2, , 2, 3, , (d) 3, , Answers, Physics, 1, 11, 21, , (a), (a), (a), , 2, 12, 22, , (*), (b), (b), , 3, 13, 23, , (d), (b), (d), , 4, 14, 24, , (c), (a), (a), , 5, 15, 25, , (c), (d), (a), , 6, 16, 26, , (a), (a), (a), , 7, 17, 27, , (c), (d), (c), , 8, 18, 28, , (d), (d), (d), , 9, 19, 29, , (c), (c), (c), , 10, 20, 30, , (a), (b), (b), , (b), (c), (d), , 3, 13, 23, , (d), (a), (c), , 4, 14, 24, , (a), (c), (c), , 5, 15, 25, , (a), (d), (c), , 6, 16, 26, , (b), (a), (b), , 7, 17, 27, , (d), (b), (d), , 8, 18, 28, , (b), (c), (c), , 9, 19, 29, , (b), (a), (d), , 10, 20, 30, , (a), (a), (c), , 3, 13, 23, , (b), (d), (a), , 4, 14, 24, , (d), (a), (a), , 5, 15, 25, , (c), (a), (c), , 6, 16, 26, , (c), (a), (c), , 7, 17, 27, , (a), (d), (b), , 8, 18, 28, , (d), (c), (b), , 9, 19, 29, , (a), (c), (b), , 10, 20, 30, , (d), (a), (b), , Chemistry, 1, 11, 21, , (b), (c), (b), , 2, 12, 22, , Mathematics, 1, 11, 21, , (b), (c), (c), , 2, 12, 22, , (a), (a), (c), , Note (*) None of the options is correct., , For Detailed Solutions Visit : https://bit.ly/2VPjAnK Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (10 January, 2019), TIME 9:30-12:30 (Shift I), , MM : 360, , PHYSICS, 1 A potentiometer wire AB having length L, and resistance 12 r is joined to a cell D of, EMF ε and internal resistance r. A cell C, ε, having emf and internal resistance 3 r is, 2, connected. The length AJ at which the, galvanometer as shown in figure shows no, deflection is, +, , D (ε,r), –, , J, , A, , 5, L, 12, , (b), , 11, L, 12, , x, on it. The, l, rod is rotated about an axis passing, through the origin (x = 0) and, perpendicular to the rod. If the rod makes, n rotations per second, then the time, averaged magnetic moment of the rod is, , linear charge density ρ(x) = ρ0, , (a) n ρ l 3, π, (c), n ρ l3, 3, , (b) π n ρ l 3, π, (d), n ρ l3, 4, , 4 A 2 W carbon resistor is color coded with, , B, , green, black, red and brown respectively., The maximum current which can be, passed through this resistor is, , + –, G, C, ε,, 2 3r, , (a), , 3 An insulating thin rod of length l has a, , (a) 0.4 mA, (c) 20 mA, (c), , 13, L, 24, , (d), , 11, L, 24, , 2 In a Young’s double slit experiment with, slit separation 0.1 mm, one observes a, 1, rad by using light, bright fringe at angle, 40, of wavelength λ1. When the light of the, wavelength λ 2 is used a bright fringe is, seen at the same angle in the same set up., Given that λ1 and λ 2 are in visible range, (380 n-m to 740 n-m), their values are, (a) 380 n-m, 525 n-m (b) 400 n-m, 500 n-m, (c) 380 n-m, 500 n-m (d) 625 n-m, 500 n-m, , (b) 63 mA, (d) 100 mA, , 5 In the given circuit, the cells have zero, internal resistance. The currents (in, Ampere) passing through resistances R1, and R2 respectively are, , R1, –, , +, , 10 V, , (a) 0.5, 0, (c) 2, 2, , R2, , 20 Ω, +, , –, , 10 V, , (b) 1, 2, (d) 0, 1, , 20 Ω
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25, , JANUARY ATTEMPT ~ 10 Jan 2019, Shift I, 6 In an electron microscope, the resolution, that can be achieved is of the order of the, wavelength of electrons used. To resolve a, width of 75, . × 10−12 m, the minimum, electron energy required is close to, (a) 500 keV, (c) 100 keV, , (b) 1 keV, (d) 25 keV, , gate circuit, the input values must be, X, P, , R, , Q, , (a) X = 0, Y = 0, (c) X = 1, Y = 1, , (b) X = 1 , Y = 0, (d) X = 0, Y = 1, , 8 Two guns A and B can fire bullets at, speeds 1 km/s and 2 km/s, respectively., From a point on a horizontal ground, they, are fired in all possible directions. The, ratio of maximum areas covered by the, bullets on the ground fired by the two guns, is, (a) 1 : 4, (c) 1 : 8, , (b) 1 : 16, (d) 1 : 2, , 9 A satellite is moving with a constant speed, v in circular orbit around the earth. An, object of mass ‘m’ is ejected from the, satellite such that it just escapes from the, gravitational pull of the earth. At the time, of ejection, the kinetic energy of the object, is, 3, mv2, 2, (c) m v2, (a), , (b) 2 mv2, (d), , 1, mv2, 2, , 10 A heat source at T = 103 K is connected to, another heat reservoir at T = 102 K by a, copper slab which is 1 m thick. Given that, the thermal conductivity of copper is, 0.1 WK −1m −1, the energy flux through it in, the steady state is, (a) 90 Wm −2, (c) 120 Wm −2, , (b) 65 Wm −2, (d) 200 Wm −2, , 11 A magnet of total magnetic moment, , 10−2 $i A-m 2 is placed in a time varying, , (a) 0.01 J, (c) 0.014 J, , (b) 0.007 J, (d) 0.028 J, , 12 To mop-clean a floor, a cleaning machine, , 7 To get output ‘1’ at R, for the given logic, , Y, , magnetic field, B$i (cos ωt ), where B = 1 T, and ω = 0125, rad/s. The work done for, ., reversing the direction of the magnetic, moment at t = 1 s is, , presses a circular mop of radius R, vertically down with a total force F and, rotates it with a constant angular speed, about its axis. If the force F is distributed, uniformly over the mop and if coefficient of, friction between the mop and the floor is µ,, the torque applied by the machine on the, mop is, 2, (a) µFR, 3, µ FR, (c), 3, , µFR, 6, µ FR, (d), 2, (b), , 13 A homogeneous solid cylindrical roller of, radius R and mass m is pulled on a cricket, pitch by a horizontal force. Assuming, rolling without slipping, angular, acceleration of the cylinder is, F, 2mR, 3F, (c), 2mR, , (a), , 2F, 3mR, F, (d), 3mR, (b), , 14 Using a nuclear counter, the count rate of, emitted particles from a radioactive source, is measured. At t = 0, it was 1600 counts, per second and t = 8 s, it was 100 counts, per second. The count rate observed as, counts per second at t = 6 s is close to, (a) 400, (c) 150, , (b) 200, (d) 360, , 15 A charge Q is distributed over three, concentric spherical shells of radii a , b, c, (a < b < c) such that their surface charge, densities are equal to one another., The total potential at a point at distance r, from their common centre, where r < a, would be, Q (a + b + c), (b), 4 πε0 (a3 + b3 + c3 ), 4 πε0 (a 2 + b2 + c2 ), ab + bc + ca, Q, Q, (d), (c), ⋅, 12 π ε0, abc, 4 πε0 (a + b + c), (a), , Q (a 2 + b2 + c2 )
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26, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 16 A parallel plate capacitor is of area 6 cm 2, and a separation 3 mm. The gap is filled, with three dielectric materials of equal, thickness (see figure) with dielectric, constants K1 = 10, K 2 = 12 and K3 = 14. The, dielectric constant of a material which give, same capacitance when fully inserted in, above capacitor, would be, , K1, , K2, , K3, , 3 mm, , then the maximum electric field associated, with it is (Take, the speed of light = 3 × 108 m/s), (a) 6 × 104 N/C, (c) 3 × 104 N/C, , (b) 4 × 104 N/C, (d) 4.5 × 104 N/C, , 20 A block of mass m is kept on a platform, which starts from rest with constant, g, acceleration upwards as shown in figure., 2, Work done by normal reaction on block in, time t is, m, , (a) 4, (c) 12, , (b) 36, (d) 14, , 17 A solid metal cube of edge length 2 cm is, moving in a positive Y -direction at a, constant speed of 6 m/s. There is a uniform, magnetic field of 0.1 T in the positive, Z-direction. The potential difference, between the two faces of the cube, perpendicular to the X-axis is, (a) 2 mV, (c) 6 mV, , (b) 12 mV, (d) 1 mV, , 18 In the cube of side ‘a’ shown in the figure,, the vector from the central point of the, face ABOD to the central point of the face, BEFO will be, z, B, , E, , A, , a, , H, , G, , F, , O, , x, , 1 $ $, a (i − k ), 2, 1, $), (c) a ($j − k, 2, , (a), , (c) 0, , g, 2, , 3mg 2t 2, 8, mg 2t 2, (d) −, 8, (b), , 21 The density of a material in SI units is, , 128 kg m −3 . In certain units in which the, unit of length is 25 cm and the unit of, mass is 50 g, the numerical value of, density of the material is, , (a) 40, (c) 640, , (b) 16, (d) 410, , 22 A train moves towards a stationary, observer with speed 34 m/s. The train, sounds a whistle and its frequency, registered by the observer is f1. If the, speed of the train is reduced to 17 m/s, the, frequency registered is f2. If speed of sound, f, is 340 m/s, then the ratio 1 is, f2, 19, 18, 20, (c), 19, , a, , 21, 20, 18, (d), 17, (b), , 23 A TV transmission tower has a height of, , 1 $ $, a ( j − i), 2, 1 $ $, (d) a (k, − i), 2, , (b), , 19 If the magnetic field of a plane, electromagnetic wave is given by, , , B = 100 × 10−6 sin 2π × 2 × 1015 t −, , , , mg 2t 2, 8, , (a), , y, , a, D, , (a), , a=, , x , ,, c , , 140 m and the height of the receiving, antenna is 40 m. What is the maximum, distance upto which signals can be, broadcasted from this tower in LOS (Line, of Sight) mode? (Take, radius of earth, = 64, . × 106 m)., (a) 65 km, (c) 40 km, , (b) 80 km, (d) 48 km
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27, , JANUARY ATTEMPT ~ 10 Jan 2019, Shift I, 24 Three Carnot engines operate in series, between a heat source at a temperature T1, and a heat sink at temperature T4 (see, figure). There are two other reservoirs at, temperatures T2 and T3 , as shown with, T1 > T2 > T3 > T4. The three engines are, equally efficient if, T1, ε1, T2, ε2, T3, , building before falling below is (Take,, g = 10 ms −2), (a) 20 m, (c) 10 m, , (b) 30 m, (d) 40 m, , 27 A uniform metallic wire has a resistance of, 18 Ω and is bent into an equilateral, triangle. Then, the resistance between any, two vertices of the triangle is, , (a) 12 Ω, (c) 2 Ω, , (b) 8 Ω, (d) 4 Ω, , 28 Two electric dipoles, A, B with respective, dipole moments d A = − 4 qa $i and, d B = − 2 qa i$ are placed on the X-axis with, a separation R, as shown in the figure, R, , ε3, , X, A, , T4, , (a), (b), (c), (d), , T2 = (T13 T4 )1/ 4 ; T3 = (T1T43 )1/ 4, T2 = (T12T4 )1/3 ; T3 = (T1T42 )1/3, T2 = (T1 T4 )1/ 2 ; T3 = (T12T4 )1/3, T2 = (T1 T42 )1/3 ; T3 = (T12T4 )1/3, , 25 A string of length 1 m and mass 5 g is, fixed at both ends. The tension in the, string is 8.0 N. The string is set into, vibration using an external vibrator of, frequency 100 Hz. The separation between, successive nodes on the string is close to, (a) 16.6 cm, (c) 10.0 cm, , (b) 33.3 cm, (d) 20.0 cm, , 26 A piece of wood of mass 0.03 kg is dropped, from the top of a 100 m height building. At, the same time, a bullet of mass 0.02 kg is, fired vertically upward with a velocity 100, ms −1 from the ground. The bullet gets, embedded in the wood. Then, the, maximum height to which the combined, system reaches above the top of the, , B, , The distance from A at which both of them, produce the same potential is, (a), (c), , 2R, 2+1, R, 2+1, , (b), (d), , 2R, 2−1, R, 2−1, , 29 Water flows into a large tank with flat, , bottom at the rate of 10−4 m3 s −1. Water is, also leaking out of a hole of area 1 cm 2 at, its bottom. If the height of the water in the, tank remains steady, then this height is, , (a) 4 cm, (c) 5.1 cm, , (b) 2.9 cm, (d) 1.7 cm, , 30 A plano-convex lens of refractive index µ1, and focal length f1 is kept in contact with, another plano-concave lens of refractive, index µ 2 and focal length f2. If the radius, of curvature of their spherical faces is R, each and f1 = 2 f2, then µ1 and µ 2 are, related as, (a) 3 µ 2 − 2 µ 1 = 1, (c) 2 µ 1 − µ 2 = 1, , (b) 2 µ 2 − µ 1 = 1, (d) µ 1 + µ 2 = 3
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28, , JEE Main 2019 ~ Solved Paper, , ONLINE, , CHEMISTRY, 1 Which of the following is not an example of, heterogeneous catalytic reaction?, (a), (b), (c), (d), , Haber’s process, Combustion of coal, Hydrogenation of vegetable oils, Ostwald’s process, , (a) CH3O, , (b) CH3O, CH3, , (c), , OCH3, , (d) CH3O, , CH3, , 2 Hall-Heroult’s process is given by, Coke, 1673 K, , (a), (b), (c), (d), , ZnO + C → Zn + CO, Cr2O3 + 2Al → Al 2O3 + 2Cr, 2Al 2O3 + 3C → 4Al + 3CO2, Cu 2+ (aq) + H2 ( g ) → Cu (s) + 2H+ (aq), , 7 The correct structure of product ‘P’ in the, following reaction is, NEt 3, Asn − Ser + (CH3CO)2 O →, P, (Excess), , O, , 3 The chemical nature of hydrogen peroxide, is, , NH2, H, N, , O, , (a) oxidising and reducing agent in both acidic, and basic medium, (b) oxidising and reducing agent in acidic, medium, but not in basic medium, (c) reducing agent in basic medium, but not in, acidic medium, (d) oxidising agent in acidic medium, but not, in basic medium, , N, H, , (a) H3C, , N, H, , O, , Ca 2+ + 2e− → Ca (s); E ° = − 287, . V, Ni, , N, H, , (c) H3C, , −, , + 2e → Ni(s); E ° = − 025, . V, , O, , NHCOCH3, O, NH, , window is, , (a) 12, (c) 4, , (a) Na, (c) Mg, , 6 The major product of the following reaction, is, CH2Cl, , (i) AlCl3 (anhyd.), (ii) H2O, , N, H, , OH, OCOCH3, , O, , 8 The metal used for making X-ray tube, , planar complex [M(F)(Cl)(SCN)(NO 2)] is, (b) 16, (d) 8, , OH, NH2, , O, , (d) H3C, , 5 The total number of isomers for a square, , CH3O, , OCOCH3, O, H, N, , O, , Zn < Mg < Ni < Ca, Ni < Zn < Mg < Ca, Ca < Zn < Mg < Ni, Ca < Mg < Zn < Ni, , OH, NHCOCH3, , O, , O, , The reducing power of the metals, increases in the order, (a), (b), (c), (d), , O, , O, , Zn 2+ + 2e− → Zn (s); E ° = − 0.76 V, , 2+, , OCOCH3, , N, H, , 4 Consider the following reduction processes:, , Mg 2+ + 2e− → Mg(s); E ° = − 236, . V, , OH, , O, OCOCH3, , O, , (b) H3C, , O, , (b) Be, (d) Ca, , 9 Consider the given plots for a reaction, obeying Arrhenius equation, (0°C < T < 300°C) : ( k and E a are rate, constant and activation energy,, respectively)
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29, , JANUARY ATTEMPT ~ 10 Jan 2019, Shift I, 14 The decreasing order of ease of alkaline, hydrolysis for the following esters is, k, , k, COOC2H5, Ea, I, , T(°C), II, , II, , I, , Kp, , IV, , III, , Both I and II are wrong, Both I and II are correct, I is wrong but II is right, I is right but II is wrong, , 10 The values of, , (a) III > II > IV > I, (c) II > III > I > IV, , (b) III > II > I > IV, (d) IV > II > III > I, , 15 The major product of the following reaction, is, Br, , for the following, , KC, reactions at 300 K are, respectively, (At 300 K, RT = 2462, . dm3 atm mol −1), N2 ( g) + O2 ( g), 2NO( g), N2O4 ( g), 2NO2 ( g), N2 ( g) + 3H2 ( g), 2NH3 ( g), , =, =, =, , (a) 1, 24.62 dm3 atm mol −1 ,, 606.0 dm 6 atm 2 mol −2, (b) 1, 24.62 dm3 atm mol −1 ,, 1.65 × 10−3 dm −6 atm −2 mol 2, (c) 24.62 dm3 atm mol −1 , 606.0 dm 6 atm −2, mol 2, 1.65 × 10−3 dm−6 atm −2 mol 2, (d) 1, 4.1 × 10−2 dm −3 atm −1 mol,, 606 dm 6 atm 2 mol −2, , KOH alc. (excess), ∆, , Ph, Br, , (a) Ph, , (b) Ph, , (c) Ph, , (d) Ph, , 16 Which dicarboxylic acid in presence of a, dehydrating agent is least reactive to give, an anhydride?, CH2, CO2H, (a), , CH2, , COOH, CH2, CH2, , lone pair(s) of electrons of Xe in XeOF 4,, respectively, are, 2, , (a) sp d and 1, (c) sp3 d and 1, , O, , 3, , (b) sp d and 2, (d) sp3 d 2 and 2, , COOH, (c), , (a) xA = 0.76; xB = 0.24 (b) xA = 0.28; xB = 0.72, (d) xA = 0.37; xB = 0.63, (c) xA = 0.4; xB = 0.6, , 13 The total number of isotopes of hydrogen, and number of radioactive isotopes among, them, respectively, are, (a) 2 and 1, (c) 2 and 0, , (b) 3 and 2, (d) 3 and 1, , (d), , CH2, CH2, , COOH, , 12 Liquids A and B form an ideal solution in, the entire composition range. At 350 K,, the vapour pressures of pure A and pure B, are 7 × 103 Pa and 12 × 103 Pa,, respectively. The composition of the, vapour in equilibrium with a solution, containing 40 mole percent of A at this, temperature is, , COOH, , (b), CO2H, , 11 The type of hybridisation and number of, 3, , COOC2H5, , COOC2H5 CH3O, , O2N, , Choose the correct option., (a), (b), (c), (d), , COOC2H5, , Cl, , C, , OH, OH, , C, O, , 17 A process has ∆H = 200 J mol −1 and, , ∆S = 40 JK −1 mol −1. Out of the values, given below, choose the minimum, temperature above which the process will, be spontaneous, , (a) 20 K, (c) 5 K, , (b) 4 K, (d) 12 K, , 18 The major product formed in the reaction, given below will be, NH2, , NaNO2, Aq. HCI, 0-5°C
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30, , JEE Main 2019 ~ Solved Paper, , ONLINE, , (a), , (b), , NO2, , OH, , NO2, , OH, , (c), , 22 The increasing order of the pK a values of, the following compounds is, OH, , OH, , OH, , OH, , (d), NO2, , 19 If dichloromethane (DCM) and water (H2O), are used for differential extraction, which, one of the following statements is correct?, (a) DCM and H2O would stay as lower and, upper layer respectively in the S.F., (b) DCM and H2O would stay as upper and, lower layer respectively in the separating, funnel (S.F.), (c) DCM and H2O will be miscible clearly, (d) DCM and H2O will make turbid/colloidal, mixture, , 20 The major product ‘X’ formed in the, following reaction is, O, , O, CH2, , C, , OCH3, , NaBH4, , CH2 CH2 OH, , CH2, , C, , O, CH2, , (c), , C, , OH, CH2 CH2 OH, , H, , 21 Which of the graphs shown below does not, represent the relationship between, incident light and the electron ejected from, metal surface?, K.E. of, eσs, , (a), , (b), 0, , 0, , Energy of, light, , Number, of eσs, , Intensity of, light, , K.E. of, eσs, , (c), Frequency of, light, , of sodium sulphate was dissolved in water, and the volume was made upto 100 mL., The mass of calcium sulphate formed and, the concentration of OH− in resulting, solution, respectively, are : (Molar mass of, Ca(OH)2 , Na 2SO4 and CaSO4 are74, 143, and 136 g mol −1, respectively; Ksp of, , (a), (b), (c), (d), , [(Et3 P)3 RhCl], [(Et3 P)3 IrCl](Et = C2H5 ), [(Ph3 P)3 RhCl], [(Ph3 P)3 IrCl], , 25 Two pi and half sigma bonds are present in, (b) N2, (d) O2, , 26 The effect of lanthanoid contraction in the, lanthanoid series of elements by and large, means, (a) increase in atomic radii and decrease in, ionic radii, (b) decrease in both atomic and ionic radii, (c) increase in both atomic and ionic radii, (d) decrease in atomic radii and increase in, ionic radii, , 27 The electronegativity of aluminium is, similar to, (a) lithium, (c) beryllium, , (d), 0, , (b) B < C < A < D, (d) B < C < D < A, , 23 A mixture of 100 mmol of Ca(OH)2 and 2 g, , (a) O+2, (c) N+2, , (d), , K.E. of, eσs, , OMe, D, , 24 Wilkinson catalyst is, OCH3, , (b), O, , (a) D < A < C < B, (c) C < B < A < D, , C, , (a) 13.6 g, 0.28 mol L −1 (b) 1.9 g, 0.28 mol L −1, (c) 13.6 g, 0.14 mol L −1 (d) 1.9 g, 0.14 mol L −1, , X, , O, OH, , (a), , NO2, B, , Ca(OH)2 is 55, . × 10−6), MeOH, , OH, , A, , (b) carbon, (d) boron, , 28 Which primitive unit cell has unequal edge, 0, , Frequency of, light, , lengths (a ≠ b ≠ c) and all axial angles, different from 90°?, , (a) Hexagonal, (c) Tetragonal, , (b) Monoclinic, (d) Triclinic
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31, , JANUARY ATTEMPT ~ 10 Jan 2019, Shift I, 29 Water filled in two glasses A and B have, BOD values of 10 and 20, respectively. The, correct statement regarding them, is, (a) A is more polluted than B, (b) A is suitable for drinking, wherease B is, not, (c) Both A and B are suitable for drinking, (d) B is more polluted than A, , 30 Which hydrogen in compound (E) is easily, replaceable during bromination reaction in, presence of light?, CH3 CH2 CH ==CH2, δ, , (a) β-hydrogen, (c) γ-hydrogen, , γ, , β, α, (E), (b) δ-hydrogen, (d) α-hydrogen, , MATHEMATICS, 1 The equation of a tangent to the hyperbola, 4x − 5 y = 20 parallel to the line x − y = 2 is, 2, , 2, , (a) x − y − 3 = 0, (c) x − y + 1 = 0, , (b) x − y + 9 = 0, (d) x − y + 7 = 0, , 2 Consider a triangular plot ABC with sides, AB = 7 m, BC = 5 m and CA = 6 m. A, vertical lamp-post at the mid-point D of, AC subtends an angle 30° at B. The height, (in m) of the lamp-post is, 2, (a), 21, 3, (c) 7 3, , (b) 2 21, (d), , 3, 21, 2, , 3, 1, dy, −π π , 3 If, +, y=, , and, , x ∈, 3 3, dx cos2 x, cos2 x, π 4, π, y = , then y − equals, 4 3, 4, 1, + e6, 3, 1, (c), + e3, 3, , (b) −, , (a), , (d), , 1, 3, , 4, 3, , $ , b = 4$i + (3 − λ )$j + 6k, $, 4 Let a = 2i$ + λ1$j + 3k, 2, , 6 If the parabolas y2 = 4b(x − c) and y2 = 8ax, have a common normal, then which one of, the following is a valid choice for the, ordered triad (a , b, c) ?, 1, (a) , 2, 0, 2, , , (b) (1, 1, 0), , (c) (1, 1, 3), , 1, (d) , 2, 3, 2, , , 7 Let z1 and z2 be any two non-zero complex, numbers such that 3|z1| = 4|z2|. If, 3z, 2z, z = 1 + 2 , then, 2z2 3z1, (a) |z| =, , 1 17, 2 2, , (c) Re(z) = 0, , (b) Im(z ) = 0, (d) |z| =, , 5, 2, , 8 A point P moves on the line 2x − 3 y + 4 = 0., If Q(1, 4) and R(3, − 2) are fixed points, then, the locus of the centroid of ∆PQR is a line, 2, 3, (c) parallel to Y -axis, (a) with slope, , 3, 2, (d) parallel to X-axis, , (b) with slope, , $ be three vectors, and c = 3$i + 6$j + (λ3 − 1)k, , 9 Consider the statement : ‘‘P (n ) : n 2 − n + 41, , such that b = 2a and a is perpendicular to, c. Then a possible value of (λ1 , λ 2 , λ3 ) is, , is prime.’’ Then, which one of the following, is true?, , (a) (1, 3, 1), 1, (c) − , 4, 0, 2, , , (b) (1, 5, 1), 1, (d) , 4, − 2, 2, , , 5 Let f : R → R be a function such that, f (x) = x + x f ′ (1) + xf ′ ′ (2) + f ′′′ (3), x ∈ R., Then, f (2) equals, 3, , (a) 30, (c) − 2, , 2, , (b) − 4, (d) 8, , (a), (b), (c), (d), , Both P (3) and P (5) are true., P (3) is false but P (5) is true., Both P (3) and P (5) are false., P (5) is false but P (3) is true., , π, 2, , 10 Let n ≥ 2 be a natural number and 0 < θ < ., 1, , Then, ∫, , (sin n θ − sin θ ) n cos θ, , dθ is equal to, sin n + 1 θ, (where C is a constant of integration)
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32, , JEE Main 2019 ~ Solved Paper, , ONLINE, 1, 1 −, , (a) 2, , n+1 , , sin, θ, n −1, n, , (b), , 1, 1 +, , , , sin n − 1 θ , n 2 − 1, , (c), , 1, 1 −, , , , sin n − 1 θ , n 2 − 1, , (d), , 1, 1 −, , , , sin n − 1 θ , n 2 + 1, , n, , n, , n, , n+1, , 16 If the third term in the binomial expansion, , +C, , n, , of (1 + xlog 2 x )5 equals 2560, then a possible, value of x is, , n+1, , +C, , n, , (a) 4 2, , n+1, , +C, , b, , 11 Let I = ∫ (x4 − 2x2 ) dx. If I is minimum, then, the ordered pair (a , b) is, (b) (0, 2 ), , (c) ( 2 , −, , (d) (−, , 2), , which when divided by 7 yield 2 or 5 as, remainder is, (b) 1465, , (c) 1356, , (d) 1365, , 13 An unbiased coin is tossed. If the outcome, is a head, then a pair of unbiased dice is, rolled and the sum of the numbers, obtained on them is noted. If the toss of, the coin results in tail, then a card from a, well-shuffled pack of nine cards numbered, 1, 2, 3, …, 9 is randomly picked and the, number on the card is noted. The, probability that the noted number is either, 7 or 8 is, (a), , 15, 72, , (b), , 13, 36, , (c), , 19, 72, , (d), , 19, 36, , 14 If a circle C passing through the point, (4, 0) touches the circle, x2 + y2 + 4x − 6 y = 12 externally at the, point (1, − 1), then the radius of C is, (a) 5, , (b) 2 5, , (c), , 57, , (d) 4, , 15 In a class of 140 students numbered 1 to, 140, all even numbered students opted, Mathematics course, those whose number, is divisible by 3 opted Physics course and, those whose number is divisible by 5 opted, Chemistry course. Then, the number of, students who did not opt for any of the, three courses is, (a) 42, (c) 38, , 20, , (b) 102, (d) 1, , (b) 18, , , , ∑ 20C, , i = 1, , (a) 100, , 2, 2), , 12 The sum of all two digit positive numbers, (a) 1256, , (a) 8, , 18 If, , a, , (a) (− 2 , 0), , (c), , 1, 8, , (d) 2 2, , x+ y+ z =5, x + 2 y + 3z = 9, x + 3 y + αz = β, has infinitely many solutions, then β − α, equals, , n+1, n, , 1, 4, , 17 If the system of equations, , +C, , n, , (b), , (d) 5, , , = k , then k equals, 20, 21, + C i − 1 , , 20, , i, , (c) 21, 3, , Ci − 1, , (b) 400, , (c) 200, , (d) 50, , 19 If the area enclosed between the curves, , y = kx2 and x = ky2 , (k > 0), is 1 square unit., Then, k is, , (a), , 3, , (b), , 1, 3, , (c), , 2, 3, , (d), , 3, 2, , 20 If the line 3x + 4 y − 24 = 0 intersects the, X-axis at the point A and the Y -axis at the, point B, then the incentre of the triangle, OAB, where O is the origin, is, (a) (4, 3), , (b) (3, 4), , (c) (4, 4), , (d) (2, 2), , 21 The mean of five observations is 5 and, their variance is 9.20. If three of the given, five observations are 1, 3 and 8, then a, ratio of other two observations is, (a) 4 : 9, (c) 10 : 3, , (b) 6 : 7, (d) 5 : 8, , 22 Consider the quadratic equation, , (c − 5)x2 − 2cx + (c − 4) = 0, c ≠ 5. Let S be the, set of all integral values of c for which one, root of the equation lies in the interval, (0, 2) and its other root lies in the interval, (2, 3). Then, the number of elements in S is, , (a) 11, , (b) 10, , (c) 12, , (d) 18, , max {|x|, x2 }, |x| ≤ 2, 23 Let f (x) = , 2 <|x| ≤ 4, 8 − 2|x|,, Let S be the set of points in the interval, (−4, 4) at which f is not differentiable., Then, S, (a) equals {−2, − 1, 0, 1, 2} (b) equals {−2, 2}, (c) is an empty set, (d) equals {−2,−1, 1, 2}
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33, , JANUARY ATTEMPT ~ 10 Jan 2019, Shift I, 24 Let A be a point on the line, , $ and, r = (1 − 3µ )i$ + (µ − 1)$j + (2 + 5µ )k, B(3, 2, 6) be a point in the space. Then, the, value of µ for which the vector AB is, parallel to the plane x − 4 y + 3z = 1 is, , (a), , 1, 4, , (b) −, , 1, 4, , (c), , 1, 8, , (d), , 28 The plane passing through the point, (4, − 1, 2) and parallel to the lines, x+ 2 y−2 z + 1, =, =, 3, 2, −1, x−2 y−3 z −4, and, also passes, =, =, 1, 2, 3, through the point, , 1, 2, , 25 Let d ∈ R, and, , 4+ d, (sin θ ) − 2 , −2, ,, (sin θ ) + 2, A=1, d, , , 5 (2 sin θ ) − d (− sin θ ) + 2 + 2d , θ ∈[θ , 2π ]. If the minimum value of det(A), is 8, then a value of d is, (a) −5, (c) 2( 2 + 1), , (a) (−1, − 1, − 1), (c) (1, 1, 1), , 29 The shortest distance between the point, 3 , , 0 and the curve y = x , (x > 0), is, 2 , , (b) −7, (d) 2( 2 + 2), , 26 If 5, 5r , 5r 2 are the lengths of the sides of a, triangle, then r cannot be equal to, (a), , 5, 4, , (b), , 7, 4, , (c), , 3, 2, , (d), , 3π, 8, , (b), , 5π, 4, , (c), , π, 2, , (a), , 3, 2, , (b), , (c), , 3, 2, , (d), , 5, 4, 5, 2, , 30 For each t ∈R, let [t ] be the greatest, , 3, 4, , integer less than or equal to t. Then,, , π, (1 −|x| + sin|1 − x|) sin [1 − x], , 2, lim, x → 1+, |1 − x|[1 − x], , π, 27 The sum of all values of θ ∈ 0, , 2, 3, satisfying sin 2 2θ + cos4 2θ = is, 4, (a), , (b) (1, 1, − 1), (d) (−1, − 1, 1), , (d) π, , (a) equals 0, , (b) does not exist, , (c) equals − 1, , (d) equals 1, , Answers, Physics, 1, 11, 21, , (c), (c), (a), , 2, 12, 22, , (d), (a), (a), , 3, 13, 23, , (d), (b), (a), , 4, 14, 24, , (c), (b), (b), , 5, 15, 25, , (a), (b), (d), , 6, 16, 26, , (d), (c), (d), , 7, 17, 27, , (b), (b), (d), , 8, 18, 28, , (b), (b), (a), , 9, 19, 29, , (c), (c), (c), , 10, 20, 30, , (a), (b), (c), , (c), (b), (b), , 3, 13, 23, , (a), (d), (b), , 4, 14, 24, , (b), (b), (c), , 5, 15, 25, , (a), (d), (c), , 6, 16, 26, , (d), (b), (b), , 7, 17, 27, , (a), (c), (c), , 8, 18, 28, , (b), (*), (d), , 9, 19, 29, , (b), (a), (d), , 10, 20, 30, , (b), (b), (c), , 3, 13, 23, , (a), (c), (a), , 4, 14, 24, , (c), (a), (a), , 5, 15, 25, , (c), (c), (a), , 6, 16, 26, , (c), (b), (b), , 7, 17, 27, , (*), (a), (c), , 8, 18, 28, , (a), (a), (c), , 9, 19, 29, , (a), (b), (d), , 10, 20, 30, , (c), (d), (a), , Chemistry, 1, 11, 21, , (b), (a), (d), , 2, 12, 22, , Mathematics, 1, 11, 21, , (c), (d), (a), , 2, 12, 22, , (a), (c), (a), , Note (*) None of the options is correct., , For Detailed Solutions Visit : https://bit.ly/2H7tXLj Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (10 January, 2019), TIME 2:30-5:30 (Shift II), , MM : 360, , PHYSICS, is given by F = 3i$ − 12$j, undergoes a, displacement of d = 4i$. If the particle had, a kinetic energy of 3 J at the beginning of, the displacement, what is its kinetic, energy at the end of the displacement ?, , pressed downward slightly and released,, it starts performing simple harmonic, motion at angular frequency ω . If the, radius of the bottle is 2.5 cm, then ω, is close to (Take, density of water, = 103 kg/m3 ), , (a) 9 J, (c) 12 J, , (a) 2. 50 rad s −1, (c) 1.25 rad s −1, , 1 A particle which is experiencing a force,, , (b) 15J, (d) 10 J, , 2 An unknown metal of mass 192 g heated, to a temperature of 100°C was immersed, into a brass calorimeter of mass 128 g, containing 240 g of water at a, temperature of 8.4°C. Calculate the, specific heat of the unknown metal, if, water temperature stabilises at 21.5°C., (Take, specific heat of brass is 394 J, kg −1K −1), , (a) 916 J kg −1 K −1, (c) 1232 J kg −1 K −1, , (b) 654 J kg −1 K −1, (d) 458 J kg −1 K −1, , 3 A current of 2 mA was passed through an, unknown resistor which dissipated a, power of 4.4 W. Dissipated power when, an ideal power supply of 11 V is, connected across it is, −4, , (a) 11 × 10 W, (c) 11 × 105 W, , −5, , (b) 11 × 10 W, (d) 11 × 10−3 W, , 4 A cylindrical plastic bottle of negligible, mass is filled with 310 mL of water and, left floating in a pond with still water. If, , (b) 5.00 rad s −1, (d) 3.75 rad s −1, , 5 Two stars of masses 3 × 1031 kg each and, at distance 2 × 1011 m rotate in a plane, about their common centre of mass O. A, meteorite passes through O moving, perpendicular to the star’s rotation plane., In order to escape from the gravitational, field of this double star, the minimum, speed that meteorite should have at O is, (Take, gravitational constant,, G = 667, . × 10−11 N-m 2 kg −2), (a) 2. 8 × 105 m/s, , (b) 3.8 × 104 m/s, , (c) 2. 4 × 104 m/s, , (d) 1. 4 × 105 m/s, , 6 Two identical spherical balls of mass M, and radius R each are stuck on two ends, of a rod of length 2R and mass M (see, figure)., The moment of inertia of the system, about the axis passing perpendicularly, through the centre of the rod is
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JANUARY ATTEMPT ~ 10 Jan 2019, Shift II, , 2R, , R, , R, , 35, A charge Q is placed at P, where OP = y, and y > > 2a. The charge Q experiences, an electrostatic force F., P, , 137, MR 2, 15, 17, (c), MR 2, 15, , 209, MR 2, 15, 152, (d), MR 2, 15, (b), , (a), , Q P′, A, , 7 The modulation frequency of an AM radio, station is 250 kHz, which is 10% of the, carrier wave. If another AM station, approaches you for license, what, broadcast frequency will you allot ?, (a) 2000 kHz, (c) 2900 kHz, , (b) 2250 kHz, (d) 2750 kHz, , 8 The actual value of resistance R , shown, in the figure is 30 Ω. This is measured in, an experiment as shown using the, V, standard formula R = , where V and I, I, are the readings of the voltmeter and, ammeter, respectively. If the measured, value of R is 5% less, then the internal, resistance of the voltmeter is, V, A, R, , (a) 600 Ω, (c) 350 Ω, , (b) 570 Ω, (d) 35 Ω, , 9 The eye can be regarded as a single, refracting surface. The radius of, curvature of this surface is equal to that, of cornea (7.8 mm). This surface, separates two media of refractive indices, 1 and 1.34. Calculate the distance from, the refracting surface at which a parallel, beam of light will come to focus., (a) 4.0 cm, (c) 3.1 cm, , (b) 2 cm, (d) 1 cm, , 10 Charges –q and +q located at A and B,, respectively, constitute an electric dipole., Distance AB = 2a, O is the mid point of, the dipole and OP is perpendicular to AB., , O, –q, , +q, , B, , If Q is now moved along the equatorial, y, line to P′ such that OP ′ = , the force on, 3, , y, Q will be close to >> 2a, , 3, F, 3, (c) 9F, , (a), , (b) 3F, (d) 27F, , 11 A hoop and a solid cylinder of same, mass and radius are made of a, permanent magnetic material with their, magnetic moment parallel to their, respective axes. But the magnetic, moment of hoop is twice of solid cylinder., They are placed in a uniform magnetic, field in such a manner that their, magnetic moments make a small angle, with the field. If the oscillation periods of, hoop and cylinder are Th and Tc, respectively, then, (a) Th = 0.5 Tc, (c) Th = 2 Tc, , (b) Th = Tc, (d) Th = 15, . Tc, , 12 Half-mole of an ideal monoatomic gas is, heated at constant pressure of 1 atm from, 20° C to 90° C . Work done by gas is close, to (Take, gas constant, R = 8.31 J/mol-K), (a) 291 J, (c) 146 J, , (b) 581 J, (d) 73 J, , 13 A rigid massless rod of length 3l has two, masses attached at each end as shown in, the figure. The rod is pivoted at point P, on the horizontal axis (see figure). When, released from initial horizontal position,, its instantaneous angular acceleration, will be
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36, , JEE Main 2019 ~ Solved Paper, , ONLINE, l, 5 Mo, , 2l, 2 Mo, , P, , g, (a), 13l, 7g, (c), 3l, , g, (b), 2l, g, (d), 3l, , 1.8 A-m is suspended from its mid point, using a thread, it makes 45° angle with, horizontal in equilibrium. To keep this, needle horizontal, the vertical force that, should be applied at one of its ends is, (a) 6. 5 × 10−5 N, (c) 1. 3 × 10−5 N, , 14 Consider the nuclear fission, , 19 Consider a Young’s double slit, , Ne20 → 2He4 + C12, , experiment as shown in figure., , Given that the binding energy/nucleon of, Ne20 , He4 and C12 are respectively,, 8.03 MeV, 7.07 MeV and 7.86 MeV,, identify the correct statement., (a), (b), (c), (d), , S1, , 15 For the circuit shown below, the current, through the Zener diode is, 5 kΩ, , Source S2, , (a) 14 mA, (c) 5 mA, , 10 kΩ, , (b) zero, (d) 9 mA, , 16 Two forces P and Q of magnitude 2F and, 3F, respectively,are at an angle θ with, each other. If the force Q is doubled, then, their resultant also gets doubled. Then,, the angle θ is, (a) 60°, (c) 30°, , (b) 120°, (d) 90°, , 17 A closed organ pipe has a fundamental, frequency of 1.5 kHz. The number of, overtones that can be distinctly heard by, a person with this organ pipe will be, (Assume that the highest frequency a, person can hear is 20,000 Hz), (a) 7, (c) 5, , (b) 4, (d) 6, , 18 At some location on earth, the horizontal, component of earth’s magnetic field is, 18 × 10−6 T. At this location, magnetic, needle of length 0.12 m and pole strength, , First minima, , Screen, , 2d, , What should be the slit separation d in, terms of wavelength λ such that the first, minima occurs directly in front of the slit, (S1 ) ?, , λ, 2(5 − 2 ), λ, (c), 2( 5 − 2), , (a), 50 V, , P, , d, , Energy of 3.6 MeV will be released., Energy of 12.4 MeV will be supplied., 8.3 MeV energy will be released., Energy of 11.9 MeV has to be supplied., , 120 V, , (b) 3. 6 × 10−5 N, (d) 1. 8 × 10−5 N, , λ, (5 − 2 ), λ, (d), ( 5 − 2), (b), , 20 A particle executes simple harmonic, motion with an amplitude of 5 cm. When, the particle is at 4 cm from the mean, position, the magnitude of its velocity in, SI units is equal to that of its, acceleration. Then, its periodic time (in, seconds) is, , 4π, 3, 7, (c) π, 3, (a), , 8π, 3, 3, (d) π, 8, (b), , 21 Four equal point charges Q each are, placed in the xy-plane at (0, 2), (4, 2), (4,, −2) and ( 0, − 2). The work required to put, a fifth charge Q at the origin of the, coordinate system will be, (a), , Q2, 4πε0, , (b), , Q2, 4 πε0, , 1 + 1 , , , , 3, , (c), , Q2, 2 2πε0, , (d), , Q2, 4 πε0, , 1 + 1 , , , , 5
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JANUARY ATTEMPT ~ 10 Jan 2019, Shift II, 22 Two vectors A and B have equal, magnitudes. The magnitude of ( A + B) is, ‘n’ times the magnitude of ( A − B). The, angle between A and B is, , n 2 − 1, , (a) sin −1 2, n + 1, n 2 − 1, , (c) cos−1 2, n + 1, , n − 1, (b) sin −1 , , n + 1, n − 1, (d) cos−1 , , n + 1, , 23 2 kg of a monoatomic gas is at a pressure, of 4 × 104 N/m 2. The density of the gas is, 8 kg/m3 . What is the order of energy of, the gas due to its thermal motion ?, (a) 106 J, (c) 104 J, , (b) 103 J, (d) 105 J, , 24 A parallel plate capacitor having, capacitance 12 pF is charged by a battery, to a potential difference of 10 V between, its plates. The charging battery is now, disconnected and a porcelain slab of, dielectric constant 6.5 is slipped between, the plates. The work done by the, capacitor on the slab is, (a) 560 pJ, (c) 692 pJ, , (b) 508 pJ, (d) 600 pJ, , 27 A metal plate of area 1 × 10−4 m 2 is, illuminated by a radiation of intensity 16, m W/m 2. The work function of the metal, is 5 eV. The energy of the incident, photons is 10 eV and only 10% of it, produces photoelectrons. The number of, emitted photoelectrons per second and, their maximum energy, respectively will, be (Take, 1 eV = 1.6 × 10−19 J), (a) 1011 and 5 eV, (c) 1010 and 5 eV, , measured by a meter scale to be, 12.6 ± 01, . cm and 34.2 ± 01, . cm,, respectively. What will be the value of its, volume in appropriate significant figures ?, (b) 4260 ± 80 cm3, (d) 4264 ± 81 cm3, , 28 The self-induced emf of a coil is 25 V., When the current in it is changed at, uniform rate from 10 A to 25 A in 1s, the, change in the energy of the inductance is, (a) 437.5 J, (c) 637.5 J, , (b) 740 J, (d) 540 J, , 29 The electric field of a plane polarised, electromagnetic wave in free space at, time t = 0 is given by an expression., E ( x , y ) = 10$j cos[(6x + 8z )], The magnetic field B ( x , z , t ) is given by, (where, c is the velocity of light), 1 $, (6k − 8$i ) cos[(6x + 8z + 10ct )], c, 1 $, (b) (6k, − 8$i ) cos[(6x + 8z − 10ct )], c, 1 $, (c) (6k, + 8$i ) cos[(6x − 8z + 10ct )], c, 1 $, (d) (6k, + 8$i ) cos[(6x + 8z − 10ct )], c, , 30 The Wheatstone bridge shown in figure, , 26 A particle starts from the origin at time, t = 0 and moves along the positive X-axis., The graph of velocity with respect to time, is shown in figure. What is the position of, the particle at time t = 5 s ?, v, (m/s), 4, , here, gets balanced when the carbon, resistor is used as R1 has the color code, (orange, red, brown). The resistors R2 and, R4 are 80 Ω and 40 Ω, respectively., Assuming that the color code for the, carbon resistors gives their accurate, values, the color code for the carbon, resistor is used as R3 would be, R1, , 3, 2, , (a) 6 m, (c) 10 m, , R2, G, , 1, 0, , (b) 1012 and 5 eV, (d) 1014 and 10 eV, , (a), , 25 The diameter and height of a cylinder are, , (a) 4300 ± 80 cm3, (c) 4264.4 ± 81.0 cm3, , 37, , R3, , 1, , 2, , 3, , 4, , 5 6, , 7, , (b) 3 m, (d) 9 m, , 8, , 9 10, , R4, , t (s), + –, , (a) brown, blue, black (b) brown, blue, brown, (c) grey, black, brown (d) red, green, brown
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38, , JEE Main 2019 ~ Solved Paper, , ONLINE, , CHEMISTRY, 1 The major product of the following, reaction is, O, CH3O, , CH3, , (i) Dil. HCl/∆, (ii) (COOH)2/, Polymerisation, , OH, , (a) —O, n, , 4 An aromatic compound ‘A’ having, molecular formula C7H 6O2 on treating, with aqueous ammonia and heating, forms compound ‘B’. The compound ‘B’ on, reaction with molecular bromine and, potassium hydroxide provides compound, ‘C’ having molecular formula C6H7N. The, structure of ‘A’ is, OHC, , CHO, , (a), , OH, , (b), OH, , O—, , (b) —O, , OH, , COOH, , (c), , n, , (d), CH==CH CHO, , OH, , (c), , 5 In the cell,, , —O, , O, , n, , OCH3, O—, , (d) —O, , n, OCOCH3, , 2 What is the IUPAC name of the, following compound ?, CH3, , CH3, H, , H, , Br, CH3, , (a) 3-bromo-3-methyl-1,2-dimethylprop-1-ene, (b) 3-bromo-1,2-dimethylbut-1-ene, (c) 2-bromo-3-methylpent-3-ene, (d) 4-bromo-3-methylpent-2-ene, , Pt(s) H 2 ( g, 1 bar) HCl( aq )|AgCl( s), Ag( s) Pt( s) the cell potential is 0.92 V, when a 10−6 molal HCl solution is used., The standard electrode potential of, ( AgCl / Ag,Cl− ) electrode is, 2.303RT, , , = 0.06 V at 298 K, Given,, F, , , (a) 0.40 V, (c) 0.94 V, , (b) 0.20 V, (d) 0.76 V, , 6 For an elementary chemical reaction,, k1, , A2, , = 2 A , the expression for ddt[A] is, k−1, , (a) 2k1 [A2 ] − k−1 [A ]2, (c) 2k1 [A2 ] − 2k−1 [A ]2, , (b) k1 [A2 ] − k−1 [A ]2, (d) k1 [A2 ] + k−1 [A ]2, , 7 The major product of the following, reaction is, NaBH4, , CH3N, , 3 A compound of formula A2B3 has the hcp, lattice. Which atom forms the hcp lattice, and what fraction of tetrahedral voids is, occupied by the other atoms ?, 2, tetrahedral voids-B, 3, 1, (b) hcp lattice-A, tetrahedral voids-B, 3, 1, (c) hcp lattice-B, tetrahedral voids-A, 3, 2, (d) hcp lattice-B, tetrahedral voids-A, 3, (a) hcp lattice- A,, , OH, , (a) CH3N, (b) CH3NH, OH, , (c) CH3NH, OH, , (d) CH3N
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JANUARY ATTEMPT ~ 10 Jan 2019, Shift II, , 39, , 8 The reaction that is not involved in the, ozone layer depletion mechanism in the, stratosphere is, , (c) O2N, , N, H, , (a) CH4 + 2O3 → 3CH2 == O + 3H2O, •, , •, , (b) Cl O( g ) + O( g ) → C l( g ) + O2 ( g ), •, , (d), N, H, , •, , hν, (c) HOCl( g ) →, OH( g ) + Cl( g ), hν, , •, , •, , NO2, , (d) CF2Cl 2 ( g ) → Cl( g ) + CF2Cl( g ), , 9 The 71st electron of an element X with an, atomic number of 71 enters into the orbital, (a) 4f, (c) 5d, , (b) 6p, (d) 6s, , 10 The amount of sugar (C12H 22O11 ) required, to prepare 2 L of its 0.1 M aqueous, solution is, (a) 17.1 g, (c) 136.8 g, , (b) 68.4 g, (d) 34.2 g, , 11 The pair that contains two PH bonds in, each of the oxoacids is, (a) H4 P2O5 and H4 P2O6 (b) H3 PO3 and H3 PO2, (c) H4 P2O5 and H3 PO3 (d) H3 PO2 and H4 P2O5, , 12 An ideal gas undergoes isothermal, compression from 5 m3 to 1 m3 against, a constant external pressure of 4 Nm −2., Heat released in this process is used, to increase the temperature of 1 mole, of Al. If molar heat capacity of Al is, 24 J mol−1K −1, the temperature of Al, increases by, 3, K, 2, (c) 2 K, , (b) 1K, , (a), , (d), , 2, K, 3, , 13 What will be the major product in the, following mononitration reaction ?, , 14 Haemoglobin and gold sol are examples of, (a) negatively and positively charged sols,, respectively, (b) negatively charged sols, (c) positively charged sols, (d) positively and negatively charged sols,, respectively, , 15 The process with negative entropy change is, (a) synthesis of ammonia from N2 and H2, , (b) dissociation of CaSO4 (s) to CaO(s) and, SO3 ( g ), (c) dissolution of iodine in water, (d) sublimation of dry ice, , 16 5.1 g NH 4 SH is introduced in 3.0 L, evacuated flask at 327° C. 30% of the solid, NH 4 SH decomposed to NH3 and H 2S as, gases. The K p of the reaction at 327° C is, (R = 0.082 atm mol −1K −1, molar mass of, S = 32 g mol −1, molar mass of N = 14 g mol −1), (a) 0. 242 × 10−4 atm 2, (c) 4. 9 × 10−3 atm 2, , (b) 0. 242 atm 2, (d) 1 × 10−4 atm 2, , 17 In the reaction of oxalate with, permanganate in acidic medium, the, number of electrons involved in producing, one molecule of CO2 is, (a) 2, (c) 1, , (b) 5, (d) 10, , 18 Among the following reactions of hydrogen, N, H, , HNO3, Conc.H2SO4, , NO2, , (a), , (a) H2 + Cl 2 → 2HCl (b) H2 + I2 → 2HI, (c) H2 + F2 → 2HF (d) H2 + Br2 → 2HBr, , 19 Sodium metal on dissolution in liquid, , N, H, , ammonia gives a deep blue solution due to, the formation of, , O2N, , (b), , with halogens, the one that requires a, catalyst is, , N, H, , (a) sodium ammonia complex, (b) sodium ion-ammonia complex, (c) sodamide, (d) ammoniated electrons
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40, , ONLINE, , 20 Which is the most suitable reagent for, the following transformation ?, OH, , CH3 CH ==CH CH2 C H CH3 →, , 25 The major product of the following, reaction is, CH3, OH, , (b) I2 / NaOH, (d) CrO2Cl 2 / CS2, , (i) aq. NaOH, (ii) CH3I, , CH3 CH ==CH CH2CO2H, (a) Tollen’s reagent, (c) Alkaline KMnO4, , JEE Main 2019 ~ Solved Paper, , CH3, , CH3, OH, , OH, , (a), , (b), , 21 The correct match between item ‘I’ and, , CH3, , item ‘II’ is, , CH3, CH3, , CH3, , Item ‘II’, (Reagent), , Item ‘I’, (Compound), (A), , Lysine, , (P) 1-naphthol, , (B), , Furfural, , (Q) Ninhydrin, , (C), , Benzyl alcohol, , (R) KMnO 4, , (D), , Styrene, , (S) Ceric ammonium, nitrate, , OH, , OCH3, , (c), , (d), CH3, , 26 The major product obtained in the, following reaction is, CO2Et, NaOEt/∆, , Codes, A, (a) Q, (c) Q, , B, R, P, , C, S, S, , D, P, R, , A, (b) R, (d) Q, , B, P, P, , C, Q, R, , D, S, S, , 22 The difference in the number of unpaired, , (a), , electrons of a metal ion in its high-spin, and low-spin octahedral complexes is two., The metal ion is, 2+, , (a) Mn, (c) Ni 2+, , CO2Et, , 2+, , (b) Fe, (d) Co2+, , (b), , CO2Et, , 23 The ground state energy of hydrogen, atom is −13.6 eV. The energy of second, excited state of He+ ion in eV is, (a) −54.4, (c) −6.04, , (c), , (b) −3.4, (d) −27.2, , CO2Et, , 24 A reaction of cobalt (III) chloride and, ethylene diamine in a 1 : 2 mole ratio, generates two isomeric products A (violet, coloured) and B (green coloured). A can, show optical activity, but B is optically, inactive. What type of isomers does A and, B represent ?, (a) Ionisation isomers, (b) Coordination isomers, (c) Geometrical isomers, (d) Linkage isomers, , (d), , CO2Et, , 27 The electrolytes usually used in the, electroplating of gold and silver,, respectively, are, , (a) [Au(OH)4 ]− and [Ag(OH)2 ]−, (b) [Au(NH3 )2 ]+ and [Ag(CN)2 ]−, , (c) [Au(CN)2 ]− and [Ag(CN)2 ]−, , (d) [Au(CN)2 ]− and [AgCl 2 ]−
