Question 1 :
A force is given by {tex} \mathrm { F } = \mathrm { at } + \mathrm { bt } ^ { 2 } , {/tex} where t is time, the dimensions of a and b are

Question 2 :
A screw gauge has {tex} 200 {/tex} equal divisions marked along the circumference of the disc and one full rotation of the disc advances on the main scale by {tex} 0.05 \mathrm { cm } . {/tex} The least count of the screw gauge is

Question 3 :
Write the dimensions of a {tex} \times b {/tex} in the relation {tex} E = \frac { b - x ^ { 2 } } { a t } , {/tex} where {tex} E {/tex} is the energy, {tex} x {/tex} is the displacement and {tex} t {/tex} is time

Question 4 :
Consider the following statements and select the correct statement(s).<br>I. Optics deal with the phenomena involving light. <br>II. Unification means physical phenomena in terms of few concepts and laws. <br>III. Macroscopic domain of Physics deals with the constitution and structure of matter at the minute scales of atoms and nuclei.<br>

Question 6 :
The density of a sphere is measured by measuring its mass and diameter. If, it is known that the maximum percentage errors in the measurement are {tex} 2 \% {/tex} and {tex} 3 \% , {/tex} then find the maximum percentage error in the measurement of density?

Question 7 :
The dimensions of {tex} \frac { 1 } { \epsilon _ { \mathrm { o } } } \frac { \mathrm { e } ^ { 2 } } { \mathrm { hc } } {/tex} are

Question 8 :
The moment of inertia of a body rotating about a given axis is {tex} 6.0 \mathrm { kg } \mathrm { m } ^ { 2 } {/tex} in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is {tex} 5 \mathrm { cm } {/tex} and the unit of mass is {tex} 10 \mathrm { g } {/tex} ?

Question 9 :
The length of one rod {tex} \ell _ { 1 } = 3.323 \mathrm { cm } {/tex} and the other is {tex} \ell _ { 2 } = 3.321 \mathrm { cm } . {/tex} Both rods were measured with one measuring instrument with least count {tex} 0.001 \mathrm { cm } {/tex} Then {tex} \left( \ell _ { 1 } - \ell _ { 2 } \right) {/tex} is

Question 10 :
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 {tex} 3 \% {/tex} each, then error in the value of resistance of the wire is