Question 3 :
The fundamental physical quantities that have same dimensions in the dimensional formulae of torque and angular momentum are
Question 5 : The area of the parallelogram represented by the vectors <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5974389b1556ddef554' height='24' width='63' > and <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c597491ec95800697427' height='24' width='55' > is-
Question 6 :
In given screw gauge, if pitch is 1 mm and circular scale has 100 divisions. When nothing is put between the jaws A and B which just closed then 13 divisions of C.S. are below the zero of reference line on linear or main scale. When a wire is placed between the jaws two linear scale divisions are clearly visible while 73 divisions on circular scale coincide with reference line. The error in this question is -
Question 7 :
The unit of {tex} L / R {/tex} is (where {tex} L = {/tex} inductance and {tex} R = {/tex} resistance)
Question 10 :
Each side a cube is measured to be 7.203 m. The volume of the cube up to appropriate significant figures is
Question 12 :
The product of pressure and volume have the same units as the product of :
Question 14 :
Electrons in a TV tube move horizontally South to North. Vertical component of earth's magnetic field points down. The electron is deflected towards
Question 15 :
The full turns of the circular scale of a screw gauge cover a distance of 1mm on its main scale. The total number of divisions on the circular scale is 50. Further it is found that the screw gauge has a zero error of -0.03mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3mm and the number of circular scale division in the line with main scale as 35. The diameter of the wire is
Question 19 :
The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of
Question 20 :
The dimensional formula for ω in the relation y = A sin ωt is-
Question 22 :
A small steel ball of radius {tex} r {/tex} is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity {tex} \eta {/tex}. After some time the velocity of the ball attains a constant value known as terminal velocity {tex} v _ { T } . {/tex} The terminal velocity depends on (i) the mass of the ball {tex} m , {/tex} (ii) {tex} \eta , {/tex} (iii) {tex} r {/tex} and (iv) acceleration due to gravity {tex} g . {/tex} Which of the following relations is dimensionally correct
Question 24 :
If x = at + bt{tex}^2{/tex}, where x is in metres and t in hours (hr), then unit of b will be
Question 26 :
If C and R denote capacity and resistance the dimensions of CR are -
Question 28 :
The dimensions of {tex} C V ^ { 2 } {/tex} matches with the dimensions of
Question 29 :
The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give<sup>
Question 30 :
Which one of the following pairs of quantities and their units is a proper match
Question 33 :
Vernier scales of Vernier calipers has 50 divisions which coincide with 49 main scale divisions. Find the Vernier constant. Given: there are 20 main scale divisions cm<sup>-1</sup>.
Question 36 :
The equation of state of some gases can be expressed as {tex}\left( P + \frac{a}{V^{2}} \right)\left( V - b \right) = \text{RT}{/tex}. Here, P is the pressure, V the volume, T the absolute temperature, and a, b, R are constants. The dimensions of ‘a’ are
Question 37 :
Of the following quantities, which one has dimensions different from the remaining three
Question 38 :
A spherometer has 20 threads per cm. Its circular scale has 100 divisions. Find the least count of spheometer
Question 41 :
Which of the following properties of laser beam can be used to measure long distances?
Question 42 :
In the following list, the only pair which have different dimensions, is
Question 44 :
If 1.76 cm<sup>3 </sup> is the volume of one cube, then the volume of twenty-five such cubes is-
Question 46 :
Density of liquid is 15.7 g/cm<sup>3</sup>. Its value in the international system of units is-
Question 48 :
Which of the following is not the name of a physical quantity ?
Question 49 :
Which one of the following instruments is not used for the measurement of length?