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JANUARY ATTEMPT ~ 10 Jan 2019, Shift II, 28 Which of the following tests cannot be, used for identifying amino acids ?, (a) Barfoed test, (b) Ninhydrin test, (c) Xanthoproteic test (d) Biuret test, , 29 The number of 2-centre-2-electron and, 3-centre-2-electron bonds in B2 H6 ,, respectively, are, (a) 4 and 2, (c) 2 and 2, , (b) 2 and 4, (d) 2 and 1, , 41, 30 Elevation in the boiling point for 1 molal, solution of glucose is 2 K . The depression, in the freezing point for 2 molal solution, of glucose in the same solvent is 2 K. The, relation between K b and K f is, , (a) Kb = 15, . Kf, (b) Kb = 0.5 K f, (c) Kb = K f, (d) Kb = 2K f, , MATHEMATICS, 1 The positive value of λ for which the, , 5 A helicopter is flying along the curve given, , coefficient of x 2 in the expression, 10, λ, , x 2 x + 2 is 720, is, , x , , by y − x3/ 2 = 7, ( x ≥ 0). A soldier positioned, 1 , at the point , 7 wants to shoot down the, 2 , , (a) 3, (c) 2 2, , helicopter when it is nearest to him. Then,, this nearest distance is, , (b) 5, (d) 4, , , , 2 Let S = ( x , y ) ∈ R 2 :, , , , y2, x2, −, = 1 ,, 1+r 1−r, , , where r ≠ ± 1. Then, S represents, (a) a hyperbola whose eccentricity is, , 2, ,, 1−r, , when 0 < r < 1., (b) a hyperbola whose eccentricity is, , 2, ,, r+1, , when 0 < r < 1., (c) an ellipse whose eccentricity is, when r > 1., , 2, ,, r+1, 1, ,, r+1, , 3 With the usual notation, in ∆ABC, if, , ∠A + ∠B = 120°, a = 3 + 1 and b = 3 − 1,, then the ratio ∠A : ∠B, is, (b) 3 : 1, (d) 5 : 3, , 4 Let α = ( λ − 2) a + b and, β = ( 4λ − 2) a + 3b be two given vectors, where vectors a and b are non-collinear., The value of λ for which vectors α and β, are collinear, is, (a) 4, (c) 3, , 7, 3, 7, 3, , 5, 6, 1, (d), 2, (b), , 6 The value of ∫, , π/ 2, , dx, , where, [x ] + [sin x ] + 4, [t ] denotes the greatest integer less than, or equal to t, is, −π/ 2, , 1, (7 π − 5), 12, 3, (c), (4 π − 3), 10, , (a), , 1, (7 π + 5), 12, 3, (d), (4 π − 3), 20, , (b), , 7 If the probability of hitting a target by a, , (d) an ellipse whose eccentricity is, when r > 1., , (a) 7 : 1, (c) 9 : 7, , 1, 3, 1, (c), 6, , (a), , (b) −3, (d) −4, , 1, shooter in any shot, is , then the, 3, minimum number of independent shots, at the target required by him so that the, probability of hitting the target at least, 5, once is greater than , is, 6, (a) 6, (c) 5, , (b) 3, (d) 4, , 8 Two sides of a parallelogram are along, the lines, x + y = 3 and x − y + 3 = 0. If its, diagonals intersect at (2, 4), then one of, its vertex is, (a) (3, 6), (c) (2, 1), , (b) (2, 6), (d) (3, 5)
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42, , ONLINE, , 9 The value of, cos, , π, , 22, , ⋅ cos, , π, , 23, , ....... cos, , 1, 1024, 1, (c), 512, , (a), , π, 210, , (b), (d), , ⋅ sin, , π, 210, , 15 Two vertices of a triangle are (0, 2) and, is, , 1, 2, , 1, 256, , (b) Third, (d) First, 3, , 16 If ∫ x5 e−4x dx =, , two functions f and g be defined as, f , g : N → N such that, n + 1, ; if n is odd, , f(n ) = 2, n, , if n is even, ;, 2, and g( n ) = n − ( −1)n . Then, fog is, (a) one-one but not onto, (b) onto but not one-one, (c) both one-one and onto, (d) neither one-one nor onto, , ∑ { 50Cr ⋅ 50 − rC25 − r } = K (50C25 ),, , r=0, , then, K is equal to, (b) 225 − 1, (d) (25)2, , where C is a constant of integration, then, f ( x ) is equal to, (a) − 4x3 − 1, (c) − 2x3 − 1, , 3 f(x), , ( x > 0) and f(1) ≠ 4., 4 x, 1, Then, lim x f , +, x, x→ 0, that f ′ ( x ) = 7 −, , 4, 7, (c) exists and equals 0 (d) exists and equals 4, (b) exists and equals, , 2, , b, , 1, , , 1, , b, , , 2, , 13 Let A = b b2 + 1 b , where b > 0. Then,, the minimum value of, (a) − 3, (c) 2 3, , det ( A), is, b, , 19, , cot−1 1 +, ∑, , , n = 1, , 23, (a), 22, 19, (c), 21, , n, , , , p=1, , , , ∑ 2 p is, , 21, (b), 19, 22, (d), 23, , 18 The tangent to the curve, y = xex passing, through the point (1, e) also passes, through the point, , 4, (a) , 2e, , 3, , (b) (3, 6e), , (c) (2, 3e), , 5, (d) , 2e, , 3, , 19 On which of the following lines lies the, point of intersection of the line,, x−4 y−5 z−3, and the plane,, =, =, 2, 2, 1, x + y + z = 2?, , x−4, y−5 z−5, =, =, 1, 1, −1, x+ 3 4− y z + 1, (b), =, =, 3, 3, −2, x−2 y−3 z+ 3, (c), =, =, 2, 2, 3, x−1 y− 3 z + 4, (d), =, =, 1, 2, −5, (a), , 20 Let f : ( −1, 1) → R be a function defined, , (b) −2 3, (d) 3, 5, , (b) 4x3 + 1, (d) − 2x3 + 1, , 17 The value of cot , , 12 Let f be a differentiable function such, , (a) does not exist, , 1 −4x 3, e, f(x) + C,, 48, , 2, , 25, , (a) 224, (c) 225, , (4, 3). If its orthocentre is at the origin, then, its third vertex lies in which quadrant?, (a) Fourth, (c) Second, , 10 Let N be the set of natural numbers and, , 11 If, , JEE Main 2019 ~ Solved Paper, , 5, , 3 i, 3 i, − . If R( z ) and, + +, 2, 2, 2, 2, , 14 Let z = , , I ( z ) respectively denote the real and, imaginary parts of z, then, (a) R (z ) > 0 and I (z ) > 0 (b) I (z ) = 0, (c) R (z ) < 0 and I (z ) > 0 (d) R (z ) = − 3, , by f ( x ) = max { − x , − 1 − x 2 }. If K be the, set of all points at which f is not, differentiable, then K has exactly, (a) three elements, (b) five elements, (c) two elements, (d) one element
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JANUARY ATTEMPT ~ 10 Jan 2019, Shift II, 21 The curve amongst the family of curves, represented by the differential equation,, ( x 2 − y 2 )dx + 2xydy = 0, which passes, through (1, 1), is, , 43, 26 Let a1 , a2 , a3 ..... , a10 be in GP with ai > 0, for i = 1, 2, ..... ,10 and S be the set of pairs, (r , k), r , k ∈ N (the set of natural numbers), for which, , (a) a circle with centre on the Y-axis, (b) a circle with centre on the X-axis, , (c) an ellipse with major axis along the, Y-axis, (d) a hyperbola with transverse axis along, the X-axis., , 22 If ∫ f ( t ) dt = x 2 +, x, , 0, , 24, 25, 6, (c), 25, , (a), , 1 2, , ∫x t, , 1, f ( t )dt , then f ′ is, 2, , 18, 25, 4, (d), 5, , (b), , 23 The number of values of θ ∈( 0, π ) for, which the system of linear equations, x + 3 y + 7z = 0,, −x + 4 y + 7z = 0,, (sin 3θ )x + (cos 2θ ) y + 2z = 0, has a non-trivial solution, is, (a) two, (c) four, , (b) three, (d) one, , 24 The plane which bisects the line segment, , loge a1r a2k, , loge a2r a3k, , loge a3r a4k, , loge a4r, loge a7r, , loge a5r, loge a8r, , loge a6r a7k = 0, k, loge a9r a10, , a5k, a8k, , a6k, a9k, , Then, the number of elements in S, is, (a) 4, (b) 2, (c) 10, (d) infinitely many, , 27 Consider the following three statements:, P : 5 is a prime number., Q : 7 is a factor of 192., R : LCM of 5 and 7 is 35., Then, the truth value of which one of the, following statements is true ?, (a) (P ∧ Q ) ∨ (~ R ), (b) P ∨ (~ Q ∧ R ), (c) (~ P ) ∨ (Q ∧ R ), (d) (~ P ) ∧ (~ Q ∧ R ), , 28 The length of the chord of the parabola, x 2 = 4 y having equation x − 2 y + 4 2 = 0, is, (a) 8 2, (c) 3 2, , (b) 2 11, (d) 6 3, , 29 If the area of an equilateral triangle, inscribed in the circle,, x2 + y2 + 10x + 12 y + c = 0, , joining the points ( −3, − 3, 4) and ( 3, 7, 6), at right angles, passes through which one, of the following points ?, , is 27 3 sq units, then c is equal to, , (a) (4, − 1, 7), (c) (−2, 3, 5), , (a) 20, (c) 13, , (b) (2, 1, 3), (d) (4, 1, − 2), , 25 If mean and standard deviation of 5, observations x1 , x2 , x3 , x4 , x5 are 10 and 3,, respectively, then the variance of 6, observations x1 , x2 , ..... x5 and − 50 is, equal to, (a) 507.5, (c) 582.5, , (b) 586.5, (d) 509.5, , (b) −25, (d) 25, , 30 The value of λ such that sum of the, squares of the roots of the quadratic, equation, x 2 + ( 3 − λ )x + 2 = λ has the, least value is, 4, 9, 15, (c), 8, (a), , (b) 1, (d) 2
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44, , ONLINE, , JEE Main 2019 ~ Solved Paper, , Answers, Physics, 1., 11., 21., , (b), (b), (d), , 2., 12., 22., , (a), (a), (c), , 3., 13., 23., , (b), (a), (c), , 4., 14., 24., , (*), (*), (b), , 5., 15., 25., , (a), (d), (b), , 6., 16., 26., , (a), (b), (d), , 7., 17., 27., , (a), (d), (a), , 8., 18., 28., , (b), (a), (a), , 9., 19., 29., , (c), (c), (b), , 10., 20., 30., , (d), (b), (b), , (d), (d), (d), , 3., 13., 23., , (c), (b), (c), , 4., 14., 24., , (c), (d), (c), , 5., 15., 25., , (b), (a), (c), , 6., 16., 26., , (c), (b), (b), , 7., 17., 27., , (c), (c), (c), , 8., 18., 28., , (a), (b), (a), , 9., 19., 29., , (c), (d), (a), , 10., 20., 30., , (b), (b), (d), , 3., 13., 23., , (a), (c), (a), , 4., 14., 24., , (d), (b), (d), , 5., 15., 25., , (c), (c), (a), , 6., 16., 26., , (d), (a), (d), , 7., 17., 27., , (c), (b), (b), , 8., 18., 28., , (a), (a), (d), , 9., 19., 29., , (c), (d), (d), , 10., 20., 30., , (b), (a), (d), , Chemistry, 1., 11., 21., , (c), (d), (c), , 2., 12., 22., , Mathematics, 1., 11., 21., , (d), (c), (b), , 2., 12., 22., , (c), (d), (a), , Note (*) None of the options is correct., , For Detailed Solutions Visit : https://bit.ly/2WuUGXp Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (11 January, 2019), TIME 9:30-12:30 (Shift I), , MM : 360, , PHYSICS, 1 A liquid of density ρ is coming out of a hose, pipe of radius a with horizontal speed v, and hits a mesh. 50% of the liquid passes, through the mesh unaffected 25% losses, all of its momentum and, 25% comes back, with the same speed. The resultant, pressure on the mesh will be, (a) ρv2, 1, (c) ρv2, 4, , 4 A slab is subjected to two forces F1 and F2, of same magnitude F as shown in the, figure. Force F2 is in xy-plane while force, F1 acts along Z-axis at the point (2i$ + 3$j)., The moment of these forces about point O, will be, , 1 2, ρv, 2, 3, (d) ρv2, 4, , z, , (b), , F1, F2, , O, , 30°, 4m, , 2 A particle undergoing simple harmonic, motion has time dependent displacement, πt, given by x(t ) = A sin . The ratio of kinetic, 90, to potential energy of this particle at, t = 210 s will be, (a) 2, 1, (c), 9, , (b) 1, (d) 3, , 3 An electromagnetic wave of intensity, , 50 Wm −2 enters in a medium of refractive, index ‘n’ without any loss. The ratio of the, magnitudes of electric fields and the ratio, of the magnitudes of magnetic fields of the, wave before and after entering into the, medium are respectively, given by, , 1, (a) , , n , n, , 1 1 , , (c) , ,, , n n, , (b) ( n , n ), 1 , (d) n ,, , , n, , y, , 6m, , x, , $ )F, (a) (3$i + 2$j − 3k, $, $, $, (c) (3i − 2 j − 3k)F, , $ )F, (b) (3$i − 2$j + 3k, $, $, $ )F, (d) (3i + 2 j + 3k, , 5 There are two long coaxial solenoids of, same length l. The inner and outer coils, have radii r1 and r2 and number of turns, per unit length n1 and n2, respectively. The, ratio of mutual inductance to the, self-inductance of the inner coil is, n2 r1, ⋅, n1 r2, n, (c) 2, n1, , (a), , n2 r22, ⋅, n1 r12, n, (d) 1, n2, (b)
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400, , 600, 700, , λ (n-m), , Dm, , Dm, , (d), 400, , λ (n-m), , 600, 700, , (c), , vertices of a right angle isosceles triangle as, shown below. The net electrostatic energy of, the configuration is zero, if the value of Q is, Q, , λ (n-m), , 600, 700, , (b), , 400, , 7 Three charges Q, +q and +q are placed at the, , (a), , 500, , (b) 7.5 × 10−4 m, (d) 7.5 m, , Dm, , 600, 700, , (a) 7.5 × 10−2 m, (c) 7.5 × 10−3 m, , Dm, , 400, , accelerated, from rest by applying a, voltage of 500 V. Calculate the radius of, the path, if a magnetic field 100 mT is, then applied., (Take, charge of the electron = 16, . × 10−19 C, and mass of the electron = 91, . × 10−31 kg), , 500, , 6 In an experiment, electrons are, , 500, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 500, , 46, , λ (n-m), , 10 In the figure shown below, the charge on, the left plate of the 10 µF capacitor is, − 30 µC. The charge on the right plate of, the 6 µF capacitor is, , +q, , +q, , −q, (b), 1+ 2, − 2q, (d), 2+1, , (a) −2q, (c) + q, , 8 An object is at a distance of 20 m from a, convex lens of focal length 0.3 m. The lens, forms an image of the object. If the object, moves away from the lens at a speed of, 5 m/s, the speed and direction of the image, will be, (a), (b), (c), (d), , 3.22 × 10−3 m/s towards the lens, 0.92 × 10−3 m/s away from the lens, 2.26 × 10−3 m/s away from the lens, 116, . × 10−3 m/s towards the lens, , 9 The variation of refractive index of a crown, glass thin prism with wavelength of the, incident light is shown. Which of the, following graphs is the correct one, if Dm is, the angle of minimum deviation ?, , 6 µF, 10 µF, , (a) + 12 µC, (c) − 12 µC, , 4 µF, , 2 µF, , (b) + 18 µC, (d) − 18 µC, , 11 If the de-Broglie wavelength of an electron, is equal to 10−3 times, the wavelength of a, photon of frequency 6 × 1014 Hz, then the, speed of electron is equal to, (Take, speed of light = 3 × 108 m/s,, Planck’s constant = 663, . × 10−34 J-s and, mass of electron = 91, . × 10−31 kg), , (a), (b), (c), (d), , 1.45 × 106 m/s, 1.8 × 106 m/s, 11, . × 106 m/s, 1.7 × 106 m/s, , 12 A satellite is revolving in a circular orbit, , 1.520, , at a height h from the earth surface such, that h << R, where R is the radius of the, earth. Assuming that the effect of earth’s, atmosphere can be neglected the minimum, increase in the speed required so that the, satellite could escape from the gravitational, field of earth is, , 1.515, , (a), , 1.535, 1.530, , n2, , 1.525, , 1.510, , 400 500 600 700, , λ (n-m), , (c), , gR, 2, 2 gR, , (b), , gR, , (d), , gR ( 2 − 1)
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47, , JANUARY ATTEMPT ~ 11 Jan 2019, Shift I, 13 Equation of travelling wave on a stretched, string of linear density 5 g/m is, y = 003, . sin(450t − 9x), where distance and, time are measured in SI units. The tension, in the string is, (a) 5 N, (c) 7.5 N, , (b) 12.5 N, (d) 10 N, , 19 In the given circuit, the current through, zener diode is close to, R1, , 500 Ω, , R2, , 1500 Ω, , 12 V, V2 = 10 V, , R2, , 14 A hydrogen atom, initially in the ground, state is excited by absorbing a photon of, wavelength 980 Å. The radius of the atom, in the excited state in terms of Bohr radius, a 0 will be (Take hc = 12500 eV-Å), (a) 4 a0, (c) 16 a0, , (b) 9 a0, (d) 25 a0, , 15 A body is projected at t = 0 with a velocity, 10 ms −1 at an angle of 60° with the, horizontal. The radius of curvature of its, trajectory at t = 1 s is R. Neglecting air, resistance and taking acceleration due to, gravity g = 10 ms −2, the value of R is, , (a) 10.3 m, (c) 5.1 m, , (b) 2.8 m, (d) 2.5 m, , (a) 6.0 mA, (c) 0, , (b) 6.7 mA, (d) 4.0 mA, , 20 The resistance of the meter bridge AB in, , given figure is 4 Ω. With a cell of emf, ε = 05, . V and rheostat resistance Rh = 2 Ω ., The null point is obtained at some point J., When the cell is replaced by another one of, emf ε = ε 2, the same null point J is found, for Rh = 6 Ω. The emf ε 2 is, ε, , A, , B, , J, , 16 The force of interaction between two atoms, x2 , ; where x is, is given by F = αβ exp −, αkT , the distance, k is the Boltzmann constant, and T is temperature and α and β are two, constants. The dimension of β is, −2, , (a) [MLT ], (c) [M2LT −4 ], , 0 2 −4, , (b) [M L T ], (d) [M2L2T −2], , 17 In a Young’s double slit experiment, the, path difference at a certain point on the, screen between two interfering waves is, 1, th of wavelength. The ratio of the, 8, intensity at this point to that at the centre, of a bright fringe is close to, (a) 0.80, (c) 0.94, , Rh, , 6V, , (a) 0.6 V, (c) 0.5 V, , (b) 0.3 V, (d) 0.4 V, , 21 Two equal resistances when connected in, series to a battery consume electric power, of 60 W. If these resistances are now, connected in parallel combination to the, same battery, the electric power consumed, will be, (a) 60 W, (c) 240 W, , (b) 30 W, (d) 120 W, , 22 In the circuit shown,, R, , (b) 0.74, (d) 0.85, , S2, , 18 A rigid diatomic ideal gas undergoes an, adiabatic process at room temperature., The relation between temperature and, volume for this process is TV x = constant,, then x is, 2, (a), 5, 5, (c), 3, , 2, (b), 3, 3, (d), 5, , L, , S1, ε, , The switch S1 is closed at time t = 0 and the, switch S2 is kept open. At some later time, (t0 ), the switch S1 is opened and S2 is
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48, , ONLINE, closed. The behaviour of the current I as a, function of time ‘t’ is given by, I, , I, , (a), , (b), to, , t, , to, , I, , t, , I, , (c), , 26 A body of mass 1 kg falls freely from a, height of 100 m on a platform of mass 3 kg, which is mounted on a spring having, spring constant k = 125, . × 106 N/m. The, body sticks to the platform and the, spring’s maximum compression is found to, be x. Given that g = 10 ms −2, the value of x, will be close to, (a) 8 cm, (c) 40 cm, , (d), to, , JEE Main 2019 ~ Solved Paper, , (b) 4 cm, (d) 80 cm, , 27 A gas mixture consists of 3 moles of oxygen, , t, , to, , t, , 23 The given graph shows variation, (with distance r from centre) of, , and 5 moles of argon at temperature T., Considering only translational and, rotational modes, the total internal energy, of the system is, (a) 12 RT, (c) 20 RT, , 28 A particle is moving along a circular path, , ro, , ro, , r, , (a) electric field of a uniformly charged, spherical shell, (b) potential of a uniformly charged, spherical shell, (c) electric field of a uniformly charged, sphere, (d) potential of a uniformly charged sphere, , 24 An amplitude modulates signal is given by, v (t ) = 10[1 + 03, . cos(22, . × 104 t )], sin(55, . × 105 t )., Here, t is in seconds. The sideband, 22, , frequencies (in kHz) are Take, π = , , 7, (a) 892.5 and 857.5, (c) 178.5 and 171.5, , (b) 15 RT, (d) 4 RT, , with a constant speed of 10 ms −1. What is, the magnitude of the change in velocity of, the particle, when it moves through an, angle of 60° around the centre of the, circle?, , (a) 10 2 m/s, (c) 10 3 m/s, , (b) 10 m/s, (d) Zero, , 29 An equilateral triangle ABC is cut from a, thin solid sheet of wood. (see figure) D, E, and F are the mid points of its sides as, shown and G is the centre of the triangle., The moment of inertia of the triangle, about an axis passing through G and, perpendicular to the plane of the triangle, is I 0. If the smaller triangle DEF is, removed from ABC, the moment of inertia, of the remaining figure about the same, axis is I. Then, , (b) 89.25 and 85.75, (d) 1785 and 1715, , A, , 25 Ice at − 20°C is added to 50 g of water at, 40°C. When the temperature of the, mixture reaches 0°C, it is found that 20 g, of ice is still unmelted. The amount of ice, added to the water was close to, (Take, specific heat of water = 42, . J/g/°C, specific heat of ice = 21, . J/g/°C and, heat of fusion of water at 0°C = 334 J/g), (a) 40 g, (c) 60 g, , (b) 50 g, (d) 100 g, , D, , B, , 3, I0, 4, I, (c) I ′ = 0, 4, (a) I ′ =, , G, , F, , E, , C, , 15, I0, 16, 9, (d) I ′ =, I0, 16, , (b) I ′ =
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49, , JANUARY ATTEMPT ~ 11 Jan 2019, Shift I, 30 In a Wheatstone bridge (see figure), resistances P and Q are approximately equal. When, R = 400 Ω, the bridge is balanced. On interchanging P and Q , the value of R for balance is, 405 Ω. The value of X is close to, B, , P, , Q, G, , A, , C, R, , K2, , X, , D, K1, , (a) 404.5 Ω, , (b) 401.5 Ω, , (c) 402.5 Ω, , (d) 403.5 Ω, , CHEMISTRY, 6 An organic compound is estimated through, , 1 An example of solid sol is, (a) gem stones, (c) butter, , Dumas method and was found to evolved, 6 moles of CO2, 4 moles of H2O and 1 mole, of nitrogen gas. The formula of the, compound is, , (b) hair cream, (d) paint, , 2 NaH is an example of, (a), (b), (c), (d), , metallic hydride, electron-rich hydride, saline hydride, molecular hydride, , 7 Match the metals (Column I) with the, , 3 The major product of the following reaction, is, , O, , NH, , (ii) DIBAL- H, , (B) Zn, N, , (b), , O, CHO, , OH, , (d), , NH2, , 4 The concentration of dissolved oxygen, (DO) in cold water can go upto, (a) 14 ppm, (c) 8 ppm, , (b) 10 ppm, (d) 16 ppm, , is/are not aromatic?, ρ, , ρ, (B), , (a) (B), (C) and (D), (c) (B), , σ, (C), , (b) (C) and (D), (d) (A) and (C), , (i), , Wilkinson catalyst, , (ii, , Chlorophyll, , (C) Rh, , (iii) Vitamin B12, , (D) Mg, , (iv) Carbonic anhydrase, , A, (a) (i), (b) (iv), (c) (iii), (d) (ii), , B, (ii), (iii), (iv), (i), , C, (iii), (i), (i), (iv), , D, (iv), (ii), (ii), (iii), , 8 A 10 mg effervescent tablet containing, , 5 Which compound(s) out of the following, , (A ), , Column II, , (A) Co, , (i) Ni/H2, , H, , (c), , coordination compound(s)/enzyme(s), (Column II)., Column I, , OEt, CN, , (a), , (b) C12H8 N, (d) C6 H8 N2, , (a) C6 H8 N, (c) C12H8 N2, , (D), , sodium bicarbonate and oxalic acid, releases 0.25 mL of CO2 at T = 29815, . K, and p = 1 bar. If molar volume of CO2 is, 25.0 L under such condition, what is the, percentage of sodium bicarbonate in, each tablet?, [Molar mass of NaHCO3 = 84 g mol −1], (a) 8.4, (c) 16.8, , (b) 0.84, (d) 33.6
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50, , JEE Main 2019 ~ Solved Paper, , ONLINE, , OH, , 9 The correct statements among (a) to (d), regarding H2 as a fuel are :, I. It produces less pollutants than petrol., II. A cylinder of compressed dihydrogen, weights ~ 30 times more than a petrol, tank producing the same amount of, energy., III. Dihydrogen is stored in tanks of metal, alloys like NaNi5 ., IV. On combustion, values of energy, released per gram of liquid dihydrogen, and LPG are 50 and 142 kJ,, respectively., (a) I, II and III only, (c) II and IV only, , (b) II, III and IV only, (d) I and III only, , 10 Consider the reaction,, N2 ( g) + 3H2 ( g), , =2NH (g), 3, , The equilibrium constant of the above, reaction is K p. If pure ammonia is left to, dissociate, the partial pressure of ammonia, at equilibrium is given by (Assume that, pNH 3 < < ptotal at equilibrium), (a), (c), , 33 / 2 K 1p/ 2P 2, , (b), , 4, K p1/ 2P 2, , (d), , 16, , 33 / 2 K 1p/ 2P 2, 16, K p1/ 2P 2, 4, , 11 Among the following compounds, which, one is found in RNA?, O, CH3, , N, H, , N, , O, , N, , N, , O, , H, , Br, , 12 The major product of the following reaction, , SO3H, , SO3H, OH, , OH, , Br, , Br, , Br, , Br, , (c), , (d), SO3H, , Br, , 13 Heat treatment of muscular pain involves, radiation of wavelength of about 900 nm., Which spectral line of H-atom is suitable, for this purpose? [RH = 1 × 105 cm–1,, , h = 66, . × 10−34 Js, c = 3 × 108 ms−1], (a) Paschen, 5 →3, (c) Lyman, ∞ → 1, , (b) Paschen, ∞ → 3, (d) Balmer, ∞ → 2, , 14 The freezing point of a diluted milk sample, is found to be −02, . ° C, while it should have, been −0.5°C for pure milk. How much, water has been added to pure milk to, make the diluted sample?, , (a), (b), (c), (d), , 2 cups of water to 3 cups of pure milk, 1 cup of water to 3 cups of pure milk, 3 cups of water to 2 cups of pure milk, 1 cup of water to 2 cups of pure milk, , 15 The correct order of the atomic radii of, C, Cs, Al and S is, (b) C < S < Cs < Al, (d) S < C < Al < Cs, , 16 The amphoteric hydroxide is, (a) Be(OH)2, (c) Sr(OH)2, , (b) Ca(OH)2, (d) Mg(OH)2, , is, Item - I, (Mixture), , Item II, (Separation method), , A. H2O : Sugar, , P., , Sublimation, , B. H2O : Aniline, , Q., , Recrystallisation, , C. H2O : Toluene, , R., , Steam distillation, , S., , Differential, extraction, , OH, Br2 (excess), , Br, Br, , O, , Me, , is, , (b), , 17 The correct match between items I and II, N Me, , (d), N, , O, , H, , O, , NH2, , (c), , NH, , (b), , Br, , (a), , (a) C < S < Al < Cs, (c) S < C < Cs < Al, , O, NH, , (a), , OH, , (a), (b), (c), (d), , (A) → (Q); (B) → (R); (C) → (S), (A) → (Q); (B) → (R); (C) → (P), (A) → (S); (B) → (R); (C) → (P), (A) → (R); (B) → (P); (C) → (S)
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51, , JANUARY ATTEMPT ~ 11 Jan 2019, Shift I, 18 Match the ores ( Column A ) with the, metals (Column B)., Column A, , Column B, , Ores, , Metals, , A., , Siderite, , P., , Zinc, , B., , Kaolinite, , Q., , Copper, , C., , Malachite, , R., , Iron, , D., , Calamine, , S., , Aluminium, , (a), (b), (c), (d), , (a) SnCl 4, (c) PbCl 4, , variable oxidation states is, (b) Cu, (d) V, , 20 The major product of the following reaction, is, COCH3, (ii) H2SO4 (dil.), , COOH, , COCH3, , (b), , HOOC, , HOOC, COCOOH, , COOH, , (c), , (d), , OHC, , HOOC, , 21 The correct match between item (I) and, item (II) is, Item - I, , Item - II, , (A) Norethindrone, , (P) Antibiotic, , (B) Ofloxacin, , (Q) Antifertility, , (C) Equanil, , (R) Hypertension, (S) Analgesics, , (a), (b), (c), (d), , (A) → (Q); (B) → (R); (C) → (S), (A) → (Q); (B) → (P); (C) → (R), (A) → (R); (B) → (P); (C) → (S), (A) → (R); (B) → (P); (C) → (R), , 22 Peroxyacetyl nitrate (PAN), an eye irritant, is produced by, (a), (b), (c), (d), , organic waste, acid rain, classical smog, photochemical smog, , (b) CCl 4, (d) SiCl 4, , 25 For the chemical reaction, X, , Y , the, standard reaction Gibbs energy depends, on temperature T (in K) as, 3, ∆ rG° (in kJ mol–1 ) = 120 − T, 8, The major component of the reaction, mixture at T is, , (a) Y if T = 280 K, (c) X if T = 315 K, , (i) KMnO4/KOH,∆, , (a), , 0.03050 kg mol −1, 0.4320 kg mol −1, 0.0432 kg mol −1, 0.0216 kg mol −1, , 24 The chloride that cannot get hydrolysed is, , 19 The element that usually does not show, , CH3, , forms face centred cubic crystals of edge, length 200 2 pm. What is the molar mass, of the solid?, [Avogadro constant = 6 × 1023 mol−1 , π = 3], (a), (b), (c), (d), , A - P; B- Q; C - R; D- S, A - R; B- S; C - P; D- Q, A - Q; B- R; C - S; D- P, A - R; B- S; C - Q; D- P, , (a) Sc, (c) Ti, , 23 A solid having density of 9 × 103 kg m−3, , -, , (b) X if T = 350 K, (d) Y if T = 300 K, , 26 Two blocks of the same metal having same, mass and at temperature T1 and T2, respectively, are brought in contact with, each other and allowed to attain thermal, equilibrium at constant pressure. The, change in entropy, ∆S, for this process is, 1, , T + T2 , (T1 + T2 ) 2 , (a) C p ln , (b) 2C p ln 1, , T1T2 , 4T1T2 , , , , , (T + T2 )2 , T1 + T2 , 2, (c) C p ln 1, (d) C p ln , , 2T1T2 , 4T1T2 , 2, , 27 The polymer obtained from the following, reaction is:, +, , NH2, , HOOC, , (i) NaNO2 /H3O, , (ii) Polymerisation, , O, , O, H, (a) —C—(CH2)4—N—, n, , (b) —O—(CH2)4—C—n, , (c) —OC(CH2)4O—, , (d) —HNC(CH2)4—C—N—, , n, , H, , n
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52, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 28 The major product of the following reaction is, Cl, (i) HBr, (ii) alc.KOH, , (b), , M x + (aq)/M(s), , O, Cl, , O, , (c), , Au 3 + (aq)/ Ag + (aq)/ Fe 3 + (aq)/ Fe 2 + (aq), Au(s), Ag(s), Fe 2 + (aq) /Fe(s), , E ° Mx + / M /V, , (d), , 1.40, , 0.80, , − 0.44, , 0.77, , If E°Zn 2 + / Zn = − 0.76 V, which cathode will, give a maximum value of E°cell per, electron transferred?, , O, , OH, , (d) y unit, , Zn(s)|Zn 2+ (aq)||M x+ (aq)|M (s), different, half cells and their standard electrode, potentials are given below., , Cl, , (a), , (b) − y unit, , 30 For the cell,, , O, OH, , y, unit, R, (c) yR unit, , (a), , 29 If a reaction follows the Arrhenius, equation, the plot lnk vs 1/(RT) gives, straight line with a gradient (−y) unit., The energy required to activate the, reactant is, , Ag +, Ag, Au3 +, (c), Au, , (a), , (b), (d), , Fe2+, Fe, Fe3 +, Fe2+, , MATHEMATICS, 1 Let [x] denote the greatest integer less, than or equal to x. Then,, lim, , tan(π sin 2 x) + (|x| − sin(x[x]))2, , x→ 0, , (a) equals π, (c) equals 0, , (b) equals π + 1, (d) does not exist, , g(x) =| f (x)| + f (|x|). Then, in the interval, (−2, 2), g is, not differentiable at one point, not differentiable at two points, differentiable at all points, not continuous, , 3 If the system of linear equations, 2x + 2 y + 3z = a, 3x − y + 5z = b, x − 3 y + 2z = c, where a , b, c are non-zero real numbers,, has more than one solution, then, (a) b − c − a = 0, (c) b − c + a = 0, , bounded by the curve x2 = 4 y and the, straight line x = 4 y − 2 is, , (a), , x2, , −2 ≤ x < 0, − 1,, 2 Let f (x) = 2, and, x − 1, 0 ≤ x ≤ 2, , (a), (b), (c), (d), , 4 The area (in sq units) of the region, , (b) a + b + c = 0, (d) b + c − a = 0, , 5 If ∫, , 7, 8, , (b), , 9, 8, , (c), , 5, 4, , 3, 4, , (d), , 1 − x2, , dx = A(x)( 1 − x2 )m + C,, x4, for a suitable chosen integer m and a, function A(x), where C is a constant of, integration, then ( A(x))m equals, , (a), , 1, 9x4, , (b), , −1, 3x3, , (c), , −1, 27x9, , 1, , (d), , 27x6, , 6 The maximum value of the function, , f (x) = 3x3 − 18x2 + 27x − 40 on the set, S = { x ∈R : x2 + 30 ≤ 11x} is, (a) 122, (c) − 222, , (b) − 122, (d) 222, , 7 Let f : R → R be defined by f (x) =, x ∈R. Then, the range of f is, , x, 1 + x2, , 1 1, (a) − , , 2 2 , , (b) (−1, 1) − {0}, , 1 1, (c) R − − , , 2 2 , , (d) R − [−1, 1], , ,
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53, , JANUARY ATTEMPT ~ 11 Jan 2019, Shift I, 8 The outcome of each of 30 items was 1, , observed ; 10 items gave an outcome − d, 2, 1, each, 10 items gave outcome each and, 2, 1, the remaining 10 items gave outcome + d, 2, each. If the variance of this outcome data, 4, is , then|d|equals, 3, , (a), , 2, 3, , 5, 2, , (b), , (c), , (d) 2, , 2, , 9 Two integers are selected at random from, the set { 1, 2, …… , 11}. Given that the, sum of selected numbers is even, the, conditional probability that both the, numbers are even is, (a), , 2, 5, , 1, 2, , (b), , (c), , 7, 10, , (d), , 5, 4, , (c) 4 5, , (d), , 3, 5, , (c) 6, , 12 Let a1 , a 2 , .... , a10 be a GP. If, a9, equals, a5, (a) 53, , (b) 2(52 ), , a3, = 25, then, a1, , 3, , 1, x + iy, (i = −1 ), where x, , , 3, 27, and y are real numbers, then y − x equals, (b) 85, , (c) – 85, , (d) – 91, , 14 If x loge (loge x) − x2 + y2 = 4( y > 0), then, at x = e is equal to, (a), (c), , e, 4 + e2, (1+ 2e ), 4 + e2, , (b), (d), , (2e − 1), 2 4 + e2, (1+ 2e ), 2 4 + e2, , (a) p ∨ r, (c) ( p ∨ r )→ ( p ∧ r ), , 137, , (b) ( p ∧ r )→ ( p ∨ r ), (d) p ∧ r, , (a) y(x) is decreasing in , 1, 2 , (b) y(x) is decreasing in (0, 1), (c) y(log e 2) = log e 4, log e 2, (d) y(log e 2) =, 4, , Cr, , C0 +, , 20, , 20, , Cr − 1, , dy, dx, , C1 +, , 20, , 20, , Cr − 2, , (a) 15, , (b) 10, , C2 + ...., , 20, , + 20C 020C r, , is maximum, is, (c) 11, , (d) 20, , 19 Two circles with equal radii are, , intersecting at the points (0, 1) and (0, −1)., The tangent at the point (0,1) to one of the, circles passes through the centre of the, other circle. Then, the distance between, the centres of these circles is, , (a) 2, (c) 1, , (d) 54, , 13 Let −2 − i =, (a) 91, , (d), , 41, , which one of the following statements is a, tautology?, , 20, , (d) 8, , (c) 4(52 ), , (c), , 18 The value of r for which, , 5, 2, , the middle term in the binomial expansion, 8, x3 3, of + equals 5670 is, x, 3, (b) 0, , (b) 13, , dy 2x + 1, −2 x, +, y = e , x > 0,, dx x , 1, where y (1) = e−2, then, 2, 1, , 11 The sum of the real values of x for which, , (a) 4, , (a) 6, , 16 If q is false and p ∧ q ←→ r is true, then, , equation, , coordinate axes at A and B. A circle is, drawn through A, B and the origin. Then,, the sum of perpendicular distances from A, and B on the tangent to the circle at the, origin is, (b), , x2 + y2 − 6x + 8 y − 103 = 0 with its sides, parallel to the coordinate axes. Then, the, distance of the vertex of this square which, is nearest to the origin is, , 17 If y(x) is the solution of the differential, , 10 The straight line x + 2 y = 1 meets the, , (a) 2 5, , 15 A square is inscribed in the circle, , (b) 2 2, (d) 2, , 20 Equation of a common tangent to the, , parabola y2 = 4x and the hyperbola xy = 2 is, , (a) x + 2 y + 4 = 0, (c) 4x + 2 y + 1 = 0, , (b) x − 2 y + 4 = 0, (d) x + y + 1 = 0, , sin 2 x, dx, −2 x , 1, +, π 2, (where, [x] denotes the greatest integer, less than or equal to x) is, , 21 The value of the integral ∫, , (a) 4 − sin 4, (c) sin 4, , (b) 4, (d) 0, , 2
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54, , (a), , 22 If one real root of the quadratic equation, , 81x + kx + 256 = 0 is cube of the other root,, then a value of k is, 2, , (a) 100, , (b) 144, , (c) −81, , (b) 2 , 1, − 1, (d) 2 3 , 1, − 1, , c, (a), 3, , (b), , c, 3, , 3, (c) y, 2, , (d), , y, 3, , 1, 3, , 1, 6, , (d), , x2, y2, +, =1, 4, 2, , (b), , (c), , x2, y2, +, =1, 2, 4, , (d), , 1, 4x2, 1, 2x2, , +, +, , 1, 2 y2, 1, 4 y2, , =1, =1, , 1, (sin k x + cosk x) for k = 1, 2, 3 ... ., k, Then, for all x ∈ R, the value of f4 (x) − f6 (x) is, equal to, , (a), , 1, 12, , (b), , 5, 12, , (c), , −1, 12, , (d), , 1, 4, , 29 The sum of an infinite geometric series, with positive terms is 3 and the sum of the, 27, cubes of its terms is . Then, the common, 19, ratio of this series is, , x −3 y + 2 z − 1, and also containing its, =, =, 2, 3, −1, projection on the plane 2x + 3 y − z = 5,, contains which one of the following points?, , (a), , 4, 9, , (b), , 2, 3, , (c), , 2, 9, , (d), , 1, 3, , $ , b = $i + λ$j + 4k, $ and, 30 Let a = $i + 2$j + 4k, , (b) (2, 2, 0), (d) (0, − 2, 2), , $ be coplanar vectors., c = 2i$ + 4$j + (λ 2 − 1) k, Then, the non-zero vector a × c is, , 0 2q r , , , q −r . If AAT = I3 , then| p|is, p −q r , , , , 26 Let A = p, , (a) − 10 $i + 5$j, (c) − 14 $i − 5$j, , (b) − 10 $i − 5$j, (d) − 14 $i + 5$j, , Answers, , Physics, (d), (a), (c), , (c), , 28 Let fk (x) =, , 25 The plane containing the line, , (a) (−2, 2, 2), (c) (2, 0, − 2), , 1, 2, , (a), , 24 In a triangle, the sum of lengths of two, sides is x and the product of the lengths of, the same two sides is y. If x2 − c2 = y, where, c is the length of the third side of the, triangle, then the circumradius of the, triangle is, , (b), , x2 + 2 y2 = 2 at all points on the ellipse, other than its four vertices, then the, mid-points of the tangents intercepted, between the coordinate axes lie on the, curve, , (d) −300, , through the points (0, − 1, 0) and (0, 0, 1), π, and making an angle with the plane, 4, y − z + 5 = 0 are, , (a) 2, − 1, 1, (c) 2, 2 , − 2, , 1, 5, , 27 If tangents are drawn to the ellipse, , 23 The direction ratios of normal to the plane, , 1, 11, 21, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 2, 12, 22, , (*), (d), (b), , 3, 13, 23, , (d), (b), (b), , 4, 14, 24, , (b), (c), (b), , 5, 15, 25, , (c), (b), (a), , 6, 16, 26, , (b), (c), (*), , 7, 17, 27, , (d), (d), (b), , 8, 18, 28, , (d), (a), (b), , 9, 19, 29, , (c), (c), (b), , 10, 20, 30, , (b), (b), (c), , (c), (c), (d), , 3, 13, 23, , (b), (b), (a), , 4, 14, 24, , (b), (c), (b), , 5, 15, 25, , (a), (a), (c), , 6, 16, 26, , (d), (a), (c), , 7, 17, 27, , (c), (a), (b), , 8, 18, 28, , (a), (d), (c), , 9, 19, 29, , (a), (a), (d), , 10, 20, 30, , (b), (a), (a), , 3, 13, 23, , (a), (a), (b,c), , 4, 14, 24, , (b), (b), (b), , 5, 15, 25, , (c), (c), (c), , 6, 16, 26, , (a), (b), (b), , 7, 17, 27, , (a), (a), (d), , 8, 18, 28, , (c), (d), (a), , 9, 19, 29, , (a), (d), (b), , 10, 20, 30, , (d), (a), (a), , Chemistry, 1, 11, 21, , (a), (a), (b), , 2, 12, 22, , Mathematics, 1, 11, 21, , (d), (b), (d), , 2, 12, 22, , (a), (d), (d), , For Detailed Solutions Visit : http://tinyurl.com/y6gyb7v9 Or, , Scan :
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JANUARY ATTEMPT ~ 11 Jan 2019, Shift II, , 55, , ONLINE QUESTION PAPER, , JEE Main 2019, (11 January, 2019), TIME 2:30-5:30 (Shift II), , MM : 360, , PHYSICS, 1 An amplitude modulated signal is plotted, below, 10 V, 8V, , V(t), , t, , 8 µs, , 100 µs, , 4 A circular disc D1 of mass M and radius R, has two identical discs D2 and D3 of the, same mass M and radius R attached, rigidly at its opposite ends (see figure)., The moment of inertia of the system about, the axis OO′ passing through the centre of, D1, as shown in the figure will be, O′, , Which one of the following best describes, the above signal?, (a), (b), (c), (d), , [1 + 9 sin(2 π × 104 t )]sin(2.5 π × 105 t )V, [9 + sin(2 π × 104 t )]sin(2.5 π × 105 t )V, [9 + sin(4 π × 104 t )]sin(5 π × 105 t )V, [9 + sin(2.5 π × 105 t )]sin(2 π × 104 t )V, , 2 Two rods A and B of identical dimensions, are at temperature 30ºC. If A is heated, upto 180ºC and B upto T º C, then new, lengths are the same. If the ratio of the, coefficients of linear expansion of A and B, is 4 : 3, then the value of T is, (a) 230ºC, (c) 200ºC, , (b) 270ºC, (d) 250ºC, , 3 A galvanometer having a resistance of, , 20 Ω and 30 divisions on both sides has, figure of merit 0.005 ampere/division. The, resistance that should be connected in, series such that it can be used as a, voltmeter upto 15 volt is, (a) 100 Ω, (c) 120 Ω, , (b) 125 Ω, (d) 80 Ω, , D2, , D3, , O, D1, , 2, (a) MR 2, 3, (c) 3MR 2, , 4, MR 2, 5, (d) MR 2, (b), , 5 The magnitude of torque on a particle of, mass 1 kg is 2.5 N-m about the origin. If, the force acting on it is 1 N and the, distance of the particle from the origin is, 5 m, then the angle between the force and, the position vector is (in radian), , π, 8, π, (c), 3, (a), , π, 4, π, (d), 6, (b), , 6. The circuit shown below contains two ideal, diodes, each with a forward resistance of, 50 Ω. If the battery voltage is 6 V, the
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56, , JEE Main 2019 ~ Solved Paper, , ONLINE, current through the 100 Ω resistance (in, ampere) is, D1, , 150Ω, 75Ω, , D2, , (b) 3.3 × 10− 2, (d) 2.3 × 10− 2, , 12 The mass and the diameter of a planet are, (b) 0.020, (d) 0.036, , 7 When 100 g of a liquid A at 100ºC is added, to 50 g of a liquid B at temperature 75ºC,, the temperature of the mixture becomes, 90ºC. The temperature of the mixture, if, 100 g of liquid A at 100ºC is added to 50 g, of liquid B at 50ºC will be, (a) 60ºC, (c) 70ºC, , cube with sides 1 cm has a magnetic dipole, moment of 20 × 10− 6 J / T when a magnetic, intensity of 60 × 103 A / m is applied. Its, magnetic susceptibility is, (a) 3.3 × 10− 4, (c) 4.3 × 10− 2, , 100Ω, 6V, , (a) 0.027, (c) 0.030, , 11 A paramagnetic substance in the form of a, , (b) 80ºC, (d) 85ºC, , three times the respective values for the, earth. The period of oscillation of a simple, pendulum on the earth is 2 s. The period of, oscillation of the same pendulum on the, planet would be, (a), , 2, s, 3, , (c) 2 3 s, , 3, s, 2, 3, (d), s, 2, , (b), , 13 A particle of mass m and charge q is in an, , 8 A string is wound around a hollow cylinder, of mass 5 kg and radius 0.5 m. If the string, is now pulled with a horizontal force of, 40 N and the cylinder is rolling without, slipping on a horizontal surface (see, figure), then the angular acceleration of, the cylinder will be (Neglect the mass and, thickness of the string), 40 N, , electric and magnetic field is given by, $., E = 2i$ + 3$j, B = 4$j + 6k, The charged particle is shifted from the, origin to the point P (x = 1; y = 1) along a, straight path. The magnitude of the total, work done is, (a) (0.35) q, (c) (2.5) q, , (b) (015, . )q, (d) 5 q, , 14 In a double-slit experiment, green light, 2, , (a) 10 rad / s, (c) 20 rad / s2, , 2, , (b) 16 rad / s, (d) 12 rad / s2, , 9 A particle moves from the point, , (20, . $i + 40, . $j ) m at t = 0 with an initial, velocity (50, . $i + 40, . $j) ms− 1. It is acted upon, by a constant force which produces a, constant acceleration (40, . $i + 40, . $j) ms− 2., What is the distance of the particle from, the origin at time 2 s?, , (a) 5 m, (c) 10 2 m, , (b) 20 2 m, (d) 15 m, , 10 A monochromatic light is incident at a, certain angle on an equilateral triangular, prism and suffers minimum deviation. If, the refractive index of the material of the, prism is 3, then the angle of incidence is, (a) 45º, (c) 60º, , (b) 90º, (d) 30º, , (5303 Å) falls on a double slit having a, separation of 1944, . µ-m and a width of, 405, . µ-m. The number of bright fringes, between the first and the second, diffraction minima is, (a) 5, (c) 9, , (b) 10, (d) 4, , 15 If speed (V ), acceleration ( A) and force (F ), are considered as fundamental units, the, dimension of Young’s modulus will be, (a) [V−4 A− 2F], (c) [V−2A2 F− 2 ], , (b) [V−2A2 F2 ], (d) [V−4 A2 F], , 16 In a hydrogen like atom, when an electron, jumps from the M-shell to the L-shell, the, wavelength of emitted radiation is λ. If an, electron jumps from N-shell to the L-shell,, the wavelength of emitted radiation will be, 27, λ, 20, 20, (c), λ, 27, (a), , 25, λ, 16, 16, (d), λ, 25, (b)
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JANUARY ATTEMPT ~ 11 Jan 2019, Shift II, 17 In the experimental set up of meter bridge, shown in the figure, the null point is, obtained at a distance of 40 cm from A. If a, 10 Ω resistor is connected in series with R1,, the null point shifts by 10 cm., The resistance that should be connected in, parallel with (R1 + 10) Ω such that the null, point shifts back to its initial position is, R1, G, B, , (b) 20 Ω, (d) 40 Ω, , 18 The region between y = 0 and y = d, $. A, contains a magnetic field B = Bk, particle of mass m and charge q enters the, mv, region with a velocity v = vi$. If d =, 2qB, then the acceleration of the charged, particle at the point of its emergence at the, other side is, qvB 3 $ 1 $ , i + j, , m 2, 2 , qvB − $j + i$ , (c), m , 2 , , (a), , qvB 1 $, 3 $, j, i−, m 2, 2 , qvB $i + $j , (d), m 2 , , (b), , 19 In a process, temperature and volume of, one mole of an ideal monoatomic gas are, varied according to the relation VT = k,, where k is a constant. In this process, the, temperature of the gas is increased by ∆T., The amount of heat absorbed by gas is, (where, R is gas constant), 1, kR∆T, 2, 1, (c), R∆ T, 2, , (a), , 2k, ∆T, 3, 3, (d), R∆ T, 2, , (b), , 20 A 27 mW laser beam has a cross-sectional, area of 10 mm2. The magnitude of the, maximum electric field in this, electromagnetic wave is given by, [Take, permittivity of space, ε 0 = 9 × 10− 12, SI units and speed of light, c = 3 × 10 m / s], 8, , (a) 1 kV/m, (c) 2 kV/m, , frame, whose shape is that of an, equilateral triangle. If the linear, dimension of each side of the frame is, increased by a factor of 3, keeping the, number of turns of the coil per unit length, of the frame the same, then the, self-inductance of the coil, , (b) 0.7 kV/m, (d) 1.4 kV/m, , increases by a factor of 3, decreases by a factor of 9 3, increases by a factor of 27, decreases by a factor of 9, , 22 A metal ball of mass 0.1 kg is heated upto, , (), , (a) 60 Ω, (c) 30 Ω, , 21 A copper wire is wound on a wooden, , (a), (b), (c), (d), , R2, , A, , 57, , 500ºC and dropped into a vessel of heat, capacity 800 JK − 1 and containing 0.5 kg, water. The initial temperature of water, and vessel is 30ºC. What is the, approximate percentage increment in the, temperature of the water?, [Take, specific heat capacities of water and, metal are respectively 4200 Jkg − 1K − 1 and, 400 Jkg − 1K − 1], (a) 25%, (c) 30%, , (b) 15%, (d) 20%, , 23 A thermometer graduated according to a, linear scale reads a value x0, when in, contact with boiling water and x0 / 3, when, in contact with ice. What is the, temperature of an object in ºC, if this, thermometer in the contact with the object, reads x0 / 2 ?, (a) 35, (c) 40, , (b) 60, (d) 25, , 24 A simple pendulum of length 1 m is, oscillating with an angular frequency, 10 rad/s. The support of the pendulum, starts oscillating up and down with a, small angular frequency of 1 rad/s and an, amplitude of 10− 2 m. The relative change, in the angular frequency of the pendulum, is best given by, (a) 1 rad/s, (c) 10− 3 rad / s, , (b) 10− 5 rad / s, (d) 10− 1 rad / s, , 25 An electric field of 1000 V/m is applied to, an electric dipole at angle of 45º. The value, of electric dipole moment is 10− 29 C-m., What is the potential energy of the electric, dipole?
