Question 1 :
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 :
Side of a cube is measured with a standard verniercallipers. The main scale reads 10 mm and first division of vernier scale coincides with that of main scale. Measured value of side of cube is -

Question 4 :
Position of a body with acceleration {tex} {' a' } {/tex} is given by {tex} x = K a ^ { m } t ^ { n } , {/tex} here {tex} t {/tex} is time. Find dimension of {tex} m {/tex} and {tex} n . {/tex}

Question 5 :
A quantity x is calculated from x = a²<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5c7b5f89758f2d4e4b4' height='41' width='25' >, If percentage error in a, b, c are &plusmn; 1%, &plusmn; 2% and &plusmn; 3% respectively. The maximum percentage error in x is -

Question 7 :
Which of the following sets can not enter into the list of fundamental quantities in any system of units?

Question 8 :
The percentage error in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum percentage error in the estimate of kinetic energy obtained by measuring mass and speed -

Question 9 :
{tex}\mathbf {Assertion}{/tex} : 'Light year' and 'Wavelength' both measure distance.<br>{tex}\mathbf {Reason}{/tex} : Both have dimensions of time.

Question 11 :
A screw gauge gives the following reading when used to measure the diameter of wire.<br>Main scale reading : 0mm<br>Circular scale reading: 52 division <br>Given that 1mm on main scale. The diameter of wire from the above date is :

Question 12 :
{tex}\mathbf {Assertion}{/tex} : Density is a derived physical quantity. {tex}\mathbf {Reason}{/tex} : Density cannot be derived from the fundamental physical quantities.

Question 13 :
The density of a cube is measured by measuring its mass and length of its sides. If the maximum errors in the measurement of its mass and length are 4% and 3% respectively, the maximum error in density is -

Question 14 :
Astronomical unit (AU) is the distance between earth and the sun. 1 AU is equal to

Question 16 :
Erg-m{tex} ^ { - 1 } {/tex} can be the unit of measure for

Question 19 :
If pressure {tex} P , {/tex} velocity {tex} V {/tex} and time {tex} T {/tex} are taken as fundamental physical quantities, the dimensional formula of force is

Question 20 :
If {tex} x = a t + b t ^ { 2 } , {/tex} where {tex} x {/tex} is the distance travelled by the body in kilometres while {tex} t {/tex} is the time in seconds, then the units of {tex} b {/tex} are

Question 21 :
The length, breadth and thickness of a strip are: <br>(10.0 &plusmn; 0.1) cm, (1.00 &plusmn; 0.01) cm and (0.100 &plusmn; 0.001) cm respectively. The most probable error in its volume will be:

Question 24 :
If h is height and g is acceleration due to gravity, then the dimensional formula of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c51d491ec9580069739b' height='44' width='32' > is the same as that of -

Question 26 :
In International System of units, there are seven base quantities whose units are defined. Which physical quantity has a prefix with its unit?

Question 29 :
What is the number of significant figures in {tex} 0.310 \times 10 ^ { 3 } {/tex}

Question 30 :
Given that y = A sin <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5ab491ec9580069743e' height='44' width='87' >, where y and x are measured in metres. Which of the following statements is correct?