Question 1 :
Which of the rectangular pair may be the components of a 13 N force?
Question 2 : 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 3 :
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 5 :
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 6 :
Two rods with lengths 20.123 cm and 18.1 cm are placed side by side. The difference in their lengths is
Question 7 : 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 8 :
A scientist performs an experiment and takes 50 readings. He repeats the same experiment and now takes 200 readings. By doing so:
Question 9 :
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 11 :
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 13 :
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 14 :
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 15 :
If L and R denote inductance and resistance, respectively, then the dimension of L/R is -
Question 16 :
Error in the measurement of radius of sphere is 2{tex} \% {/tex}. Then error in the calculation of volume will be
Question 17 :
{tex}\mathbf {Assertion}{/tex} : : Mass, length and time are fundamental physical quantities. <br>{tex}\mathbf {Reason}{/tex} : They are independent of each other.
Question 18 :
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 19 :
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 20 :
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 21 : 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 23 :
If velocity, force and time are taken to be fundamental quantities find dimensions formula for (a) mass
Question 24 :
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 25 :
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 26 : 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 27 : 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 28 :
The dimensional formula of kinetic energy is the same as that of -
Question 29 :
Taking into account the significant figures, what is the value of 9.99 m + 0.0099 m
Question 31 :
The dimensions of h/e (h = Planck's constant and e = electronic charge) are same as that of :
Question 32 :
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 33 :
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 36 :
Which of the following physical quantities has same unit in all the three system of units?
Question 37 :
Dimensions of one or more pairs are same. Identify the pairs-
Question 38 :
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 39 : 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>
Question 42 :
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 44 :
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 46 :
{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 47 :
Which of the following relation cannot be derived using dimensional analysis (Neglect value of constant) -