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58, , ONLINE, (a) − 9 × 10− 20 J, (c) − 20 × 10− 18 J, , (b) − 10 × 10− 29 J, (d) − 7 × 10− 27 J, , JEE Main 2019 ~ Solved Paper, , Which of the combinations shown in, figures below will achieve the desired, value?, , 26 In the circuit shown, the potential, difference between A and B is, M, 5Ω, A, , 1Ω, , 1V, , 1Ω, , 2V, , 1Ω, , 3V, , D, N, , (a) 3 V, (c) 6 V, , C, , (b) 1 V, (d) 2 V, , (c), , (c), , (d), , 29 In a photoelectric experiment, the, , straight line with momentum p. Starting, at time t = 0, a force F = kt acts in the same, direction on the moving particle during, time interval T, so that its momentum, changes from p to 3p. Here, k is a constant., The value of T is, 2p, k, 2k, p, , (b), , B, , 27 A particle of mass m is moving in a, , (a), , (a), 10Ω, , p, k, k, (d) 2, p, , wavelength of the light incident on a metal, is changed from 300 n-m to 400 n-m. The, decrease in the stopping potential is close, hc, , to , = 1240 n-mV, e, , (a) 0.5 V, (c) 1.5 V, , (b) 2.0 V, (d) 1.0 V, , 30 A pendulum is executing simple harmonic, , (b) 2, , 28 Seven capacitors, each of capacitance 2 µF, are to be connected in a configuration to, 6, obtain an effective capacitance of µF., 13, , motion and its maximum kinetic energy is, K1. If the length of the pendulum is doubled, and it performs simple harmonic motion, with the same amplitude as in the first case,, its maximum kinetic energy is K 2. Then, (a) K 2 = 2K1, (c) K 2 =, , K1, 4, , (b) K 2 =, , K1, 2, , (d) K 2 = K1, , CHEMISTRY, 1 The relative stability of + 1 oxidation state, of group 13 elements follows the order, (a), (b), (c), (d), , Al < Ga < Tl < In, Al < Ga < In < Tl, Tl < In < Ga < Al, Ga < Al < In < Tl, , 4 The correct match between Item I and, Item II is, Item I, Ester test, , P., , Tyr, , B., , Carbylamine test Q., , Asp, , C., , Phthalein dye, test, , R., , Ser, , S., , Lys, , 2 The hydride that is not electron deficient is, (a) AlH3, (c) SiH4, , (b) B2H6, (d) GaH3, , 3 The higher concentration of which gas in, air can cause stiffness of flower buds?, (a) SO2, (c) CO2, , (b) CO, (d) NO2, , Item II, , A., , (a), (b), (c), (d), , A → Q; B → S; C → R, A → R, B → Q; C → P, A → R; B → S; C → Q, A → Q; B → S; C → P
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JANUARY ATTEMPT ~ 11 Jan 2019, Shift II, 5 The correct match between Item I and, Item II is, Item I, , Item II, , A., , Allosteric, effect, , P., , Molecule binding to the, active site of enzyme., , B., , Competitive Q. Molecule crucial for, inhibitor, communication in the, body., , C., , Receptor, , R. Molecule binding to a site, other than the active site, of enzyme., , D., , Poison, , S., , (a), (b), (c), (d), , Molecule binding to the, enzyme covalently., , A → P; B → R; C → S; D → Q, A → P, B → R; C → Q; D → S, A → R; B → P; C → S; D → Q, A → R; B → P; C → Q; D → S, , 59, In the above sequence of reactions, A and, D, respectively, are, (a), (b), (c), (d), , KI and KMnO4, MnO2 and KIO3, KI and K2MnO4, KIO3 and MnO2, , 10 25 mL of the given HCl solution requires, 30 mL of 0.1 M sodium carbonate solution., What is the volume of this HCl solution, required to titrate 30 mL of 0.2 M aqueous, NaOH solution?, (a) 75 mL, (c) 12.5 mL, , (b) 25 mL, (d) 50 mL, , 11 The major product of the following reaction, is, HO, , (i) HCI, (ii) AlCl3 (Anhyd.), , 6 Which of the following compounds will, produce a precipitate with AgNO3 ?, Br, , HO, , Cl, , (a), , (b), , Br, (a), , (b), , N, Br, , Br, , Cl, , HO, , (d), , (c), , (d), , (c), , 12 The homopolymer formed from, 4-hydroxybutanoic acid is, , 7 The coordination number of Th in, , K 4 [Th(C2O4 )4 (OH2 )2 ] is (C2O24 − = Oxalato), , (a) 14, (c) 8, , (b) 10, (d) 6, , 8 The reaction, 2 X → B is a zeroth order, reaction. If the initial concentration of X is, 0.2 M, the half-life is 6 h. When the initial, concentration of X is 0.5 M, the time, required to reach its final concentration of, 0.2 M will be, (a) 7.2 h, (c) 12.0 h, , (b) 18.0 h, (d) 9.0 h, , 4 KOH, O 2, , 9 A → 2B + 2H2O, (Green), , 3B , → 2C + MnO2 + 2H2O, 4 HCl, , (Purple), , H 2O, KI, , 2C → 2 A + 2KOH + D, , (a) —OC(CH2)3—O—, , (b) —C(CH2)2C—, , (c) —C(CH2)3—O—, , (d) —C(CH2)2C—O—n, , n, , n, , n, , 13 Among the colloids cheese (C), milk (M), and smoke (S), the correct combination of, the dispersed phase and dispersion, medium, respectively is, (a) C : liquid in solid; M : liquid in liquid;, S : solid in gas, (b) C : solid in liquid; M : liquid in liquid;, S : gas in solid, (c) C : liquid in solid; M : liquid in solid;, S : solid in gas, (d) C : solid in liquid; M : solid in liquid;, S : solid in gas
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60, , JEE Main 2019 ~ Solved Paper, , ONLINE, , OH, , 14 In the following compound,, NH2, dN, e N, H, , OH, , a, , (c), , CH3, , (d), , CH3, , N b, , NO2 OH, N, c, , 18 The reaction,, , the favourable site/s for protonation, is/are, (a) (a) and (e), (c) (a) and (d), , (b) (b), (c) and (d), (d) (a), , 15 Given the equilibrium constant, (KC ) of the reaction :, , Cu (s) + 2Ag + (aq) → Cu 2 + (aq) + 2Ag(s), , °, of this, is 10 × 1015 , calculate the E cell, , reaction at 298 K., RT, , , at 298 K = 0059, V, 2303, ., ., , , F, (a) 0.4736 V, (c) 0.4736 mV, , (b) 0.04736 mV, (d) 0.04736 V, , 16 Which of the following compounds reacts, with ethyl magnesium bromide and also, decolourises bromine water solution, OCH3, , CN, CH2—CO2CH3, , (a), , CH, , (b), OH, , CH2, CN, , (c), , NH2 OH, , (d), , MgO(s) + C(s) → Mg(s) + CO( g), for which, ∆ r H º = + 491.1 kJ mol− 1 and, ∆ rSº = 1980, . JK − 1mol− 1, is not feasible at, 298 K. Temperature above which reaction, will be feasible is, , (a), (b), (c), (d), , 2040.5 K, 1890.0 K, 2380.5 K, 2480.3 K, , 19 Taj Mahal is being slowly disfigured and, discoloured. This is primarily due to, (a), (b), (c), (d), , water pollution, soil pollution, global warming, acid rain, , 20 The standard reaction Gibbs energy for a, chemical reaction at an absolute, temperature T is given by, ∆ rGº = A − BT, Where A and B are non-zero constants., Which of the following is true about this, reaction?, (a), (b), (c), (d), , Endothermic if, A < 0 and B > 0, Exothermic if, B < 0, Exothermic if, A > 0 and B < 0, Endothermic if, A > 0, , 21 The correct option with respect to the, Pauling electronegativity values of the, elements is, , 17 The major product obtained in the, following reaction is, , (a) P > S, (c) Te > Se, , OH, LiAlH4, (excess), , 22 The de-Broglie wavelength (λ ) associated, , CH3, , with a photoelectron varies with the, frequency (ν ) of the incident radiation as,, [ν 0 is threshold frequency], , NO2, , OH, , (a), , OH, , CH3, NO2 OH, , (b) Si < Al, (d) Ga < Ge, , (a) λ ∝, , 1, (ν − ν0, , (b), , CH3, NH2 OH, , (c) λ ∝, , 1, )4, , 1, (ν − ν0 ), , (b) λ ∝, , 1, 3, , (ν − ν0 ) 2, (d) λ ∝, , 1, 1, , (ν − ν0 ) 2
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JANUARY ATTEMPT ~ 11 Jan 2019, Shift II, 23 A compound ‘X’ on treatment with, Br2 / NaOH, provided C3 H9N, which gives, positive carbylamine test. Compound ‘X’ is, (a) CH3 COCH2NHCH3 (b) CH3 CH2CH2CONH2, (c) CH3 CON(CH3 )2, (d) CH3 CH2COCH2NH2, , 61, 26 K 2HgI4 is 40% ionised in aqueous solution., The value of its van’t Hoff factor (i) is, (a) 1.6, (c) 2.2, , (b) 1.8, (d) 2.0, , 27 The number of bridging CO ligand(s) and, Co Co bond(s) in Co2 (CO)8, respectively, are, , 24 The major product obtained in the, following conversion is, , (a) 2 and 0, (c) 4 and 0, , CH3, O, , 28 For the equilibrium,, , Br2 (1 eqv.), MeOH, , 2H2O, H3 O+ + OH− , the value of ∆Gº, at 298 K is approximately, , -, , (a) − 80 kJ mol − 1, (c) 80 kJ mol − 1, , (a) CH3, , CH3, , (b), , the corresponding items in Column II., , O OMe, , Column I, Br, , (i), , O, , O, , Br, , calcination is, ∆ Fe O + XH O, (a) Fe2O3 ⋅ XH2O →, 2 3, 2, , B. Castner-Kellner, process, , (iii) NaOH, , C. Solvay process, , (iv) Ca 3Al 2O 6, , D. Temporary hardness, , (a), (b), (c), (d), , 25 The reaction that does not define, , Column II, , Na 2CO 3 ⋅ 10H2O A. Portland cement, ingredient, , (ii) Mg(HCO 3 ) 2, , CH3, , (d), , CH3, Br, , (b) 100 kJ mol − 1, (d) − 100 kJ mol − 1, , 29 Match the following items in Column I with, , O, Br, OMe, , (c), , (b) 0 and 2, (d) 2 and 1, , (i) - (D); (ii) - (A); (iii) - (B); (iv) - (C), (i) - (B); (ii) - (C); (iii) - (A); (iv) - (D), (i) - (C); (ii) - (B); (iii) - (D); (iv) - (A), (i) - (C); (ii) - (D); (iii) - (B); (iv) - (A), , 30 The radius of the largest sphere which fits, , ∆ CaO + MgO + 2CO, (c) CaCO3 ⋅ MgCO3 →, 2, , properly at the centre of the edge of a body, centred cubic unit cell is, (Edge length is represented by ‘a’), , ∆, (d) 2Cu 2S + 3O2 →, 2Cu 2O + 2SO2, , (a) 0.134 a, (c) 0.047 a, , (b) ZnCO3, , ∆ ZnO, →, , + CO2, , (b) 0.027 a, (d) 0.067 a, , MATHEMATICS, 1 Let f (x) =, , x, , −, , d−x, , a +x, b + (d − x), where a, b and d are non-zero real, constants. Then,, , (a), (b), (c), (d), , 2, , 2, , 2, , 2, , , x ∈ R,, , f is an increasing function of x, f ′ is not a continuous function of x, f is a decreasing function of x, f is neither increasing nor decreasing, function of x, , 2 Let K be the set of all real values of x,, where the function, f (x) = sin| x| −| x| + 2(x − π ) cos| x|is not, differentiable. Then, the set K is equal to, (a) {0}, (c) { π }, , (b) φ (an empty set), (d) {0, π }, , 3 Let z be a complex number such that, | z| + z = 3 + i (where i = − 1).
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62, , JEE Main 2019 ~ Solved Paper, , ONLINE, Then,| z|is equal to, 34, 3, 41, 4, , (a), (c), , 9 The area (in sq units) in the first quadrant, bounded by the parabola, y = x2 + 1, the, tangent to it at the point, (2, 5) and the coordinate axes is, , 5, 3, 5, (d), 4, , (b), , positive integers. The maximum value of, xm yn, is, the expression, (1 + x2m ) (1 + y2n ), 1, (a), 2, 1, (c), 4, , m+ n, (d), 6mn, , 1, defined by f (x) = 1 − . Then, f is, x, injective only, both injective as well as surjective, not injective but it is surjective, neither injective nor surjective, , 6 Let (x + 10)50 + (x − 10)50, = a 0 + a1x + a 2x2 + K + a50x50, for all x ∈ R;, a, then 2 is equal to, a0, (a) 12.25, (c) 12.00, , (b) 12.50, (d) 12.75, , 7 Let A and B be two invertible matrices of, , order 3 × 3. If det( ABAT ) = 8 and, det( AB− 1 ) = 8, then det(BA− 1BT ) is equal to, 1, 4, (d) 16, , (a) 1, (c), , (b), , 1, 16, , 8 The integral ∫, , π /4, , dx, , π /6, , sin 2x(tan5 x + cot5 x), , equals, 1 π, −1 1 , − tan , , 3 3, 5 4, 1, 1 , (b), tan − 1 , , 9 3, 20, 1π, −1 1 , (c), − tan , , 9 3, 10 4, π, (d), 40, (a), , 187, 24, 37, (d), 24, (b), , 10 If 19th term of a non-zero AP is zero, then, its (49th term) : (29th term) is, , (b) 1, , 5 Let a function f : (0, ∞) → (0, ∞) be, , (a), (b), (c), (d), , 14, 3, 8, (c), 3, , (a), , 4 Let x, y be positive real numbers and m, n, , (a) 1 : 3, (c) 2 : 1, , (b) 4 : 1, (d) 3 : 1, , 11 If the point (2, α , β) lies on the plane which, passes through the points (3, 4, 2) and, (7, 0, 6) and is perpendicular to the plane, 2x − 5 y = 15, then 2α − 3β is equal to, (a) 17, (c) 5, , (b) 7, (d) 12, , 12 A circle cuts a chord of length 4a on the, X-axis and passes through a point on the, Y-axis, distant 2b from the origin. Then,, the locus of the centre of this circle, is, (a) a parabola, (c) a straight line, , (b) an ellipse, (d) a hyperbola, , 13 Let Sn = 1 + q + q2 + K + qn and, 2, , q + 1, q + 1 q + 1, Tn = 1 + , ,, +K+ , +, 2 , 2 2 , where q is a real number and q ≠ 1. If, 101, C1 + 101C 2 ⋅ S1 + K + 101C101 ⋅ S100 = αT100,, then α is equal to, (a) 2100, (c) 200, , n, , (b) 202, (d) 299, , 14 All x satisfying the inequality, , (cot− 1 x)2 − 7(cot− 1 x) + 10 > 0, lie in the, interval, , (a), (b), (c), (d), , (− ∞ , cot 5) ∪ (cot 2, ∞ ), (cot 5, cot 4), (cot 2, ∞ ), (− ∞ , cot 5) ∪ (cot 4, cot 2), , 15 The number of functions f from {1, 2, 3, …, , 20} onto {1, 2, 3, … , 20} such that f (k) is, a multiple of 3, whenever k is a multiple of, 4, is, (a) (15)! × 6!, (c) 5! × 6!, , (b) 56 × 15, (d) 65 × (15)!
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JANUARY ATTEMPT ~ 11 Jan 2019, Shift II, 16 Let the length of the latus rectum of an, ellipse with its major axis along X-axis and, centre at the origin, be 8. If the distance, between the foci of this ellipse is equal to, the length of its minor axis, then which one, of the following points lies on it?, (a) (4 2 , 2 3 ), (c) (4 2 , 2 2 ), , (b) (4 3 , 2 2 ), (d) (4 3 , 2 3 ), , 17 Let α and β be the roots of the quadratic, equation, x2 sin θ − x(sin θ cos θ + 1) + cos θ = 0, (0 < θ < 45º ) and α < β. Then,, ∞ , (− 1)n , n, α, +, , is equal to, ∑, βn , n = 0, 1, −, 1 − cosθ 1 +, 1, (c), −, 1 + cosθ 1 −, (a), , 1, 1, 1, (b), +, sin θ, 1 − cosθ 1 + sin θ, 1, 1, 1, (d), +, sin θ, 1 + cosθ 1 − sin θ, , a−b−c, 2a, 18 If, 2b, b−c−a, 2c, , 2c, , 2a, 2b, c−a −b, , = (a + b + c) (x + a + b + c)2, x ≠ 0 and, a + b + c ≠ 0, then x is equal to, (a), (b), (c), (d), , − (a + b + c), − 2(a + b + c), 2(a + b + c), abc, , 19 The solution of the differential equation,, dy, = (x − y)2, when y(1) = 1, is, dx, 2− y, = 2( y − 1), 2− x, , (a) log e, , 1+ x − y, (b) − log e, =x+ y−2, 1− x + y, (c) log e, , 2− x, =x− y, 2− y, , (d) − log e, , 1− x + y, = 2(x − 1), 1+ x − y, , 20 Contrapositive of the statement “If two, numbers are not equal, then their squares, are not equal” is, (a) If the squares of two numbers are not, equal, then the numbers are not equal., (b) If the squares of two numbers are equal,, then the numbers are equal., , 63, (c) If the squares of two numbers are not, equal, then the numbers are equal., (d) If the squares of two numbers are equal,, then the numbers are not equal., , 21 lim, , x cot(4x), , x → 0 sin 2, , x cot2 (2x), , (a) 0, (c) 4, , is equal to, (b) 1, (d) 2, , 22 A bag contains 30 white balls and 10 red, balls. 16 balls are drawn one by one, randomly from the bag with replacement., If X be the number of white balls drawn,, , , mean of X, then , is equal to, standard deviation of X , 4 3, 3, (c) 3 2, , (a), , (b) 4, (d) 4 3, , 23 If the area of the triangle whose one vertex, is at the vertex of the parabola,, y2 + 4(x − a 2 ) = 0 and the other two vertices, are the points of intersection of the, parabola and Y -axis, is 250 sq units, then, a value of ‘a’ is, (a) 5 5, (c) 5(21/3 ), , (b) 5, (d) (10)2/3, , x−3 y+ 1 z −6, and, =, =, 1, 3, −1, x+ 5 y−2 z −3, intersect at the point R., =, =, −6, 7, 4, The reflection of R in the xy-plane has, coordinates, , 24 Two lines, , (a) (2, − 4, − 7), (c) (− 2, 4, 7), , (b) (2, − 4, 7), (d) (2, 4, 7), , x+1, dx = f (x) 2x − 1 + C, where C is, 2x − 1, a constant of integration, then f (x) is equal, to, , 25 If ∫, , 2, (x + 2), 3, 2, (c) (x − 4), 3, (a), , 1, (x + 4), 3, 1, (d) (x + 1), 3, (b), , 26 If a hyperbola has length of its conjugate, axis equal to 5 and the distance between, its foci is 13, then the eccentricity of the, hyperbola is, 13, 12, 13, (c), 8, , (a), , (b) 2, (d), , 13, 6
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64, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 27 Let S = {1, 2, K , 20}. A subset B of S is said, , 29 Let 3 $i + $j, $i + 3$j and β$i + (1 − β)$j, respectively be the position vectors of the, points A, B and C with respect to the origin, O. If the distance of C from the bisector of, 3, the acute angle between OA and OB is, ,, 2, then the sum of all possible values of β is, , to be “nice”, if the sum of the elements of B, is 203. Then, the probability that a, randomly chosen subset of S is ‘‘nice’’, is, (a), (c), , 6, , (b), , 220, 7, , (d), , 220, , 4, 220, 5, 220, , (a) 1, (c) 4, , 28 If in a parallelogram ABDC, the, coordinates of A, B and C are respectively, (1, 2), (3, 4) and (2, 5), then the equation of, the diagonal AD is, (a), (b), (c), (d), , (b) 3, (d) 2, , b+ c c+ a a + b, for a ∆ABC, =, =, 11, 12, 13, with usual notation. If, cos A cos B cos C, , then the ordered, =, =, α, β, γ, triad (α , β, γ ) has a value, , 30 Given,, , 3x + 5 y − 13 = 0, 3x − 5 y + 7 = 0, 5x − 3 y + 1 = 0, 5x + 3 y − 11 = 0, , (a) (19, 7, 25), (c) (5, 12, 13), , (b) (3, 4, 5), (d) (7, 19, 25), , Answers, Physics, 1., 11., 21., , (b), (a), (c), , 2., 12., 22., , (a), (c), (d), , 3., 13., 23., , (d), (d), (d), , 4., 14., 24., , (c), (a), (c), , 5., 15., 25., , (d), (d), (d), , 6., 16., 26., , (b), (c), (d), , 7., 17., 27., , (b), (a), (b), , 8., 18., 28., , (b), (*), (c), , 9., 19., 29., , (b), (c), (d), , 10., 20., 30., , (c), (d), (b), , (c), (c), (d), , 3., 13., 23., , (a), (a), (b), , 4., 14., 24., , (d), (b), (b), , 5., 15., 25., , (d), (a), (d), , 6., 16., 26., , (a), (c), (b), , 7., 17., 27., , (b), (b), (d), , 8., 18., 28., , (b), (d), (c), , 9., 19., 29., , (b), (d), (d), , 10., 20., 30., , (b), (d), (d), , 3., 13., 23., , (b), (a), (b), , 4., 14., 24., , (c), (c), (a), , 5., 15., 25., , (d), (a), (b), , 6., 16., 26., , (a), (b), (a), , 7., 17., 27., , (c), (b), (d), , 8., 18., 28., , (c), (b), (c), , 9., 19., 29., , (d), (d), (a), , 10., 20., 30., , (d), (b), (d), , Chemistry, 1., 11., 21., , (b), (a), (d), , 2., 12., 22., , Mathematics, 1., 11., 21., , (a), (b), (b), , 2., 12., 22., , (b), (a), (d), , Note (*) None of the options is correct., , For Detailed Solutions Visit : http://tinyurl.com/y2u5qf3w Or, , Scan :
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65, , JANUARY ATTEMPT ~ 12 Jan 2019, Shift I, , ONLINE QUESTION PAPER, , JEE Main 2019, (12 January, 2019), TIME 9:30-12:30 (Shift I), , MM : 360, , PHYSICS, 1 For the given cyclic process CAB as shown, for a gas, the work done is, C, , 6.0, , A, , 5, p (Pa), , 40 A, perpendicular out of the page, 20 A, perpendicular into the page, 20 A, perpendicular out of the page, 40 A, perpendicular into the page, , 3 A person standing on an open ground, , 4, , hears the sound of a jet aeroplane, coming, from north at an angle 60° with ground, level. But he finds the aeroplane right, vertically above his position. If v is the, speed of sound, then speed of the plane is, , 3, 2, 1, , B, 1, , (a) 5 J, , (a), (b), (c), (d), , 2, , 3, , (b) 10 J, , 5 3, V (m ), , 4, , (c) 1 J, , (d) 30 J, , 2 As shown in the figure, two infinitely long,, identical wires are bent by 90° and placed, in such a way that the segments LP and, QM are along the X-axis, while segments, PS and QN are parallel to the Y -axis. If, OP = OQ = 4 cm and the magnitude of the, magnetic field at O is 10−4 T and the two, wires carry equal currents (see figure), the, magnitude of the current in each wire and, the direction of the magnetic field at O will, be (Take, µ 0 = 4π × 10−7 NA −2 ), , 3, v, 2, 2v, (c), 3, , (a), , (b) v, (d), , v, 2, , 4 The galvanometer deflection, when key K1, is closed but K 2 is open equals θ 0 (see, figure). On closing K 2 also and adjusting, R2 to 5 Ω, the deflection in galvanometer, θ, becomes 0 . The resistance of the, 5, galvanometer is given by (neglect the, internal resistance of battery) :, R2, , K2, R1=220Ω, , y, , S, , G, , L, , P, , O, , Q, M, , x, K1, , N, , (a) 22Ω, , (b) 5Ω, , (c) 25Ω, , (d) 12Ω
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66, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 5 A cylinder of radius R is surrounded by a, cylindrical shell of inner radius R and, outer radius 2R. The thermal conductivity, of the material of the inner cylinder is K1, and that of the outer cylinder is K 2., Assuming no loss of heat, the effective, thermal conductivity of the system for heat, flowing along the length of the cylinder is, K + K2, K + 3K 2, (a) 1, (b) 1, 2, 4, 2K 1 + 3K 2, (c), (d) K 1 + K 2, 5, , 6 Two light identical springs of spring, constant k are attached horizontally at the, two ends of an uniform horizontal rod AB, of length l and mass m. The rod is pivoted, at its centre ‘O’ and can rotate freely in, horizontal plane. The other ends of the two, springs are fixed to rigid supports as, shown in figure., A, y, , O, , 8 The output of the given logic circuit is, A, Y, B, , (b) A B, (d) AB + A B, , (a) AB, (c) AB + AB, , 9 The least count of the main scale of a screw, gauge is 1 mm. The minimum number of, divisions on its circular scale required to, measure 5 µm diameter of a wire is, (a) 50, (c) 500, , (b) 200, (d) 100, , 10 A point source of light, S is placed at a, distance L in front of the centre of plane, mirror of width d which is hanging, vertically on a wall. A man walks in front, of the mirror along a line parallel to the, mirror, at a distance 2L as shown below., The distance over which the man can, see the image of the light source in the, mirror is, , x, S, , d, , L, , B, , 2L, , The rod is gently pushed through a small, angle and released. The frequency of, resulting oscillation is, 1 2k, 2π m, 1 6k, (c), 2π m, (a), , 1, 2π, 1, (d), 2π, (b), , 3k, m, k, m, , 7 Two electric bulbs rated at 25 W, 220 V and, 100 W, 220 V are connected in series across, a 220 V voltage source. If the 25 W and, 100 W bulbs draw powers P1 and P2, respectively, then, (a) P1 = 16 W , P2 = 4W, (b) P1 = 4 W , P2 = 16W, (c) P1 = 9 W , P2 = 16W, (d) P1 = 16 W , P2 = 9W, , d, (a), 2, , (b) d, , (c) 3d, , (d) 2d, , 11 A passenger train of length 60 m travels at, a speed of 80 km/hr. Another freight train, of length 120 m travels at a speed of, 30 km/hr. The ratio of times taken by the, passenger train to completely cross the, freight train when : (i) they are moving in, the same direction and (ii) in the opposite, direction is, (a), , 3, 2, , (b), , 25, 11, , (c), , 11, 5, , (d), , 5, 2, , 12 An ideal gas occupies a volume of 2 m3 at a, pressure of 3 × 106 Pa. The energy of the, gas is, (a) 6 × 104 J, (c) 9 × 106 J, , (b) 108 J, (d) 3 × 102 J
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67, , JANUARY ATTEMPT ~ 12 Jan 2019, Shift I, 13 A simple pendulum is made of a string of, length l and a bob of mass m, is released, from a small angle θ 0 . It strikes a block of, mass M, kept on a horizontal surface at its, lowest point of oscillations, elastically. It, bounces back and goes up to an angle θ1., Then, M is given by, θ + θ1 , (a) m 0, , θ0 − θ1 , , (b), , m θ0 − θ1 , , , 2 θ0 + θ1 , , θ − θ1 , (c) m 0, , θ0 + θ1 , , (d), , m, 2, , 1 2, kr . If, 2, Bohr’s quantization conditions are applied,, radii of possible orbitals and energy levels, vary with quantum number n as, , in a central potential field U (r ) =, , 1, , n2, 1, (d) rn ∝ n , En ∝, n, , (c) rn ∝ n , En ∝ n, , 15 A proton and an α-particle (with their, masses in the ratio of 1 : 4 and charges in, the ratio of 1 : 2) are accelerated from rest, through a potential difference V. If a, uniform magnetic field B is set up, perpendicular to their velocities, the ratio, of the radii rp : rα of the circular paths, described by them will be, (b) 1 : 3, (d) 1 : 2, , (a) 1 : 2, (c) 1 : 3, , (b) 6 V/m, (d) 24 V/m, , 18 A straight rod of length L extends from, , θ0 + θ1 , , , θ0 − θ1 , , (b) rn ∝ n 2 , En ∝, , glass slab of refractive index 1.5. If 4% of, light gets reflected and the amplitude of, the electric field of the incident light is, 30 V/m, then the amplitude of the electric, field for the wave propogating in the glass, medium will be, (a) 30 V/m, (c) 10 V/m, , 14 A particle of mass m moves in a circular orbit, , (a) rn ∝ n , En ∝ n, , 17 A light wave is incident normally on a, , 16 In the figure shown, a circuit contains two, , x = a to x = L + a. The gravitational force it, exerts on a point mass m at x = 0, if the, mass per unit length of the rod is A + Bx2 ,, is given by, , , 1, 1, (a) Gm A , − − BL, a, +, L, a, , , , , 1, , 1, (b) Gm A , − + BL, , a + L a, 1, , 1 , (c) Gm A −, + BL, a a + L, , 1, , 1 , (d) Gm A −, − BL, a a + L, , , 19 A 100 V carrier wave is made to vary, between 160 V and 40 V by a modulating, signal. What is the modulation index?, (a) 0.4, , (b) 0.5, , (c) 0.6, , (d) 0.3, , 20 In the figure shown, after the switch ‘S ’ is, turned from position ‘A’ to position ‘B ’, the, energy dissipated in the circuit in terms of, capacitance ‘C ’ and total charge ‘Q ’ is, , identical resistors with resistance R = 5 Ω, and an inductance with L = 2 mH. An ideal, battery of 15 V is connected in the circuit., , A, , B, , S, ε, , S, , R, 15 V, , 3C, , C, , L, , (a), R, , 3 Q2, ⋅, 4 C, , (b), , 5 Q2, ., 8 C, , (c), , 1 Q2, 3 Q2, (d) ⋅, ⋅, 8 C, 8 C, , 21 An ideal battery of 4 V and resistance R, What will be the current through the, battery long after the switch is closed?, (a) 6 A, (c) 5.5 A, , (b) 3 A, (d) 7.5 A, , are connected in series in the primary, circuit of a potentiometer of length 1 m, and resistance 5 Ω. The value of R to, give a potential difference of 5 mV, across 10 cm of potentiometer wire is, (a) 395 Ω, , (b) 495 Ω, , (c) 490 Ω, , (d) 480 Ω
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68, , ONLINE, , 22 A particle A of mass ‘m’ and charge ‘q’ is, accelerated by a potential difference of, 50 V. Another particle B of mass ‘4m’ and, charge ‘q’ is accelerated by a potential, difference of 2500 V. The ratio of, λ, de-Broglie wavelengths A is close to, λB, (a) 4.47, , (b) 10.00, , (c) 0.07, , JEE Main 2019 ~ Solved Paper, , 26 Determine the electric dipole moment of, the system of three charges, placed on the, vertices of an equilateral triangle as, shown in the figure., , –2q, , y, , (d) 14.14, , l, , l, , 23 Let the moment of inertia of a hollow, cylinder of length 30 cm (inner radius, 10 cm and outer radius 20 cm) about its, axis be I. The radius of a thin cylinder of, the same mass such that its moment of, inertia about its axis is also I, is, (a) 16 cm, , (b) 14 cm, , (c) 12 cm (d) 18 cm, , 24 A travelling harmonic wave is represented, by the equation y (x, t ) = 10−3 sin (50t + 2x),, where x and y are in metre and t is in, second. Which of the following is a correct, statement about the wave?, (a) The wave is propagating along the, negative X-axis with speed 25 ms −1., (b) The wave is propagating along the, positive X-axis with speed 25 ms −1., (c) The wave is propagating along the, positive X-axis with speed 100 ms −1., (d) The wave is propagating along the, negative X-axis with speed 100 ms −1., , 25 There is uniform spherically symmetric, surface charge density at a distance R0, from the origin. The charge distribution is, initially at rest and starts expanding, because of mutual repulsion. The figure, that represents best the speed v[R(t )] of the, distribution as a function of its, instantaneous radius R(t ) is, , (a), , v [R(t)], vo, , R(t), v [R(t)], , (d), , (c), Ro, , 27 A satellite of mass M is in a circular orbit, of radius R about the centre of the earth. A, meteorite of the same mass falling towards, the earth collides with the satellite, completely inelastically. The speeds of the, satellite and the meteorite are the same, just before the collision. The subsequent, motion of the combined body will be, (a) in the same circular orbit of radius R, (b) in an elliptical orbit, (c) such that it escapes to infinity, (d) in a circular orbit of a different radius, , 28 What is the position and nature of image, formed by lens combination shown in, figure? (where, f1 and f2 are focal lengths), 2 cm, A, , R(t), , B, , O, 20 cm, f2 = –5 cm, , 20, cm from point B at right, real, 3, (b) 70 cm from point B at right, real, (c) 40 cm from point B at right, real, (a), , Ro, , R(t), , (b) 2ql $j, $i + $j, (d) (ql), 2, , f1 = + 5 cm, , (b), , Ro, , x, , l, , $j − $i, (a) 3 ql, 2, (c) − 3 ql $j, , v [R(t)], , v [R(t)], , +q, , +q, , Ro, , R(t), , (d) 70 cm from point B at left, virtual, , 29 In a meter bridge, the wire of length 1m, has a non-uniform cross-section such that, dR, of its resistance R with, the variation, dl, 1, dR, length l is, ∝ . Two equal resistance, dl, l
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69, , JANUARY ATTEMPT ~ 12 Jan 2019, Shift I, are connected as shown in the figure. The, galvanometer has zero deflection when the, jockey is at point P. What is the length AP?, , R′, , 30 The position vector of the centre of mass, rcm of an asymmetric uniform bar of, negligible area of cross-section as shown in, figure is, , R′, 2m, L, , G, , m, , m, , P, L, , A, , B, l, , (a) 0.3 m, (c) 0.2 m, , 2L, , 3L, , 13 $, 5, 11 $, 3, L x + L y$ (b) r =, L x + L y$, 8, 8, 8, 8, 3 $ 11 $, 5 $ 13 $, (c) r = L x +, L y (d) r = L x +, Ly, 8, 8, 8, 8, , (a) r =, , 1–l, , (b) 0.25 m, (d) 0.35 m, , CHEMISTRY, 1 What is the work function of the metal, if, the light of wavelength 4000 Å generates, photoelectron of velocity 6 × 105 ms−1 from it?, (Mass of electron = 9 × 10−31 kg, Velocity of light = 3 × 108 ms−1, Planck’s constant = 6626, × 10−34 Js, ., Charge of electron = 16, . × 10, (a) 4.0 eV, (c) 0.9 eV, , −19, , −1, , JeV ), , (b) 2.1 eV, (d) 3.1 eV, , 2 Given, Gas : H2 , CH4 , CO2 , SO2, Critical temperature/K, , X. X upon hydrolysis with water yields, H2O2 and O2 along with another product., The metal is, (a) Li, , (b) Mg, , (b) asparagine, (d) histidine, , 7 Among the following four aromatic, compounds, which one will have the lowest, melting point?, O, OH, OH, , (a), , (b) Mn O bond, (d) Mn Mn, , 4 The hardness of a water sample (in terms, of equivalents of CaCO3 ) containing, 10−3 M CaSO4 is, (Molar mass of CaSO4 = 136 g mol−1), (a) 100 ppm, (c) 50 ppm, , (b) 10 ppm, (d) 90 ppm, , (b), , O, CH3, , (c), , due to the presence of, (a) Mn C bond, (c) C O bond, , (d) Na, , basic amino acid is, (a) serine, (c) lysine, , (b) SO2, (d) H2, , 3 Mn 2 (CO)10 is an organometallic compound, , (c) Rb, , 6 Among the following compounds, most, , 33 190 304 630, , On the basis of data given above, predict, which of the following gases shows least, adsorption on a definite amount of, charcoal?, (a) CH4, (c) CO2, , 5 A metal on combustion in excess air forms, , O, O, , OH, , (d), , CH3, , 8 The correct order for acid strength of, compounds, CH ≡≡ CH, CH3 –– C ≡≡ CH and CH2 == CH2, is as follows :, (a) CH3 C≡≡ CH > CH2 == CH2 > HC≡≡ CH, (b) CH3 −− C ≡≡ CH > CH ≡≡ CH > CH2 == CH2, (c) HC ≡≡ CH > CH3 −− C ≡≡ CH > CH2 == CH2, (d) CH≡≡ C H > CH2 == CH2 > CH3 −− C≡≡ CH
