Question 1 :
Out of the following which pair of quantities do not have same dimensions
Question 2 :
Main scale of a vernier calliper has 100 divisions in 5 cm. Its vernier scale has 25 divisions in one cm. The least count is
Question 3 :
If a vector {tex} 2 \hat { i } + 3 \hat { j } + 8 \hat { k } {/tex} is perpendicular to the vector {tex} 4 \hat { j } - \hat { 4 i } + \alpha \hat { k } {/tex} then the value of {tex} \alpha {/tex} is
Question 5 :
If {tex} R {/tex} and {tex} L {/tex} represent respectively resistance and self inductance, which of the following combinations has the dimensions of frequency
Question 6 :
The length, breadth and thickness of a block are measured as 125.5 cm, 5.0 cm and 0.32 cm respectively. Which one of the following measurements is most accurate
Question 8 :
The percentage errors in the measurement of mass and speed are {tex} 2 \% {/tex} and {tex} 3 \% {/tex} respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed
Question 9 :
The quantities {tex} A {/tex} and {tex} B {/tex} are related by the relation, {tex} m = A / B {/tex} where {tex} m {/tex} is the linear density and {tex} A {/tex} is the force. The dimensions of {tex} B {/tex} are of
Question 11 :
When a wire is placed between studs of a screw gauge then no main scale division is completed and 34 circular scale division coincides with the reference line. If pitch is 0.5 mm and there is 50 divisions on head scale. Then diameter of wire is -
Question 12 :
The physical quantity which has dimensional formula as that of {tex} \frac { \text { Energy } } { \text { Mass } \times \text { Length } } {/tex} is
Question 13 : What is the dimensional formula of<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5bf4389b1556ddef580' height='40' width='108' >?
Question 14 :
Which one of the following does not have the same dimensions
Question 16 :
The dimension of magnetic field in {tex} \mathrm { M } , \mathrm { L } , \mathrm { T } {/tex} and {tex} \mathrm { C } {/tex} (coulomb) is given as
Question 19 :
If {tex} | \vec { A } \times \vec { B } | = \sqrt { 3 } \vec { A } \cdot \vec { B } , {/tex} then the value of {tex} | \vec { A } + \vec { B } | {/tex} is
Question 20 :
If energy E, velocity V and time t are chosen as fundamental quantities, then the dimensional formula of surface tension is
Question 21 :
The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of
Question 22 :
Wind is blowing {tex} \mathrm { NE } {/tex} with 18{tex} \sqrt { 2 } \mathrm { km } \mathrm { h } ^ { - 1 } {/tex} and steamer is heading due west with 18{tex} \mathrm { km } \mathrm { h } ^ { - 1 } {/tex}. In which direction is the flag on the mast fluttering?
Question 23 :
Two capacitors {tex} C _ { 1 } = 5.2 \mu F{/tex} and {tex} 0.1 \mu F{/tex} and {tex} C _ { 2 } = 12.2 \mu F {/tex} are joined (i) In series (ii) In parallel. Find the net capacitance in these two cases.
Question 24 :
In the past, there were attempts to use metric system in the measurement of time, which could not succeed. In this system, whole day was divided into 10 decimal hours, each consisting of 100 decimal minutes and the day starting was at midnight. If one such watch using this system shows 6 decimal hours and 50 decimal minutes then this time in our traditional system is:
Question 25 :
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 26 :
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 27 :
The speed of light {tex} ( c ) , {/tex} gravitational constant {tex} ( G ) {/tex} and Planck's constant {tex} ( h ) {/tex} are taken as the fundamental units in a system. The dimension of time in this new system should be
Question 28 :
The dimension of quantity {tex} ( L / R C V ) {/tex} is
Question 29 :
Find a vector {tex} \vec { x } {/tex} which is perpendicular to both {tex} \vec { A } {/tex} and {tex} \vec { B } {/tex} but has magnitude equal to that of {tex} \vec { B } {/tex} . Rule: Inter change coeff. of {tex} \hat { i } {/tex} and {tex} \hat { j } {/tex} and change sign of one of the vectors. {tex} \vec { A } = 3 \hat { i } - 2 \hat { j } + \hat { k } , \vec { B } = 4 \hat { i } + 3 \hat { j } - 2 \hat { k } {/tex}
Question 30 :
A body of mass {tex} m = 3.513 \mathrm { kg } {/tex} is moving along the x-axis with a speed of {tex} 5.00 \mathrm { ms } ^ { - 1 } . {/tex} The magnitude of its momentum is recorded as
Question 31 :
A dust particle oscillates in air with a time period which depends on atmospheric pressure {tex} P {/tex}, density of air {tex} d {/tex} and energy of the particle {tex} E , {/tex} then time period is proportional to
Question 32 :
If velocity {tex} v {/tex}, acceleration {tex} A {/tex} and force {tex} F {/tex} are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of {tex} v , A {/tex} and {tex} F {/tex} would be
Question 33 :
The acceleration of a particle as seen from two frames {tex} S _ { 1 } {/tex} and {tex} S _ { 2 } {/tex} has equal magnitude {tex} 5 \mathrm { ms } ^ { - 2 } . {/tex}
Question 35 :
Pitch of screw gauge is 1 mm. There are 100 divisions on circular scale. While measuring diameter of wire the linear scale reads 1 mm and 45<sup>th</sup> division of circular scale coincides with reference line of main scale. Length of wire is 5.0 cm measured by metre scale. The surface area of wire to correct significant figure is
Question 36 :
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 39 :
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 40 :
Which of the following units denotes the dimensions {tex} \left[ M L ^ { 2 } / Q ^ { 2 } \right] , {/tex} where {tex} Q {/tex} denotes the electric charge?
Question 41 :
The dimensions of h/e (h = Planck's constant and e = electronic charge) are same as that of :
Question 42 :
{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 43 :
Error in the measurement of radius of sphere is 2{tex} \% {/tex}. Then error in the calculation of volume will be
Question 45 :
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 46 :
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 47 :
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 48 : 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 49 :
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 50 :
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 52 :
If velocity, force and time are taken to be fundamental quantities find dimensions formula for (a) mass
Question 53 :
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 54 :
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 56 : 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 57 :
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 58 :
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 60 :
Which of the rectangular pair may be the components of a 13 N force?