Question 50 :
A student measures quantities a, b and c and then calculates S by the formula S = ab<sup>2</sup>/c<sup>3</sup>. If the error in a, b, c are 1%, 3% and 2% respectively, the maximum error in S can be-
Question 51 :
If a copper wire is stretched to make its radius decrease by 0.1{tex} \% {/tex}, then the percentage increase in resistance is approximately
Question 53 :
A man starts from {tex} O {/tex} moves 500{tex} \mathrm { m } {/tex} turns by {tex} 60 ^ { \circ } {/tex} and moves 500{tex} \mathrm { m } {/tex} again turns by {tex} 60 ^ { \circ } {/tex} and moves 500{tex} \mathrm { m } {/tex} and so on. Find the displacement after (i){tex} 5{tex} \mathrm { th } {/tex} turn, (ii) {tex}3{tex} \mathrm { rd } {/tex} turn
Question 54 :
A chocolate cookie is a circular disk of diameter {tex} 8.50\pm 0.02 \mathrm { cm } {/tex} and thickness {tex} 0.050 \pm 0.005 \mathrm { cm } . {/tex} The average volume in {tex} \mathrm { cm } ^ { 3 } {/tex} is
Question 55 :
A dust particle oscillates in air with a time period which depends on atmospheric pressure P, density of air d and energy of the particle E, then time period is proportional to
Question 56 :
Two resistances of 400 {tex}\Omega{/tex} and 800 {tex}\Omega{/tex} connected in series with a 6 volt battery of negligible internal resistance. A voltmeter of resistance 10,000 {tex}\Omega{/tex} is used to measure the potential difference across 400 {tex}\Omega{/tex}. The error in the measurement of potential difference in volts approximately is
Question 57 :
The current voltage relation of diode is given by {tex}I =(e1000 V/T- l) mA{/tex}, where the applied voltage {tex} V{/tex} is in volts and the temperature {tex}T{/tex} is in degree Kelvin. If a student makes an error measuring {tex} ± 0.01 V{/tex} while measuring the current of {tex} 5 mA{/tex} at {tex}300 K,{/tex} what will be the error in the value of current in {tex}mA?{/tex}
Question 58 :
The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of
Question 59 :
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3{tex} \% {/tex} each, then error in the value of resistance of the wire is
Question 60 :
A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is {tex} 90 \mathrm { s } , 91 \mathrm { s } , 95 \mathrm { s } , {/tex} and {tex}92 \mathrm { s } {/tex} . If the minimum division in the measuring clock is 1{tex} \mathrm { s } {/tex}, then the reported mean time should be:
Question 61 :
The {tex} ( x , y , z ) {/tex} co-ordinates of two points {tex} A {/tex} and {tex} B {/tex} are given respectively as {tex} ( 0,3 , - 1 ) {/tex} and {tex} ( - 2,6,4 ) . {/tex} The displacement vector from {tex} A {/tex} to {tex} B {/tex} is given by
Question 63 :
A screw gauge with a pitch of {tex} 0.5mm{/tex} and a circular scale with 50 divisions is made 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 {tex} 0.5mm {/tex} and the 25th division coincides with the main scale line.
Question 64 :
{tex}Assertion:{/tex} Specific gravity of a fluid is a dimensionless quantity
<br>{tex}Reason: {/tex} It is the ratio of density of fluid to density of water.
Question 66 :
Which of the rectangular pair may be the components of a 13 N force?
Question 67 :
The angles which the vector {tex} \vec { A } = 3 \hat { i } + 6 \hat { j } + 2 \hat { k } {/tex} makes with the co-ordinate axes are
Question 68 :
Energy due to position of a particle is given by, {tex} U = \frac { \alpha \sqrt { y } } { y + \beta } , {/tex} where {tex} \alpha {/tex} and {tex} \beta {/tex} are constants, {tex} y {/tex} is distance. The dimensions of {tex} ( \alpha \times \beta ) {/tex} are
Question 69 :
A scientist performs an experiment and takes 50 readings. He repeats the same experiment and now takes 200 readings. By doing so:
Question 71 :
Dimensions of one or more pairs are same. Identify the pairs-
Question 72 :
The dimensions of h/e (h = Planck's constant and e = electronic charge) are same as that of :
Question 74 : What is the final reading of callipers as shown -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c65b4389b1556ddef620' height='97' width='176' >
Question 75 : The velocity of a particle is given by v = a + <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c571b5f89758f2d4e454' height='37' width='15' > + ct<sup>2</sup><br>The unit of b will be
Question 76 : Dimensional formula <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5cfb5f89758f2d4e4bb' height='17' width='48' > does not represent the physical quantity -
Question 78 : Match the Column I with Column II <table><tr><th>Column I Physical quantity</th> <th>Column II Name of unit</th> </tr><tr><td>(A) Conductance</td> <td>(p) Gray</td> </tr> <tr><td>(B) Magnetic induction </td> <td>(q) Lumen</td> </tr> <tr><td>(C) Absorbed dose</td> <td>(r) Tesla</td> </tr> <tr><td>(D) Luminous flux</td> <td>(s) Siemens</td></tr></table>
Question 79 :
Pitch of a screw gauge is 0.5 mm and its least count is 0.01 mm. Calculate no. of divisions on its head scale.