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70, , ONLINE, , The cell reaction is, , 9 Decomposition of X exhibits a rate, , constant of 0.05 µg/year. How many years, are required for the decomposition of 5 µg, of X into 2.5 µg?, , (a) 20, , (b) 25, , (c) 40, , (d) 50, , 10 The increasing order of reactivity of the, following compounds towards reaction, with alkyl halides directly is, O, , NH2, , NH2, , NH2, , NH, O, (B), , (A ), , (C), , (D), , (a) (A) < (C) < (D) < (B) (b) (B) < (A) < (C) < (D), (c) (B) < (A) < (D) < (C) (d) (A) < (B) < (C) < (D), , 11 The element with Z = 120 (not yet, discovered) will be an/a, (a) transition metal, (b) inner-transition metal, (c) alkaline earth metal (d) alkali metal, , 12 The major product of the following reaction, is, , CN, , CHO, , CHO, , (b), O, , O, O, CH, , (c), , CHO, , NH, , (d), OH, OH, , (b) − 384.0, (d) 192.0, , 15 In the following reaction,, Aldehyde + Alcohol HCl, → Acetal, Aldehyde, Alcohol, HCHO, CH3CHO, , t, , BuOH, MeOH, , The best combination is, (a) CH3 CHO and MeOH, (b) CH3 CHO and t BuOH, (c) HCHO and MeOH, (d) HCHO and t BuOH, , 16 The molecule that has minimum/no role in, the formation of photochemical smog, is, (b) CH2 == O, (d) O3, , 17 Poly-β-hydroxybutyrate-Co-β-, , O, , (a), , −, , The standard reaction enthalpy (∆ r H O ) at, 300 K in kJ mol −1 is, [Use, R = 8 JK −1 mol−1, and F = 96,000 C mol−1 ], , (a) N2, (c) NO, , (i) DIBAL-H, (ii) H3O+, , O, , Zn (s) + Cu 2+ (aq) → Zn 2+ (aq) + Cu (s), , (a) − 412.8, (c) 206.4, , CN, , O, , JEE Main 2019 ~ Solved Paper, , OH, CHO, , OH, , 13 CH3CH2 C CH3 cannot be prepared by, , Ph, (a) CH3 CH2COCH3 + PhMgX, (b) PhCOCH3 + CH3 CH2MgX, (c) PhCOCH2CH3 + CH3 MgX, (d) HCHO + PhCH(CH3 ) CH2MgX, , 14 The standard electrode potential E O− and, −, dE O, , its temperature coefficient , for a, dT, , , cell are 2V and − 5 × 10−4 VK −1 at 300 K, respectively., , hydroxyvalerate (PHBV) is a copolymer, of ……, (a) 3-hydroxybutanoic acid and, 2-hydroxypentanoic acid, (b) 2-hydroxybutanoic acid and, 3-hydroxypentanoic acid, (c) 3-hydroxybutanoic acid and, 4-hydroxypentanoic acid, (d) 3-hydroxybutanoic acid and, 3-hydroxypentanoic acid, , 18 In the Hall-Heroult process, aluminium is, formed at the cathode. The cathode is, made out of, (a) platinum, (c) pure aluminium, , (b) carbon, (d) copper, , 19 Iodine reacts with concentrated HNO3 to, yield Y along with other products. The, oxidation state of iodine in Y , is, (a) 1, (c) 7, , (b) 3, (d) 5, , 20 For a diatomic ideal gas in a closed, system, which of the following plots does
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71, , JANUARY ATTEMPT ~ 12 Jan 2019, Shift I, not correctly describe the relation between, various thermodynamic quantities?, Cp, , (a), , Cv, , (b), , X is equal to freezing point of 12% aqueous, solution of Y . If molecular weight of X is A,, then molecular weight of Y is, (a) 4A, , (b) 2A, , T, , (a) Co2+ and Fe2+, (c) V2+ and Co2+, , - B( g) + C( g); K, D(s) - C( g) + E ( g); K, A(s), , p2, , = y atm2, , The total pressure when both the solids, dissociate simultaneously is, (a) x + y atm, (c) (x + y) atm, , 2, , (b) d 2 2 and d 2, x −y, z, (d) dxz and d 2 2, −y, , 23 Water samples with BOD values of 4 ppm, and 18 ppm, respectively, are, , are, , O, , O, , H 3C, H3 C, , (i) Cl2/CCl4, , (a), , Cl, CH3O, , (b), Cl, , CH3, , CH3 ; B=, , CH3, O, , CH3, , CH3, , CH3 ; B=, , CH3, , A=, HO, , O, OH, , C, , HC, (c) A= 3, , (d) CH3O, Cl, , H 3C, , neutralise 25 mL of sodium hydroxide, solution. The amount of NaOH in 50 mL of, the given sodium hydroxide solution is, (d) 10 g, , O, CH3, H, , H, ; B=, H3C, , CH3, , CH3, , O, , 25 50 mL of 0.5 M oxalic acid is needed to, , (c) 20 g, , O, , O, , Cl, CH3O, , [A ], , CH3, A=, HO, , Dil. NaOH, , [B], , O, , (ii) AlCl3 (anhyd.), , (b) 80 g, , H, , CH3, H3O+, ∆, , [A], , CH3O, , (c), , (b) 2 pA = 3 pB, (d) 3 pA = 2 pB, , (a) pA = 2 pB, (c) pA = 3 pB, , 24 The major product of the following reaction is, , (b), , (d) 4, , 30 In the following reactions, products A and B, , (a) clean and clean, (b) highly polluted and clean, (c) highly polluted and highly polluted, (d) clean and highly polluted, , CH3O, , (c) 1, , gas B. The compressibility factor of gas A, is thrice than that of gas B at same, temperature. The pressures of the gases, for equal number of moles are, , facing the ligands in K3 [Co(CN)6 ] are, x, , (b) 16, , 29 The volume of gas A is twice than that of, , 22 The metal d-orbitals that are directly, (a) dxz , dyz and d 2, z, (c) dxy , dxz and dyz, , 1, 4, , (a), , (b) x + y atm, (d) 2( x + y ) atm, 2, , K, , - 2C + D,, , the initial concentration of B was 1.5 times, of the concentration of A, but the equilibrium, concentrations of A and B were found to be, equal. The equilibrium constant (K) for the, aforesaid chemical reaction is, , = x atm2, , p1, , (b) Cr2+ and Mn 2+, (d) V2+ and Fe2+, , 28 In a chemical reaction, A + 2B, , V, , 21 Two solids dissociate as follows:, , (a) 40 g, , (d) A, , spin-only magnetic moment of 3.9 BM for, the complex [M (H2O)6 ]Cl2, is, , Cv, , (d), , U, T, , (a), , (c) 3A, , 27 The pair of metal ions that can given a, , p, , (c), , 26 Freezing point of a 4% aqueous solution of, , OH, , (d), , A= H3C, H 3C, , C, , O, H, , H2C, , H, , ; B=, CH3, , H 3C, , CH3
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72, , JEE Main 2019 ~ Solved Paper, , ONLINE, , MATHEMATICS, 1 Let P(4, − 4) and Q(9, 6) be two points on, the parabola, y2 = 4x and let X be any point, on the arc POQ of this parabola, where O is, the vertex of this parabola, such that the, area of ∆PXQ is maximum. Then, this, maximum area (in sq units) is, (a), , 125, 2, , (b), , 75, 2, , (c), , 625, 4, , (d), , 125, 4, , 2 Consider three boxes, each containing 10, balls labelled 1, 2, …, 10. Suppose one ball, is randomly drawn from each of the boxes., Denote by ni , the label of the ball drawn, from the ith box, (i = 1, 2, 3). Then, the, number of ways in which the balls can be, chosen such that n1 < n2 < n3 is, (a) 82, , (b) 120, , (c) 240, , (d) 164, , 3 Let y = y(x) be the solution of the, differential equation,, dy, x, + y = x log e x, (x > 1). If, dx, 2 y(2) = log e 4 − 1, then y(e) is equal to, (a) −, , e, 2, , (b) −, , e2, 2, , (c), , e, 4, , (d), , e2, 4, , 4 The sum of the distinct real values of µ, for, , 7 A ratio of the 5th term from the beginning, to the 5th term from the end in the, 10, 1, , , 1 , is, binomial expansion of 23 +, 1, , , 3, , , 2(3), 1, , 1, , (a) 1 : 2(6)3, , (b) 1 : 4(16)3, , 1, , (c) 4(36)3 : 1, , 1, , (d) 2(36)3 : 1, , 8 Let S = {1, 2, 3, ... , 100}. The number of, non-empty subsets A of S such that the, product of elements in A is even, is, (a) 250 (250 − 1), (c) 250 + 1, , (b) 250 − 1, (d) 2100 − 1, , 9 The maximum area (in sq. units) of a, rectangle having its base on the X-axis and, its other two vertices on the parabola,, y = 12 − x2 such that the rectangle lies, inside the parabola, is, (a) 36, (c) 32, , (b) 20 2, (d) 18 3, , 10 The integral ∫ cos (loge x) dx is equal to, (where C is a constant of integration), x, [cos(log e x) + sin(log e x)] + C, 2, , $ i$ + µ$j + k, $,, which the vectors, µ$i + $j + k,, $i + $j + µk, $ are coplanar, is, , (a), , (a) 2, (c) 1, , (c) x [cos(log e x) − sin(log e x)] + C, x, (d) [sin(log e x) − cos(log e x)] + C, 2, , (b) 0, (d) − 1, , 5 Let C1 and C 2 be the centres of the circles, x2 + y2 − 2x − 2 y − 2 = 0 and, x2 + y2 − 6x − 6 y + 14 = 0 respectively. If P, and Q are the points of intersection of, these circles, then the area (in sq units) of, the quadrilateral PC1QC 2 is, (a) 8, (c) 6, , (b) 4, (d) 9, , 6 If the straight line, 2x − 3 y + 17 = 0 is, perpendicular to the line passing through, the points (7, 17) and (15, β), then β equals, 35, 3, 35, (c) −, 3, , (a), , (b) − 5, (d) 5, , (b) x [cos(log e x) + sin(log e x)] + C, , 11 lim, x→, , π, 4, , cot3 x − tan x, is, π, cos x + , , 4, , (a) 4 2, (c) 8, , (b) 4, (d) 8 2, , 12 An ordered pair (α , β) for which the system, of linear equations, (1 + α )x + βy + z = 2, αx + (1 + β) y + z = 3, ax + βy + 2z = 2, has a unique solution, is, (a) (2, 4), (c) (1, − 3), , (b) (− 4, 2), (d) (−3, 1)
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73, , JANUARY ATTEMPT ~ 12 Jan 2019, Shift I, 13 If the sum of the deviations of 50, observations from 30 is 50, then the mean, of these observations is, (a) 50, (c) 51, , (b) 30, (d) 31, , 14 For x > 1, if (2x)2 y = 4e2x − 2 y , then, (1 + log e 2x)2, , dy, is equal to, dx, , x log e 2x + log e 2, x, (c) x log e 2x, (a), , x log e 2x − log e 2, x, (d) log e 2x, (b), , 15 The maximum value of, , π, 3 cos θ + 5 sin θ − , , 6, for any real value of θ is, , 79, 2, (c) 31, , (a), , (b) 34, (d) 19, , 16 The area (in sq units) of the region, , bounded by the parabola, y = x2 + 2 and the, lines, y = x + 1, x = 0 and x = 3, is, , 15, 2, 21, (c), 2, , 17, 4, 15, (d), 4, , (a), , (b), , 17 The Boolean expression, , 20 If λ be the ratio of the roots of the, quadratic equation in x,, 3m2x2 + m(m − 4)x + 2 = 0,, then the least value of m for which, 1, λ + = 1, is, λ, (a) − 2 + 2, (c) 4 − 3 2, , 21 Considering only the principal values of, inverse functions, the set, π, A = x ≥ 0 : tan −1 (2x) + tan −1 (3x) = , 4, , (a) is an empty set, (b) is a singleton, (c) contains more than two elements, (d) contains two elements, , 22 If the vertices of a hyperbola be at (−2, 0), and (2, 0) and one of its foci be at (−3, 0),, then which one of the following points does, not lie on this hyperbola?, (a) (2 6 , 5), (c) (4, 15 ), , z −α, (α ∈R) is a purely imaginary, z+α, number and|z| = 2, then a value of α is, , (a) 2, , (a) p ∧ q, (c) p ∧ (~ q), , (c) 1, , 18 If a variable line, 3x + 4 y − λ = 0 is such, that the two circles, x2 + y2 − 2x − 2 y + 1 = 0 and, x2 + y2 − 18x − 2 y + 78 = 0, are on its opposite sides, then the set of all, values of λ is the interval, (a) [13, 23], (c) [12, 21], , (b) (2, 17), (d) (23, 31), , 19 The perpendicular distance from the origin, to the plane containing the two lines,, x+ 2 y−2 z + 5, x −1 y − 4 z + 4, and, ,, =, =, =, =, 3, 5, 7, 1, 4, 7, is, (a) 11 6, (c) 11, , 11, (b), 6, (d) 6 11, , (b) (6, 5 2 ), (d) (− 6, 2 10 ), , 23 If, , (( p ∧ q) ∨ ( p ∨ ~ q)) ∧ (~ p∧ ~ q) is, equivalent to, (b) p ∨ (~ q), (d) (~ p ) ∧ (~ q), , (b) 4 − 2 3, (d) 2 − 3, , 1, 2, (d) 2, , (b), , 1 0 0, 24 Let P = 3 1 0 and Q = [qij ] be two 3 × 3, , , 9 3 1, matrices such that Q − P 5 = I3 . Then,, q21 + q31, is equal to, q32, (a) 10, (c) 9, , (b) 135, (d) 15, , 25 In a random experiment, a fair die is, rolled until two fours are obtained in, succession. The probability that the, experiment will end in the fifth throw of, the die is equal to, (a), , 175, 6, , (c), , 5, , 200, 6, , 5, , (b), (d), , 225, 65, 150, 65
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74, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 26 Let S be the set of all points in (− π , π ) at, , 28 The product of three consecutive terms of a, GP is 512. If 4 is added to each of the first, and the second of these terms, the three, terms now form an AP. Then, the sum of, the original three terms of the given GP is, , which the function, f (x) = min {sin x, cos x}, is not differentiable. Then, S is a subset of, which of the following?, π, π, (a) − , 0, , 4, 4, π, π π π, (b) − , − , , , 4 4 2, 2, 3π, (c) −, ,−, 4, 3π, (d) −, ,−, 4, , (a) 36, (c) 32, , 1 + 2 + 3 + ... + k, . If, k, 5, 2, =, S12 + S22 + ... + S10, A, then A is equal to, 12, , 29 Let Sk =, , π 3π π , ,, , , 4 4 4, π π 3π , , ,, , 2 2 4 , , (a) 156, (c) 283, , 27 A tetrahedron has vertices P(1, 2, 1),, Q(2, 1, 3), R(− 1, 1, 2) and O(0, 0, 0). The angle, between the faces OPQ and PQR is, 7, (a) cos−1 , 31, , 9, (b) cos−1 , 35 , , 19 , , 35 , , 17 , , 31, , (c) cos−1, , (b) 28, (d) 24, , (d) cos−1, , (b) 301, (d) 303, , 30 Let f and g be continuous functions on, [0, a] such that f (x) = f (a − x) and, a, g(x) + g(a − x) = 4, then ∫ f (x) g(x) dx is, 0, equal to, a, , a, , (a) 4∫ f (x) dx, , (b) ∫ f (x) dx, , (c) 2∫ f (x) dx, , (d) − 3∫ f (x) dx, , 0, a, , 0, , a, , 0, , 0, , Answers, Physics, 1., 11., 21., , (b), (c), (a), , 2., 12., 22., , (b), (c), (d), , 3., 13., 23., , (d), (a), (a), , 4., 14., 24., , (a), (c), (a), , 5., 15., 25., , (b), (a), (c), , 6., 16., 26., , (c), (a), (c), , 7., 17., 27., , (a), (d), (b), , 8., 18., 28., , (a), (c), (b), , 9., 19., 29., , (b), (c), (b), , 10., 20., 30., , (c), (d), (a), , (d), (d), (b), , 3., 13., 23., , (a), (d), (d), , 4., 14., 24., , (a), (a), (c), , 5., 15., 25., , (c), (c), (*), , 6., 16., 26., , (c), (a), (c), , 7., 17., 27., , (b), (d), (c), , 8., 18., 28., , (c), (b), (d), , 9., 19., 29., , (d), (d), (b), , 10., 20., 30., , (b), (a), (b), , 3., 13., 23., , (c), (d), (d), , 4., 14., 24., , (d), (b), (a), , 5., 15., 25., , (b), (d), (a), , 6., 16., 26., , (d), (a), (c), , 7., 17., 27., , (c), (d), (c), , 8., 18., 28., , (a), (c), (b), , 9., 19., 29., , (c), (b), (d), , 10., 20., 30., , (a), (c), (c), , Chemistry, 1., 11., 21., , (b), (c), (d), , 2., 12., 22., , Mathematics, 1., 11., 21., , (d), (c), (b), , 2., 12., 22., , (b), (a), (b), , Note (*) None of the options is correct., , For Detailed Solutions Visit : https://bit.ly/2VokMiu Or, , Scan :
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ONLINE QUESTION PAPER, , JEE Main 2019, (12 January, 2019), TIME 2:30-5:30 (Shift II), , MM : 360, , PHYSICS, 4 A simple harmonic motion is represented by, , 1 To double the covering range of a TV, transmission tower, its height should be, multiplied by, , y = 5(sin 3 πt + 3 cos 3πt ) cm. The amplitude, and time period of the motion are, , (a), , (a) 10 cm,, , (b) 4, 1, (d), 2, , 2, , (c) 2, , (c) 5 cm,, , 2 The charge on a capacitor plate in a, , 2, s, 3, 2, (d) 10 cm, s, 3, , (b) 5 cm,, , 3, s, 2, , 5 In the given circuit diagram, the currents, , circuit as a function of time is shown in, the figure., , . A and I5 = 04, . A, are, I1 = − 0.3 A, I 4 = 08, flowing as shown. The currents I 2, I3 and I 6, respectively, are, , 6, 5, q(µC), , 3, s, 2, , I6 Q, , P, , 4, , I3, , 3, 2, 0, , 2, , 4, t(s), , 6, , 8, , What is the value of current at t = 4 s?, (a) 2 µA, (c) Zero, , (b) 15, . µA, (d) 3 µA, , 3 Two satellites A and B have masses m, and 2m respectively. A is in a circular, orbit of radius R and B is in a circular, orbit of radius 2R around the earth. The, ratio of their kinetic energies, TA / TB is, (a), (c), , 1, 2, , (b) 2, 1, 2, , (d) 1, , I5, , I2, S I, 4, , I1, , R, , (a) 1.1 A, 0.4 A, 0.4 A (b) 1.1 A, − 0.4 A, 0.4 A, (c) 0.4 A, 1.1 A, 0.4 A (d) − 0.4 A, 0.4 A, 1.1 A, , 6 A load of mass M kg is suspended from a steel, wire of length 2 m and radius 1.0 mm in, Searle’s apparatus experiment. The increase, in length produced in the wire is 4.0 mm. Now,, the load is fully immersed in a liquid of, relative density 2. The relative density of the, material of load is 8. The new value of increase, in length of the steel wire is, (a) zero, (c) 4.0 mm, , (b) 5.0 mm, (d) 3.0 mm
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76, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 7 The moment of inertia of a solid sphere,, about an axis parallel to its diameter and, at a distance of x from it, is ‘I (x)’. Which, one of the graphs represents the variation, of I (x) with x correctly?, I(x), , I(x), , (a), , (b), O, , x, , I(x), , (c), , O, I(x), , x, , x, , O, , x, , has 25 divisions in it. When a current of, 4 × 10− 4 A passes through it, its needle, (pointer) deflects by one division. To use, this galvanometer as a voltmeter of range, 2.5 V, it should be connected to a, resistance of, (a) 250 Ω, (c) 200 Ω, , (b) 6200 Ω, (d) 6250 Ω, , 12 Formation of real image using a biconvex, , (d), O, , 11 A galvanometer whose resistance is 50 Ω,, , lens is shown below. If the whole set up is, immersed in water without disturbing the, object and the screen positions, what will, one observe on the screen?, , 8 An ideal gas is enclosed in a cylinder at, pressure of 2 atm and temperature, 300 K., The mean time between two successive, collisions is 6 × 10− 8 s. If the pressure is, doubled and temperature is increased to, 500 K, the mean time between two, successive collisions will be close to, (a) 4 × 10− 8 s, (c) 2 × 10− 7 s, , (b) 3 × 10− 6 s, (d) 0.5 × 10− 8 s, , 9 A vertical closed cylinder is separated into, two parts by a frictionless piston of mass m, and of negligible thickness. The piston is, free to move along the length of the, cylinder. The length of the cylinder above, the piston is l1 and that below the piston is, l2, such that l1 > l2. Each part of the, cylinder contains n moles of an ideal gas at, equal temperature T. If the piston is, stationary, its mass m, will be given by, (where, R is universal gas constant and g, is the acceleration due to gravity), (a), , nRT l1 − l2 , , , g l1 l2 , , (b), , nRT 1, 1, + , g l2 l1 , , (c), , RT 2l1 + l2 , , , g l1 l2 , , (d), , RT l1 − 3l2 , , , ng l1 l2 , , Screen, 2f, f, , 2f, , f, , (a) No change, (b) Magnified image, (c) Image disappears (d) Erect real image, , 13 Let l, r , c, and v represent inductance,, resistance, capacitance and voltage,, l, in SI, respectively. The dimension of, rcv, units will be, (a) [LT 2 ], (c) [A− 1 ], , (b) [LTA], (d) [LA− 2 ], , 14 A particle of mass 20 g is released with an, initial velocity 5 m/s along the curve from, the point A, as shown in the figure. The, point A is at height h from point B. The, particle slides along the frictionless, surface. When the particle reaches point B,, its angular momentum about O will be, (Take, g = 10 m / s2), O, a = 10 m, , 10 A parallel plate capacitor with plates of, area 1 m2 each, are at a separation of 0.1 m., If the electric field between the plates is, 100 N/C, the magnitude of charge on each, , C2 , plate is Take, ε 0 = 885, . × 10− 12, , N − m2 , , − 10, , (a) 9.85 × 10, C, (c) 7.85 × 10− 10 C, , − 10, , (b) 8.85 × 10, C, (d) 6.85 × 10− 10 C, , A, h = 10 m, B, 2, , (a) 8 kg - m / s, (c) 2 kg - m2 / s, , (b) 3 kg - m2 / s, (d) 6 kg - m2 / s
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JANUARY ATTEMPT ~ 12 Jan 2019, Shift II, 15 In a Frank-Hertz experiment, an electron, of energy 5.6 eV passes through mercury, vapour and emerges with an energy 0.7 eV., The minimum wavelength of photons, emitted by mercury atoms is close to, (a) 250 nm, (c) 1700 nm, , (b) 2020 nm, (d) 220 nm, , 16 A block kept on a rough inclined plane, as, shown in the figure, remains at rest upto a, maximum force 2 N down the inclined, plane. The maximum external force up the, inclined plane that does not move the, block is 10 N. The coefficient of static, friction between the block and the plane is, (Take, g = 10 m / s2), 10, , 77, 20 A 10 m long horizontal wire extends from, North-East to South-West. It is falling, with a speed of 50, . ms− 1 at right angles to, the horizontal component of the earth’s, magnetic field of 03, . × 10− 4 Wb / m2. The, value of the induced emf in wire is, (a) 15, . × 10− 3 V, (c) 0.3 × 10− 3 V, , 21 Two particles A and B are moving on two, concentric circles of radii R1 and R2 with, equal angular speed ω. At t = 0, their, positions and direction of motion are, shown in the figure, Y, , N, , A, , R2, , 2N, 30°, , (a), , 2, 3, , (c), , 3, 4, , 3, 2, 1, (d), 2, 2, , surface of the sun is about 10 W / m . The, rms value of the corresponding magnetic, field is closest to, (b) 102 T, (d) 10− 2 T, , 18 An α-particle of mass m suffers, one-dimensional elastic collision with a, nucleus at rest of unknown mass. It is, scattered directly backwards losing 64% of, its initial kinetic energy. The mass of the, nucleus is, (b) 4 m, (d) 2 m, , (b) − ω(R1 + R2 )$i, (c) ω(R − R )i$, 1, , nucleus is 232, 90 Th. At the end, there are 6, α-particles and 4 β-particles which are, emitted. If the end nucleus is AZ X, A and Z, are given by, (b) A = 208; Z = 82, (d) A = 208; Z = 80, , 2, , (d) ω(R2 − R1 )i$, , 22 A soap bubble, blown by a mechanical, pump at the mouth of a tube, increases in, volume, with time, at a constant rate. The, graph that correctly depicts the time, dependence of pressure inside the bubble, is given by, p, , p, , (a), , (b), , 19 In a radioactive decay chain, the initial, , (a) A = 202; Z = 80, (c) A = 200; Z = 81, , B, , (a) ω(R1 + R2 )$i, 8, , (a) 1.5 m, (c) 3.5 m, , X, , R1, , π, The relative velocity vA − vB at t =, is, 2ω, given by, , (b), , 17 The mean intensity of radiation on the, , (a) 1 T, (c) 10− 4 T, , (b) 11, . × 10− 3 V, (d) 2.5 × 10− 3 V, , 1, t3, , 1, t, , p, (c), , (d), , t, , p, , log (t)
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78, , ONLINE, , 23, , I2, , 27 In the circuit shown, find C if the effective, , R2, , C, L, , JEE Main 2019 ~ Solved Paper, , capacitance of the whole circuit is to be, 05, . µF. All values in the circuit are in µF., , R1 I1, , C, , 2, , A, , 3, In the above circuit, C =, µF, R2 = 20 Ω,, 2, 3, H and R1 = 10 Ω. Current in L - R1, L=, 10, path is I1 and in C - R2 path is I 2.The, voltage of AC source is given by, V = 200 2 sin(100t ) volts. The phase, difference between I1 and I 2 is, (a) 30º, (c) 0º, , 2, , a liquid. When the vessel is rotated about, its own vertical axis, the liquid rises up, near the wall. If the radius of vessel is, 5 cm and its rotational speed is 2 rotations, per second, then the difference in the, heights between the centre and the sides, (in cm) will be, (b) 1.2, (d) 2.0, , m3 . Its magnetic susceptibility at, temperature 350 K is 28, . × 10− 4. Its, susceptibility at 300 K is, (b) 3.672 × 10, (d) 3.267 × 10− 4, , vary from 0 to 5.0 V, VCC = 5 V, βDC = 200,, . V., RB = 100 k Ω, RC = 1 k Ω and VBE = 10, The minimum base current and the input, voltage at which the transistor will go to, saturation, will be, respectively, , 4, ν, 3, 3ν, (c), 2, , (a), , IC, , RC, , VBB, , v0, IE, , (b) 2 ν, (d), , 5ν, 3, , VCC, , refractive index µ 2, radius of curvature R), fits exactly into a plano-concave lens (focal, length f1, refractive index µ1, radius of, curvature R). Their plane surfaces are, parallel to each other. Then, the focal, length of the combination will be, , (a) f1 − f2, (a) 25 µA and 2.8 V, (c) 20 µA and 3.5 V, , (b) 341 ms− 1, (d) 335 ms− 1, , 30 A plano-convex lens (focal length f2,, , C, E, , vi, , 7, µF, 11, , illuminated with monochromatic light of, frequency v, the stopping potential for the, photocurrent is − V0 / 2. When the surface, is illuminated by monochromatic light of, frequency ν / 2, the stopping potential is, − V0. The threshold frequency for, photoelectric emission is, , −4, , B, , (d), , 29 When a certain photosensitive surface is, , 26 In the figure, given that VBB supply can, , RB, , (b) 4 µF, , end. It is still used in the laboratory to, determine velocity of sound in air. A, tuning fork of frequency 512 Hz produces, first resonance when the tube is filled with, water to a mark 11 cm below a reference, mark. near the open end of the tube. The, experiment is repeated with another fork, of frequency 256 Hz which produces first, resonance when water reaches a mark, 27 cm below the reference mark. The, velocity of sound in air, obtained in the, experiment is close to, (a) 328 ms− 1, (c) 322 ms− 1, , 25 A paramagnetic material has 1028 atoms/, , (a) 3.726 × 10, (c) 2.672 × 10− 4, , 2, , 28 A resonance tube is old and has jagged, , 24 A long cylindrical vessel is half-filled with, , −4, , 2, , B, , 6, (a) µF, 5, 7, (c), µF, 10, , (b) 60º, (d) 90º, , (a) 0.1, (c) 0.4, , 1, , 2, , 2, , (b) 25 µA and 3.5 V, (d) 20 µA and 2.8 V, , (c) f1 + f2, , R, µ 2 − µ1, 2f1 f2, (d), f1 + f2, , (b)
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80, , ONLINE, , 11 The correct structure of histidine in a, , (c) CH3O, , strongly acidic solution (pH = 2) is, ρ, , (a) H3N, , ρ, , σ, COO, ρ, NH2, , CH, , (b) H3N, , ρ, , CH, , (d) H3N, , CH, , COOH, , NH, NH, , Nρ, H, , 12 The compound that is not a common, component of photochemical smog is, (a) CF2Cl 2, , (b) H3 C C OONO2, , O, , (c) CH2 == CHCHO, , (d) O3, , 13 The pair that does not require calcination, is, (a), (b), (c), (d), , ZnO and MgO, ZnO and Fe2O3 ⋅ xH2O, ZnCO3 and CaO, Fe2O3 and CaCO3 ⋅ MgCO3, , 14 The element that does not show catenation, is, (a) Ge, (c) Si, , (b) Sn, (d) Pb, , 15 8 g of NaOH is dissolved in 18 g of H2O., Mole fraction of NaOH in solution and, molality (in mol kg − 1) of the solution, respectively are, (a) 0.2, 11.11, (c) 0.2, 22.20, , (b) 0.167, 22.20, (d) 0.167, 11.11, , CH2, , CH3, , is, (a) Tyndall effect can be used to distinguish, between a colloidal solution and a true, solution, (b) It is possible to cause artificial rain by, throwing electrified sand carrying, charge opposite to the one on clouds from, an aeroplane, (c) Lyophilic sol can be coagulated by, adding an electrolyte, (d) Latex is a colloidal solution of rubber, particles which are positively charged, , 18 The correct statement(s) among I to III, with respect to potassium ions that are, abundant within the cell fluids is/are, I. They activate many enzymes., II. They participate in the oxidation of, glucose to produce ATP., III. Along with sodium ions, they are, responsible for the transmission of, nerve signals., (a) I, and III only, (c) I and II only, , (b) I, II and III, (d) III only, , (a) 600 - 750 nm, (c) 0.8 - 15, . nm, , (b) 400 - 550 nm, (d) 200 - 315 nm, , 20 The correct order of atomic radii is, CH, , CH, , HBr (excess), CH3, Heat, , CH, , CH2, , CH3, , Br, , (b) HO, , CH, , ozone layer protects us from the sun’s, radiation that falls in the wavelength, region of, , conversion is, , (a) CH3O, , (d) HO, , 19 The upper stratosphere consisting of the, , 16 The major product in the following, CH3O, , CH3, , Br, , +, , NH, , CH, , 17 Among the following, the false statement, , ρ, , σ, COO, , CH2, , Br, , N, , N, , (c) H3N, , COOH, ρ, NH2, , CH, , JEE Main 2019 ~ Solved Paper, , CH2, , CH, Br, , CH3, , ?, , (a) Ho > N > Eu > Ce (b) N > Ce > Eu > Ho, (c) Eu > Ce > Ho > N (d) Ce > Eu > Ho > N, , 21 Molecules of benzoic acid (C6H5COOH), dimerise in benzene. ‘w’ g of the acid, dissolved in 30 g of benzene shows a, depression in freezing point equal to 2 K., If the percentage association of the acid to, form dimer in the solution is 80, then w is
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JANUARY ATTEMPT ~ 12 Jan 2019, Shift II, (Given that K f = 5 K kg mol− 1, molar mass, −1, , of benzoic acid = 122 g mol ), (a) 1.8 g, (c) 2.4 g, , 81, (a) (C ), (D ), (c) (B ), (C ), (D ), , (b) (B ), (D ), (d) (B ), (C ), , 25 The major product of the following reaction, , (b) 1.0 g, (d) 1.5 g, , is, , CH2CH3, , 22 For a reaction, consider the plot of ln k, versus 1 / T given in the figure. If the rate, constant of this reaction at 400 K is, 10− 5 s− 1, then the rate constant at 500 K is, , H3C, , Cl, , C, , NaOEt, ∆, , COOCH2CH3, Slope = –4606, , (a) CH3 CH2C == CH2, , CO2CH2CH3, , ln k, , (b), , 1/ T, , (a) 4 × 10− 4 s− 1, (c) 10− 4 s− 1, , (b) 10− 6 s− 1, (d) 2 × 10− 4 s− 1, , CO2CH2CH3, , CH3 C == CHCH3, CH2CH3, , 23 The increasing order of the reactivity of, the following with LiAlH4 is, , (c) H3C, , O, , COOCH2CH3, , (A), C2H5, , OCH2CH3, , C, , OCH2CH3, , NH2, O, , (d) H3C H2C, , C, , CO2CH2CH3, , (B), C2H5, , CH3, , OCH3, , 26 The major product of the following reaction, , O, , is, , (C), C2H5, O, , O, , H 3C, , Cl, , NH2, , O, , O, , (D), C2H5, , (a), (b), (c), (d), , O, , C2H5, , O, , (A ) < (B ) < (D ) < (C ), (A ) < (B ) < (C ) < (D ), (B ) < (A ) < (D ) < (C ), (B ) < (A ) < (C ) < (D ), , (a) CH3, , O, O, O, , (b) HO, , 24 The aldehydes which will not form, Grignard product with one equivalent, Grignard reagents are, CHO, , CHO, (B), , (A), , (c), , HO, O, , HO2C, CHO, , CHO, (C), HO3CO, , (D), HOH2C, , (d), , O, , CH3, O, , O, , (i) NaNO2/H+, (ii) CrO3/H+, (iii) H2SO4 (conc.), ∆
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82, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 27 The combination of plots which does not, represent isothermal expansion of an ideal, gas is, , (a) 1.0, (c) 0.40, , (b) 0.75, (d) 1.50, , 29 The major product of the following reaction, is, O, , p, , p, , NaBH4, EtOH, , O, , 1/Vm, (A ), , O, , Vm, (B), , O, , OH, , (a), pVm, , (b), OH, , OH, , U, , (c), O, , p, (C), , (a) (A ) and (C ), (c) (B ) and (D ), , O, , Vm, (D), , (b) (B ) and (C ), (d) (A ) and (D ), , 28 If the de-Broglie wavelength of the, electron in n th Bohr orbit in a hydrogenic, atom is equal to 15, . πa 0 (a 0 is Bohr radius),, then the value of n /Z is, , (d), OEt, , 30 Λ°m for NaCl, HCl and NaA are 126.4,, , 425.9 and 1005, . S cm2 mol− 1, respectively., If the conductivity of 0.001 M HA is, 5 × 10− 5 S cm− 1, degree of dissociation of, HA is, (a) 0.25, (c) 0.75, , (b) 0.50, (d) 0.125, , MATHEMATICS, 1 lim, , x→1−, , π − 2 sin − 1 x, is equal to, 1−x, , (a), , π, 2, , (b), , (c), , π, , (d), , 2, π, 1, 2π, , 2 Let S be the set of all real values of λ such, that a plane passing through the points, (− λ2 , 1, 1), (1, − λ2 , 1) and (1, 1, − λ2 ) also, passes through the point (− 1, − 1, 1). Then,, S is equal to, (a) { 3 , −, (c) {1, − 1}, , 3}, , (b) {3, − 3}, (d) { 3 }, , 3 If a circle of radius R passes through the, , 4 If an angle between the line,, , x+ 1 y−2 z −3, and the plane,, =, =, 2, 1, −2, 2 2, x − 2 y − kz = 3 is cos− 1 , , then a value, 3 , of k is, , 5, 3, 3, (c) −, 5, (a), , 3, 5, 5, (d) −, 3, , (b), , 5 The expression ~ (~ p → q) is logically, equivalent to, (a) p ∧ ~ q, (c) ~ p ∧ q, , (b) p ∧ q, (d) ~ p ∧ ~ q, , 6 The set of all values of λ for which the, , origin O and intersects the coordinate axes, at A and B, then the locus of the foot of, perpendicular from O on AB is, , system of linear equations x − 2 y − 2z = λx,, x + 2 y + z = λy and − x − y = λz, has a non-trivial solution, , (a) (x2 + y2 )2 = 4R 2x2 y2, (b) (x2 + y2 )3 = 4R 2x2 y2, (c) (x2 + y2 )(x + y) = R 2xy, (d) (x2 + y2 )2 = 4Rx2 y2, , (a), (b), (c), (d), , contains exactly two elements., contains more than two elements., is a singleton., is an empty set.
