Question 1 :
If radius of the sphere is {tex} ( 5.3 \pm 0.1 ) c m {/tex}. Then percentage error in its volume will be

Question 2 :
The force {tex} F {/tex} on a sphere of radius '{tex}a{/tex}' moving in a medium with velocity {tex} ^ { \prime } v ^ { \prime } {/tex} is given by {tex} F = 6 \pi \eta a v {/tex}. The dimensions of {tex} \eta {/tex} are

Question 3 :
The velocity of a freely falling body changes as {tex} g ^ { p } h ^ { q } {/tex} where {tex} g {/tex} is acceleration due to gravity and {tex} h {/tex} is the height. The values of {tex} p {/tex} and {tex} q {/tex} are

Question 5 :
The equation of a wave is given by {tex} Y = A \sin \omega \left( \frac { x } { v } - k \right) {/tex} where {tex} \omega {/tex} is the angular velocity and {tex} v {/tex} is the linear velocity. The dimension of {tex} k {/tex} is

Question 8 :
The vernier constant of a travelling microscope is 0.001 cm. If 49 main scale divisions coincide with 50 main scale divisions, then the value of 1 main scale division is -

Question 9 :
Find the dimensions of {tex} \frac { B ^ { 2 } } { \mu _ { o } } {/tex}

Question 10 :
Which one of the following represents the correct dimensions of the coefficient of viscosity?<br>

Question 13 :
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 14 :
A physcial quantity {tex} x {/tex} depends on quantities {tex} y {/tex} and {tex} z {/tex} as follows: {tex} x = A y + B \tan C z , {/tex} where {tex} A , B {/tex} and {tex} C {/tex} are constants. Which of the following do not have the same dimensions

Question 15 :
The position vector of a particle is {tex} \vec { r } = a [ \cos \omega t \hat { i } + {/tex} {tex} \sin \omega t \hat { j } ] {/tex} . The velocity of the particle is

Question 16 :
{tex}\mathbf {Assertion}{/tex} : In the relation {tex} f = \frac {1}{2l} \sqrt {\frac {T}{m}} {/tex}, where symbols have standard meaning, {tex}m{/tex} represent linear mass density.<br>{tex}\mathbf {Reason}{/tex} : The frequency has the dimensions of inverse of time.

Question 17 :
The force F is given in terms of time t and displacement x by the equation F = AcosBx + CsinDt. The dimensional formula of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5c0491ec95800697453' height='36' width='17' > is-

Question 18 :
The distance of a galaxy from the earth is of the order of 10²⁵m. The time taken by light to reach the earth from the galaxy is

Question 19 :
Error in the measurement of radius of sphere is 2%. Then error in the calculation of volume will be

Question 20 :
An aeroplane moves 400 m towards the north, 300 m towards west and then 1200 m vertically upwards, then its displacement from the initial position is:

Question 23 :
Which one of the following physical quantities is not a fundamental quantity?

Question 24 :
The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is

Question 25 :
If the unit of force is 100 N, unit of length is 10 m and unit of time is 100 s, what is the unit of mass in this system of units?

Question 26 :
The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is

Question 28 :
Which of the following statements is not correct regarding conservation laws?

Question 29 :
A spherometer has 250 equal divisions marked along the periphery of its disc and one full rotation of the disc advances on the main scale by 0.0625 cm. The least count of the spherometer is

Question 30 :
To measure the length of cylinder, a student uses the vernier calipers, whose main scale reads in millimeter and its vernier is divided into 10 divisions which coincide with 9 divisions of the main scale. He observed that when the two jaws of the instrument touch each other the eighth division of the vernier scale coincides with any one of the mains scale division and the zero of the vernier lies to the right of the zero of main scale. When he placed a cylinder tightly along its length between the two jaws the zero of the vernier scale lies slightly to the left of 42 mm and the fourth vernier division coincides with a scale division. The length of the cylinder measured by the student is-

Question 31 :
The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by relation of the type f = cm^xk^y, where c is a dimensional constant. The value of x and y are-

Question 33 :
A person was weighting 102.1 kg last week and gained 0.28 kg this week. His weight as of now is correctly expressed as:

Question 34 :
Dimensions of {tex} \frac { 1 } { \mu _ { 0 } \varepsilon _ { 0 } } , {/tex} where symbols have their usual meaning, are

Question 38 :
{tex}\mathbf {Assertion}{/tex} : Density is a derived physical quantity. {tex}\mathbf {Reason}{/tex} : Density cannot be derived from the fundamental physical quantities.

Question 39 :
Erg-m{tex} ^ { - 1 } {/tex} can be the unit of measure for

Question 41 :
Dimensional formula {tex} M L ^ { - 1 } T ^ { - 2 } {/tex} does not represent the physical quantity

Question 42 :
Which one of the following is not a unit of young's modulus

Question 43 :
An athletic coach told his team that muscle times speed equals power. What dimensions does he view for muscle

Question 45 :
A physical quantity is given by {tex} X = M ^ { a } L ^ { b } T ^ { c } . {/tex} The percentage error in measurement of {tex} M , L {/tex} and {tex} T {/tex} are {tex} \alpha , \beta {/tex} and {tex} \gamma {/tex} respectively. Then maximum percentage error in the quantity {tex} X {/tex} is

Question 48 :
A cube has a side 1.2 &times; 10{tex}^{-2}{/tex}m. Its volume will be recorded as

Question 50 :
A calorie is a unit of heat and equals 4.2 J. Suppose we employ a system of units in which of the unit of mass is &alpha; kg, the unit of length is &beta;metre and the unit of time is &gamma; second. In this new system, 1 calorie =