Question 80 :
Which of the following relation cannot be derived using dimensional analysis (Neglect value of constant) -
Question 81 :
{tex}\mathbf {Assertion}{/tex} : : Mass, length and time are fundamental physical quantities. <br>{tex}\mathbf {Reason}{/tex} : They are independent of each other.
Question 82 :
Calculate the area of the triangle determined by the two vectors {tex} \vec { A } = 3 \hat { i } + 4 \hat { j } {/tex} and {tex} \vec { B } = - 3 \hat { i } + 7 \hat { j } {/tex}
Question 83 :
Given {tex} \vec { A } = 2 \hat { i } + p \hat { j } + q \hat { k } {/tex} and {tex} \vec { B } = 5 \hat { i } + 7 \hat { j } + 3 \hat { k } . {/tex} If {tex} \vec { A } \| \vec { B } , {/tex} then the values of {tex} p {/tex} and {tex} q {/tex} are, respectively,
Question 84 :
Unit vector parallel to the resultant of vectors {tex} \vec { A } = 4 \hat { i } - 3 \hat { j } {/tex} and {tex} \vec { B } = 8 \hat { i } + 8 \hat { j } {/tex} will be
Question 85 :
The density of wood is 0.5 g cm<sup>-3</sup> in cgs system of units. The corresponding value in SI units is-
Question 86 :
Which of the following physical quantities has same unit in all the three system of units?
Question 87 :
Two rods with lengths 20.123 cm and 18.1 cm are placed side by side. The difference in their lengths is
Question 88 :
The component of vector {tex} \vec { A } = 2 \hat { i } + 3 \hat { j } {/tex} along the vector {tex} \hat { i } + \hat { j } {/tex} is
Question 89 :
The projection of a vector {tex} \vec { r } = 3 \hat { i } + \hat { j } + 2 \hat { k } {/tex} on the {tex} x - y {/tex} plane has magnitude
Question 91 :
Two forces {tex} \vec { F } _ { 1 } = 500 \mathrm { N } {/tex} due east and {tex} \vec { F } _ { 2 } = 250 \mathrm { N } {/tex} due north have their common initial point. {tex} \vec { F } _ { 2 } - \vec { F } _ { 1 } {/tex} is
Question 93 :
The equation of a wave is y = a sin (At - Bx + C), where A, B and C are constants. The dimensions of A, B and C are respectively
Question 94 :
Taking into account the significant figures, what is the value of 9.99 m + 0.0099 m
Question 95 :
If velocity, force and time are taken to be fundamental quantities find dimensions formula for (a) mass
Question 96 :
Error in the measurement of radius of sphere is 2{tex} \% {/tex}. Then error in the calculation of volume will be
Question 97 : In the given relation P = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5f3491ec95800697483' height='40' width='41' >, where P is power, x is distance and t is time, the dimensions of 'a' will be -
Question 98 :
The value of {tex} n {/tex} so that vectors {tex} 2 \hat { i } + 3 \hat { j } - 2 \hat { k } , 5 \hat { i } + n \hat { j } + \hat { k } {/tex} and {tex} - \hat { i } + 2 \hat { j } + 3 \hat { k } {/tex} may be coplanar, will be
Question 99 :
Two resistances of 400 Ω and 800 Ω connected in series with a 6 volt battery of negligible internal resistance. A voltmeter of resistance 10,000Ω is used to measure the potential difference across 400 Ω. The error in the measurement of potential difference in volts approximately is
Question 100 :
The dimensional formula of kinetic energy is the same as that of -
Question 101 :
If L and R denote inductance and resistance, respectively, then the dimension of L/R is -
Question 103 :
A sample of gas is at 0°C. To what temperature it must be raised in order to double the r.m.s. speed of the molecule-
Question 105 : A block of mass {tex} m {/tex} is connected to three springs, each of spring constant {tex} k {/tex} as shown in Fig. 1.26. The block is pulled by {tex} x {/tex} in the direction of {tex} C . {/tex} Find resultant spring constant.<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d5809e541fcca588ca358b7"><br>