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JANUARY ATTEMPT ~ 12 Jan 2019, Shift II, 7 Let Z be the set of integers. If, , 13 If the function f given by, , 2, , A = { x ∈ Z : 2( x + 2) ( x − 5 x + 6) = 1} and, B = { x ∈ Z : − 3 < 2x − 1 < 9}, then the, number of subsets of the set A × B, is, (a) 212, (c) 215, , 83, , f (x) = x3 − 3(a − 2) x2 + 3ax + 7,, for some a ∈ R is increasing in (0, 1] and, decreasing in [1, 5), then a root of the, f (x) − 14, equation,, = 0 (x ≠ 1) is, (x − 1)2, , (b) 218, (d) 210, , 8 In a class of 60 students, 40 opted for, , (a) − 7, (c) 7, , (b) 6, (d) 5, , NCC, 30 opted for NSS and 20 opted for, both NCC and NSS. If one of these, students is selected at random, then the, probability that the student selected has, opted neither for NCC nor for NSS is, , 14 If n C 4, n C5 and n C 6 are in AP, then n can, , 1, (a), 6, 2, (c), 3, , 15 Let f be a differentiable function such that, , 1, (b), 3, 5, (d), 6, , 9 If a curve passes through the point (1, − 2), and has slope of the tangent at any point, x2 − 2 y, , then the curve also, (x, y) on it as, x, passes through the point, (b) (− 1, 2), (d) (3, 0), , (a) ( 3 , 0), (c) (− 2 , 1), , , , 10 lim , , n, , + 12, is equal to, n → ∞ n2, , (a) tan − 1 (3), (c) π / 4, , +, , n, n 2 + 22, , +, , n, n 2 + 32, , + ... +, , 1, , 5n , , (b) tan − 1 (2), (d) π /2, , 11 In a game, a man wins ` 100 if he gets 5 or, 6 on a throw of a fair die and loses ` 50 for, getting any other number on the die. If he, decides to throw the die either till he gets, a five or a six or to a maximum of three, throws, then his expected gain/loss (in, rupees) is, (a), , 400, loss, 3, , (c) 0, , 400, loss, 9, 400, gain, (d), 3, , (b), , 12 If sin 4 α + 4 cos4 β + 2 = 4 2 sin α cos β;, α, β ∈[0, π ], then cos(α + β) − cos(α − β) is, equal to, (a) − 1, (c) − 2, , (b) 2, (d) 0, , be, (a) 9, (c) 14, , (b) 11, (d) 12, , f (1) = 2 and f ′ (x) = f (x) for all x ∈ R. If, h (x) = f ( f (x)), then h′ (1) is equal to, (a) 4e2, (c) 2e, , (b) 4e, (d) 2e2, , 16 The mean and the variance of five, observations are 4 and 5.20, respectively., If three of the observations are 3, 4 and 4,, then the absolute value of the difference of, the other two observations, is, (a) 1, (c) 5, , (b) 7, (d) 3, , 17 The number of integral values of m for, which the quadratic expression,, (1 + 2m) x2 − 2(1 + 3m)x + 4(1 + m), x ∈ R, is, always positive, is, (a) 6, (c) 7, , (b) 8, (d) 3, , 18 The total number of irrational terms in the, binomial expansion of (71/ 5 − 31/ 10 )60 is, , (a) 49, (c) 54, , (b) 48, (d) 55, , , , 1, , 19 If A = − sin θ, , sin θ, 1, , 1 , sin θ ; then for all, , 1 , − sin θ, , , − 1, π, 3, 5π, θ ∈ , , , det( A) lies in the interval, 4 4, 3, (a) , 3, 2 , 3, (c) 0, , 2 , , 5, (b) , 4, 2 , 5, (d) 1, , 2
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84, , JEE Main 2019 ~ Solved Paper, , ONLINE, , 20 Let a, b and c be three unit vectors, out of, , which vectors b and c are non-parallel. If α, and β are the angles which vector a makes, with vectors b and c respectively and, 1, a × (b × c) = b, then|α − β|is equal to, 2, , (a) 30º, (c) 90º, , (b) 45º, (d) 60º, , 21 If the sum of the first 15 terms of the, series, 3, , 3, , 3, , 3, , 3 + 1 1 + 2 1 + 33 + 3 3 + ..., , , , , 4, 4, 2, 4, is equal to 225 k, then k is equal to, (a) 108, (c) 54, , (b) 27, (d) 9, , x, , 22 The integral ∫ , 1 e, , e, , 2x, , , , equal to, , e, − , x, , x, , , log e x dx is, , , 3, 1, (a), −e− 2, 2, 2e, 1 1, 1, (b) − + − 2, 2 e 2e, 1, 1, (c), −e− 2, 2, e, 3 1, 1, (d), − −, 2 e 2e2, , 23 The integral ∫, , (b), (c), (d), , (a) 1, (c) 2, , (b) 2, (d) 0, , 26 The equation of a tangent to the parabola,, x2 = 8 y, which makes an angle θ with the, positive direction of X-axis, is, , (a), (b), (c), (d), , y = x tan θ − 2 cot θ, x = y cot θ + 2 tan θ, y = x tan θ + 2 cot θ, x = y cot θ − 2 tan θ, , 27 If the angle of elevation of a cloud from a, point P which is 25 m above a lake be 30º, and the angle of depression of reflection of, the cloud in the lake from P be 60º, then, the height of the cloud (in meters) from the, surface of the lake is, (b) 60, (d) 42, , 28 Let S and S′ be the foci of an ellipse and B, be any one of the extremities of its minor, axis. If ∆S′ BS is a right angled triangle, with right angle at B and area, (∆S′ BS ) = 8 sq units, then the length of a, latus rectum of the ellipse is, , 3x13 + 2x11, 4, , x4, 6(2x + 3x + 1), x12, 4, , satisfying| z1 | = 9 and| z2 − 3 − 4i | = 4., Then, the minimum value of| z1 − z2 |is, , (a) 50, (c) 45, , dx is equal, , (2x + 3x + 1), to (where C is a constant of integration), , (a), , 25 Let z1 and z2 be two complex numbers, , 2, , 3, , 6(2x4 + 3x2 + 1)3, x4, (2x + 3x2 + 1)3, 4, , x12, (2x4 + 3x2 + 1)3, , 2, , 4, , +C, +C, , +C, +C, , 24 The tangent to the curve y = x2 − 5x + 5,, , (a) 2 2, (c) 2, , (b) 4 2, (d) 4, , 29 There are m men and two women, participating in a chess tournament. Each, participant plays two games with every, other participant. If the number of games, played by the men between themselves, exceeds the number of games played, between the men and the women by 84,, then the value of m is, (a) 12, (c) 9, , (b) 11, (d) 7, , 30 If a straight line passing through the point, , parallel to the line 2 y = 4x + 1, also passes, through the point, , P(− 3, 4) is such that its intercepted portion, between the coordinate axes is bisected at, P, then its equation is, , 1 7, (a) , , 4 2, 1, (c) − , 7, 8 , , (a), (b), (c), (d), , 7 1, (b) , , 2 4, 1, (d) , − 7, 8, , , x− y+ 7= 0, 4x − 3 y + 24 = 0, 3x − 4 y + 25 = 0, 4x + 3 y = 0
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JANUARY ATTEMPT ~ 12 Jan 2019, Shift II, , 85, , Answers, Physics, 1., 11., 21., , (b), (c), (d), , 2., 12., 22., , (c), (c), (b), , 3., 13., 23., , (d), (c), (a), , 4., 14., 24., , (d), (d), (d), , 5., 15., 25., , (a), (a), (d), , 6., 16., 26., , (d), (b), (b), , 7., 17., 27., , (b), (c), (d), , 8., 18., 28., , (a), (b), (a), , 9., 19., 29., , (a), (b), (c), , 10., 20., 30., , (b), (a), (b), , (c), (a), (c), , 3., 13., 23., , (d), (a), (a), , 4., 14., 24., , (d), (d), (b), , 5., 15., 25., , (c), (d), (b), , 6., 16., 26., , (d), (d), (c), , 7., 17., 27., , (b), (d), (c), , 8., 18., 28., , (c), (b), (b), , 9., 19., 29., , (b), (d), (a), , 10., 20., 30., , (d), (c), (d), , 3., 13., 23., , (b), (c), (b), , 4., 14., 24., , (a), (c), (d), , 5., 15., 25., , (d), (b), (d), , 6., 16., 26., , (c), (b), (b), , 7., 17., 27., , (c), (c), (a), , 8., 18., 28., , (a), (c), (d), , 9., 19., 29., , (a), (a), (a), , 10., 20., 30., , (b), (a), (b), , Chemistry, 1., 11., 21., , (c), (d), (c), , 2., 12., 22., , Mathematics, 1., 11., 21., , (b), (c), (b), , 2., 12., 22., , (a), (c), (a), , For Detailed Solutions Visit : https://bit.ly/2YhJ2Qq Or, , Scan :
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JEE MAIN, , SOLVED PAPER 2018, PHYSICS, 1. The density of a material in the shape of a, cube is determined by measuring three sides, of the cube and its mass. If the relative errors, in measuring the mass and length are, respectively 1.5% and 1% , the maximum, error in determining the density is, (a) 2.5%, (c) 4.5%, , (b) 3.5%, (d) 6%, , represent the same motion. One of them does, it incorrectly. Pick it up., Distance, , (a), , Position, , Time, , (b), , Position, Time, , (a) −, , k, 4a2, , (b), , k, 2 a2, , (d) −, , (c) zero, , 3 k, 2 a2, , initial speed v0 strikes a stationary particle of, the same mass. If the final total kinetic, energy is 50% greater than the original, kinetic energy, the magnitude of the relative, velocity between the two particles after, collision, is, v0, 4, v, (c) 0, 2, , (a), Velocity, , (c), , radius a under the action of an attractive, k, potential U = − 2 . Its total energy is, 2r, , 5. In a collinear collision, a particle with an, , 2. All the graphs below are intended to, , Velocity, , 4. A particle is moving in a circular path of, , (b) 2 v 0, (d), , v0, 2, , Time, , (d), , 6. Seven identical circular planar discs, each of, 3. Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a, frictionless pulley, are moving as shown in, the figure. The coefficient of friction of, horizontal surface is 0.15. The minimum, weight m that should be put on top of m2 to, stop the motion is, m, m2, , mass M and radius R are welded, symmetrically as shown in the figure. The, moment of inertia of the arrangement about, the axis normal to the plane and passing, through the point P is, P, O, , T, , T, m1, m 1g, , (a) 18.3 kg, , (b) 27.3 kg (c) 43.3 kg (d) 10.3 kg, , 19, MR 2, 2, 73, (c) MR 2, 2, (a), , 55, MR 2, 2, 181, (d), MR 2, 2, , (b)
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2, , JEE MAIN Solved Paper 2018, , 7. From a uniform circular disc of radius R and, R, mass 9 M, a small disc of radius is removed, 3, as shown in the figure. The moment of, inertia of the remaining disc about an axis, perpendicular to the plane of the disc and, passing through centre of disc is, , 11. The mass of a hydrogen molecule is, , 3.32 × 10 −27 kg. If 10 23 hydrogen molecules, strike per second, a fixed wall of area 2 cm 2, at an angle of 45° to the normal and rebound, elastically with a speed of 10 3 m/s, then the, pressure on the wall is nearly, (a) 2.35 × 103 N/m 2, , (b) 470, . × 103 N/m 2, , (c) 2.35 × 10 N/m, , (d) 470, . × 102 N/m 2, , 2, , 12. A silver atom in a solid oscillates in simple, , 2R, 3, , harmonic motion in some direction with a, frequency of 10 12 per second. What is the, force constant of the bonds connecting one, atom with the other? (Take, molecular, weight of silver = 108 and Avogadro number, = 6 .02 × 10 23 g mol −1 ), , R, , 40, MR 2, 9, 37, (d), MR 2, 9, , (a) 4MR 2, , (b), , (c) 10MR 2, , (a) 6.4 N/m, (c) 2.2 N/m, , a circular orbit of radius R in a central force, inversely proportional to the nth power of R., If the period of rotation of the particle is T,, then :, n, , +1, , (a) T ∝ R 3 / 2 for any n, , (b) T ∝ R 2, , (c) T ∝ R( n + 1)/ 2, , (d) T ∝ R n / 2, , Ka, 3mg, , (c), , mg, 3Ka, , (d), , mg, Ka, , 10. Two moles of an ideal monoatomic gas, occupies a volume V at 27°C. The gas expands, adiabatically to a volume 2 V. Calculate (i), the final temperature of the gas and (ii), change in its internal energy., (a) (i) 189 K (ii) 2.7 kJ, (c) (i) 189 K (ii) −2.7 kJ, , 9 .27 × 10 10 Pa. What will be the fundamental, frequency of the longitudinal vibrations?, (b) 2.5 kHz (c) 10 kHz, , (d) 7.5 kHz, , 14. Three concentric metal shells A , B and C of, , material of bulk modulus K is surrounded by, a liquid in a cylindrical container. A massless, piston of area a floats on the surface of the, liquid, covering entire cross-section of, cylindrical container. When a mass m is, placed on the surface of the piston to, compress the liquid, the fractional decrement, dr , in the radius of the sphere, is, r, (b), , its middle point and is set into longitudinal, vibrations. The density of granite is, 2.7 × 10 3 kg/m 3 and its Young’s modulus is, , (a) 5 kHz, , 9. A solid sphere of radius r made of a soft, , Ka, mg, , (b) 7.1 N/m, (d) 5.5 N/m, , 13. A granite rod of 60 cm length is clamped at, , 8. A particle is moving with a uniform speed in, , (a), , 2, , (b) (i) 195 K (ii) −2.7 kJ, (d) (i) 195 K (ii) 2.7 kJ, , respective radii a , b and c (a < b < c) have, surface charge densities + σ , − σ and +σ,, respectively. The potential of shell B is, σ a2, , ε0 , σ b2, (c) , ε0 , (a), , , − b2, + c, a, , , − c2, + a, b, , , σ a2, , ε0 , σ b2, (d) , ε0 , (b), , , − b2, + c, b, , , − c2, + a, c, , , 15. A parallel plate capacitor of capacitance 90 pF, is connected to a battery of emf 20 V. If a, 5, 3, is inserted between the plates, the magnitude, of the induced charge will be, , dielectric material of dielectric constant K =, , (a) 1.2 nC, , (b) 0.3 nC, , (c) 2.4 nC, , (d) 0.9 nC, , 16. In an AC circuit, the instantaneous emf and, current are given by, π, , e = 100 sin 30 t, i = 20 sin 30 t − , , 4
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JEE MAIN Solved Paper 2018, In one cycle of AC, the average power, consumed by the circuit and the wattless, current are, respectively, (a) 50 , 10, , (b), , 1000, 50, , 10 (c), , 0 (d) 50 , 0, 2, 2, , 17. Two batteries with emf 12 V and 13 V are, connected in parallel across a load resistor of, 10 Ω. The internal resistances of the two, batteries are 1 Ω and 2 Ω, respectively. The, voltage across the load lies between, (a) 11.6 V and 11.7 V, (c) 11.4 V and 11.5 V, , (b) 11.5 V and 11.6 V, (d) 11.7 V and 11.8 V, , 18. An electron, a proton and an alpha particle, having the same kinetic energy are moving in, circular orbits of radii re , rp , rα respectively, in, a uniform magnetic field B. The relation, between re , rp , rα is, (a) re > rp = rα, (c) re < rp < rα, , (b) re < rp = rα, (d) re < rα < rp, , a current I, is m and the magnetic field at the, centre of the loop is B1 . When the dipole, moment is doubled by keeping the current, constant, the magnetic field at the centre of, B, the loop is B2 . The ratio 1 is, B2, (a) 2, , (b) 3, , (c) 2, , (d), , 1, 2, , 20. For an R-L-C circuit driven with voltage of, amplitude vm and frequency ω 0 =, , 1, , LC, current exhibits resonance. The quality, factor, Q is given by, ω0 L, R, R, (c), ω0C, , (a), , If ε r1 and ε r2 refer to relative permittivities of, air and medium respectively, which of the, following options is correct?, (a), (c), , εr1, , εr 2, εr1, εr 2, , =4, , (b), , 1, 4, , (d), , =, , , the, , ω0 R, L, CR, (d), ω0, (b), , 21. An EM wave from air enters a medium. The, , , z , electric fields are E1 = E 01 x$ cos 2 πν − t in, c , , air and E2 = E 02 x$ cos[ k(2 z − ct)] in medium,, where the wave number k and frequency ν, refer to their values in air. The medium is, non-magnetic., , εr1, , εr 2, εr1, εr 2, , =2, =, , 1, 2, , 22. Unpolarised light of intensity I passes, through an ideal polariser A. Another, identical polariser B is placed behind A. The, I, intensity of light beyond B is found to be ., 2, Now, another identical polariser C is placed, between A and B. The intensity beyond B is, 1, now found to be . The angle between, 8, polariser A and C is, (a) 0°, (c) 45°, , 19. The dipole moment of a circular loop carrying, , 3, , (b) 30°, (d) 60°, , 23. The angular width of the central maximum, in a single slit diffraction pattern is 60°. The, width of the slit is 1 µm. The slit is, illuminated by monochromatic plane waves., If another slit of same width is made near it,, Young’s fringes can be observed on a screen, placed at a distance 50 cm from the slits. If, the observed fringe width is 1 cm, what is slit, separation distance? (i.e. distance between, the centres of each slit.), (a) 25 µm, (c) 75 µm, , (b) 50 µm, (d) 100 µm, , 24. An electron from various excited states of, hydrogen atom emit radiation to come to the, ground state. Let λ n , λ g be the de-Broglie, wavelength of the electron in the nth state, and the ground state, respectively. Let Λ n be, the wavelength of the emitted photon in the, transition from the nth state to the ground, state. For large n, (A , B are constants), (a) Λn ≈ A +, , B, λ2n, , (b) Λn ≈ A + Bλ2n, (c) Λ2n ≈ A + Bλ2n, (d) Λ2n ≈ λ
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4, , JEE MAIN Solved Paper 2018, , 25. If the series limit frequency of the Lyman, , series is ν L , then the series limit frequency of, the Pfund series is, (b) 16 νL, ν, (d) L, 25, , (a) 25 νL, ν, (c) L, 16, , 26. It is found that, if a neutron suffers an elastic, collinear collision with deuterium at rest,, fractional loss of its energy is Pd ; while for its, similar collision with carbon nucleus at rest,, fractional loss of energy is Pc . The values of Pd, and Pc are respectively, (a) (.89, .28), (c) (0, 0), , (b) (.28, .89), (d) (0, 1), , 27. The reading of the ammeter for a silicon, diode in the given circuit is, 200Ω, , 28. A telephonic communication service is, working at carrier frequency of 10 GHz. Only, 10% of it is utilised for transmission. How, many telephonic channels can be transmitted, simultaneously, if each channel requires a, bandwidth of 5 kHz?, (a) 2 × 103, , (b) 2 × 104, , (c) 2 × 10, , (d) 2 × 106, , 5, , 29. In a potentiometer experiment, it is found, that no current passes through the, galvanometer when the terminals of the cell, are connected across 52 cm of the, potentiometer wire. If the cell is shunted by a, resistance of 5 Ω, a balance is found when, the cell is connected across 40 cm of the wire., Find the internal resistance of the cell., (a) 1 Ω, (c) 2 Ω, , (b) 15, . Ω, (d) 2.5 Ω, , 30. On interchanging the resistances, the balance, , 3V, , (a) 0, (c) 11.5 mA, , (b) 15 mA, (d) 13.5 mA, , point of a meter bridge shifts to the left by, 10 cm. The resistance of their series, combination is 1 kΩ. How much was the, resistance on the left slot before, interchanging the resistances?, (a) 990 Ω, (c) 550 Ω, , (b) 505 Ω, (d) 910 Ω
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CHEMISTRY, 31. The ratio of mass per cent of C and H of an, organic compound (C x H yO z ) is 6 : 1. If one, molecule of the above compound (C x H yO z ), contains half as much oxygen as required to, burn one molecule of compound Cx H y, completely to CO2 and H2O. The empirical, formula of compound Cx H yO z is, (a) C 3H6O 3 (b) C 2H4O, , (c) C 3H4O 2 (d) C 2H4O 3, , 32. Which type of ‘defect’ has the presence of, (a) Schottky defect, (b) Vacancy defect, (c) Frenkel defect, (d) Metal deficiency defect, , 33. According to molecular orbital theory, which, of the following will not be a viable, molecule?, (b) He +2, , (c) H−2, , and 0.20 M HCl. If the equilibrium constants, for the formation of HS− from H2S is, , 10, . × 10 −7 and that of S2− from HS− ions is, , . × 10 −13 then the concentration of S2− ions, 12, in aqueous solution is :, (a) 5 × 10−8 (b) 3 × 10−20 (c) 6 × 10−21 (d) 5 × 10−19, , 38. An aqueous solution contains an unknown, , concentration of Ba2 + . When 50 mL of a 1 M, solution of Na2SO4 is added, BaSO4 just, begins to precipitate. The final volume is, 500 mL. The solubility product of BaSO4 is, 1 × 10 −10 . What is the original concentration, , cations in the interstitial sites?, , (a) He 2+, 2, , 37. An aqueous solution contains 0.10 M H2S, , (d) H2−, 2, , of Ba 2+ ?, (a) 5 × 10−9 M, −9, , (c) 11, . × 10, , M, , (b) 2 × 10−9 M, (d) 10, . × 10−10 M, , 39. At 518°C, the rate of decomposition of a, 34. Which of the following lines correctly show, the temperature dependence of equilibrium, constant, K, for an exothermic reaction?, In K, , A, B, , 1, T(K), , (0, 0), , (a) 2, , D, , (a) A and B (b) B and C (c) C and D (d) A and D, , 35. The combustion of benzene (), l gives CO2 ( g ), and H2O(), l . Given that heat of combustion of, benzene at constant volume is, −3263.9 kJ mol −1 at 25° C; heat of, combustion (in kJ mol −1 ) of benzene at, constant pressure will be, (R = 8.314 JK −1 mol −1), (b) −452.46 (c) 3260, , (d) −3267.6, , 36. For 1 molal aqueous solution of the following, compounds, which one will show the highest, freezing point?, (a) [Co(H2O)6 ]Cl 3, (b) [Co(H2O)5 Cl]Cl 2 ⋅ H2O, (c) [Co(H2O)4 Cl 2 ]Cl ⋅ 2H2O, (d) [Co(H2O)3 Cl 3 ]⋅ 3H2O, , (b) 3, , (c) 1, , (d) 0, , 40. How long (approximate) should water be, , ××, ××, ××, C, ××, ××, ××, , (a) 4152.6, , sample of gaseous acetaldehyde, initially at a, pressure of 363 Torr, was 1.00 Torr s −1 when, 5% had reacted and 0.5 Torr s −1 when 33%, had reacted. The order of the reaction is :, , electrolysed by passing through 100 amperes, current so that the oxygen released can, completely burn 27.66 g of diborane?, (Atomic weight of B = 10 .8 µ), (a) 6.4 hours, (c) 3.2 hours, , (b) 0.8 hours, (d) 1.6 hours, , 41. The recommended concentration of fluoride, ion in drinking water is up to 1 ppm as, fluoride ion is required to make teeth enamel, harder by converting [3Ca3 (PO4 )2 ⋅ Ca(OH)2 ], to :, (a) [CaF2 ], (c) [3Ca 3 (PO 4 )2 ⋅ CaF2 ], , (b) [3(CaF2 ) ⋅ Ca(OH)2 ], (d) [3{Ca 3 (PO 4 )2 } ⋅ CaF2 ], , 42. Which of the following compounds, contain(s) no covalent bond(s)?, KCl, PH3 , O2 , B2H6 , H2SO4, (a) KCl, B 2H6 , PH3, (c) KCl, , (b) KCl, H2SO 4, (d) KCl, B 2H6
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6, , JEE MAIN Solved Paper 2018, , 43. Which of the following are Lewis acids?, (b) AlCl 3 and SiCl 4, (d) BCl 3 and AlCl 3, , (a) PH3 and BCl 3, (c) PH3 and SiCl 4, , 44. Total number of lone pair of electron in, I−3 ion is, , (a) 3, , (b) 6, , (c) 9, , (d) 12, , 45. Which of the following salts is the most basic, in aqueous solution?, (a) Al(CN)3, (c) FeCl 3, , (b) CH3COOK, (d) Pb(CH3COO)2, , 46. Hydrogen peroxide oxidises [Fe(CN)6 ]4 − to, [Fe(CN)6 ]3 − in acidic medium but reduces, 3−, , 4−, , [Fe(CN)6 ] to [Fe(CN)6 ] in alkaline, medium. The other products formed are,, respectively., (a) (H2O + O 2 ) and H2O, (b) (H2O + O 2 ) and (H2O + OH− ), (c) H2O and (H2O + O 2 ), (d) H2O and (H2O + OH− ), , III. Only one isomer is produced if the, reactant complex ion is a trans-isomer., IV. Only one isomer is produced if the, reactant complex ion is a cis-isomer., The correct statements are, (a) (I) and (II), (c) (III) and (IV), , 51. Glucose on prolonged heating with HI gives, (a) n-hexane, (c) Hexanoic acid, , reduction of alkynes with, (a) H2 -Pd/C, BaSO 4, (c) Na/liq. NH3, , suitable for Kjeldahl’s method for nitrogen, estimation?, NH2, (b), N, , (b) +3, +2 and +4, (d) +3, 0 and +4, , 48. The compound that does not produce, nitrogen gas by the thermal decomposition is, (b) (NH4 )2 Cr2O 7, (d) (NH4 )2 SO 4, , white gelatinous precipitate ‘X ’ is obtained,, which is soluble in excess of NaOH., Compound ‘X ’ when heated strongly gives an, oxide which is used in chromatography as an, adsorbent. The metal ‘M’ is, (b) Ca, , (c) Al, , (c), , (d), , 54. Phenol on treatment with CO2 in the, presence of NaOH followed by acidification, produces compound X as the major product., X on treatment with (CH3CO)2 O in the presence, of catalytic amount of H2SO4 produces:, O, O, , (a), , (b), , CO2H, O, C, , I. Two isomers are produces if the reactant, complex ion is a cis-isomer., II. Two isomers are produced if the reactant, complex ion is a trans-isomer., , O, , CH3, , CO2H, , O, OH, , −, , [Co(NH3 )4 Br2 ] + Br →, [Co(NH3 )3 Br3 ] + NH3, , CH3, , CO2H, , statements :, +, , O, CH3, , O, , (d) Fe, , 50. Consider the following reaction and, , N+2Cl–, , NO2, , 49. When metal ‘M’ is treated with NaOH, a, , (a) Zn, , (b) NaBH4, (d) Sn-HCl, , 53. Which of the following compounds will be, , (a), , [Cr(C 6 H6 )2 ], and K2 [Cr(CN)2 (O)2 (O2 )(NH3 )], respectively are, , (a) Ba(N3 )2, (c) NH4NO 2, , (b) 1-hexene, (d) 6-iodohexanal, , 52. The trans-alkenes are formed by the, , 47. The oxidation states of Cr, in [Cr(H2O)6 ]Cl3 ,, (a) +3, +4 and +6, (c) +3, 0 and +6, , (b) (I) and (III), (d) (II) and (IV), , (c), , (d), CO2H, CH3, , O, O
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JEE MAIN Solved Paper 2018, 55. An alkali is titrated against an acid with, , 58. The increasing order of basicity of the, , methyl orange as indicator, which of the, following is a correct combination?, , following compounds is, NH2, , I., , Base, , Acid, , End point, , Weak, , Strong, , Colourless to pink, , 7, , NH, , II., NH2, , (a), , IV., , III., , (b), , Strong, , Strong, , Pinkish red to yellow, , (c), , Weak, , Strong, , Yellow to pinkish red, , (d), , Strong, , Strong, , Pink to colourless, , NHCH3, , NH, , (a) (I) < (II) < (III) < (IV) (b) (II) < (I) < (III) < (IV), (c) (II) < (I) < (IV) < (III) (d) (IV) < (II) < (I) < (III), , 59. The major product formed in the following, reaction is, , 56. The predominant form of histamine present, in human blood is (pK a , Histidine = 6 .0), H, N, , NH2, , (a), , H, N, (b), , (c), , r, NH3, OH, , I, , (b), I, , OH, , r, NH3, , (d), , r, N, H, , O, , (a), , H, N, , NH2, , HI, Heat, , r, N, , N, H, H, N, , O, , N, OH, , (c), , 57. Phenol reacts with methyl chloroformate in, the presence of NaOH to form product A., A reacts with Br 2 to form product B. A and B, are respectively, Br, , OH, (a), , OCH3, , 60. The major product of the following reaction, is, Br, NaOMe, MeOH, , OCH3, , O, , O, , O, , O, , O, , (b), , and, , O, , OMe, , O, , (a), , O, Br, , O, , O, (c), , O, , O, and, , O, , (b), , O, Br, (c), , OH, (d), , OCH3, O, , OH, OMe, , and, , OCH3, Br, , O, , OH, , I, , OH, , and, , I, , (d), , (d)
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MATHEMATICS, 61. Two sets A and B are as under, , 67. The sum of the coefficients of all odd degree, , A = {(a, b ) ∈ R × R :|a − 5| < 1 and, | b − 5| < 1};, B = {(a, b ) ∈ R × R : 4(a − 6 )2 + 9( b − 5 )2≤ 36}., Then,, (a) B ⊂ A, (b) A ⊂ B, (c) A ∩ B = φ (an empty set), (d) neither A ⊂ B nor B ⊂ A, , (d) 2, , 2x, 2x , x − 4, , 64. If 2 x, 2 x = (A + Bx)(x − A)2 ,, x−4, , , 2x, x − 4, 2x, then the ordered pair (A , B) is equal to, (c) (−4, 5), , (d) (4, 5), , 3 x + ky − 2 z = 0, has a non-zero solution ( x, y, z ), then xz / y2, is equal to, (d) 30, , 66. From 6 different novels and 3 different, dictionaries, 4 novels and 1 dictionary are to, be selected and arranged in a row on a shelf,, so that the dictionary is always in the middle., The number of such arrangements is, (a) atleast 1000, (b) less than 500, (c) atleast 500 but less than 750, (d) atleast 750 but less than 1000, , If, , 2, = 140 m, then m is equal to, a 22 + … + a17, , (a) 66, , (b) 68, , (c) 34, , (d) 33, , 12 + 2 ⋅ 2 2 + 3 2 + 2 ⋅ 4 2 + 5 2 + 2 ⋅ 6 2 + …, If B − 2 A = 100 λ, then λ is equal to, (a) 232, (c) 464, , (b) 248, (d) 496, , 70. For each t ∈R, let [ t] be the greatest integer, less than or equal to t. Then,, 1 2 , 15 , lim x + + … + , +, x x, x→ 0, x , (a) is equal to 0, (c) is equal to 120, , (b) is equal to 15, (d) does not exist (in R), , (a) φ (an empty set), (c) { π}, , 2x + 4y − 3z = 0, , (c) −30, , a 9 + a 43 = 66 ., , not differentiable at t}. Then, the set S is, equal to, , x + ky + 3 z = 0, , (b) 10, , and, , 71. Let S = (t ∈ R : f (x) = | x − π |(, ⋅ e|x| − 1)sin| x | is, , 65. If the system of linear equations, , (a) −10, , k=0, a12 +, , be the sum of the first 40 terms of the series, , equation x 2 − x + 1 = 0 , then α101 + β107 is, equal to, , (a) (−4, − 5) (b) (−4, 3), , (b) 0, (d) 2, , 69. Let A be the sum of the first 20 terms and B, , 63. If α , β ∈C are the distinct roots of the, , (c) 1, , (a) −1, (c) 1, , x 3 − 1 , (x > 1) is, , 12, , x ( x − 6) + 6 = 0 . Then, S, , (b) 0, , 5, , x 3 − 1 + x −, , ∑ a 4k + 1 = 416, , (a) is an empty set, (b) contains exactly one element, (c) contains exactly two elements, (d) contains exactly four elements, , (a) −1, , 5, , x +, , , 68. Let a1 , a 2 , a 3, …, a 49 be in AP such that, , 62. Let S = { x ∈ R : x ≥ 0 and, 2| x − 3| +, , terms in the expansion of, , (b) {0}, (d) {0, π}, , 72. If the curves y 2 = 6 x , 9 x 2 + by 2 = 16 intersect, each other at right angles, then the value of b, is, (a) 6, , (b), , 73. Let f (x) = x 2 +, , 7, 2, , (c) 4, , 1, x, , 2, , and g(x) = x −, , (d), , 9, 2, , 1, ,, x, , f (x), , then the, g(x), local minimum value of h(x) is, x ∈ R − { −1, 0 , 1}. If h(x) =, , (a) 3, (c) −2 2, , (b) −3, (d) 2 2
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JEE MAIN Solved Paper 2018, , 79. Let the orthocentre and centroid of a triangle, , 74. The integral, sin 2 x cos 2 x, , ∫ (sin5 x + cos 3 x sin2 x + sin3 x cos 2 x, , dx, , + cos 5 x)2, is equal to, , 1, −1, (b), +C, +C, 3(1 + tan3 x), 3(1 + tan3 x), 1, −1, (c), (d), +C, +C, 3, 1 + cot 3 x, 1 + cot x, (where C is a constant of integration), (a), , π, 2, , 75. The value of, , (a), , sin 2 x, , ∫ 1 + 2x, , dx is, π, 2, π, (d), 4, , (b), , (c) 4π, , 76. Let g(x) = cos x 2, f (x) =, , x and α , β (α < β) be, the roots of the quadratic equation, 18 x 2 − 9 πx + π 2 = 0 . Then, the area (in sq, units) bounded by the curve y = (gof )(x) and, the lines x = α, x = β and y = 0, is, 1, (a) ( 3 − 1), 2, 1, (c) ( 3 − 2 ), 2, , 1, (b) ( 3 + 1), 2, 1, (d) ( 2 − 1), 2, , 77. Let y = y(x) be the solution of the differential, dy, + y cos x = 4 x , x ∈(0 , π)., dx, π, = 0 , then y is equal to, 6, , equation sin x, π, If y , 2, , 4, π2, 9 3, 8, (c) − π 2, 9, (a), , −8 2, π, 9 3, 4, (d) − π 2, 9, (b), , 78. A straight line through a fixed point (2, 3), intersects the coordinate axes at distinct, points P and Q. If O is the origin and the, rectangle OPRQ is completed, then the locus, of R is, (a) 3 x + 2 y = 6, (c) 3 x + 2 y = xy, , be A(−3 , 5) and B(3 , 3), respectively. If C is the, circumcentre of this triangle, then the radius, of the circle having line segment AC as, diameter, is, (a) 10, 5, (c) 3, 2, , (b) 2 x + 3 y = xy, (d) 3 x + 2 y = 6 xy, , (b) 2 10, 3 5, (d), 2, , 80. If the tangent at (1, 7) to the curve x 2 = y − 6, touches the circle x 2 + y 2 + 16 x + 12 y + c = 0 ,, then the value of c is, (a) 195, , π, −, 2, , π, 8, , 9, , (b) 185, , (c) 85, , (d) 95, , 81. Tangent and normal are drawn at P(16 , 16) on, the parabola y 2 = 16 x , which intersect the, axis of the parabola at A and B, respectively., If C is the centre of the circle through the, points P, A and B and ∠CPB = θ, then a value, of tanθ is, (a), , 1, 2, , (b) 2, , (c) 3, , (d), , 4, 3, , 82. Tangents are drawn to the hyperbola, 4 x 2 − y 2 = 36 at the points P and Q. If these, tangents intersect at the point T(0, 3), then, the area (in sq units) of ∆PTQ is, (a) 45 5, (c) 60 3, , (b) 54 3, (d) 36 5, , 83. If L1 is the line of intersection of the planes, , 2 x − 2 y + 3 z − 2 = 0 , x − y + z + 1 = 0 and L 2 is, the line of intersection of the planes, x + 2 y − z − 3 = 0, 3 x − y + 2 z − 1 = 0 , then the, distance of the origin from the plane,, containing the lines L1 and L 2 is, (a), , 1, 4 2, , (b), , 1, 3 2, , (c), , 1, 2 2, , (d), , 1, 2, , 84. The length of the projection of the line, , segment joining the points (5, −1, 4) and, (4 , − 1, 3) on the plane, x + y + z = 7 is, 2, 3, 1, (c), 3, (a), , (b), (d), , 2, 3, 2, 3
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10, , JEE MAIN Solved Paper 2018, , 85. Let u be a vector coplanar with the vectors, , 88. If sum of all the solutions of the equation, , $ If u is, a = 2 $i + 3 $j − k$ and b = $j + k., , , 1, π, , π, 8 cos x ⋅ cos + x ⋅ cos − x − , 2, 6, , 6, , , perpendicular to a and u ⋅ b = 24, then|u|2 is, equal to, (a) 336, , (b) 315, , (c) 256, , = 1 in [0, π ] is kπ, then k is equal to, , (d) 84, , 2, (a), 3, , 86. A bag contains 4 red and 6 black balls. A ball, is drawn at random from the bag, its colour, is observed and this ball along with two, additional balls of the same colour are, returned to the bag. If now a ball is drawn at, random from the bag, then the probability, that this drawn ball is red, is, 3, 10, , (a), , 87. If, , (b), , 2, 5, , (c), , 9, , 9, , i =1, , i =1, , 1, 5, , (d), , (c) 2, , (c), , 8, 9, , (d), , 20, 9, , m. A TV tower stands at the mid-point of QR., If the angles of elevation of the top of the, tower at P , Q and R are respectively 45°, 30°, and 30°, then the height of the tower (in m), is, (a) 100, (c) 100 3, , (b) 50, (d) 50 2, , 90. The boolean expression ~ (p ∨ q) ∨ (~ p ∧ q) is, equivalent to, , the standard deviation of the 9 items, x1 , x 2 , …, x 9 is, (b) 4, , 13, 9, , 89. PQR is a triangular park with PQ = PR = 200, , 3, 4, , ∑(x i − 5) = 9 and ∑(x i − 5)2 = 45, then, , (a) 9, , (b), , (a) ~ p, (c) q, , (d) 3, , (b) p, (d) ~q, , Answers, Physics, 1. (c), 11. (a), , 2. (b), 12. (b), , 3. (b), 13. (a), , 4. (c), 14. (b), , 5. (b), 15. (a), , 6. (d), 16. (b), , 7. (a), 17. (b), , 8. (c), 18. (b), , 9. (c), 19. (c), , 10. (c), , (c), , (c), , (a), , (a), , (d), , (a), , (c), , (c), , (b), , 30. (c), , 21., , 22., , 23., , 24., , 25., , 26., , 27., , 28., , 29., , 20. (a), , Chemistry, 31. (d), , 32. (c), , 33. (d), , 34. (a), , 35. (d), , 36. (d), , 37. (b), , 38. (c), , 39. (a), , 40. (c), , 41. (c), , 42. (c), , 43. (d), , 44. (c), , 45. (b), , 46. (c), , 47. (c), , 48. (d), , 49. (c), , 50. (b), , 51. (a), , 52. (c), , 53. (b), , 54. (a), , 55. (c), , 56. (d), , 57. (c), , 58. (c), , 59. (d), , 60. (b), , Mathematics, 61. (b), , 62. (c), , 63. (c), , 64. (c), , 65. (b), , 66. (a), , 67. (d), , 68. (c), , 69. (b), , 70. (c), , 71. (a), , 72. (d), , 73. (d), , 74. (b), , 75. (d), , 76. (a), , 77. (c), , 78. (c), , 79. (c), , 80. (d), , 81. (b), , 82. (a), , 83. (b), , 84. (d), , 85. (a), , 86. (b), , 87. (c), , 88. (b), , 89. (a), , 90. (a), , For solutions scan, the QR code
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] OFFLINE ], , SOLVED PAPER 2017, , JEE MAIN, Joint Entrance Examinaton, INSTRUCTIONS, , 1. This test consists of 90 questions., 2. Each question is allotted 4 marks for correct response., 3. Candidates will be awarded marks as stated above in instruction no. 2 for correct response of each question., 1 marks will be deducted for indicating incorrect response of each question. No deduction from the total, score will be made if no response is indicated for an item in the answer sheet., 4. There is only one correct response for each question. Filling up more than one response in any question will, be treated as wrong response and marks for wrong response will be deducted according as per instructions, , Physics, 1. An observer is moving with half the speed of, , 4. A body of mass m = 10 -2 kg is moving in a, , light towards a stationary microwave source, emitting waves at frequency 10 GHz. What is, the frequency of the microwave measured by, the observer? (speed of light = 3 ´ 108 ms -1), , medium and experiences a frictional force, F = - kv2 . Its initial speed is v0 = 10 ms -1. If,, after 10 s, its energy is 1 mv20 , the value of k, 8, will be, , (a) 12.1 GHz, (c) 15.3 GHz, , (a) 10-3 kgs -1, , (b) 17.3 GHz, (d) 10.1 GHz, , (b) 10-4 kgm-1, , 2. The following observations were taken for, determining surface tension T of water by, capillary method. Diameter of capillary,, m, rise, of, water,, d = 1.25 ´ 10 -2, h = 1.45 ´ 10 -2 m. Using g = 9.80 m/s 2 and, rhg, the simplified relation T =, ´ 103 N/ m,, 2, the possible error in surface tension is closest, to, (a) 1.5%, , (b) 2.4%, , (c) 10%, , (d) 0.15%, , (c) 10-1kgm-1s -1, (d) 10-3 kgm-1, , 5. C p and C V are specific heats at constant, pressure and constant volume, respectively., It is observed that C p - C V = a for hydrogen, gas C p - C V = b for nitrogen gas. The correct, relation between a and b is, (a) a = b, (c) a = 28 b, , (b) a = 14 b, 1, (d) a =, b, 14, , 3. Some energy levels, of a molecule are, shown in the, figure. The ratio of, the wavelengths, r = l 1 / l2 is given, by, 2, (a) r =, 3, 1, (c) r =, 3, , 3, (b) r =, 4, 4, (d) r =, 3, , –E, , 6. The moment of inertia of a uniform cylinder, , λ2, , –2 E, , of length l and radius R about its, perpendicular bisector is I. What is the ratio, l / R such that the moment of inertia is, minimum?, , –3 E, , (a), , –4/3E, λ1, , 3, 2, 3, (c), 2, , (b) 1, (d), , 3, 2
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12, , JEE MAIN Solved Paper 2017, , 7. A radioactive nucleus A with a half-life T,, decays into a nucleus B. At t = 0, there is no, nucleus B. After sometime t, the ratio of the, number of B to that of A is 0.3. Then, t is given, by, log 13, ., loge 2, T, (c) t =, log 13, ., , (a) t = T, , 11. In the below circuit, the current in each, resistance is, 2V, , (b) t = T log 13, ., (d) t =, , 1Ω, , 2V, , (a) In a balanced Wheatstone bridge, if the cell and, the galvanometer are exchanged, the null point is, disturbed, (b) A rheostat can be used as a potential divider, (c) Kirchhoff’s second law represents energy, conservation, (d) Wheatstone bridge is the most sensitive when all, the four resistances are of the same order of, magnitude, , 9. A capacitance of 2 mF is required in an, electrical circuit across a potential difference, of 1kV. A large number of 1 mF capacitors are, available which can withstand a potential, difference of not more than 300 V. The, minimum number of capacitors required to, achieve this is, (b) 24, (d) 2, , 10. In the given circuit diagram, when the, current reaches steady state in the circuit, the, charge on the capacitor of capacitance C will, be, E, , r, r1, , C, , r1, (r2 + r ), r2, (b) CE, (r + r2 ), r1, (c) CE, (r1 + r ), (d) CE, , 1Ω, , 1Ω, , (a) 0.25 A, , 2V, , 2V, , (b) 0.5 A, , (c) 0 A, , (d) 1 A, , 12. In amplitude modulation, sinusoidal carrier, frequency used is denoted by wc and the signal, frequency is denoted by wm . The bandwidth, ( Dwm ) of the signal is such that Dwm << wc ., Which of the following frequencies is not, contained in the modulated wave?, (a) wc, (c) wc - wm, , (b) wm + wc, (d) wm, , 13. In a common emitter amplifier circuit using, an n-p-n transistor, the phase difference, between the input and the output voltages, will be, (a) 90°, , (b) 135°, , (c) 180°, , (d) 45°, , 14. A copper ball of mass 100 g is at a, temperature T. It is dropped in a copper, calorimeter of mass 100 g, filled with 170 g of, water at room temperature. Subsequently,, the temperature of the system is found to be, 75°C. T is (Given, room temperature = 30°C,, specific heat of copper = 0.1 cal/g°C), (a) 885°C, (c) 825°C, , (b) 1250°C, (d) 800°C, , 15. In a Young’s double slit experiment, slits are, r2, , (a) CE, , 2V, , T loge 2, 2 log 13, ., , 8. Which of the following statements is false?, , (a) 16, (c) 32, , 2V, , separated by 0.5 mm and the screen is placed, 150 cm away. A beam of light consisting of, two wavelengths, 650 nm and 520 nm, is, used to obtain interference fringes on the, screen. The least distance from the common, central maximum to the point where the, bright fringes due to both the wavelengths, coincide, is, (a) 7.8 mm, (c) 15.6 mm, , (b) 9.75 mm, (d) 1.56 mm
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JEE MAIN Solved Paper 2017, , 20. An electron beam is accelerated by a, , 1, , field E2 = 3 E1$j, it experiences a torque, T2 = - T1. The angle q is, (b) 60°, , (c) 90°, , (d) 30°, , 17. A slender uniform rod of mass M and length l, is pivoted at one end so that it can rotate in a, vertical plane (see the figure). There is, negligible friction at the pivot. The free end is, held vertically above the pivot and then, released. The angular acceleration of the rod, when it makes an angle q with the vertical, is, , (a), , (b), log V, , (c), , log V, , (d), , z, , logλmin, , (a) 45°, , logλmin, , potential difference V to hit a metallic target, to produce X-rays. It produces continuous as, well as characteristic X-rays. If l min is the, smallest possible wavelength of X-rays in the, spectrum, the variation of log l min with, log V is correctly represented in, logλmin, , moment p, which makes angle q with, respect to X-axis. When subjected to an, electric field E1 = Ei$, it experiences a torque, T = tk$ . When subjected to another electric, , logλmin, , 16. An electric dipole has a fixed dipole, , 13, , log V, , log V, , 21. The temperature of an open room of volume, 30 m3 increases from 17°C to 27°C due to the, sunshine. The atmospheric pressure in the, room remains 1 ´ 105 Pa. If n i and n f are the, number of molecules in the room before and, after heating, then n f - n i will be, , θ, x, , 2g, (a), sin q, 3l, (c), , 3g, (b), cos q, 2l, , 2g, cos q, 3l, , (d), , (a) 138, . ´ 1023, , 3g, sinq, 2l, , (c) -2.5 ´ 10, , 18. An external pressure P is applied on a cube at, 0°C so that it is equally compressed from all, sides. K is the bulk modulus of the material of, the cube and a is its coefficient of linear, expansion. Suppose we want to bring the, cube to its original size by heating. The, temperature should be raised by, (a), , P, aK, , (b), , 3a, PK, , (c) 3PKa, , (b) 2.5 ´ 1025, , 25, , (d), , P, 3aK, , (d) -161, . ´ 1023, , 22. In a coil of resistance 100 W, a current is, induced by changing the magnetic flux, through it as shown in the figure. The, magnitude of change in flux through the coil, is, 10, Current, (A), , 19. A diverging lens with magnitude of focal, length 25 cm is placed at a distance of 15 cm, from a converging lens of magnitude of focal, length 20 cm. A beam of parallel light falls on, the diverging lens. The final image formed is, (a) virtual and at a distance of 40 cm from convergent, lens, (b) real and at a distance of 40 cm from the divergent, lens, (c) real and at a distance of 6 cm from the convergent, lens, (d) real and at a distance of 40 cm from convergent, lens, , Time, (s), , (a) 225 Wb, (c) 275 Wb, , 0.5, , (b) 250 Wb, (d) 200 Wb, , 23. When a current of 5 mA is passed through a, galvanometer having a coil of resistance 15 W,, it shows full scale deflection. The value of the, resistance to be put in series with the
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14, , JEE MAIN Solved Paper 2017, galvanometer to convert it into a voltmeter of, range 0-10 V is, 3, , 3, , (a) 2.045 ´ 10 W, , (b) 2.535 ´ 10 W, , (c) 4.005 ´ 103 W, , (d) 1985, ., ´ 103 W, , 24. A time dependent force F = 6 t acts on a, particle of mass 1 kg. If the particle starts, from rest, the work done by the force during, the first 1 s will be, (a) 22 J, , (b) 9 J, , (c) 18 J, , (d) 4.5 J, , 28. A particle A of mass m and initial velocity v, m, which is, 2, at rest. The collision is head on, and elastic., The ratio of the de-Broglie wavelengths l A to, l B after the collision is, collides with a particle B of mass, , lA 2, =, lB 3, l, 1, (d) A =, 3, lB, , lA, =2, lB, l, 1, (c) A =, lB 2, (a), , (b), , 25. A magnetic needle of magnetic moment, , 29. A particle is executing simple harmonic, , 6.7 ´ 10 -2 Am2 and moment of inertia, 7.5 ´ 10 -6 kg, m2 is performing simple, harmonic oscillations in a magnetic field of, 0.01 T. Time taken for 10 complete, oscillations is, , motion with a time period T. At time t = 0, it, is at its position of equilibrium. The kinetic, energy-time graph of the particle will look,, like, , (a) 8.89 s, , (b) 6.98 s, , (c) 8.76 s, , KE, , (d) 6.65 s, , 26. The variation of acceleration due to gravity g, , (a), , with distance d from centre of the Earth is, best represented by (R = Earth’s radius), g, , t, , KE, , g, , (a), , (b), , (b), d, O, , T, , O, , O, , T/2, , T, , t, , d, , R, , O, , g, , R, KE, , g, , (c), , (d), (c), d, , d, O, , O, , R, , O, , T, , T/4 T/2, t, , R, , 27. A body is thrown vertically upwards. Which, , KE, , one of the following graphs correctly, represent the velocity vs time?, (d), v, , (a), , O, , t, , (b), , T/2, , T, , T, t, , v, t, , 30. A man grows into a giant such that his linear, dimensions increase by a factor of 9., Assuming that his density remains same, the, stress in the leg will change by a factor of, , v, , (c), , 1, 9, 1, (c), 81, , v, t, , (a), , (d), , t, , (b) 81, (d) 9
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Chemistry, 31. Which of the following compounds will give, significant amount of meta-product during, mononitration reaction?, OH, , OCOCH3, , (a), , (a) 15 kg, , (b) 37.5 kg (c) 7.5 kg, , tert-BuONa followed by addition of bromine, water, fails to decolourise the colour of, bromine ?, NHCOCH3, , C6H5, , O, , (a), , (c), , Br, , (b) isobaric work, (d) isothermal work, , 33. The increasing order of reactivity of the, following halides for the S N 1 reaction is, I. CH3CH(Cl)CH2CH3, III. p -H3CO ¾ C 6 H4 ¾ CH2Cl, (b) (II) < (I) < (III), (d) (II) < (III) < (I), , 34. The radius of the second Bohr orbit for, hydrogen atom is (Planck’s constant, ( h ) = 6.6262 ´ 10 - 34 Js; mass of electron, = 9.1091 ´ 10 - 31 kg ; charge of electron, (e ) = 1.60210 ´ 10 - 19 C; permitivity of, vacuum ( Î0 ) = 8.854185 ´ 10 -12kg - 1 m - 3A 2 ), (b) 4.76 Å, , (c) 0.529 Å (d) 2.12 Å, , 35. pKa of a weak acid (HA) and pK b of a weak, base (BOH) are 3.2 and 3.4, respectively. The, pH of their salt (AB) solution is, (a) 7.2, , (b) 6.9, , (c) 7.0, , (d) 1.0, , 36. The formation of which of the following, polymers involves hydrolysis reaction?, (a) Nylon-6, (c) Nylon-6, 6, , (c), , (d), Br, , (b) Bakelite, (d) Terylene, , 37. The most abundant elements by mass in the, body of a healthy human adult are Oxygen, (61.4%); Carbon (22.9%), Hydrogen (10.0 %);, and Nitrogen (2.6%). The weight which a, , Br, , 39. In, , the following reactions,, respectively acting as a/an, (i) ZnO + Na2O ¾® Na2 ZnO2, (ii) ZnO + CO2 ¾® ZnCO3, (a) base and acid, (c) acid and acid, , II. CH3CH2CH2Cl, (a) (III) < (II) < (I), (c) (I) < (III) < (II), , Br, , O, , 32. DU is equal to, , (a) 1.65 Å, , (b), , (d), , (a) isochoric work, (c) adiabatic work, , (d) 10 kg, , 38. Which of the following, upon treatment with, , (b), NH2, , 75 kg person would gain if all 1H atoms are, replaced by 2H atoms is, , ZnO, , is, , (b) base and base, (d) acid and base, , 40. Both lithium and magnesium display several, similar properties due to the diagonal, relationship; however, the one which is, incorrect is, (a) Both form basic carbonates, (b) Both form soluble bicarbonates, (c) Both form nitrides, (d) nitrates of both Li and Mg yield NO 2 and O 2 on, heating, , 41. 3-methyl-pent-2-ene on reaction with HBr in, presence of peroxide forms an addition, product., The, number, of, possible, stereoisomers for the product is, (a) six, , (b) zero, , (c) two, , (d) four, , 42. A metal crystallises in a face centred cubic, structure. If the edge length of its unit cell is, ‘a’, the closest approach between two atoms in, metallic crystal will be, (a) 2 a, , (b) 2 2 a, , (c) 2 a, , (d), , a, 2, , 43. Two reactions R1 and R2 have identical preexponential factors. Activation energy of R1, exceeds that of R2 by 10 kJ mol- 1. If k 1 and k 2, are rate constants for reactions R1 and R2 ,
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JEE MAIN Solved Paper 2017, 52. Which of the following species is not, , OH, , 17, , OH, , paramagnetic?, (a), , (a) NO, (b) CO, (c) O 2, (d) B 2, , CHO, , CHO, , COOH, (c), , 0.45°C when 0.2 g of acetic acid is added to, 20 g of benzene. If acetic acid associates to, form a dimer in benzene, percentage, association of acetic acid in benzene will be, (K f for benzene = 5.12 K kg mol - 1), (a) 64.6 %, (b) 80.4 %, (c) 74.6 %, (d) 94.6 %, , CHO, , CHO, , 53. The freezing point of benzene decreases by, , (d), , CHO, , COOH, , CHO, , 57. A water sample has ppm level concentration, of following anions, F - = 10; SO24 - = 100; NO3- = 50, the anion/anions that make/makes the water, sample unsuitable for drinking is/are, (a) Only NO -3, (b) Both SO 24 - and NO -3, , 54. Which of the following molecules is least, resonance stabilised?, (a), , excess HCl produces 0.01186 mole of CO2 ., The molar mass of M2CO3 in g mol - 1 is, (a) 1186, (c) 118.6, , (d), , N, , (c) Only F (d) Only SO 24 -, , 58. 1 g of a carbonate (M2CO3 ) on treatment with, , (b), O, , (c), , (b), , (b) 84.3, (d) 11.86, , O, , 55. On treatment of 100 mL of 0.1 M solution of, , 59. Given, E°Cl, , 2 / Cl, , -, , = 1.36 V, E°Cr 3 + / Cr = - 0.74 V, , CoCl3 .6H2O with excess of AgNO3 ; 1.2 ´ 1022, ions are precipitated. The complex is, , E°, , (a) [Co(H2O)4 Cl 2 ] Cl .2H2O, (b) [Co(H2O)3 Cl 3 ]. 3H2O, (c) [Co(H2O)6 ]Cl 3, (d) [Co(H2O)5 Cl] Cl 2 .H2O, , Among the following, the strongest reducing, agent is, , 56. The major product obtained in the following, reaction is, , Cr 2 O2 - / Cr3 +, 7, , = 1.33 V, E°MnO- / Mn 2 + = 1.51 V, , (a) Cr, , (b) Mn2 +, , (c) Cr 3 +, , (d) Cl -, , 60. The group having isoelectronic species is, (a) O 2 - , F - , Na +, Mg 2 +, , O, , (b) O - , F - , Na, Mg+, , O, DIBAL-H, , (c) O 2 - , F - , Na, Mg 2 +, (d) O - , F - , Na +, Mg 2 +, , COOH, , 4
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Mathematics, 61. If S is the set of distinct values of b for which, the following system of linear equations, x + y + z = 1,, x + ay + z = 1, and, ax + by + z = 0, has no solution, then S is, (a) an infinite set, (b) a finite set containing two or more elements, (c) singleton set, (d) a empty set, , 62. The statement ( p ® q ) ® [(~ p ® q ) ® q ] is, (a) a tautology, (b) equivalent to ~ p ® q, (c) equivalent to p ® ~ q, (d) a fallacy, , value of cos 4x is, 3, 5, , (b), , 1, 3, , (c), , 2, 9, , (d) -, , 7, 9, , 64. For three events A, B and C, if P(exactly one, of A or B occurs) = P(exactly one of B or C, 1, occurs) = P (exactly one of C or A occurs) =, 4, and P (all the three events occur, 1, , then the probability, simultaneously) =, 16, that atleast one of the events occurs, is, (a), , 7, 32, , (b), , 7, 16, , (c), , 7, 64, , (d), , 3, 16, , 65. Let w be a complex number such that, 2 w + 1 = z, where z = - 3. If, 1, 1, 1, 2, 1 - w - 1 w2 = 3 k, then k is equal to, 1, w2, w7, (a) - z, , (b) z, , (c) - 1, , (d) 1, , 66. Let k be an integer such that the triangle with, vertices ( k , - 3 k ), (5, k ) and ( - k , 2 ) has area, 28 sq units. Then, the orthocentre of this, triangle is at the point, 1, 3, (a) æç2, - ö÷ (b) æç1, ö÷, è, è 4ø, 2ø, , flower-bed in the form of a circular sector,, then the maximum area (in sq m) of the, flower-bed is, (a) 12.5, (c) 25, , (b) 10, (d) 30, , 68. The area (in sq units) of the region, {( x, y ) : x ³ 0, x + y £ 3, x2 £ 4 y and, y £ 1+ x } is, 59, 12, 7, (c), 3, , 3, 2, 5, (d), 2, (b), , (a), , 69. If the image of the point P(1, - 2, 3 ) in the, , 63. If 5 (tan2 x - cos 2 x ) = 2 cos 2 x + 9, then the, (a) -, , 67. If 20 m of wire is available for fencing off a, , 3, 1, (c) æç1, - ö÷ (d) æç2, ö÷, è, è 2ø, 4ø, , measured, 2 x + 3 y - 4 z + 22 = 0, x y z, parallel to the line = = is Q, then PQ is, 1 4 5, equal to, plane, , (a) 3 5, , (b) 2 42, , (c) 42, , (d) 6 5, , æ 1ö, x Î ç 0, ÷ ,, è 4ø, , 70. For, , if, , the, , derivative, , of, , æ 6x x ö, tan -1 ç, ÷ is x × g ( x ), then g ( x )equals, è 1 - 9 x3 ø, (a), (c), , 9, , (b), , 1 + 9 x3, 3x, , (d), , 1 - 9 x3, , 3x, , x, , 1 - 9 x3, 3, 1 + 9 x3, , dy, + ( y + 1 ) cos x = 0 and, dx, æpö, y(0 ) = 1, then y ç ÷ is equal to, è2 ø, , 71. If (2 + sin x), , (a), , 1, 3, , (c) -, , (b) 1, 3, , (d), , 2, 3, , 4, 3, , 72. Let a vertical tower AB have its end A on the, level ground. Let C be the mid-point of AB, and P be a point on the ground such that, AP = 2 AB. If ÐBPC = b, then tan b is equal to, (a), , 6, 7, , (b), , 1, 4, , (c), , 2, 9, , (d), , 4, 9
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JEE MAIN Solved Paper 2017, é2, , 73. If A = ê, ë -4, , -3 ù, , then adj (3 A2 + 12 A ) is, 1 úû, , equal to, é 51 63ù, (b) ê, ú, ë 84 72 û, é 72 - 63ù, (d) ê, ú, ë - 84 51 û, , é 72 - 84ù, (a) ê, ú, ë - 63 51 û, é 51 84ù, (c) ê, ú, ë 63 72 û, , 74. For any three positive real numbers a, b and c,, if 9 (25a2 + b2 ) + 25 (c2 - 3ac ) = 15 b (3a + c ),, then, (a) b, c and a are in GP, (c) a, b and c are in AP, , (b) b, c and a are in AP, (d) a, b and c are in GP, , 75. The distance of the point (1, 3, -7 ) from the, plane passing through the point (1, - 1, - 1 ), having normal perpendicular to both the, lines, x -1 y +2 z-4, x -2 y +1, and, =, =, =, =, 1, 3, 2, -2, -1, z+7, , is, -1, 20, units, 74, 5, units, (c), 83, , 10, units, 83, 10, (d), units, 74, , (a), , (b), , 76. Let In = ò tan n x dx ( n > 1 ). If, 5, , 5, , I4 + I6 = a tan x + bx + C , where C is a, constant of integration, then the ordered pair, (a, b ) is equal to, 1, (a) æç - , 1ö÷, è 5 ø, 1, (c) æç , - 1ö÷, è5, ø, , 1, (b) æç , 0ö÷, è5 ø, 1, (d) æç - , 0ö÷, è 5 ø, , 77. The eccentricity of an ellipse whose centre is, at the origin is 1/2. If one of its directrices is, x = - 4, then the equation of the normal to it, æ 3ö, at ç1, ÷ is, è 2ø, (a) 2 y - x = 2, (c) 4 x + 2 y = 7, , (b) 4 x - 2 y = 1, (d) x + 2 y = 4, , 78. If a hyperbola passes through the point, P( 2 , 3 ) and has foci at ( ± 2, 0 ), then the, tangent to this hyperbola at P also passes, through the point, , 19, , (b) (2 2 , 3 3 ), (d) (- 2 , - 3 ), , (a) (3 2 , 2 3 ), (c) ( 3, 2 ), , é 1 1ù, defined as, ,, ë 2 2 úû, , 79. The function f : R ® ê f(x) =, , x, 1 + x2, , is, , (a) invertible, (b) injective but not surjective, (c) surjective but not injective, (d) neither injective nor surjective, , 80. lim, , x ® p/ 2, , (a), , 1, 24, , cot x - cos x, ( p - 2 x )3, (b), , 1, 16, , equals, (c), , 1, 8, , (d), , 1, 4, , $ b = i$ + $j and c be a vector, 81. Let a = 2 $i + $j - 2 k,, such that | c - a| = 3 , |( a ´ b ) ´ c| = 3 and, the angle between c and a ´ b is 30°. Then,, a × c is equal to, (a), , 25, 8, , (b) 2, , (c) 5, , (d), , 1, 8, , 82. The, , normal, to, the, curve, y( x - 2 ) ( x - 3 ) = x + 6 at the point, where the, curve intersects the Y-axis passes through the, point, 1 1, (b) æç , ö÷, è2 2 ø, 1 1, (d) æç , ö÷, è2 3 ø, , 1, 1, (a) æç - , - ö÷, è 2, 2ø, 1, 1, (c) æç , - ö÷, è2, 3ø, , 83. If two different numbers are taken from the, set {0, 1, 2, 3, …, 10}, then the probability, that their sum as well as absolute difference, are both multiple of 4, is, (a), , 6, 55, , (b), , 12, 55, , (c), , 14, 45, , (d), , 7, 55, , 84. A man X has 7 friends, 4 of them are ladies, and 3 are men. His wife Y also has 7 friends, 3, of them are ladies and 4 are men. Assume X, and Y have no common friends. Then, the, total number of ways in which X and Y, together can throw a party inviting 3 ladies, and 3 men, so that 3 friends of each of X and, Y are in this party, is, (a) 485, , (b) 468, , (c) 469, , (d) 484
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20, , JEE MAIN Solved Paper 2017, , 85. The value of (21C 1 -, , C 1 ) + (21C 2 + ( C 3 - C 3 ) + ( C 4 - 10C 4 ) + . . . +, (21C 10 - 10C 10 ) is, 21, , 10, , (a) 2 21 - 211, (c) 2, , 20, , -2, , 10, , 10, , C2 ), , 88. The radius of a circle having minimum area,, which touches the curve y = 4 - x2 and the, lines y =| x |, is, , 21, , (d) 2, , 20, , 10, , -2, , 86. A box contains 15 green and 10 yellow balls., , 89. For a positive integer n, if the quadratic, equation, x( x + 1 ) + ( x + 1 ) ( x + 2 ) + . . ., + ( x + n - 1 ) ( x + n ) = 10 n, , If 10 balls are randomly drawn one-by-one, with replacement, then the variance of the, number of green balls drawn is, (a) 12/5, , (b) 6, , (c) 4, , has two consecutive integral solutions, then, n is equal to, , (d) 6/25, , (a) 12, (c) 10, , 87. Let a, b, c Î R. If f ( x ) = ax2 + bx + c be such, that a + b + c = 3 and, f ( x + y ) = f ( x ) + f ( y ) + xy, " x, y Î R, then, 10, , å f ( n ) is, , equal to, , (a) 330, , (b) 165, , n =1, , (c) 190, , (d) 255, , 90., , 3 p/ 4, , òp/4, , (b) 9, (d) 11, , dx, is equal to, 1 + cos x, , (a) - 2, (c) 4, , (b) 2, (d) - 1, , Answers, , Physics, 1. (b), 11. (c), 21. (c), , (b) 2 ( 2 - 1), (d) 4 ( 2 + 1), , (a) 2 ( 2 + 1), (c) 4 ( 2 - 1), , (b) 2 21 - 210, , 9, , 2. (a), 12. (d), 22. (b), , 3. (c), 13. (c), 23. (d), , 4. (b), 14. (a), 24. (d), , 5. (b), 15. (a), 25. (d), , 6. (d), 16. (b), 26. (c), , 7. (a), 17. (d), 27. (b), , 8. (a), 18. (d), 28. (a), , 9. (c), 19. (d), 29. (c), , 10. (b), 20. (d), 30. (d), , 33. (b), 43. (d), 53. (d), , 34. (d), 44. (a), 54. (d), , 35. (b), 45. (b), 55. (d), , 36. (a), 46. (a), 56. (a), , 37. (c), 47. (c), 57. (c), , 38. (a), 48. (a), 58. (b), , 39. (d), 49. (c), 59. (a), , 40. (a), 50. (b), 60. (a), , 63. (d), 73. (b), 83. (a), , 64. (b), 74. (c), 84. (a), , 65. (a), 75. (b), 85. (d), , 66. (d), 76. (b), 86. (a), , 67. (c), 77. (b), 87. (a), , 68. (d), 78. (b), 88. (c), , 69. (b), 79. (c), 89. (d), , 70. (a), 80. (b), 90. (b), , Chemistry, 31. (c), 41. (d), 51. (d), , 32. (c), 42. (d), 52. (b), , Mathematics, 61. (d), 71. (a), 81. (b), , 62. (a), 72. (c), 82. (b), , For solutions scan, the QR code
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] OFFLINE ], , SOLVED PAPER 2016, , JEE MAIN, Joint Entrance Examinaton, INSTRUCTIONS, , 1. This test consists of 90 questions., 2. Each question is allotted 4 marks for correct response., 3. Candidates will be awarded marks as stated above in instruction no. 2 for correct response of each question., 1 marks will be deducted for indicating incorrect response of each question. No deduction from the total, score will be made if no response is indicated for an item in the answer sheet., 4. There is only one correct response for each question. Filling up more than one response in any question will, be treated as wrong response and marks for wrong response will be deducted according as per instructions, , Physics, 1. A student measures the time period of 100, oscillations of a simple pendulum four times., The data set is 90s, 91s, 92s and 95s. If the, minimum division in the measuring clock is, 1s, then the reported mean time should be, (a) (92 ± 2 )s, (c) (92 ± 18, . )s, , (b) (92 ± 5 )s, (d) (92 ± 3)s, , 2. A particle of mass m is moving along the side, of a square of side a , with a uniform speed v, in the X-Y plane as shown in the figure., Y, , a, v, , D, a v, , v, a, , A, , C, v a, B, , R, 45º, O, , X, , Which of the following statements is false for, the angular momentum L about the origin?, (a) L = -, , mv $, R k , when the particle is moving from A, 2, , to B, R, (b) L = mv æç, + aö÷ k$ , when the particle is moving, è 2, ø, from B to C, , R, (c) L = mv æç, - aö÷ k$ , when the particle is moving, è 2, ø, from C to D, mv $, (d) L =, R k , when the particle is moving from, 2, D to A, , 3. A point particle of, , P, , mass m, moves, along the uniformly h=2m, rough track PQR as, R, 30º, shown in the figure., O, The coefficient of Horizontal, Q, friction, between surface, the particle and the, rough track equals m. The particle is released,, from rest , from the point P and it comes to, rest at a point R. The energies, lost by the ball,, over the parts, PQ and QR, of the track, are, equal to each other, and no energy is lost, when particle changes direction from PQ to, QR. The values of the coefficient of friction m, and the distance x( = QR), are respectively, close to, (a) 0.2 and 6.5 m, (b) 0.2 and 3.5 m, (c) 0.29 and 3.5 m, (d) 0.29 and 6.5 m
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22, , JEE MAIN Solved Paper 2016, , 4. A person trying to lose weight by burning fat, , 7. A pendulum clock loses 12 s a day if the, , lifts a mass of 10 kg upto a height of 1 m, 1000, times. Assume that the potential energy lost, each time he lowers the mass is dissipated., How much fat will he use up considering the, work done only when the weight is lifted up?, Fat supplies 3.8 ´ 107 J of energy per kg, which is converted to mechanical energy, with a 20% of efficiency rate. (Take,, g = 9. 8 ms -2 ), , temperature is 40°C and gains 4 s in a day if, the temperature is 20°C. The temperature at, which the clock will show correct time, and, the coefficient of linear expansion (a) of the, metal of the pendulum shaft are, respectively, , (a) 2.45 ´ 10-3 kg, , (a) 25°C, a = 1.85 ´ 10-5 /° C, (b) 60°C, a = 1.85 ´ 10-4 /° C, (c) 30°C, a = 1.85 ´ 10-3 /° C, (d) 55°C, a = 1.85 ´ 10-2 /° C, , (b) 6.45 ´ 10-3 kg, , 8. An ideal gas undergoes a quasistatic,, , (c) 9.89 ´ 10-3 kg, , reversible process in which its molar heat, capacity C remains constant. If during this, process the relation of pressure p and volume, V is given by pV n = constant, then n is given, by (Here C p and C V are molar specific heat at, constant pressure and constant volume,, respectively), , -3, , (d) 12.89 ´ 10, , kg, , 5. A roller is made by joining together two, corners at their vertices O. It is kept on two, rails AB and CD which are placed a, symmetrically (see the figure), with its axis, perpendicular to CD and its centre O at the, centre of line joining AB and CD (see the, figure). It is given a light path, so that it starts, rolling with its centre O moving parallel to, CD in the direction shown. As it moves, the, roller will tend to, B, , D, , (a) n =, (c) n =, , Cp, , (b) n =, , CV, Cp - C, , C - Cp, , C - CV, C - CV, (d) n =, C - Cp, , C - CV, , 9. n moles of an ideal gas undergoes a process A, and B as shown in the figure. The maximum, temperature of the gas during the process will, be, p, , O, , A, , 2 p0, , A, , p0, , C, , (a) turn left, (b) turn right, (c) go straight, (d) turn left and right alternately, , V0, , (a), , 6. A satellite is revolving in a circular orbit at a, height h from the Earth’s surface (radius of, Earth R, h < < R ). The minimum increase in, its orbital velocity required, so that the, satellite could escape from the Earth’s, gravitational field, is close to (Neglect the, effect of atmosphere), (a), (b), (c), (d), , 2gR, gR, gR /2, gR ( 2 - 1), , B, , 9 p0 V0, 4 nR, , (b), , 3 p0 V0, 2 nR, , 2V0, , (c), , 9 p0 V0, 2 nR, , V, , (d), , 9 p0 V0, nR, , 10. A particle performs simple harmonic motion, with amplitude A . Its speed is trebled at the, 2, instant that it is at a distance A from, 3, equilibrium position. The new amplitude of, the motion is, (a), , A, 3, , 41, , (c) A 3, , (b) 3A, (d), , 7, A, 3
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JEE MAIN Solved Paper 2016, , 23, , 11. A uniform string of length 20 m is suspended, , 14. The temperature dependence of resistances, , from a rigid support. A short wave pulse is, introduced at its lowest end. It starts moving, up the string. The time taken to reach the, support is (Take, g = 10 ms- 2 ), , of Cu and undoped Si in the temperature, range 300-400 K, is best described by, , (a) 2 p 2 s, (c) 2 2 s, , (b) 2 s, (d) 2 s, , 12. The region between two concentric spheres, of radii a and b, respectively (see the figure),, A, has volume charge density r = , where A is, r, a constant and r is the distance from the, centre. At the centre of the spheres is a point, charge Q. The value of A such that the electric, field in the region between the spheres will be, constant is, , (a) linear increase for Cu, linear increase for Si, (b) linear increase for Cu, exponential increase for Si, (c) linear increase for Cu, exponential decrease for Si, (d) linear decrease for Cu, linear decrease for Si, , 15. Two identical wires A and B, each of length l,, carry the same current I. Wire A is bent into a, circle of radius R and wire B is bent to form a, square of side a. If BA and BB are the values of, magnetic field at the centres of the circle and, B, square respectively, then the ratio A is, BB, (a), , p2, 8, , (b), , p2, 16 2, , (c), , p2, 16, , (d), , p2, 8 2, , 16. Hysteresis loops for two magnetic materials A, and B are as given below:, B, , a, , Q, , b, , (a), (c), , Q, , (b), , 2 pa2, 2Q, , (d), , B, , H, , H, , Q, 2 p( b 2 - a2 ), 2Q, , (A), , (B), , 13. A combination of capacitors is set-up as, , These materials are used to make magnets for, electric generators, transformer core and, electromagnet core. Then, it is proper to use, , shown in the figure. The magnitude of the, electric field, due to a point charge Q (having, a charge equal to the sum of the charges on, the 4 mF and 9 mF capacitors), at a point, distance 30 m from it, would equal to, , 17. An arc lamp requires a direct current of 10 A, , p( a2 - b 2 ), , 3 µF, , 4 µF, , 9 µF, , 2 µF, + –, 8V, , (a) 240 N/C, (b) 360 N/C, (c) 420 N/C, (d) 480 N/C, , pa2, , (a) A for electric generators and transformers, (b) A for electromagnets and Bfor electric generators, (c) A for transformers and B for electric generators, (d) B for electromagnets and transformers, , at 80 V to function. If it is connected to a, 220 V (rms), 50 Hz AC supply, the series, inductor needed for it to work is close to, (a) 80 H, (c) 0.044 H, , (b) 0.08 H, (d) 0.065 H, , 18. Arrange, , the following electromagnetic, radiations per quantum in the order of, increasing energy., A. Blue light, C. X-ray, (a) D, B, A, C, (c) C, A, B, D, , B. Yellow light, D. Radio wave, (b) A, B, D, C, (d) B, A, D, C
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24, , JEE MAIN Solved Paper 2016, , 19. An observer looks at a distance tree of height, 10 m with a telescope of magnifying power of, 20. To the observer the tree appears, (a) 10 times taller, (c) 20 times taller, , (b) 10 times nearer, (d) 20 times nearer, , 20. The box of a pin hole camera, of length L, has, a hole of radius a. It is assumed that when the, hole is illuminated by a parallel beam of light, of wavelength l the spread of the spot, (obtained on the opposite wall of the camera), is the sum of its geometrical spread and the, spread due to diffraction. The spot would, then have its minimum size (say b min ) when, (a) a =, , æ 2 l2 ö, l2, ÷÷, and bmin = çç, L, è L ø, , æ 2 l2 ö, ÷÷, lL and bmin = çç, è L ø, (c) a = lL and bmin = 4lL, l2, (d) a =, and bmin = 4lL, L, (b) a =, , 21. Radiation of wavelength l is incident on a, photocell. The fastest emitted electron has, 3l, ,, speed v. If the wavelength is changed to, 4, the speed of the fastest emitted electron will, be, 1/ 2, , 1/ 2, , 4, (b) < v æç ö÷, è 3ø, , 1/ 2, , 3, (d) = v æç ö÷, è 4ø, , 4, (a) > v æç ö÷, è 3ø, , 1/ 2, , 4, (c) = v æç ö÷, è 3ø, , B are 20 min and 40 min, respectively., Initially, the samples have equal number of, nuclei. After 80 min, the ratio of decayed, numbers of A and B nuclei will be, (b) 4 : 1, (d) 5 : 4, , 23. If a, b, c and d are inputs to a gate and x is its, output, then as per the following time graph,, the gate is, a., , b., , c., , d., , x., , (a) NOT, , (b) AND, , (c) OR, , (a) In amplitude modulation, the amplitude of the, high frequency carrier wave is made to vary in, proportion to the amplitude of the audio signal, (b) In amplitude modulation, the frequency of the, high frequency carrier wave is made to vary in, proportion to the amplitude of the audio signal, (c) In frequency modulation, the amplitude of the, high frequency carrier wave is made to vary in, proportion to the amplitude of the audio signal, (d) In frequency modulation, the amplitude of the, high frequency carrier wave is made to vary in, proportion to the frequency of the audio signal, , 25. A screw gauge with a pitch of 0.5 mm and a, circular scale with 50 divisions is used to, measure the thickness of a thin sheet of, aluminium. Before starting the measurement,, it is found that when the two jaws of the, screw gauge are brought in contact, the 45th, division coincides with the main scale line, and that the zero of the main scale is barely, visible. What is the thickness of the sheet, if, the main scale reading is 0.5 mm and the, 25th division coincides with the main scale, line?, (a) 0.75 mm, (c) 0.70 mm, , (d) NAND, , (b) 0.80 mm, (d) 0.50 mm, , 26. A pipe open at both ends has a fundamental, frequency f in air. The pipe is dipped, vertically in water, so that half of it is in, water. The fundamental frequency of the air, column is now, (a), , 22. Half-lives of two radioactive elements A and, , (a) 1 : 16, (c) 1 : 4, , 24. Choose the correct statement., , f, 2, , (b), , 3f, 4, , (c) 2f, , (d) f, , 27. A galvanometer having a coil resistance of, 100 W gives a full scale deflection when a, current of 1 mA is passed through it. The, value of the resistance which can convert this, galvanometer into ammeter giving a full scale, deflection for a current of 10 A, is, (a) 0.01 W, , (b) 2 W, , (c) 0.1 W, , (d) 3 W, , 28. In an experiment for determination of, refractive index of glass of a prism by i-d plot,, it was found that a ray incident at an angle, 35° suffers a deviation of 40° and that it, emerges at an angle 79°. In that case, which of, the following is closest to the maximum, possible value of the refractive index?, (a) 1.5, , (b) 1.6, , (c) 1.7, , (d) 1.8
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JEE MAIN Solved Paper 2016, 29. Identify the semiconductor devices whose, characteristics are as given below, in the, order (a),(b),(c),(d)., I, , I, , (a), , V, , (b), , V, , 25, , (a) Simple diode, Zener diode, Solar cell, Light, dependent resistance, (b) Zener diode, Simple diode, Light dependent, resistance, Solar cell, (c) Solar cell, Light dependent resistance, Zener, diode, Simple diode, (d) Zener diode, Solar cell, Simple diode, Light, dependent resistance, , 30. For a common emitter configuration, if a and, b have their usual meanings, the incorrect, relationship between a and b is, 1 1, = +1, a b, b, (b) a =, 1- b, b, (c) a =, 1+ b, , (a), I, , I, Dark, , (c), , Resistance, V, , (d), , V, Intensity, of light, , Illuminated, , (d) a =, , b2, 1+ b2, , Chemistry, 1. A stream of electrons from a heated filament, was passed between two charged plates kept, at a potential difference V esu. If e and m are, charge and mass of an electron, respectively,, then the value of h / l (where, l is wavelength, associated with electron wave) is given by, (a) 2 meV, (c) 2 mev, , (b) mev, (d) mev, , 2. 2-chloro-2-methylpentane on reaction with, sodium methoxide in methanol yields, CH3, ½, I. C 2 H5CH2 C ¾ OC H3, ½, CH3, II. C 2 H5CH2 C == CH2, ½, CH3, III. C 2 H5CH == C ¾ CH3, ½, CH3, (a) Both I and III, (c) Both I and II, , (b) Only III, (d) All of these, , 3. Which of the following compounds is, metallic and ferromagnetic?, (a) CrO 2, (b) VO 2, (c) MnO 2, (d) TiO 2, , 4. Which of the following statements about low, density polythene is false?, (a) It is a poor conductor of electricity, (b) Its synthesis required dioxygen or a peroxide, initiator as a catalyst, (c) It is used in the manufacture of buckets, dustbins, etc, (d) Its synthesis requires high pressure, , 5. For a linear plot of log ( x / m ) versus log p in, a Freundlich adsorption isotherm, which of, the following statements is correct? (k and n, are constants), (a) 1/n appears as the intercept, (b) Only 1/n appears as the slope, 1, (c) log æç ö÷ appears as the intercept, è nø, (d) Both k and 1/n appear in the slope term
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26, , JEE MAIN Solved Paper 2016, , 6. The heats of combustion of carbon and, , 13. The pair having the same magnetic moment, , carbon, monoxide, are, and, - 393.5, - 283.5 kJ mol-1, respectively. The heat of, formation (in kJ) of carbon monoxide per mole, is, , is, [at. no. Cr = 24, Mn = 25, Fe = 26 and Co = 27], , (a) 676.5, (c) -110.5, , (c) [CoCl 4 ]2- and [Fe(H2O)6 ]2+, , (b) -676.5, (d) 110.5, , (a) [Cr(H2O)6 ]2+ and [Fe(H2O)6 ]2+, (b) [Mn(H2O)6 ]2+ and [Cr(H2O)6 ]2+, (d) [Cr(H2O)6 ]2+ and [CoCl 4 ]2-, , 7. The hottest region of Bunsen flame shown in, the figure given below is, , CO2H, OH, Cl is, , H, 14. The absolute configuration of H, , Region 4, Region 3, Region 2, Region 1, , CH3, , (a) (2 S, 3 R), (c) (2 R, 3 R), , (b) (2 S, 3 S), (d) (2 R, 3 S), , 15. The equilibrium constant at 298 K for a, (a) region 2 (b) region 3 (c) region 4 (d) region 1, , 8. Which of the following is an anionic, detergent?, , (d) 7.6, , 10. The distillation technique most suited for, separating glycerol from spent lye in the soap, industry is, (a) fractional distillation, (b) steam distillation, (c) distillation under reduced pressure, (d) simple distillation, , (c) NO 2, , (d) 0.182, , (b) Galena, (d) Magnetite, , 17. At 300 K and 1 atm, 15 mL of a gaseous, hydrocarbon requires 375 mL air containing, 20% O2 by volume for complete combustion., After combustion, the gases occupy 330 mL., Assuming that the water formed is in liquid, form and the volumes were measured at the, same temperature and pressure, the formula, of the hydrocarbon is, (b) C 4H8, , (c) C 4H10, , (d) C 3H6, , 18. The pair in which phosphorus atoms have a, , of sp hybridisation is, (b) NO -3, , (a) Siderite, (c) Malachite, , (a) C3 H8, , 11. The species in which the N-atom is in a state, (a) NO -2, , (c) 1.182, , concentrated by froth floatation method?, , water. The vapour pressure of water (in torr), for this aqueous solution is, (c) 759.0, , (b) 1.818, , 16. Which one of the following ores is best, , 9. 18 g of glucose (C6H12O6 ) is added to 178.2 g, , (b) 752.4, , -, , (a) 0.818, , (a) Sodium lauryl sulphate, (b) Cetyltrimethyl ammonium bromide, (c) Glyceryl oleate, (d) Sodium stearate, , (a) 76.0, , reaction, A + B, C + D is 100. If the initial, concentrations of all the four species were, 1 M each, then equilibrium concentration of, D (in mol L-1) will be, , (d) NO +2, , 12. Decomposition of H2O2 follows a first order, reaction. In 50 min, the concentration of, H2O2 decreases from 0.5 to 0.125 M in one, such, decomposition., When, the, concentration of H2O2 reaches 0.05 M, the, rate of formation of O2 will be, (a) 6.93 ´ 10-4 mol min-1 (b) 2.66 L min-1 at STP, (c) 134, . ´ 10-2 mol min-1 (d) 6.93 ´ 10-2 mol min-1, , formal oxidation state of +3 is, (a) pyrophosphorous and hypophosphoric acids, (b) orthophosphorous and hypophosphoric acids, (c) pyrophosphorous and pyrophosphoric acids, (d) orthophosphorous and pyrophosphorous acids, , 19. Which one of the following complexes shows, optical isomerism?, (a) cis [Co(en)2 Cl 2 ]Cl, (b) trans [Co(en)2 Cl 2 ]Cl, (c) [Co(NH3 )4 Cl 2 ]Cl, (d) [Co(NH3 )3 Cl 3 ], (en = ethylenediamine)
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JEE MAIN Solved Paper 2016, 20. The reaction of zinc with dilute and, , 27, , 27. In the Hofmann-bromamide degradation, , concentrated nitric acid, respectively,, produce, , reaction, the number of moles of NaOH and, Br2 used per mole of amine produced are, , (a) NO 2 and NO, , (a) four moles of NaOH and two moles of Br2, (b) two moles of NaOH and two moles of Br2, (c) four moles of NaOH and one mole of Br2, (d) one mole of NaOH and one mole of Br2, , (b) NO and N2O, (c) NO 2 and N2O, (d) N2O and NO 2, , 21. Which one of the following statements about, water is false?, (a) Water can act both as an acid and as a base, (b) There is extensive intramolecular hydrogen, bonding in the condensed phase, (c) Ice formed by heavy water sinks in normal water, (d) Water is oxidised to oxygen during, photosynthesis, , 22. The concentration of fluoride, lead, nitrate, and iron in a water sample from an, underground lake was found to be 1000 ppb,, 40 ppb, 100 ppm and 0.2 ppm, respectively., This water is unsuitable for drinking due to, high concentration of, (a) lead, (b) nitrate, (c) iron, (d) fluoride, , 28. Two closed bulbs of equal volume (V), containing an ideal gas initially at pressure p i, and temperature T1 are connected through a, narrow tube of negligible volume as shown in, the figure below. The temperature of one of, the bulbs is then raised to T2 . The final, pressure p f is, T1, pi, V, , T1, , T2, pi, V, , T2, pf, V, , pf, V, , æ T ö, (a) 2 pi ç 1 ÷, è T1 + T2 ø, , æ T ö, (b) 2 pi ç 2 ÷, è T1 + T2 ø, , æ TT ö, (c) 2 pi ç 1 2 ÷, è T1 + T2 ø, , æ TT ö, (d) pi ç 1 2 ÷, è T1 + T2 ø, , 29. The, , 23. The main oxides formed on combustion of Li,, Na and K in excess of air respectively are, , reaction of propene with HOCl, proceeds, through, the, (Cl2 + H2O), intermediate, +, , (a) CH3 ¾ CH ¾ CH2 ¾ Cl, , (a) LiO 2 , Na 2O 2 and K 2O, (b) Li 2O 2 , Na 2O 2 and KO 2, (c) Li 2O, Na 2O 2 and KO 2, (d) Li 2O , Na 2O and KO 2, , +, , (b) CH3 ¾ CH(OH)¾ CH2, +, , (c) CH3 ¾ CHCl ¾ CH2, +, , 24. Thiol group is present in, , (d) CH3 ¾ CH ¾CH2 ¾ OH, , 30. The product of the reaction given below is, , (a) cystine, (b) cysteine, (c) methionine, (d) cytosine, , (i) NBS/hν, , X, , (ii) H2O/K2CO3, , 25. Galvanisation is applying a coating of, (a) Cr, (c) Zn, , (b) Cu, (d) Pb, , O, , OH, (b), , (a), , 26. Which of the following atoms has the highest, first ionisation energy?, (a) Na, (b) K, (c) Sc, (d) Rb, , CO2H, (c), , (d)
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Mathematics, æ1 ö, èxø, , 8. If the 2nd, 5th and 9th terms of a, , 1. If f ( x ) + 2 f ç ÷ = 3 x,, x ¹ 0 and S = {x Î R : f ( x ) = f ( - x )}; then S, (a) is an empty set, (b) contains exactly one element, (c) contains exactly two elements, (d) contains more than two elements, , 2. A value of q for which, p, 3, , 2 + 3 i sin q, is purely, 1 - 2 i sin q, , (b), , æ 3ö, (c) sin-1 ç ÷, è 4 ø, , p, 6, , 1, (d) sin-1 æç ö÷, è 3ø, , 3. The sum of all real values of x satisfying the, equation ( x2 - 5 x + 5 )x, (a) 3, (c) 6, , 2, , + 4 x - 60, , = 1 is, , (b) - 4, (d) 5, , é 5a, , - bù, and A adj A = AA T, then, 2 úû, 5a + b is equal to, , 4. If A = ê, ë3, (a) - 1, , (b) 5, , (c) 4, , (d) 13, , 5. The, , system, of, linear, equations, x + ly - z = 0; lx - y - z = 0; x + y - lz = 0, has a non-trivial solution for, , having five letters, formed using the letters of, the word SMALL and arranged as in a, dictionary, then the position of the word, SMALL is, (c) 52nd, , (d) 58th, , 7. If the number of terms in the expansion of, n, , 2, 4 ö, æ, ç1 - + 2 ÷ , x ¹ 0, is 28, then the sum of, è, x x ø, the coefficients of all the terms in this, expansion is, (a) 64, , (b) 2187, , (c) 243, , 4, 3, 7, (d), 4, (b), , 9. If the sum of the first ten terms of the series, 2, , 2, , 2, , 2, , æ 4ö, æ 1ö, æ 2ö, æ 3ö, 2, ç1 ÷ + ç2 ÷ + ç3 ÷ + 4 + ç4 ÷ + K, is, è 5ø, è 5ø, è 5ø, è 5ø, 16, m, then m is equal to, 5, (a) 102, , (b) 101, , (c) 100, , (d) 99, , 10. Let p = lim (1 + tan2 x )1/ 2 x , then log p is, x ®0+, , equal to, (a) 2, 1, (c), 2, , (b) 1, 1, (d), 4, , 11. For, , x Î R,, f ( x ) = |log 2 - sin x|, g ( x ) = f ( f ( x )), then, , and, , (a) g is not differentiable at x = 0, (b) g ¢(0) = cos (log 2 ), (c) g ¢(0) = - cos (log 2 ), (d) g is differentiable at x = 0 and, g ¢(0) = - sin (log 2 ), , 12. Considerf ( x ) = tan -1 ç, , 6. If all the words (with or without meaning), , (b) 59th, , 8, 5, , æ 1 + sin x ö, æ pö, ÷ , x Î ç 0, ÷ ., è 2ø, è 1 - sin x ø, , (a) infinitely many values of l, (b) exactly one value of l, (c) exactly two values of l, (d) exactly three values of l, , (a) 46th, , (a), , (c) 1, , imaginary, is, (a), , non-constant AP are in GP, then the, common ratio of this GP is, , (d) 729, , A normal to y = f ( x ) at x =, , p, also passes, 6, , through the point, (a) (0, 0), p, (c) æç , 0ö÷, è6 ø, , 2p ö, (b) æç 0,, ÷, è 3ø, p, (d) æç , 0ö÷, è4 ø, , 13. A wire of length 2 units is cut into two parts, which are bent respectively to form a square, of side = x units and a circle of radius = r, units. If the sum of the areas of the square and, the circle so formed is minimum, then, (a) 2 x = (p + 4)r, (c) x = 2 r, , (b) (4 - p )x = pr, (d) 2 x = r
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JEE MAIN Solved Paper 2016, 2 x 12 + 5 x9, , 14. The integral ò, (a), (c), , 5, , 3, , 2, , ( x + x + 1), x, , dx is equal to, , 3, , (x + x + 1), , - x5, 5, , 3, , +C, , (b), , x10, 5, , 2( x + x3 + 1)2, 10, , 5, , 2( x5 + x3 + 1)2, , +C, , +C, , (d), , - x, , 2( x5 + x3 + 1)2, , +C, , where, C is an arbitrary constant., 1/ n, , æ ( n + 1 )( n + 2 ) K 3 n ö, ÷, n ®¥ è, ø, n2 n, , 15. lim ç, (a), (c), , 18, , (b), , e4, 9, , is equal to, , e2, , 16. The area (in sq units) of the region, {( x, y ) : y2 ³ 2 x, y ³ 0} is, 4, 3, 4 2, (c) p 3, (a) p -, , and, , x2 + y2 £ 4 x,, , x ³ 0,, , 8, 3, p 2 2, (d) 2, 3, , (b) p -, , 17. If a curve y = f ( x ) passes through the point (1,, - 1) and satisfies the differential equation,, æ 1ö, y(1 + xy )dx = xdy, then f ç - ÷ is equal to, è 2ø, (a) (c), , 2, 5, , 2, 5, , (b) (d), , 4, 5, , 4, 5, , 18. Two sides of a rhombus are along the lines,, x - y + 1 = 0 and 7 x - y - 5 = 0. If its, diagonals intersect at (- 1, - 2), then which, one of the following is a vertex of this, rhombus?, (a) (- 3, - 9), , (b) (- 3, - 8), , 1, 8, (c) æç , - ö÷, è3, 3ø, , 10 7, (d) æç - , - ö÷, è 3, 3ø, , 19. The centres of those circles which touch the, circle, x2 + y2 - 8 x - 8 y - 4 = 0, externally, and also touch the X-axis, lie on, (a) a circle, (b) an ellipse which is not a circle, (c) a hyperbola, (d) a parabola, , 20. If one of the diameters of the circle, given by, , the equation, x2 + y2 - 4 x + 6 y - 12 = 0, is a, chord of a circle S, whose centre is at ( -3, 2 ),, then the radius of S is, (b) 5 3, (d) 10, , (a) 5 2, (c) 5, , 21. Let P be the point on the parabola, y2 = 8 x,, which is at a minimum distance from the, centre C of the circle, x2 + ( y + 6 )2 = 1. Then,, the equation of the circle, passing through C, and having its centre at P is, (a) x2 + y2 - 4 x + 8 y + 12 = 0, (b) x2 + y2 - x + 4 y - 12 = 0, x, (c) x2 + y2 - + 2 y - 24 = 0, 4, (d) x2 + y2 - 4 x + 9 y + 18 = 0, , 27, , (d) 3log 3 - 2, , e2, , 29, , 22. The eccentricity of the hyperbola whose, length of the latusrectum is equal to 8 and the, length of its conjugate axis is equal to half of, the distance between its foci, is, 4, 3, 2, (c), 3, , (b), , (a), , 4, 3, , (d) 3, , 23. The distance of the point (1, - 5, 9) from the, plane x - y + z = 5 measured along the line, x = y = z is, (a) 3 10, , (b) 10 3, , (c), , 10, 3, , (d), , 20, 3, , x -3 y +2 z+4, lies in the, =, =, 2, 3, -1, plane lx + my - z = 9, then l2 + m 2 is equal, to, , 24. If the line, , (a) 26, (c) 5, , (b) 18, (d) 2, , $ b$ and c$ be three unit vectors such that, 25. Let a,, 3 $, a$ ´ ( b$ ´ c$ ) =, ( b + c$ ). If b$ is not parallel to, 2, $ then the angle between a$ and b$ is, c,, (a), , 3p, 4, , (b), , p, 2, , (c), , 2p, 3, , (d), , 5p, 6, , 26. If the standard deviation of the numbers 2, 3,, a and 11 is 3.5, then which of the following is, true?, (a) 3a2 - 26a + 55 = 0, 2, , (c) 3a - 34a + 91 = 0, , (b) 3a2 - 32 a + 84 = 0, (d) 3a2 - 23a + 44 = 0
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30, , JEE MAIN Solved Paper 2016, , 27. Let two fair six-faced dice A and B be thrown, , 29. A man is walking towards a vertical pillar in a, , simultaneously. If E1 is the event that die A, shows up four, E2 is the event that die B, shows up two and E3 is the event that the sum, of numbers on both dice is odd, then which of, the following statements is not true?, , straight path, at a uniform speed. At a certain, point A on the path, he observes that the, angle of elevation of the top of the pillar is, 30°. After walking for 10 min from A in the, same direction, at a point B, he observes that, the angle of elevation of the top of the pillar is, 60°. Then, the time taken (in minutes) by, him, from B to reach the pillar, is, , (a) E1 and E2 are independent, (b) E2 and E3 are independent, (c) E1 and E3 are independent, (d) E1, E2 and E3 are independent, , (a) 6, (c) 20, , 28. If 0 £ x < 2 p, then the number of real, values of x, which satisfy the equation, cos x + cos 2 x + cos 3 x + cos 4 x = 0, is, (a) 3, (c) 7, , (b) 10, (d) 5, , 30. The Boolean expression, ( p Ù ~ q ) Ú q Ú (~ p Ù q ) is equivalent to, , (b) 5, (d) 9, , (a) ~ p Ù q, (c) p Ú q, , (b) p Ù q, (d) p Ú ~ q, , Answers, Physics, 1. (a), 11. (c), , 2. (b,d), 12. (a), , 3. (c), 13. (c), , 4. (d), 14. (c), , 5. (a), 15. (d), , 6. (d), 16. (d), , 7. (a), 17. (d), , 8. (b), 18. (a), , 9. (a), 19. (c), , 10. (d), 20. (c), , 21. (a), , 22. (d), , 23. (c), , 24. (b), , 25. (a), , 26. (d), , 27. (a), , 28. (a), , 29. (a), , 30. (a,c), , Chemistry, 1., , (c), , 11. (d), 21. (b), , 2., , (d), , 12. (a), 22. (b), , 3., , (a), , 4., , (c), , 5., , (b), , 6., , (c), , 7., , (a), , 8., , (a), , 9., , (b), , 10. (c), , 13. (a), 23. (c), , 14. (a), 24. (b), , 15. (b), 25. (c), , 16. (b), 26. (c), , 17. (*), 27. (c), , 18. (d), 28. (b), , 19. (a), 29. (a), , 20. (d), 30. (a), , Mathematics, 1. (c), 11. (b), , 2. (d), 12. (b), , 3. (a), 13. (c), , 4. (b), 14. (b), , 5. (d), 15. (b), , 6. (d), 16. (b), , 7. (d), 17. (d), , 8. (b), 18. (c), , 9. (b), 19. (d), , 10. (c), 20. (b), , 21. (a), , 22. (c), , 23. (b), , 24. (d), , 25. (d), , 26. (b), , 27. (d), , 28. (c), , 29. (d), , 30. (c), , For solutions scan, the QR code
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Solved Paper 2015, , JEE, Main, Joint Entrance Examination, Instructions, 1. This test consists of 90 questions., 2. There are three parts in the question paper A, B, C consisting of Physics, Chemistry & Mathematics having 30 questions in each, part of equal weightage. Each question is allotted 4 marks for correct response., 3. Candidates will be awarded marks as stated above in instruction no. 2 for correct response of each question. 1 marks will be, deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response, is indicated for an item in the answer sheet., 4. There is only one correct response for each question. Filling up more than one response in any question will be treated as, wrong response and marks for wrong response will be deducted according as per instructions., , Physics, 1. Two stones are thrown up simultaneously, from the edge of a cliff 240 m high with initial, speed of 10 m/s and 40 m/s respectively., Which of the following graph best represents, the time variation of relative position of the, second stone with respect to the first?, Assume stones do not rebound after hitting, the ground and neglect air resistance, take, g = 10 m /s 2 ), 240, , (y2 – y1)m, , 240, , 8, , 12, , t(s), , (y2 – y1)m, , (c), 8 12, 240, , L, . Measured value of L, g, is 20.0 cm known to 1 mm accuracy and time, for 100 oscillations of the pendulum is found, to be 90 s using a wrist watch of 1s resolution., The accuracy in the determination of g is, , pendulum is T = 2p, , (a) 2%, (c) 1%, , (b) 3%, (d) 5%, , 3. Given in the figure are two blocks A and B of, , (a), t, , 2. The period of oscillation of a simple, , weight 20 N and 100 N respectively. These, are being pressed against a wall by a force F as, shown in figure. If the coefficient of friction, between the blocks is 0.1 and between block, B and the wall is 0.15, the frictional force, applied by the wall in block B is, , t(s), , (y2 – y1)m, , F, , (b), , A, , B, , 20N 100N, , 240, , t(s), , 12, (y2 – y1)m, , (d), 8, , 12, , t(s), , (a) 100 N, (c) 120 N, , (b) 80 N, (d) 150 N
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32, , JEE MAIN Solved Paper 2015, , 4. A particle of mass m moving in the, , 8. A pendulum made of a uniform wire of, , x-direction with speed 2v is hit by another, particle of mass 2m moving in the y-direction, with speed v. If the collision is perfectly, inelastic, the percentage loss in the energy, during the collision is close to, , cross-sectional area A has time period T., When an additional mass M is added to its, bob, the time period changes TM . If the, Young’s modulus of the material of the wire, 1, is equal to (g = gravitational, is Y, then, Y, acceleration), , (a) 44%, (c) 56%, , (b) 50%, (d) 62%, , 5. Distance of the centre of mass of a solid, uniform cone from its vertex is z0 . If the, radius of its base is R and its height is h,, then z0 is equal to, h2, 4R, 5h, (c), 8, (a), , 3h, 4, 3h2, (d), 8R, (b), , 6. From a solid sphere of mass M and radius R, a, cube of maximum possible volume is cut., Moment of inertia of cube about an axis, passing through its centre and perpendicular, to one of its faces is, (a), , MR 2, 32 2p, , (b), , MR 2, 16 2p, , (c), , 4MR 2, 9 3p, , (d), , 4MR 2, 3 3p, , 7. From a solid sphere of mass M and radius R, a, æ Rö, spherical portion of radius ç ÷ is removed as, è2 ø, shown in the figure. Taking gravitational, potential V = 0 at r = ¥, the potential at the, centre of the cavity thus formed is, (G = gravitational constant), , - GM, 2R, - GM, (b), R, - 2GM, (c), 3R, - 2GM, (d), R, (a), , ù, é T 2, (a) ê æç M ö÷ - 1ú, ø, è, úû, êë T, ù, é æT ö 2, (b) ê ç M ÷ - 1ú, úû, êë è T ø, 2ù, é, T, (c) ê1 - æç M ö÷ ú, èT ø ú, êë, û, 2, é, æT ö ù, (d) ê1 - ç ÷ ú, ê, è TM ø ú, û, ë, , A, Mg, Mg, A, A, Mg, A, Mg, , 9. Consider a spherical shell of radius R at, temperature T. The black body radiation, inside it can be considered as an ideal gas of, photons with internal energy per unit volume, 1 æ Uö, U, µ T4 and pressure p = ç ÷. If the, u=, 3 èVø, V, shell now undergoes an adiabatic expansion,, the relation between T and R is, (a) T µ e - R, 1, (c) T µ, R, , (b) T µ e - 3 R, 1, (d) T µ 3, R, , 10. A solid body of constant heat capacity 1 J/°C, is being heated by keeping it in contact with, reservoirs in two ways, (i) Sequentially keeping in contact with, 2 reservoirs such that each reservoir, supplies same amount of heat., (ii) Sequentially keeping in contact with, 8 reservoirs such that each reservoir, supplies same amount of heat., In both the cases, body is brought from initial, temperature 100°C to final temperature, 200°C. Entropy change of the body in the two, cases respectively, is, (a) In2, 4In2, (b) In2, In2, (c) In2, 2In2, (d) 2In2, 8In2
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JEE MAIN Solved Paper 2015, , 33, , 11. Consider an ideal gas confined in an isolated, , 15. A uniformly charged solid sphere of radius R, , closed chamber. As the gas undergoes an, adiabatic expansion, the average time of, collision between molecules increases as V q ,, where V is the volume of the gas. The, Cp ö, æ, value of q is ç g =, ÷, CV ø, è, , has potential V0 (measured with respect to ¥), on its surface. For this sphere, the, equipotential, surfaces with potentials, 3 V0 5 V0 3 V0, V, and 0 have radius R1,, ,, ,, 2, 4, 4, 4, R2 , R3 , and R4 respectively. Then,, , (a), , 3g + 5, 6, , (b), , 3g - 5, 6, , (c), , g+1, 2, , (d), , g -1, 2, , 12. For a simple pendulum, a graph is plotted, between its Kinetic Energy (KE) and Potential, Energy (PE) against its displacement d., Which one of the following represents these, correctly? (graphs are schematic and not, drawn to scale), E, , E, , PE, , KE, , (a), , PE, , 16. In the given circuit, charge Q2 on the 2 mF, capacitor changes as C is varied from 1 mF to, 3mF. Q2 as a function of C is given properly by, (figures are drawn schematically and are not, to scale), , (b), KE, , d, E, , E, KE, , (c), , (a) R1 = 0 and R 2 > (R 4 - R 3 ), (b) R1 ¹ 0 and (R 2 - R 1) > (R 4 - R 3 ), (c) R1 = 0 and R 2 < (R 4 - R 3 ), (d) 2 R < R 4, , 1µ F, , d, C, , PE, , 2µ F, d, , KE, , (d), , PE, E, , 13. A train is moving on a straight track with, -1, , speed 20 ms . It is blowing its whistle at the, frequency of 1000 Hz. The percentage change, in the frequency heard by a person standing, near the track as the train passes him is close, to (speed of sound = 320 ms - 1), (a) 6%, , (b) 12%, , (c) 18%, , surface charge s in the upper half and, negative surface charge - s in the lower half., The electric field lines around the cylinder, will look like figure given in (figures are, schematic and not drawn to scale), +++++, +, –– ––, –– ––, , (b), , (a), , +++ ++, +, –– –, –, –– ––, , Q2, 1µF, , 3 µF, , (c), , (d), , ++++, +, –, –– –+, ––––, , C, , 1 µF, , Charge, , 3µF, , C, , 3 µF, , C, , Charge, , (c) Q2, , (d) Q2, 1µF, , 3 µF, , C, , 1µF, , 17. When 5V potential difference is applied, across a wire of length 0.1m, the drift speed of, electrons is 2.5 ´ 10 - 4 ms -1 . If the electron, density in the wire is 8 ´ 1028 m - 3 the, resistivity of the material is close to, (a) 1.6 ´ 10- 8 Wm, (b) 1.6 ´ 10- 7 Wm, , ++ +++, +, –– ––, –– ––, , Charge, , (b), , Q2, , (d) 24%, , 14. A long cylindrical shell carries positive, , (a), , Charge, , (c) 1.6 ´ 10- 6 Wm, (d) 1.6 ´ 10- 5 Wm
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34, , JEE MAIN Solved Paper 2015, , 18. In the circuit shown below, the current in the, 1W resistor is, 6V, , 21. A rectangular loop of sides 10 cm and 5 cm, carrying a current I of 12 A is placed in, different orientations as shown in the figures, below., , P 2Ω, , z, B, , 9V, , I, , (a), , I, , x, , (a) 1.3 A, from P to Q, (b) 0 A, (c) 0.13 A, from Q to P, (d) 0.13 A, from P to Q, , z, , I, , (c), , B, , y (b), , I, , Q 3Ω, , 3Ω, , z, , I, , 1Ω, , x, , I B, I, , current I in the same direction. Let F1 be the, magnetic force on the inner solenoid due to, the outer one and F2 be the magnetic force on, the outer solenoid due to the inner one. Then,, (a) F1 = F2 = 0, (b) F1 is radially inwards and F2 is radially outwards, (c) F1 is radially inwards and F2 = 0, (d) F1 is radially outwards and F2 = 0, , 20. Two long current carrying thin wires, both, with current I, are held by insulating threads, of length L and are in equilibrium as shown, in the figure, with threads making an angle q, with the vertical. If wires have mass l per, unit length then, the value of I is (g =, gravitational acceleration), , I, , y, , z, , I, , I, , x, x, , 19. Two coaxial solenoids of different radii carry, , I, , B, , y (d), , I, , I, , I, , I, , y, I, , If there is a uniform magnetic field of 0.3 T in, the positive z-direction in which orientations, the loop would be in (i) stable equilibrium, and (ii) unstable equilibrium?, (a) (a) and (b) respectively, (b) (a) and (c) respectively, (c) (b) and (d) respectively, (d) (b) and (c) respectively, , 22. An inductor ( L = 0.03 H) and a resistor, ( R = 0.15 kW) are connected in series to a, battery of 15V EMF in a circuit shown below., The key K 1 has been kept closed for a long, time. Then at t = 0, K1 is opened and key K2 is, closed simultaneously. At t = 1 ms, the, current in the circuit will be (e 5 ~, = 150 ), 0.03H, , 0.15 kΩ, , K2, , L, θ, , K1, 15V, , I, , (a) sin q, , plgL, m 0 cos q, , plgL, (b) 2 sin q, m 0 cos q, (c) 2, (d), , pgL, tan q, m0, plgL, tan q, m0, , I, , (a) 100 mA, (b) 67 mA, (c) 6.7 mA, (d) 0.67mA, , 23. A red LED emits light at 0.1 W uniformly, around it. The amplitude of the electric field, of the light at a distance of 1 m from the diode, is, (a) 1.73 V/m, (b) 2.45 V/m, (c) 5.48 V/m, (d) 7.75 V/m
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35, , JEE MAIN Solved Paper 2015, 24. Monochromatic light is incident on a glass, , 28. Match List-I (fundamental experiment) with, , prism of angle A. If the refractive index of the, material of the prism is m, a ray incident at an, angle q, on the face AB would get transmitted, through the face AC of the prism provided, , List-II (its conclusion) and select the correct, option from the choices given below the list., , A, θ, , B, , C, , é, æ, æ 1 ööù, (a) q > sin- 1 êm sinç A - sin- 1 ç ÷ ÷ ú, è m ø ø úû, è, êë, é, æ, æ 1 ööù, (b) q < sin- 1 êm sinç A - sin- 1 ç ÷ ÷ ú, è m ø ø úû, è, êë, é, æ, æ 1 ööù, (c) q > cos - 1 êm sinç A + sin- 1 ç ÷ ÷ ú, è m ø ø úû, è, êë, é, æ, æ 1 ööù, (d) q < cos - 1 êm sinç A + sin- 1 ç ÷ ÷ ú, è m ø ø úû, è, êë, , 25. On a hot summer night, the refractive index, of air is smallest near the ground and, increases with height from the ground. When, a light beam is directed horizontally, the, Huygens principle leads us to conclude that, as it travels, the light beam, , List I, , List II, , A. Franck-Hertz, 1. Particle nature of light, experiment, B. Photo-electric, 2. Discrete energy levels of, experiment, atom, C. Davisson-Germer 3. Wave nature of electron, experiment, 4. Structure of atom, A, (a) 1, (c) 2, , B, 4, 1, , C, 3, 3, , A, (b) 2, (d) 4, , modulated on a carrier wave of frequency, 2MHz. The frequencies of the resultant signal, is/are, (a) 2 MHz only, (b) 2005 kHz and 1995 kHz, (c) 2005 kHz 2000 kHz and 1995 kHz, (d) 2000 kHz and 1995 kHz, , 30. An LCR circuit is equivalent to a damped, pendulum. In an LCR circuit, the capacitor is, charged to Q0 and then connected to the L, and R as shown below., R, , L, , 26. Assuming human pupil to have a radius of, , (a) 1 mm, , (b) 30 mm, , (c) 100 mm (d) 300 mm, , 27. As an electron makes a transition from an, excited state to the ground state of a hydrogen, like atom/ion, (a) its kinetic energy increases but potential energy, and total energy decrease, (b) kinetic energy, potential energy and total energy, decrease, (c) kinetic energy decreases, potential energy, increases but total energy remains same, (d) kinetic energy and total energy decrease but, potential energy increases, , C, 3, 2, , 29. A signal of 5 kHz frequency is amplitude, , (a) becomes narrower, (b) goes horizontally without any deflection, (c) bends downwards, (d) bends upwards, , 0.25 cm and a comfortable viewing distance, of 25 cm, the minimum separation between, two objects that human eye can resolve at 500, nm wavelength is, , B, 4, 3, , C, , If a student plots graphs of the square of, maximum charge (Q2Max ) on the capacitor, with time (t) for two different values L 1 and, L 2 ( L 1 > L 2 ) of L, then which of the following, represents this graph correctly? (plots are, schematic and not drawn to scale), L1, , 2, , (a)QMax, , L2, , Q2, , (c), , t, L1, , Max, , L2, , 2, , (b)QMax, , Q2, , (d), , L2, t, , Max, , L1, , t, , Q0(For both L1and L2), t
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Chemistry, 1. The molecular formula of a commercial resin, , 7. The standard Gibbs energy change at 300K, , used for exchanging ions in water softening is, C 8 H7SO3 Na (mol. wt. = 206). What would be, the maximum uptake of Ca2 + ions by the, resin when expressed in mole per gram resin?, , for the reaction, 2A, B + C is 2494. 2 J. At, a given time, the composition of the reaction, 1, mixture is [ A ] = , [ B] = 2, 2, 1, and [C ] = . The reaction proceeds in the, 2, [ R = 8.314 JK / mol, e = 2.718 ], , 1, 103, 2, (c), 309, , 1, 206, 1, (d), 412, , (b), , (a), , 2. Sodium metal crystallises in a body centred, cubic lattice with a unit cell edge of 4.29 Å., The radius of sodium atom is approximately, (a) 1.86 Å, , (b) 3.22 Å, , (c) 5.72 Å, , (d) 0.93 Å, , 3. Which of the following is the energy of a, possible excited state of hydrogen?, (a) + 13.6 eV, (b) - 6.8 eV, (c) - 3.4 eV, (d) + 6.8 eV, , (a) forward direction because Q > Kc, (b) reverse direction because Q > Kc, (c) forward direction because Q < Kc, (d) reverse direction because Q < Kc, , 8. Two Faraday of electricity is passed through, a solution of CuSO4 . The mass of copper, deposited at the cathode is, (at. mass of Cu = 63.5 u), (a) 0g, , (b) 63.5g, , intermolecular interaction that is, dependent on the inverse cube of distance, between the molecules is, (b) ion-dipole interaction, (d) hydrogen bond, , 5. The following reaction is performed at 298K, 2NO(g ) + O2 (g ), , # 2NO (g ), 2, , The standard free energy of formation of NO, (g) is 86.6 kJ/mol at 298 K. What is the, standard free energy of formation of NO2 (g ), at 298 K? ( K p = 1.6 ´ 10 12 ), (a) R(298) ln (1.6 ´ 1012 ) - 86600, 12, , (d) 127g, , (a) low probability of simultaneous collision of all the, reacting species, (b) increase in entropy and activation energy as, more molecules are involved, (c) shifting of equilibrium towards reactants due to, elastic collisions, (d) loss of active species on collision, , 10. 3 g of activated charcoal was added to 50 mL, of acetic acid solution (0.06 N) in a flask., After an hour it was filtered and the strength, of the filtrate was found to be 0.042 N. The, amount of acetic acid adsorbed (per gram of, charcoal) is, (a) 18 mg, , (b) 36 mg, , respectively are, (a) 1.36, 1.40 and 1.71, (c) 1.71, 1.40 and 1.36, , 6. The vapour pressure of acetone at 20°C is, 185 torr. When 1.2 g of a non-volatile, substance was dissolved in 100 g of acetone at, 20°C, its vapour pressure was 183 torr. The, molar mass ( g mol –1 ) of the substance is, (b) 64, (d) 488, , (d) 54 mg, , 11. The ionic radii (in Å) of N , O2 – and F -, , In (1.6 ´ 1012 ), (c) 86600 R(298), (d) 0.5 [2 ´ 86600 - R(298) In (1.6 ´ 1012 )], , (c) 42 mg, 3-, , (b) 86600+ R(298) In (1.6 ´ 10 ), , (a) 32, (c) 128, , (c) 2g, , 9. Higher order (>3) reactions are rare due to, , 4. The, , (a) ion-ion interaction, (c) London force, , #, , (b) 1.36, 1.71 and 1.40, (d) 1.71, 1.36 and 1.40, , 12. In the context of the Hall-Heroult process for, the extraction of Al, which of the following, statements is false?, (a) CO and CO 2 are produced in this process, (b) Al 2O 3 is mixed with CaF2 which lowers the, melting point of the mixture and brings, conductivity, (c) Al 3+ is reduced at the cathode to form Al, (d) Na 3 AIF6 serves as the electrolyte
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JEE MAIN Solved Paper 2015, 13. From the following statements regarding, H2O2 , choose the incorrect statement., (a) It can act only as an oxidising agent, (b) It decomposed on exposure to light, (c) It has to be stored in plastic or wax lined glass, bottles in dark, (d) It has to be kept away from dust, , 14. Which one of the following alkaline earth, metal sulphates has its hydration enthalpy, greater than its lattice enthalpy?, (a) CaSO 4, (c) BaSO 4, , (b) BeSO 4, (d) SrSO 4, , 15. Which among the following is the most, reactive?, (a) Cl 2, (c) I 2, , (b) Br2, (d) ICl, , 16. Match the catalysts to the correct processes., Catalyst, , Process, , (A) TiCl 3, , (i), , Wacker process, , (B) PdCl 2, , (ii) Ziegler- Natta, polymerisation, , (C) CuCl 2, , (iii) Contact process, , (D) V2O 5, , (iv) Deacon's process, , (a) (A)- (iii), (B) - (ii), (C) - (iv), (D) - (i), (b) (A)- (ii), (B) - (i), (C) - (iv), (D) - (iii), (c) (A)- (ii), (B) - (iii), (C) - (iv), (D) - (i), (d) (A)- (iii), (B) - (i), (C) - (ii), (D) - (iv), , 20. Assertion (A) Nitrogen and oxygen are the, main components in the atmosphere but, these do not react to form oxides of nitrogen., Reason (R) The reaction between nitrogen, and oxygen requires high temperature., (a) Both Assertion and Reason are correct and the, reason is the correct explanation for the, Assertion., (b) Both Assertion and Reason are correct but the, reason is not the correct explanation for the, Assertion., (c) The Assertion is incorrect but the Reason is, correct., (d) Both the Assertion and Reason are incorrect., , 21. In Carius method of estimation of halogens,, 250 mg of an organic compound gave 141 mg, of AgBr. The percentage of bromine in the, compound is, (at. mass Ag = 108, Br = 80), (a) 24, , (b) 36, , (c) 48, , exhibit geometrical isomerism?, (a) 1-phenyl-2-butene, (b) 3-phenyl-1-butene, (c) 2-phenyl-1-butene, (d) 1, 1-diphenyl-1-propane, , 23. Which, , compound, would, give, 5-keto-2-methyl hexanal upon ozonolysis?, CH3, , CH3, CH3, , (a), , (b), CH3, CH3, , CH3, , 18. The number of geometric isomers that can, exist for square planar [Pt (Cl) (py) (NH3 ), (NH2OH)]+ is (py = pyridine), (a) 2, (c) 4, , (d) 60, , 22. Which of the following compound will, , 17. Which one has the highest boiling point?, (a) He, (b) Ne, (c) Kr, (d) Xe, , 37, , (b) 3, (d) 6, , 19. The colour of KMnO4 is due to, (a) M ® L charge transfer transition, (b) d - d transition, (c) L ® M charge transfer transition, * transition, (d) s - s, , (c), , (d), , H3C, , CH3, , 24. The synthesis of alkyl fluorides is best, accomplished by, (a) free radical fluorination, (b) Sandmeyer’s reaction, (c) Finkelstein reaction, (d) Swarts reaction
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38, , JEE MAIN Solved Paper 2015, , 25. In the following sequence of reaction,, KMnO, , SOCl, , 27. Which polymer is used in the manufacture of, paints and lacquers?, , H / Pd, , 4, 2, 2, Toluene ¾¾®, A ¾¾®, B ¾¾®, C, BaSO, , (a) Bakelite, (b) Glyptal, (c) Polypropene, (d) Polyvinyl chloride, , 4, , The product C is, (b) C 6H5CH3, (d) C 6H5CHO, , (a) C 6H5 COOH, (c) C 6H5CH2OH, , 28. Which of the vitamins given below is water, , 26. In the reaction,, , soluble?, , NH2, NaNO2 / HCl, 0.5°C, , D, , CuCN / KCN, ∇, , (a) Vitamin C, (b) Vitamin D, (c) Vitamin E, (d) Vitamin K, , E + N2, , CH3, The product E is, , 29. Which of the following compounds is not an, antacid?, , COOH, (a), , (b) H3C, , CH3, , 30. Which of the following compounds is not, , CH3, , coloured yellow?, , CH3, , CN, (c), , (a) Aluminium hydroxide, (b) Cimetidine, (c) Phenelzine, (d) Ranitidine, , (a) Zn2 [Fe(CN)6 ], (b) K 3 [Co(NO 2 )6 ], (c) (NH4 )3 [As(Mo 3O10 )4 ], (d) BaCrO 4, , (d), , CH3, , Mathematics, 1. Let A and B be two sets containing four and, , 3. Let a and b be the roots of equation, , two elements respectively. Then, the number, of subsets of the set A ´ B, each having atleast, three elements are, , x2 - 6 x - 2 = 0. If a n = a n - b n , for n ³ 1,, a - 2 a8, is equal to, then the value of 10, 2 a9, , (a) 219, , (b) 256, , (c) 275, , (d) 510, , 2. A complex number z is said to be, unimodular, if| z| = 1. Suppose z 1 and z2 are, z - 2 z2, complex numbers such that 1, is, 2 - z 1z2, unimodular and z2 is not unimodular. Then,, the point z 1 lies on a, (a) straight line parallel to X-axis., (b) straight line parallel to Y-axis., (c) circle of radius 2., (d) circle of radius 2., , (a) 6, (c) 3, , (b) -6, (d) -3, , é1 2, , 2 ù, , 4. If A = ê2 1 -2 ú is a matrix satisfying the, , ê, ú, êëa 2 b úû, equation AA T = 9 I, where I is 3 ´ 3 identity, matrix, then the ordered pair (a, b ) is equal to, (a) (2, - 1), (c) (2, 1), , (b) (-2, 1), (d) (-2, - 1)
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JEE MAIN Solved Paper 2015, 5. The set of all values of l for which the system, of linear equations 2 x 1 - 2 x2 + x3 = lx 1,, 2 x 1 - 3 x2 + 2 x3 = lx2 and - x + 2 x = lx, 1, 2, 3, has a non-trivial solution,, (a) is an empty set, (b) is a singleton set, (c) contains two elements, (d) contains more than two elements, , 39, , 12. The normal to the curve x2 + 2 xy - 3 y2 = 0 at, (1, 1 ), (a) does not meet the curve again, (b) meets the curve again in the second quadrant, (c) meets the curve again in the third quadrant, (d) meets the curve again in the fourth quadrant, , 13. Let f ( x ) be a polynomial of degree four having, , can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is, , extreme values at x = 1 and x = 2. If, f(x)ù, é, lim ê1 + 2 ú = 3, then f(2 ) is equal to, x ®0 ë, x û, , (a) 216, (c) 120, , (a) -8, (c) 0, , 6. The number of integers greater than 6000 that, , (b) 192, (d) 72, , 7. The sum of coefficients of integral powers of, 50, , x in the binomial expansion of (1 - 2 x ), 1, (a) (350 + 1), 2, 1, (c) (350 - 1), 2, , is, , 1, (b) (350 ), 2, 1, (d) (2 50 + 1), 2, , 8. If m is the AM of two distinct real numbers l, and n( l, n > 1 ) and G 1, G 2 and G 3 are three, geometric means between l and n , then, G 41 + 2G 42 + G 43 equals, 2, , (a) 4 l mn, 2, , (c) 4 lmn, , 2, , (b) 4 lm n, (d) 4 l 2 m2 n2, , 9. The sum of first 9 terms of the series, 13 13 + 23, 13 + 23 + 33, + . . . is, +, +, 1, 1 +3, 1 +3 +5, (a) 71, (c) 142, , 10. lim, x ®0, , (b) 96, (d) 192, , (1 - cos 2 x )(3 + cos x ), is equal to, x tan 4 x, , (a) 4, (c) 2, , (b) 3, 1, (d), 2, , ìk x + 1 , 0 £ x £ 3, 11. If the function g ( x ) = í, î mx + 2 , 3 < x £ 5, is differentiable, then the value of k + m is, (a) 2, (c), , 10, 3, , (b), , 16, 5, , (d) 4, , (b) -4, (d) 4, , dx, , 14. The integral ò, , 2, , 4, , x (x +, 1, 1ö 4, , (c) -( x +, , 1, 1)4, , equals, , 1, , æ x4 +, (a) çç 4 ÷÷ + c, è x ø, 4, , 3, 1 )4, , (b) ( x4 + 1)4 + c, 1, , æ x4 +, (d) - çç 4, è x, , +c, , 15. The integral ò, , log x2, , 4, , 2, , 1ö 4, ÷÷ + c, ø, , 2, , log x + log(36 - 12 x + x2 ), , dx, , is equal to, (a) 2, (c) 1, , (b) 4, (d) 6, , 16. The area (in sq units) of the region described, by {( x, y ) : y2 £ 2 x and y ³ 4 x - 1} is, (a), , 7, 32, , (b), , 5, 64, , (c), , 15, 64, , (d), , 9, 32, , 17. Let y( x ) be the solution of the differential, dy, + y = 2 x log x, ( x ³ 1 )., dx, Then, y(e ) is equal to, , equation ( x log x ), (a) e, (c) 2, , (b) 0, (d) 2e, , 18. The, , number of points having both, coordinates as integers that lie in the interior, of the triangle with vertices (0, 0), (0, 41) and, (41, 0) is, (a) 901, (c) 820, , (b) 861, (d) 780
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40, , JEE MAIN Solved Paper 2015, , 19. Locus of the image of the point (2, 3) in the, , 25. Let a, b and c be three non-zero vectors such, , line (2 x - 3 y + 4 ) + k ( x - 2 y + 3 ) = 0, k Î R,, is a, , that no two of them are collinear and, 1, (a ´ b ) ´ c = | b||c|a. If q is the angle, 3, between vectors b and c, then a value of sin q, is, , (a) straight line parallel to X-axis., (b) straight line parallel to Y-axis., (c) circle of radius 2., (d) circle of radius 3., , 20. The number of common tangents to the, circles, x2 + y2 -4 x - 6 y -12 = 0, 2, 2, x + y + 6 x +18 y + 26 = 0 is, (a) 1, (c) 3, , and, , (b) 2, (d) 4, , 21. The area (in sq units) of the quadrilateral, formed by the tangents at the end points of, 2, x2 y, the latera recta to the ellipse, +, = 1 is, 9, 5, 27, 4, 27, (c), 2, (a), , (b) 18, (d) 27, , 22. Let O be the vertex and Q be any point on the, parabola x2 = 8 y. If the point P divides the, line segment OQ internally in the ratio 1 : 3,, then the locus of P is, 2, , (a) x = y, (b) y2 = x, (c) y2 = 2 x, , 23. The distance of the point (1, 0, 2) from the, point, of intersection of the line, x -2 y +1 z-2, and, the, plane, =, =, 3, 4, 12, x - y + z = 16 is, (b) 8, (d) 13, , 24. The equation of the plane containing the line, 2 x - 5 y + z = 3, x + y + 4 z = 5 and parallel to, the plane x + 3 y + 6 z = 1 is, (a) 2 x + 6 y + 12 z = 13, (b) x + 3 y + 6 z = - 7, (c) x + 3 y + 6 z = 7, (d) 2 x + 6 y + 12 z = - 13, , - 2, 3, -2 3, (d), 3, , (b), , 26. If 12 identical balls are to be placed in 3, identical boxes, then the probability that one, of the boxes contains exactly 3 balls, is, 11, , (a), , 55 æ 2 ö, ç ÷, 3 è 3ø, , 10, , 2, (b) 55æç ö÷, è 3ø, , 12, , 1, (c) 220æç ö÷, è 3ø, , 11, , 1, (d) 22 æç ö÷, è 3ø, , 27. The mean of the data set comprising of 16, observations is 16. If one of the observation, valued 16 is deleted and three new, observations valued 3, 4 and 5 are added to, the data, then the mean of the resultant data, is, (a) 16.8, , (b) 16.0, , (c) 15.8, , (d) 14.0, , 28. If the angles of elevation of the top of a tower, from three collinear points A, B and C on a, line leading to the foot of the tower are 30°,, 45° and 60° respectively, then the ratio, AB : BC is, (a) 3 : 1, (c) 1 : 3, , (d) x2 = 2 y, , (a) 2 14, (c) 3 21, , 2 2, 3, 2, (c), 3, (a), , (b) 3 : 2, (d) 2 : 3, , æ 2x ö, ÷, where, è 1 - x2 ø, , 29. Let tan -1 y = tan -1 x + tan -1 ç, | x| <, (a), (c), , 1, 3, , . Then, a value of y is, , 3 x - x3, 1 - 3x, , 2, , 3x - x, 1 + 3x, , (b), , 3 x + x3, , (d), , 3 x + x3, , 3, , 2, , 1 - 3 x2, 1 + 3 x2, , 30. The negation of ~ s Ú (~ r Ù s ) is equivalent to, (a) s Ù ~ r, (b) s Ù (r Ù ~ s ), (c) s Ú (r Ú ~ s ), (d) s Ù r
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Answers, Physics, 1. (c), 11. (c), , 2. (b), 12. (b), , 3. (c), 13. (b), , 4. (c), 14. (a), , 5. (b), 15. (c,d), , 6. (c), 16. (b), , 7. (b), 17. (d), , 8. (a), 18. (c), , 9. (c), 19. (a), , 10. (b), 20. (b), , 21. (c), , 22. (d), , 23. (b), , 24. (a), , 25. (d), , 26. (b), , 27. (a), , 28. (c), , 29. (c), , 30. (a), , Chemistry, 1. (d), 11. (c), , 2. (a), 12. (d), , 3. (c), 13. (a), , 4. (b), 14. (b), , 5. (d), 15. (d), , 6. (b), 16. (b), , 7. (b), 17. (d), , 8. (b), 18. (b), , 9. (a), 19. (c), , 10. (a), 20. (a), , 21. (a), , 22. (a), , 23. (b), , 24. (d), , 25. (d), , 26. (c), , 27. (b), , 28. (a), , 29. (c), , 30. (a), , Mathematics, 1. (a), 11. (a), , 2. (c), 12. (d), , 3. (c), 13. (c), , 4. (d), 14. (d), , 5. (c), 15. (c), , 6. (b), 16. (d), , 7. (a), 17. (c), , 8. (b), 18. (d), , 9. (b), 19. (c), , 10. (c), 20. (c), , 21. (d), , 22. (d), , 23. (d), , 24. (c), , 25. (a), , 26. (a), , 27. (d), , 28. (a), , 29. (a), , 30. (d), , For solutions scan, the QR code
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Solved Paper 2014, , JEE Main, Joint Entrance Examination, Time : 3 hrs, , MM : 360, , Instructions, 1., , This test consists of 90 questions., , 2., , There are three parts in the question paper A,B,C consisting of Physics, Chemistry and Mathematics, having 30 questions in each part of equal weightage. Each question is allotted 4 marks for correct, response., , 3., , Candidates will be awarded marks as stated above in instruction 2 for correct response of each, question. 1/4 mark will be deducted for indicating incorrect response for an item in the answer sheet., , 4., , There is only one correct response for each question. Filling up more than one response in any, question will be treated as wrong response and marks for wrong response will be deducted, accordingly as per instructions., , Physics, 1. The current voltage relation of diode is, , 3. A mass m supported by a, , given by I = ( e, − 1) mA, where the, applied voltage V is in volt and the, temperature T is in kelvin. If a student, makes an error measuring ± 0.01 V while, measuring the current of 5 mA at 300K,, what will be the error in the value of, current in mA?, , massless string wound, around a uniform hollow m, cylinder of mass m and, radius R. If the string does, not slip on the cylinder,, with what acceleration will, the mass fall on release?, , (a) 0.2 mA, (c) 0.5 mA, , (a), , 1000 V / T, , (b) 0.02 mA, (d) 0.05 mA, , 2. From a tower of height H, a particle is, thrown vertically upwards with a speed u., The time taken by the particle to hit the, ground, is n times that taken by it to reach, the highest point of its path. The relation, between H, u and n is, (a) 2 gH = n2u 2, , (b) gH = (n − 2 )2 u 2, , (c) 2 gH = nu (n − 2 ), , (d) gH = (n − 2 )2 u 2, , 2, , 2g, 3, , (b), , g, 2, , (c), , 5g, 6, , R, , m, , (d) g, , 4. A block of mass m is placed on a surface, with a vertical cross-section given by, y = x 3 / 6. If the coefficient of friction is 0.5,, the maximum height above the ground at, which the block can be placed without, slipping is, (a), , 1, m, 6, , (b), , 2, m, 3, , (c), , 1, m, 3, , (d), , 1, m, 2
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JEE MAIN Solved Paper 2014, 5. When a rubber band is stretched by a, distance x, it exerts a restoring force of, magnitude F = a x + bx 2 , where a and b, are constants. The work done in stretching, the unstretched rubber-band by L is, (a) a L2 + bL3, (c), , aL2, bL3, +, 2, 3, , 1 2, (aL + bL3 ), 2, 2, 1 aL, bL3 , (d) , +, , 2 2, 3 , (b), , 6. A bob of mass m attached to an, inextensible string of length l is suspended, from a vertical support. The bob rotates in, a horizontal circle with an angular speed ω, rad/s about the vertical support. About the, point of suspension, (a) angular momentum is conserved, (b) angular momentum changes in magnitude but, not in direction, (c) angular momentum changes in direction but not, in magnitude, (d) angular momentum changes both in direction, and magnitude, , 7. Four particles, each of mass M and, equidistant from each other, move along a, circle of radius R under the action of their, mutual gravitational attraction, the speed, of each particle is, (a), , GM, R, , (b), , 2 2, , (c), , GM, (1 + 2 2 ), R, , (d), , 1 GM, (1 + 2 2 ), 2 R, , 9. There is a circular tube, in a vertical plane. Two, liquids which do not, mix and of densities d1, α, d2, and d2 are filled in the, tube., Each, liquid, d1, subtends 90° angle at, centre. Radius joining their interface, makes an angle α with vertical. Ratio d1 / d2, is, 1 + sinα, 1 − sinα, 1 + tanα, (c), 1 − tanα, (a), , 1 + cos α, 1 − cos α, 1 + sinα, (d), 1 − cos α, (b), , 10. On heating water, bubbles beings formed, at the bottom of the vessel detach and rise., Take the bubbles to be, spheres of radius R and, making a circular contact of, radius r with the bottom of the, R, vessel. If r <<R and the, 2r, surface tension of water is T,, value of r just before bubbles detach is, (density of water is ρ), (a) R 2, , ρw g, 3T, , (b) R 2, , ρw g, 6T, , (c) R 2, , ρw g, T, , (d) R 2, , 3ρw g, T, , 11. Three rods of copper, brass and steel are, , GM, R, , 8. The pressure that has to be applied to the, ends of a steel wire of length 10 cm to keep, its length constant when its temperature is, raised by 100°C is (For steel, Young’s, modulus is 2 × 1011Nm −2 and coefficient of, thermal expansion is 1.1 × 10 −5 K −1), (a) 2.2 × 108 Pa, (c) 2.2 × 107 Pa, , 43, , (b) 2.2 × 109 Pa, (d) 2.2 × 106 Pa, , welded together to form a Y-shaped, structure. Area of cross-section of each rod, is 4 cm2 . End of copper rod is maintained, at 100°C whereas ends of brass and steel, are kept at 0°C. Lengths of the copper,, brass and steel rods are 46, 13 and 12 cm, respectively. The rods are thermally, insulated from surroundings except at, ends. Thermal conductivities of copper,, brass and steel are 0.92, 0.26 and 0.12 in, CGS units, respectively. Rate of heat flow, through copper rod is, (a) 1.2 cal/s, (c) 4.8 cal/s, , (b) 2.4 cal/s, (d) 6.0 cal/s
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44, , JEE MAIN Solved Paper 2014, , 12. One mole of diatomic, , P, , 17. A parallel plate capacitor is made of two, , B, , 800 K, ideal gas undergoes a, cyclic process ABC as, shown in figure. The, 600 K, C, A, process BC is adiabatic., 400 K, V, The temperatures at A,, B and C are 400 K, 800 K and 600 K,, respectively., Choose, the, correct, statement., , (a) The change in internal energy in whole cyclic, process is 250 R, (b) The change in internal energy in the process CA, is 700 R, (c) The change in internal energy in the process AB, is −350 R, (d) The change in internal energy in the process BC, is −500 R, , 13. An open glass tube is immersed in, mercury in such a way that a length of, 8 cm extends above the mercury level. The, open end of the tube is then closed and, sealed and the tube is raised vertically up, by additional 46 cm. What will be length of, the air column above mercury in the tube, now? (Atmospheric pressure = 76 cm of, Hg), , circular plates separated by a distance of, 5 mm and with a dielectric of dielectric, constant 2.2 between them. When the, electric field in the dielectric is, 3 × 104 V/m, the charge density of the, positive plate will be close to, (a) 6 × 10−7 C/m 2, , (b) 3 × 10−7 C/m 2, , (c) 3 × 10 C/m, , (d) 6 × 104 C/m 2, , 4, , 2, , 18. In a large building, there are 15 bulbs of, 40 W, 5 bulbs of 100 W, 5 fans of 80 W and, 1 heater of 1 kW. The voltage of the, electric mains is 220 V. The minimum, capacity of the main fuse of the building, will be, (a) 8 A, , (b) 10 A, , (c) 12 A, , (d) 14 A, , 19. A conductor lies along the z-axis at, −1.5 ≤ z < 1.5 m and carries a fixed current, of 10.0 A in −az direction (see figure). For a, field B = 3.0 × 10 −4 e−0.2 x ay T,, find the, , power required to move the conductor at, constant speed to x = 2.0 m, y = 0 in, 5 × 10 −3 s. Assume parallel motion along, the x-axis., , (a) 16 cm (b) 22 cm (c) 38 cm (d) 6 cm, , z, , 14. A particle moves with simple harmonic, , 1.5, , motion in a straight line. In first τ sec, after, starting from rest it travels a distance a and, in next τ sec, it travels 2a, in same, direction, then, (a), (b), (c), (d), , amplitude of motion is 3a, time period of oscillations is 8π, amplitude of motion is 4a, time period of oscillations is 6π, , l, B, , y, , 2.0, –1.5, , x, , 15. A pipe of length 85 cm is closed from one, end. Find the number of possible natural, oscillations of air column in the pipe, whose frequencies lie below 1250 Hz. The, velocity of sound in air is 340 m/s., (a) 12, , (b) 8, , (c) 6, , (d) 4, , 16. Assume that an electric field E = 30 x 2 i$, exists in space. Then, the potential, difference VA − VO, where VO is the, potential at the origin and VA the potential, at x = 2 m, is, (a) 120 J, , (b) −120 J (c) −80 J, , (d) 80 J, , (a) 1.57 W, (c) 14.85 W, , (b) 2.97 W, (d) 29.7 W, , 20. The coercivity of a small magnet where the, ferromagnet, gets, demagnetised, is, 3 × 103 Am −1. The current required to be, passed in a solenoid of length 10 cm and, number of turns 100, so that the magnet, gets demagnetised when inside the, solenoid is, (a) 30 mA, (c) 3 A, , (b) 60 mA, (d) 6 A
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JEE MAIN Solved Paper 2014, 21. In the circuit shown here, the point C is, kept connected to point A till the current, flowing through the circuit becomes, constant. Afterward, suddenly point C is, disconnected from point A and connected, to point B at time t = 0. Ratio of the voltage, across resistance and the inductor at, t = L / R will be equal to, A, , R, , C, , 45, , (a) The entire spectrum of visible light will come out, of the water at an angle of 90° to the normal, (b) The spectrum of visible light whose frequency is, less than that of green light will come out of the, air medium., (c) The spectrum of visible light whose frequency is, more than that of green light will come out to the, air medium., (d) The entire spectrum of visible light will come out, of the water at various angles to the normal., , 25. Two beams, A and B, of plane polarised, L, B, , (a), , e, 1− e, , (b) 1, , (c) −1, , (d), , 1− e, e, , 22. During the propagation of, electromagnetic waves in a medium,, (a) electric energy density is double of the magnetic, energy density, (b) electric energy density is half of the magnetic, energy density, (c) electric energy density is equal to the magnetic, energy density, (d) Both electric and magnetic energy densities are, zero, , 23. A thin convex lens made from crown glass, µ = 3 has focal length f. When, , 2, it is measured in two different liquids, 4, 5, having refractive indices and . It has, 3, 3, the focal lengths f1 and f2 , respectively. The, correct relation between the focal length is, (a), (b), (c), (d), , f1 = f2 < f, f1 > f and f2 becomes negative, f2 > f and f1 becomes negative, f1 and f2 both become negative, , 24. A green light is incident from the water to, the air-water interface at the critical angle, (θ). Select the correct statement., , light with mutually perpendicular planes, of polarisation are seen through a polaroid., From the position when the beam A has, maximum intensity (and beam B has zero, intensity), a rotation of polaroid through, 30° makes the two beams appear equally, bright. If the initial intensities of the two, beams are I A and IB respectively, then, I A / IB equals, (a) 3, , (b), , 3, 2, , (c) 1, , (d), , 1, 3, , 26. The radiation corresponding to 3 → 2, transition of hydrogen atom falls on a, metal surface to produce photoelectrons., These electrons are made to enter a, magnetic field of 3 × 10 −4 T. If the radius of, the largest circular path followed by these, electrons is 10.0 mm, the work function of, the metal is close to, (a) 1.8 eV, , (b) 1.1 eV (c) 0.8 eV, , (d) 1.6 eV, , 1, , 27. Hydrogen (1H ), deuterium (1H2 ), singly, , ionised helium(2 He4 )+ and doubly ionised, lithium (3 Li8 )+ + all have one electron, around the nucleus. Consider an electron, transition from n = 2 to n = 1. If the, wavelengths of emitted radiation are, λ 1, λ 2 , λ 3 and λ 4 , respectively for four, elements, then approximately which one, of the following is correct?, (a), (b), (c), (d), , 4λ1 = 2 λ 2 = 2 λ 3 = λ 4, λ1 = 2 λ 2 = 2 λ 3 = λ 4, λ1 = λ 2 = 4λ 3 = 9λ 4, λ1 = 2 λ 2 = 3λ 3 = 4λ 4
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46, , JEE MAIN Solved Paper 2014, , 28. The forward biased diode connection is, +2V, , (a), (b), (c), , 30. Match List I (Electromagnetic wave type), with List II (Its association/application), and select the correct option from the, choices given below the lists., , –2V, , –3V, , –3V, , 2V, , 4V, , –2V, , +2V, , List I, , List II, , A., , Infrared waves, , B., , Radio waves, , 2. For broadcasting, , 29. A student measured the length of a rod and, , C., , X-rays, , 3. To detect fracture of bones, , wrote it as 3.50 cm. Which instrument did, he use to measure it?, , D., , Ultraviolet, , 4. Absorbed by the ozone layer of, the atmosphere, , (d), , (a) A meter scale, (b) A vernier calliper where the 10 divisions in, vernier scale matches with 9 divisions in main, scale and main scale has 10 divisions in 1 cm, (c) A screw gauge having 100 divisions in the, circular scale and pitch as 1 mm, (d) A screw gauge having 50 divisions in the, circular scale and pitch as 1 mm, , (a), (b), (c), (d), , Codes, A, 4, 1, 3, 1, , 1. To treat muscular strain, , B, 3, 2, 2, 2, , C, 2, 4, 1, 3, , D, 1, 3, 4, 4, , Chemistry, 31. The correct set of four quantum numbers, , 34. For the estimation of nitrogen, 1.4 g of an, , for the valence electrons of rubidium atom, ( Z = 37) is, , organic compound was digested by, Kjeldahl's method and the evolved ammonia, M, sulphuric acid., was absorbed in 60 mL of, 10, The unreacted acid required 20 mL of M /10, sodium, hydroxide, for, complete, neutralisation. The percentage of nitrogen, in the compound is, , 1, 2, 1, (c) 5, 1, ,1, +, 2, , (a) 5, 0, 0, +, , 1, 2, 1, (d) 5, 0, 1, +, 2, (b) 5, 1, 0, +, , 32. If Z is a compressibility factor, van der, Waals’ equation at low pressure can be, written as, RT, (a) Z = 1 +, pb, pb, (c) Z = 1 −, RT, , a, (b) Z = 1 −, VRT, pb, (d) Z = 1 +, RT, , 33. CsCl crystallises in body centred cubic, lattice. If ‘a’ its edge length, then which of, the following expressions is correct?, (a) r, , Cs +, , (b) r, , Cs +, , (c) r, , Cs +, , (d) r, , Cs, , +, , + rCl − = 3a, 3a, + rCl − =, 2, 3, + rCl − =, a, 2, + rCl − = 3a, , (a) 6%, (c) 3%, , (b) 10%, (d) 5%, , 35. Resistance of 0.2 M solution of an, electrolyte is 50 Ω . The specific, conductance of the solution of 0.5 M, solution of same electrolyte is 1.4 S m −1, and resistance of same solution of the, same electrolyte is 280 Ω . The molar, conductivity of 0.5 M solution of the, electrolyte in Sm 2mol−1 is, (a) 5 × 10−4, , (b) 5 × 10−3, , (c) 5 × 10, , (d) 5 × 102, , 3
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JEE MAIN Solved Paper 2014, 36. For the complete combustion of ethanol,, C2H 5OH( l)+ 3O2( g) → 2CO2( g)+ 3H2O( l),, the amount of heat produced as measured, in bomb calorimeter, is 1364.47 kJ mol−1 at, 25°C. Assuming ideality the enthalpy of, combustion, ∆ C H, for the reaction will be, , 40. For, , the non-stoichiometric reaction, 2 A + B → C + D, the following kinetic data, were obtained in three separate, experiments, all at 298 K., Initial rate of, Initial, Initial, concen tration concentration formation of C, ( B), ( A), (mol L −1S −1), , (R = 8.314 J K –1mol –1), , (i), , 0.1 M, , 0.1 M, , 1.2 × 10 −3, , (ii), , 0.1 M, , 0.2 M, , 1.2 × 10 −3, , (iii), , 0.2 M, , 0.1 M, , 2 . 4 × 10 −3, , (a) − 1366. 95 kJ mol −1, (b) − 1361. 95 kJ mol −1, (c) − 1460. 50 kJ mol −1, (d) − 1350. 50 kJ mol −1, , The rate law for the formation of C is, , 37. The equivalent conductance of NaCl at, concentration C and at infinite dilution are, λ C and λ ∞ , respectively. The correct, relationship between λ C and λ ∞ is given, as (where, the constant B is positive), (a), (b), (c), (d), , λC, λC, λC, λC, , = λ∞, = λ∞, = λ∞, = λ∞, , 47, , + (B)C, − (B)C, − (B) C, + (B ) C, , dC, = k[ A][B], dt, dC, (c), = k[ A][B]2, dt, , (a), , dC, = k[ A]2 [B], dt, dC, (d), = k[ A], dt, , (b), , 41. Among the following oxoacids, the correct, decreasing order of acid strength is, (a), (b), (c), (d), , HOCl > HClO2 > HClO3 > HClO4, HClO4 > HOCl > HClO2 > HClO3, HClO4 > HClO3 > HClO2 > HOCl, HClO2 > HClO4 > HClO3 > HOCl, , 38. Consider separate solution of 0.500 M, , 42. The metal that cannot be obtained by, , C2H5OH (aq), 0.100 M Mg 3(PO4 )2 (aq),, 0.250 M KBr(aq) and 0.125 M Na3PO4 (aq), at 25°C. Which statement is true about, these solution, assuming all salts to be, strong electrolytes?, , electrolysis of an aqueous solution of its, salts is, , (a) They all have the same osmotic pressure, (b) 0.100 M Mg 3 (PO 4 )2 (aq) has the highest osmotic, pressure, (c) 0.125 M Na 3PO 4 (aq) has the highest osmotic, pressure, (d) 0.500 M C 2H5OH (aq) has the highest osmotic, pressure, , 39. For the reaction,, SO2( g) +, , 1, O ( g) q, 2 2, , SO3( g), , 1, 2, , 43. The octahedral complex of a metal ion M 3 +, with four monodentate ligands L1, L2 , L3, and L4 absorb wavelengths in the region of, red, green, yellow and blue, respectively., The increasing order of ligand strength of, the four ligands is, (a), (b), (c), (d), , L4 < L3 , L2 < L1, L1 < L3 < L2 < L4, L3 < L2 < L4 < L1, L1 < L2 < L4 < L3, , shown by NO?, , where, the symbols have usual meaning,, then the value of x is (assuming ideality), (c), , (b) Ca, (d) Cr, , 44. Which of the following properties is not, , if Kp = KC( RT )x, , (a) − 1, , (a) Ag, (c) Cu, , (b) −, (d) 1, , 1, 2, , (a) It is diamagnetic in gaseous state, (b) It is a neutral oxide, (c) It combines with oxygen to form nitrogen, dioxide, (d) Its bond order is 2.5
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JEE MAIN Solved Paper 2014, 55. Sodium phenoxide when heated with CO2, under pressure at 125°C yields a product, which on acetylation produces C., ONa, , 49, , 57. For which of the following molecule, significant µ ≠ 0 ?, , Cl, , CN, , OH, , SH, , Cl, , CN, , OH, , SH, , I, , II, , III, , IV, , +, , 125 °, , H, + CO2 → B , → C, 5 atm, , Ac2 O, , The major product C would be, OH, , OCOCH3, COOH, , (a), , COCH3, , (b), , (a) Only I, (c) Only III, , (b) I and II, (d) III and IV, , 58. Which one is classified as a condensation, polymer?, , COCH3, , (a) Dacron, (c) Teflon, , OCOCH3, , OH, , (b) Neoprene, (d) Acrylonitrile, , 59. Which one of the following bases is not, present in DNA?, , (c), , COOCH3, , (d), , COOH, , (a) Quinoline, (c) Cytosine, , (b) Adenine, (d) Thymine, , 60. In the reaction,, 56. Considering the basic strength of amines, in aqueous solution, which one has the, smallest pKb value?, (b) CH3NH2, (d) C6H5NH2, , (a) (CH3 )2 NH, (c) (CH3 )3 N, , LiAlH4, , PCl 5, , Alc. KOH, , CH3COOH → A → B → C, The product C is, (a) acetaldehyde, (c) ethylene, , (b) acetylene, (d) acetyl chloride, , Mathematics, and, X = {4 n −3 n − 1 : n ∈ N}, Y = {9 ( n − 1) : n ∈ N}; where N is the set of, natural numbers, then X ∪ Y is equal to, , 61. If, , (a) N, (c) X, , (b) Y − X, (d) Y, , 62. If z is a complex number such that| z| ≥ 2,, then the minimum value of z +, , 1, 2, , 5, (a) is equal to, 2, (b) lies in the interval (1, 2), 5, 2, 3, 5, (d) is strictly greater than but less than, 2, 2, , (c) is strictly greater than, , and, the, equation, a∈R, −3 ( x − [ x ])2 + 2 ( x − [ x ]) + a2 = 0 (where,[ x ], denotes the greatest integer ≤ x) has no, integral solution, then all possible values, of a lie in the interval, , 63. If, , (a) (−1, 0) ∪ (0, 1), (c) (−2 , − 1), , (b) (1, 2 ), (d) (−∞, − 2 ) ∪ (2 , ∞ ), , 64. Let α and β be the roots of equation, px 2 + qx + r = 0, p ≠ 0. If p, q and r are in, AP and, , 1 1, + = 4, then the value of|α − β|, α β, , is, (a), , 61, 9, , (b), , 2 17, 9, , (c), , 34, 9, , (d), , 2 13, 9
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50, , JEE MAIN Solved Paper 2014, , 65. If α, β ≠ 0 and f( n) = α n + β n and, , 72. If g is the inverse of a function f and, , 3, 1 + f(1) 1 + f(2), 1 + f(1) 1 + f(2) 1 + f(3), 1 + f(2) 1 + f(3) 1 + f(4), , f ′( x ) =, , = K(1 − α)2(1 − β)2 (α − β)2 ,, 1, (b), αβ, , (a) αβ, , (d) −1, , (c) 1, , −1, , AA = A A and B = A A , then BB is, equal to, T, , (a) I + B, , (b) 5 x4, , 1, 1 + {g ( x)}5, , T, , (c) B−1, , (b) I, , T, , (d) (B−1 )T, , 67. If the coefficients of x 3 and x 4 in the, expansion of (1 + ax + bx 2 )(1 − 2 x )18 in, powers of x are both zero, then ( a, b) is, equal to, 251, (a) 16,, , , 3 , 272 , (c) 14,, , , 3 , , 251, (b) 14,, , , 3 , 272 , (d) 16,, , , 3 , , (a) 2/′, f (c ) = g ′(c ), (c) f ′(c ) = g ′(c ), , 74. If x = − 1 and x = 2 are extreme points of, f( x ) = α log| x | + βx 2 + x , then, 1, 2, 1, (c) α = 2 , β = −, 2, , (a) α = − 6, β =, , π, 4, π, (d), 2, 1, , 8, , 2, , (a) ( x − 1) e, (c) ( x +, , x+, , 1, x, , 1, x+, x, 1) e, , 76. The integral, 9, , 121, 10, (c) 100, , (c) 4 3 − 4, , 441, 100, (d) 110, , (b), , positive numbers form an, increasing GP. If the middle term in this, GP is doubled, then new numbers are in, AP. Then, the common ratio of the GP is, , sin( π cos2 x ), is equal to, x→ 0, x2, , 71. lim, , π, 2, , (c) − π, , +C, , ∫, , (b) xe, (d), , x+, , 1, x, , +C, , 1, x+, x, − xe, , 1 + 4 sin2, , +C, , x, x, − 4 sin dx is, 2, 2, , 2π, −4−4 3, 3, π, (d) 4 3 − 4 −, 3, (b), , 77. The area of the region described by, , 70. Three, , (b) 3 +, (d) 2 +, , 1, 2, , equal to, (a) π − 4, , (a) 2 + 3, (c) 2 − 3, , +C, , 0, , 7, , = k(10)9 , then k is equal to, (a), , (d) α = 2 , β =, , 1, 2, , to, , π, , 69. If(10) + 2(11) (10) + 3(11) (10) + ... + 10(11), 9, , (b) α = − 6, β = −, , x, , (b), , (a), , (b) 2 f ′(c ) = 3g ′(c ), (d) f ′(c ) = 2 g ′(c ), , 1, , direction cosines satisfy the equations, l + m + n = 0 and l2 = m2 + n2 is, π, 3, π, (c), 6, , (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and, f(1) = 6, then for some c ∈] 0, 1[, , x+, 75. The integral ∫ 1 + x − 1 e x dx is equal, , , , 68. The angle between the lines whose, , (a), , (d) 1 + {g ( x)}5, , 73. If f and g are differentiable functions in, , 66. If A is a 3 × 3 non-singular matrix such that, T, , (a) 1 + x5, (c), , then K is equal to, , 1, , then g ′( x ) is equal to, 1 + x5, , 2, 3, , A = {( x , y ) : x 2 + y 2 ≤ 1 and y 2 ≤ 1 − x } is, (a), , π 4, +, 2, 3, , (b), , π 4, π 2, (c) −, −, 2 3, 2 3, , π 2, +, 2, 3, , (d), , 78. Let the population of rabbits surviving at, a time t be governed by the differential, dp(t) 1, equation, = p(t) − 200. If p(0) = 100,, 2, dt, then p(t) is equal to, t, , (b) 1, , (a) 400 − 300e 2, , (d) π, , (c) 600 − 500e 2, , (b) 300 − 200e, , −, , t, 2, , −, , t, 2, , t, , (d) 400 − 300e
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JEE MAIN Solved Paper 2014, 79. If PS is the median of the triangle with, , vertices P (2 , 2), Q (6, − 1) and R(7, 3), then, equation of the line passing through (1, − 1), and parallel to PS is, (a) 4 x − 7 y − 11 = 0, (c) 4 x + 7 y + 3 = 0, , (b) 2 x + 9 y + 7 = 0, (d) 2 x − 9 y − 11 = 0, , 80. Let a, b, c and d be non-zero numbers. If the, point of intersection of the lines, 4 ax + 2 ay + c = 0 and 5 bx + 2 by + d = 0, lies in the fourth quadrant and is, equidistant from the two axes, then, (a) 2 bc − 3ad = 0, (c) 2 ad − 3bc = 0, , (b) 2 bc + 3ad = 0, (d) 3bc + 2 ad = 0, , 81. The locus of the foot of perpendicular, drawn from the centre of the ellipse, x 2 + 3 y 2 = 6 on any tangent to it is, (a) ( x2 − y2 )2 = 6 x2 + 2 y2, (c) ( x2 + y2 )2 = 6 x2 + 2 y2, , radius 1. If T is the circle centred at (0, y ), passing through origin and touching the, circle C externally, then the radius of T is, equal to, (b), , 3, 2, , (c), , 1, 2, , (d), , 1, 4, , parabolas y 2 = 4 x and x 2 = − 32 y is, 1, 2, , (b), , 3, 2, , (c), , 84. The image of the line, , 1, 8, , (d), , 2, 3, , x −1 y − 3 z − 4, =, =, 3, 1, −5, , in the plane 2 x − y + z + 3 = 0 is the line, , x+ 3, =, 3, x+ 3, (b), =, −3, x−3, (c), =, 3, x−3, (d), =, −3, (a), , y−5, =, 1, y−5, =, −1, y+ 5, =, 1, y+ 5, =, −1, , z−2, −5, z+2, 5, z−2, −5, z−2, 5, , (b) 1, (d) 3, , 86. Let A and B be two events such that, 1, 1, 1, P ( A ∪ B) = , P ( A ∩ B) = and P ( A) = ,, 6, 4, 4, where A stands for the complement of the, event A. Then , the events A and B are, (a) independent but not equally likely, (b) independent and equally likely, (c) mutually exclusive and independent, (d) equally likely but not independent, , 87. The variance of first 50 even natural, numbers is, 833, 4, , (b) 833, (d), , 437, 4, , and k ≥ 1, then f4 ( x ) − f6 ( x ) is equal to, , 1, 6, 1, (c), 4, , (a), , 1, 3, 1, (d), 12, (b), , 89. A bird is sitting on the top of a vertical pole, , 83. The slope of the line touching both the, (a), , (a) 0, (c) 2, , 88. If fk( x ) = 1 / k (sin k x + cosk x ), where x ∈ R, , 82. Let C be the circle with centre at (1, 1) and, , 3, 2, , equal to, , (c) 437, , (d) ( x2 + y2 )2 = 6 x2 − 2 y2, , (a), , 85. If [ a × b b × c c × a ] = λ [ a b c ]2 , then λ is, , (a), , (b) ( x2 − y2 )2 = 6 x2 − 2 y2, , 51, , 20 m high and its elevation from a point O, on the ground is 45°. It flies off horizontally, straight away from the point O. After 1s,, the elevation of the bird from O is reduced, to 30°. Then, the speed (in m/s) of the bird, is, (a) 40( 2 − 1), (b) 40( 3 − 2 ), (c) 20 2, (d) 20( 3 − 1), , 90. The statement ~( p ↔ ~ q) is, (a) equivalent to p ↔ q, (b) equivalent to ~ p ↔ q, (c) a tautology, (d) a fallacy
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Answers, 1., 11., 21., 31., 41., 51., 61., 71., 81., , (a), (c), (c), (a), (c), (b), (d), (d), (c), , 2., 12., 22., 32., 42., 52., 62., 72., 82., , (c), (d), (c), (b), (b), (d), (b), (d), (d), , 3., 13., 23., 33., 43., 53., 63., 73., 83., , (b), (a), (b), (c), (b), (d), (a), (d), (a), , 4., 14., 24., 34., 44., 54., 64., 74., 84., , (a), (d), (d), (b), (a), (c), (d), (c), (a), , 5., 15., 25., 35., 45., 55., 65., 75., 85., , (c), (c), (d), (a), (d), (a), (c), (b), (b), , NOTE ‘*’ Means, none options are not correct., , For solutions scan, the QR code, , 6., 16., 26., 36., 46., 56., 66., 76., 86., , (c), (c), (b), (a), (b), (a), (b), (d), (a), , 7., 17., 27., 37., 47., 57., 67., 77., 87., , (d), (a), (c), (c), (b), (d), (d), (a), (b), , 8., 18., 28., 38., 48., 58., 68., 78., 88., , (a), (c), (a), (a), (a), (a), (a), (a), (d), , 9., 19., 29., 39., 49., 59., 69., 79., 89., , (c), (b), (b), (b), (d), (a), (c), (b), (d), , 10., 20., 30., 40., 50., 60., 70., 80., 90., , (*), (c), (d), (d), (b), (c), (d), (c), (a)
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Solved Paper 2013, , JEE Main, Joint Entrance Examination, Time : 3 hrs, , MM : 360, , Instructions, 1., , This test consists of 90 questions., , 2., , There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics, having 30 questions in each part of equal weightage. Each question is allotted 4 marks for correct, response., , 3., , Candidates will be awarded marks as stated above for correct response of each question. 1/4 mark will, be deducted for indicating incorrect response of each question. No deduction from the total score will, be made if no response is indicated for an item in the answer sheet., , 4., , There is only one correct response for each question. Filling up more than one response in any, question will be treated as wrong response and marks for wrong response will be deducted according, as per instructions., , Physics, 1. A uniform cylinder of length L and mass M, having cross-sectional area, A is, suspended, with its length vertical from a, fixed point by a massless spring such that, it is half submerged in a liquid of density σ, at equilibrium position. The extension x0, of the spring when it is in equilibrium is, Mg, k, Mg, (b), k, Mg, (c), k, Mg, (d), k, (a), , 1 − LAσ , , M , LA, σ, 1 −, , , 2M , 1 + LAσ , , M , , 2. A metallic rod of, , 2l, , l, , length l is tied to a, ω, string of length 2l, and made to rotate, with angular speed, ω on a horizontal, table with one end of the string fixed. If, there is a vertical magnetic field B in the, region, the emf induced across the ends of, the rod is, 2B ω l3, 2, 4Bω l 2, (c), 2, , (a), , 3B ω l 3, 2, 5Bω l 2, (d), 2, , (b)
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54, , JEE MAIN Solved Paper 2013, , 3. This question has Statement I and, , 7. Two capacitors C1 and C2 are charged to, , Statement II. Of the four choices given, after the statements, choose the one that, best describes the two statements., Statement I A point particle of mass m, moving with speed v collides with, stationary point particle of mass M. If the, maximum energy loss possible is given as, 1, m , f mv 2 , then f = , ., , 2, M + m, , 120 V and 200 V respectively. It is found, that by connecting them together the, potential on each one can be made zero., Then,, , Statement II Maximum energy loss, occurs when the particles get stuck, together as a result of the collision., (a) Statement I is true, Statement II is true;, Statement II is the correct explanation of, Statement I, (b) Statement I is true, Statement II is true;, Statement II is not the correct explanation of, Statement I, (c) Statement I is true, Statement II is false, (d) Statement I is false, Statement II is true, , 4. Let[ ε0 ] denotes the dimensional formula of, the permittivity of vacuum. If M = mass,, L = length, T = time and A = electric, current, then, (a) [ε0 ] = [M−1 L−3 T2 A ], (b) [ε0 ] = [M−1 L−3 T4 A 2 ], −2 2, , −1, , (b) 3C1 = 5C 2, (d) 9C1 = 4C 2, , 8. A sonometer wire of length 1.5 m is made, of steel. The tension in it produces an, elastic strain of 1%. What is the, fundamental frequency of steel, if density, and elasticity of steel are 7.7 × 103 kg/m3, and 2.2 × 1011 N /m 2 respectively?, (a) 188.5 Hz, (c) 200.5 Hz, , (b) 178.2 Hz, (d) 770 Hz, , 9. A circular loop of radius 0.3 cm lies, parallel to a much bigger circular loop of, radius 20 cm. The centre of the smaller, loop is on the axis of the bigger loop. The, distance between their centres is 15 cm. If, a current of 2.0 A flows through the smaller, loop, then the flux linked with bigger loop, is, (a) 9.1 × 10−11 Wb, , (b) 6 × 10−11 Wb, , (c) 3.3 × 10−11 Wb, , (d) 6.6 × 10−9 Wb, , 10. Diameter of a plano-convex lens is 6 cm, , −2, , (c) [ε0 ] = [M L T A ], (d) [ε0 ] = [M−1 L2 T−1 A 2 ], , 5. A projectile is given an initial velocity of, ( $i + 2 $j) m/s, where $i is along the ground and, $j is along the vertical. If g = 10 m/s2 , the, equation of its trajectory is, (a) y = x − 5 x2, (b) y = 2 x − 5 x2, , and thickness at the centre is 3 mm. If, speed of light in material of lens is, 2 × 108 m/s, the focal length of the lens is, (a) 15 cm (b) 20 cm (c) 30 cm (d) 10 cm, , 11. What is the minimum energy required to, launch a satellite of mass m from the, surface of a planet of mass M and radius R, in a circular orbit at an altitude of 2R?, (a), , (c) 4 y = 2 x − 5 x2, (d) 4 y = 2 x − 25 x2, , 5GmM, 2 GmM, GmM, (b), (c), 2R, 6R, 3R, , (d), , GmM, 3R, , 12. A diode detector is used to detect an, , 6. The amplitude of a damped oscillator, decreases to 0.9 times its original, magnitude is 5 s. In another 10 s, it will, decrease to α times its original magnitude,, where α equals, (a) 0.7, (c) 0.729, , (a) 5C1 = 3C 2, (c) 3C1 + 5C 2 = 0, , (b) 0.81, (d) 0.6, , amplitude modulated wave of 60%, modulation by using a condenser of, capacity 250 pico farad in parallel with a, load resistance 100 kΩ. Find the maximum, modulated frequency which could be, detected by it., (a) 10.62 MHz, (c) 5.31 MHz, , (b) 10.62 kHz, (d) 5.31 kHz
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JEE MAIN Solved Paper 2013, 13. A beam of unpolarised light of intensity I0, is passed through a polaroid A and then, through another polaroid B which is, oriented so that its principal plane makes, an angle of 45° relative to that of A. The, intensity of the emergent light is, (b) I0 /2, (d) I0 / 8, , (a) I0, (c) I0 / 4, , 14. The supply voltage to room is 120 V. The, , resistance of the lead wires is 6 Ω. A 60 W, bulb is already switched on. What is the, decrease of voltage across the bulb, when, a 240 W heater is switched on in parallel to, the bulb?, (a) Zero, (c) 13.3 V, , (b) 2.9 V, (d) 10.04 V, , 15. The shown p-V diagram represents the, thermodynamic cycle of an engine,, operating with an ideal monoatomic gas., The amount of heat, extracted from the, source in a single cycle is, , the cylinder have equal cross-sectional, area A. When the piston is in equilibrium,, the volume of the gas is V0 and its pressure, is p0 . The piston is slightly displaced from, the equilibrium position and released., Assuming that the system is completely, isolated from its surrounding, the piston, executes a simple harmonic motion with, frequency, (a), , 1 Aγ p0, 2 π V0 M, , (c), , 1, 2π, , B, , p0, , C, D, , A, , 2V0, , (a) p0 V0, , 13, (b) p0 V0, 2, , 11, (c) p0 V0, 2, , (d) 4 p0 V0, , 16. A hoop of radius r and mass m rotating, , with an angular velocity ω0 is placed on a, rough horizontal surface. The initial, velocity of the centre of the hoop is zero., What will be the velocity of the centre of, the hoop when it ceases to slip?, rω0, 4, rω0, (c), 2, , (a), , (b), , rω0, 3, , (d) rω0, , 17. An ideal gas enclosed in a vertical, cylindrical container supports a freely, moving piston of mass M. The piston and, , 1 V0 Mp0, 2 π A2 γ, , (d), , 1, 2π, , MV0, Aγ p0, , θ and then allowed to cool in a room which, is at temperature θ0 . The graph between, the temperature T of the metal and time t, will be closed to, T, , (a) T, , (b) θ, 0, t, , O, , T, , T, , (c) θ, 0, , (d) θ, 0, , O, , V0, , A 2 γp0, MV0, , (b), , 18. If a piece of metal is heated to temperature, , O, , 2p0, , 55, , t, , O, , t, , t, , 19. This question has Statement I and, Statement II. Of the four choices given, after the statements, choose the one that, best describes the two statements., Statement I Higher the range, greater is, the resistance of ammeter., Statement II To increase the range of, ammeter, additional shunt needs to be, used across it., (a) Statement I is true, Statement II is true; Statement, II is the correct explanation of Statement I, (b) Statement I is true, Statement II is true;, Statement II is not the correct explanation of, Statement I, (c) Statement I is true, Statement II is false, (d) Statement I is false, Statement II is true
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56, , JEE MAIN Solved Paper 2013, , 20. In an L-C-R circuit, , 24. The I-V characteristic of an LED is, , V, , as shown, both, S1, switches are open R, C, initially., Now,, switch S1 and S2 ,, S2, L, kept open. (q is, charge on the, capacitor and τ = RC is capacitance time, constant). Which of the following, statement is correct?, (a) Work done by the battery is half of the energy, dissipated in the resistor, (b) At t = τ, q = CV /2, (c) At t = 2τ, q = CV (1 − e −2 ), τ, (d) At t = , q = CV (1 − e −1 ), 2, , 21. Two coherent point, , Screen, , sources S1 and S2 are, separated by a small, distance d as shown., The fringes obtained, on the screen will be, (a) points, (c) semi-circle, , d, S1 S2, D, , (b) straight lines, (d) concentric circles, , 22. The magnetic field in a travelling, electromagnetic wave has a peak value of, 20 nT. The peak value of electric field, strength is, (a) 3 V / m, (c) 9 V / m, , (b) 6 V / m, (d) 12 V / m, , 23. The anode voltage of a photocells kept, fixed. The wavelength λ of the light falling, on the cathode is gradually changed. The, plate current I of photocell varies as, follows, I, , R YG B, , (b) Y, , R, , O, , O, , V, , V, V, , (c) I, , (d), , O, , V, , R, Y, G, B, , I, , decrease in its surface energy, so that its, temperature remains unchanged. What, should be the minimum radius of the drop, for this to be possible? The surface tension, is T , denstiy of liquid is ρ and L is its latent, heat of vapourisation, (a) ρL /T, (c) T /ρL, , (b) T /ρL, (d) 2 T /ρL, , 26. In a hydrogen like atom, electron makes, transition from an energy level with, quantum number n to another with, quantum number ( n − 1., ) If n >> 1, the, frequency of radiation emitted is, proportional to, (a), , 1, n, , (c), , 1, n3 / 2, , 1, n2, 1, (d) 3, n, (b), , 27. The graph between angle of deviation (δ), and angle of incidence (i) for a triangular, prism is represented by, δ, , δ, , (a), , (b), , (b), O, , λ, , λ, I, , I, , (c), λ, , O, , i, , δ, , λ, , i, , δ, , (c), , (d), , O, - Red, - Yellow, - Green, - Blue, , 25. Assume that a drop of liquid evaporates by, , I, , (a), , B, G, , (a) I, , (d), O, , i, , O, , i
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JEE MAIN Solved Paper 2013, 28. Two charges, each equal to q, are kept at, x = − a and x = a on the X-axis. A particle, q, is placed at, 2, the origin. If charge q0 is given a small, displacement ( y << a) along the Y-axis, the, net force acting on the particle is, proportional to, of mass m and charge q0 = −, , (a) y, , (b) − y, , (c), , 1, y, , (d) −, , 1, y, , 29. Two short bar magnets of length 1 cm each, , have magnetic moments 1.20 Am 2 and, 1.00 Am 2 respectively. They are placed on, a horizontal table parallel to each other, with their N poles pointing towards the, south. They have a common magnetic, equator and are separated by a distance of, 20.0 cm. The value of the resultant, horizontal magnetic induction at the, , 57, , mid-point O of the line joining their, centres is close to (horizontal component, of the earth’s magnetic induction is, 3.6 × 10 −5 Wb/m 2 ), (a) 3.6 × 10−5 Wb / m2 (b) 2.56 × 10−4 Wb / m2, (c) 3.50 × 10−4 Wb / m2 (d) 5.80 × 10−4 Wb / m2, , 30. A charge Q is uniformly distributed over a, long rod AB of length L as shown in the, figure. The electric potential at the point O, lying at distance L from the end A is, A, , O, , B, , L, , L, , (a), , Q, 8 π ε0 L, , (b), , 3Q, 4 π ε0 L, , (c), , Q, 4 π ε0 L ln 2, , (d), , Q ln 2, 4 π ε0 L, , Chemistry, 31. Which of the following complex species is, , 35. A piston filled with 0.04 mole of an ideal, , not expected to exhibit optical isomerism?, , gas expands reversibly from 50.0 mL to, 375 mL at a constant temperature of, 37.0°C. As it does so, it absorbs 208 J of, heat. The values of q and W for the, process will be, (R = 8.314 J / molK, ln 7.5 =2.01), , (a) [Co(en)3 ]3+, (c) [Co (NH3 )3Cl 3 ], , (b) [Co(en)2 Cl 2 ]+, , (d) [Co(en)(NH3 )2 Cl 2 ]+, , 32. Which one of the following molecules is, expected, to, behaviour?, (a) C 2, (c) O 2, , exhibit, , diamagnetic, , (b) N 2, (d) S 2, , 33. A solution of ( −)-1-chloro-1-phenylethane, in toluene racemises slowly in the, presence of a small amount of SbCl5 , due, to the formation of, (a) carbanion, (c) carbocation, , (b) carbene, (d) free radical, , ° 3+, 34. Given, ECr, = − 0.74 V ;, /Cr, ° − /Mn 2+ = 1.51 V, EMnO, , (a), (b), (c), (d), , q, q, q, q, , = + 208 J, W, = − 208 J, W, = − 208 J, W, = + 208 J, W, , = − 208 J, = − 208 J, = + 208 J, = + 208 J, , 36. The molarity of a solution obtained by, mixing 750 mL of 0.5 (M) HCl with, 250 mL of 2(M) HCl will be, (a) 0.875 M, (c) 1.75 M, , (b) 1.00 M, (d) 0.0975 M, , 37. Arrange the following compounds in the, order of decreasing acidity, OH, OH, OH, , OH, , 4, , °, ECr, 2, , O72 − /Cr 3+, , ° − = 1.36 V, = 1.33 V ; ECl, /Cl, , Based on the data given above, strongest, oxidising agent will be, (a) Cl, (c) Mn 2+, , (b) Cr 3+, (d) MnO −4, , ;, , ;, , Cl, , CH3, , (I), , (II), , (a) II > IV > I > III, (c) III > I > II > IV, , ;, , NO2, (III), , OCH3, (IV), , (b) I > II > III > IV, (d) IV > III > I > II
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58, , JEE MAIN Solved Paper 2013, , 38. For gaseous state, if most probable speed, is denoted by C *, average speed by C and, mean square speed by C, then for a large, number of molecules, the ratios of these, speeds are, (a), (b), (c), (d), , 39. The rate of a reaction double when its, temperature changes from 300 K to 310 K., Activation energy of such a reaction will be, ( R = 8.314 JK −1 mol−1 and log 2 = 0.301), (b) 48.6 kJ mol −1, (d) 60.5 kJ mol −1, , 40. A compound with molecular mass 180 is, acylated with CH3 COCl to get a, compound with molecular mass 390. The, number of amino groups present per, molecule of the former compound is, (a) 2, (c) 4, , (b) 5, (d) 6, , not represent the correct order of the, property stated against it?, (a) V < Cr < Mn < Fe : paramagnetic, behaviour, (b) Ni 2+ < Co 2+ < Fe 2+ < Mn2+ : ionic size, (c) Co 3+ < Fe 3+ < Cr 3+ < Sc 3+ : stability in, aqueous solution, (d) Sc < Ti < Cr < Mn : number of oxidation states, 2+, , 2+, , 2+, , 42. The order of stability of the following, carbocations, , CH, , CH2; CH3, , (I), , CH2, , CH2;, , is, , (II), (III), , (a) III > II > I, (c) I > II > III, , (a), (b), (c), (d), , ONCl and ONO − are not isoelectronic, O 3 molecule is bent, Ozone is violet-black in solid state, Ozone is diamagnetic gas, , 45. A gaseous hydrocarbon gives upon, combustion 0.72 g of water and 3.08 g of, CO2 . The empirical formula of the, hydrocarbon is, (a) C 2H4, (c) C 6H5, , (b) C 3H4, (d) C 7 H8, , 46. In which of the following pairs of, molecules/ions, both the species are not, likely to exist?, (a) H+2 , He 2−, 2, H22 + ,, , He 2, , (b) H −2 , He 22 −, , (d) H−2 , He 2+, 2, , 47. Which of the following exists as covalent, crystals in the solid state?, (a) Iodine, (c) Sulphur, , (b) Silicon, (d) Phosphorus, , 48. Synthesis of each molecule of glucose in, photosynthesis involves, (a) 18 molecules of ATP, (b) 10 molecules of ATP, (c) 8 molecules of ATP, (d) 6 molecules of ATP, , 49. The coagulating power of electrolytes, CH2, , CH2, , (b) 2, 5 and 8, (d) 5, 2 and 8, , 44. Which of the following is the wrong, , (c), , 41. Which of the following arrangements does, 2+, , (a) 5, 2 and 16, (c) 2, 5 and 16, , statement?, , C * : C : C = 1.225 : 1.128 : 1, C * : C : C = 1.128 : 1.225 : 1, C * : C : C = 1 : 1.128 : 1.225, C * : C : C = 1 : 1.225 : 1.128, , (a) 53.6 kJ mol −1, (c) 58.5 kJ mol −1, , The values of x , y and z in the reaction are, respectively, , (b) II > III > I, (d) III > I > II, , (a), (b), (c), (d), , Al 3+ < Ba 2 + < Na +, Na + < Ba 2+ < Al 3+, Ba 2+ < Na 2+ < Al 3+, Al 3+ < Na + < Ba 2+, , 50. Which of the following represents the, correct order of increasing first ionisation, enthalpy for Ca, Ba, S, Se and Ar?, , 43. Consider the following reaction,, xMnO4− + yC2O24 − + zH+ → xMn2+, + 2yCO2 +, , having ions Na + , Al3 + and Ba2 + for arsenic, sulphide sol increases in the order, , z, HO, 2 2, , (a), (b), (c), (d), , Ca < S < Ba < Se < Ar, S < Se < Ca < Ba < Ar, Ba < Ca < Se < S < Ar, Ca < Ba < S < Se < Ar
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JEE MAIN Solved Paper 2013, 51. Energy of an electron is given by, E = − 2.178 × 10−18, , Z2 , J 2, n , , Wavelength of light required to excite an, electron in an hydrogen atom from level, n = 1 to n = 2 will be (h = 6.62 × 103 −4 Js, and c = 3.0 × 108 ms−1), −7, , (a) 1.214 × 10, , m, , (b) 2.816 × 10−7 m, (c) 6.500 × 10−7 m, −7, , (d) 8.500 × 10, , m, , 52. Compound ( A), C8 H9 Br gives a white, precipitate when warmed with alcoholic, AgNO3 . Oxidation of (A) gives an acid (B),, C8 H6 O4 . (B) easily forms anhydride on, heating. Identify the compound (A)., CH2Br, (a), , C2H5, (b), Br, , CH3, CH2Br, (c), , (d), , CH2Br, CH3, , CH3, , 53. Four successive members of the first row, transition elements listed below with, atomic numbers. Which one of them is, °, expected to have the highest EM, 3+, / M 2+, value?, (a) Cr (Z = 24), (c) Fe (Z = 26), , (b) Mn (Z = 25), (d) Co (Z = 27), , 54. How many litres of water must be added to, 1 L of an aqueous solution of HCl with a, pH of 1 to create an aqueous solution with, pH of 2?, (a) 0.1 L, , (b) 0.9 L, , (c) 2.0 L, , (d) 9.0 L, , 59, , 55. The first ionisation potential of Na is, 5.1 eV. The value of electron gain enthalpy, of Na+ will be, (a) − 2.55 eV, , (b) − 5.1 eV, , (c) − 10.2 eV, , (d) + 2.55 eV, , 56. An organic compound A upon reacting, with NH 3 gives B. On heating, B gives C. C, in the presence of KOH reacts with Br2 to, give CH3CH2NH2 . A is, (a) CH3COOH, (b) CH3CH2CH2COOH, (c) CH3 CH COOH (d) CH3CH2COOH, , CH3, , 57. Stability of the species Li2 , Li2− and Li2+, increases in the order of, (a) Li 2 < Li 2+ < Li 2−, (c) Li 2 < Li −2 < Li +2, , (b) Li –2 < Li +2 < Li 2, (d) Li −2 < Li 2 < Li 2+, , 58. An unknown alcohol is treated with the, “Lucas reagent” to determine whether the, alcohol is primary, secondary or tertiary., Which alcohol reacts fastest and by what, mechanism?, (a) Secondary alcohol by SN1, (b) Tertiary alcohol by SN1, (c) Secondary alcohol by SN2, (d) Tertiary alcohol by SN2, , 59. The gas leaked from a storage tank of the, Union Carbide plant in Bhopal gas tragedy, was, (a) Methylisocyanate, (c) Ammonia, , (b) Methylamine, (d) Phosgene, , 60. Experimentally it was found that a metal, oxide has formula M0.98O. Metal M,, present as M 2+ and M 3+ in its oxide., Fraction of the metal which exists as M3 +, would be, (a) 7.01%, (c) 6.05%, , (b) 4.08%, (d) 5.08%
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Mathematics, 61. Distance between two parallel planes, , 67. The sum of first 20 terms of the sequence, , 2 x + y + 2 z = 8 and 4 x + 2 y + 4 z + 5 = 0 is, , 0.7, 0.77, 0.777,…, is, , 3, (a), 2, , (a), , 5, (b), 2, , 7, (c), 2, , 9, (d), 2, , 62. At present, a firm is manufacturing, 2000 items. It is estimated that the rate of, change of production P with respect to, additional number of workers x is given by, dP, = 100 − 12 x . If the firm employees, dx, 25 more workers, then the new level of, production of items is, (a) 2500, (c) 3500, , (b) 3000, (d) 4500, , 63. Let A and B be two sets containing, 2 elements and 4 elements respectively., The number of subsets of A × B having 3 or, more elements is, (a) 256, , (b) 220, , (c) 219, , (d) 211, , 64. If the lines, , x −2 y −3 z −4, x −1 y − 4 z − 5, and, =, =, =, =, 1, 1, −k, k, 2, 1, are coplanar, then k can have, (a), (b), (c), (d), , any value, exactly one value, exactly two values, exactly three values, , 18, , (b), , 72, , 68. A ray of light along x + 3 y = 3 gets, reflected upon reaching X-axis,, equation of the reflected ray is, , the, , (a) y = x + 3, (b) 3 y = x − 3, (c) y = 3 x − 3, (d) 3 y = x − 1, , 69. The number of values of k, for which the, system of equations, (k + 1)x + 8y = 4k, kx + (k + 3)y = 3k − 1, has no solution, is, (a) infinite, (c) 2, , (b) 1, (d) 3, , 70. If the equations x 2 + 2 x + 3 = 0 and, ax 2 + bx + c = 0, a, b, c ∈ R, have a common, root, then a : b : c is, , 65. If the vectors AB = 3 $i + 4 ^, and, k, AC = 5 i$ − 2 $j + 4 k$ are the sides of a ∆ABC,, then the length of the median through A is, (a), , 7, (179 − 10− 20 ), 81, 7, (b) (99 − 10− 20 ), 9, 7, (c), (179 + 10− 20 ), 81, 7, (d) (99 + 10− 20 ), 9, , (c), , 33, , (d), , 45, , 66. The real number k for which the equation,, 2 x 3 + 3 x + k = 0 has two distinct real roots, , (a) 1 : 2 : 3, (c) 1 : 3 : 2, , (b) 3 : 2 : 1, (d) 3 : 1 : 2, , 71. The circle passing through (1, − 2) and, touching the axis of x at (3, 0) also passes, through the point, (a) (− 5, 2 ), (c) (5, − 2 ), , (b) (2, − 5), (d) (− 2, 5), , 72. If x , y and z are in AP and tan − 1 x, tan − 1 y, , in [0, 1], , and tan − 1 z are also in AP, then, , (a), (b), (c), (d), , (a), (b), (c), (d), , lies between 1 and 2, lies between 2 and 3, lies between − 1and 0, does not exist, , x= y= z, 2 x = 3y = 6z, 6x = 3y = 2 z, 6x = 4y = 3z
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JEE MAIN Solved Paper 2013, 73. Statement I ( p ∧ ~ q) ∧ (~ p ∧ q) is a, fallacy., Statement II ( p → q) ↔ (~ q → ~ p) is a, tautology., (a) Statement I is true, Statement II is true;, Statement II is a correct explanation for, Statement I, (b) Statement I is true, Statement II is true;, Statement II is not a correct explanation for, Statement I, (c) Statement I is true, Statement II is false, (d) Statement I is false, Statement II is true, , 74. If ∫ f( x ) dx = ψ( x ), then ∫ x 5 f( x 3 )dx is equal, to, , lim, , x→0, , (a) −, , 1, 4, , 1, 2, , (c) 1, , ∫π /6, , (d) 2, , b, , ∫a f(x) dx = ∫a f(a + b − x) dx, (a) Statement I is true, Statement II is true;, Statement II is a correct explanation for Statement I, (b) Statement I is true, Statement II is true;, Statement II is not a correct explanation for, Statement I, (c) Statement I is true, Statement II is false, (d) Statement I is false, Statement II is true, , 77. The equation of the circle passing through, having centre at (0, 3) is, , 79. The x-coordinate of the incentre of the, triangle that has the coordinates of, mid-points of its sides as (0, 1), (1, 1) and, (1, 0) is, , 2, , , x +1, x −1 , −, , 2 /3, x, − x 1/ 3 + 1 x − x 1/ 2 , , dx, is equal to π /6 ., 1 + tan x, , the foci of the ellipse, , 13, 35, 10, (d) 5, 3, (b), , (d) 1 − 2, , Statement II, b, , 17, 35, 11, (c) 5, 3, (a), , 80. The term independent of x in expansion of, , 76. Statement I The value of the integral, π /3, , 5 questions. Each question has three, alternative answers of which exactly one is, correct. The probability that a student will, get 4 or more correct answers just by, guessing is, , (c) 1 +, , (1 − cos 2 x )(3 + cos x ), is equal to, x tan 4 x, (b), , 78. A multiple choice examination has, , (a) 2 + 2, (b) 2 − 2, , 1 3, [ x ψ( x3 ) − ∫ x2 ψ( x3 ) dx] + C, 3, 1 3, (b), x ψ( x3 ) − 3 ∫ x3 ψ( x3 ) dx + C, 3, 1, (c) x3 ψ( x3 ) − ∫ x2 ψ( x3 ) dx + C, 3, 1, (d) [ x3 ψ( x3 ) − ∫ x3 ψ( x3 ) dx] + C, 3, (a), , 75., , 61, , x 2 y2, +, = 1 and, 16, 9, , (a) x2 + y2 − 6 y − 7 = 0 (b) x2 + y2 − 6 y + 7 = 0, (c) x2 + y2 − 6 y − 5 = 0 (d) x2 + y2 − 6 y + 5 = 0, , (a) 4, (c) 210, , 10, , is, , (b) 120, (d) 310, , 81. The area (in square units) bounded by the, curves y = x , 2 y − x + 3 = 0, X-axis and, lying in the first quadrant is, (a) 9, (c) 18, , (b) 36, 27, (d), 4, , 82. Let Tn be the number of all possible, triangles formed by joining vertices of an, n-sided regular polygon. If Tn + 1 − Tn = 10,, then the value of n is, (a) 7, (c) 10, , (b) 5, (d) 8, , 83. If z is a complex number of unit modulus, 1 + z, and argument θ, then arg , is equal to, 1 + z , , (a) − θ, π, (b), −θ, 2, (c) θ, (d) π − θ
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62, , JEE MAIN Solved Paper 2013, (a) Statement I is true, Statement II is true;, Statement II is a correct explanation for, Statement I, (b) Statement I is true, Statement II is true;, Statement II is not a correct explanation for, Statement I, (c) Statement I is true, Statement II is false, (d) Statement I is false, Statement II is true, , 84. ABCD is a trapezium such that AB and CD, are parallel and BC ⊥ CD. If ∠ ADB = θ,, BC = p and CD = q, then AB is equal to, (a), (c), , ( p2 + q 2 ) sin θ, pcos θ + q sin θ, , (b), , p2 + q 2, p cos θ + q sin θ, 2, , 2, , (d), , p2 + q 2 cos θ, p cos θ + q sin θ, ( p2 + q 2 ) sin θ, ( p cos θ + q sin θ)2, , 1 α 3, 85. If P = 1 3 3 is the adjoint of a 3 × 3, 2 4 4, matrix A and| A | = 4 , then α is equal to, (a) 4, (c) 5, , 88. If y = sec (tan − 1 x ), then, to, 1, 2, (c) 1, (a), , (b) 11, (d) 0, , 86. The intercepts on X-axis made by tangents, x, , to the curve, y = ∫ | t | dt, x ∈ R, which are, 0, parallel to the line y = 2 x , are equal to, (a) ± 1, (c) ± 3, , (b), (d), , 1, 2, 2, , tan A, cot A, 89. The expression, can, +, 1 − cot A 1 − tan A, be written as, (a), (b), (c), (d), , (b) ± 2, (d) ± 4, , 87. Given A circle, 2 x 2 + 2 y 2 = 5 and a, parabola, y 2 = 4 5 x ., Statement I An equation of a common, tangent to these curves is y = x + 5., , dy, at x = 1is equal, dx, , sin A cos A + 1, sec A cosec A + 1, tan A + cot A, sec A + cosec A, , 90. All the students of a class performed poorly, in Mathematics. The teacher decided to, give grace marks of 10 to each of the, students. Which of the following statistical, measures will not change even after the, grace marks were given?, , Statement II If the line,, 5, y = mx +, ( m ≠ 0) is the common, m, tangent, then m satisfies, m4 − 3 m2 + 2 = 0., , (a) Mean, (c) Mode, , (b) Median, (d) Variance, , Answers, 1., 11., 21., 31., 41., 51., 61., 71., 81., , (c), (a), (d), (c), (a), (a), (c), (c), (a), , 2., 12., 22., 32., 42., 52., 62., 72., 82., , (d), (b), (b), (a,b), (d), (d), (c), (a), (b), , 3., 13., 23., 33., 43., 53., 63., 73., 83., , (d), (c), (d), (c), (c), (d), (c), (b), (c), , 4., 14., 24., 34., 44., 54., 64., 74., 84., , (b), (d), (a), (d), (*), (d), (c), (c), (a), , 5., 15., 25., 35., 45., 55., 65., 75., 85., , (b), (b), (d), (a), (d), (b), (c), (d), (b), , For solutions scan, the QR code, , 6., 16., 26., 36., 46., 56., 66., 76., 86., , (c), (c), (d), (a), (c), (d), (d), (d), (a), , 7., 17., 27., 37., 47., 57., 67., 77., 87., , (b), (c), (c), (c), (b), (b), (c), (a), (b), , 8., 18., 28., 38., 48., 58., 68., 78., 88., , (b), (c), (a), (c), (a), (b), (b), (c), (a), , 9., 19., 29., 39., 49., 59., 69., 79., 89., , (a), (d), (b), (a), (b), (a), (b), (b), (b), , 10., 20., 30., 40., 50., 60., 70., 80., 90., , (c), (c), (d), (b), (c), (b), (a), (c), (d)
