The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1\, cm$ and $34.2 \pm 0.1\, cm$,respectively. What will be the value of its volume in appropriate significant figures?

Match List-$I$ with List-$II$:

$LIST$-$I$	$LIST$-$II$
$(A)$ Surface tension	$(I)$ $kg m^{-1} s^{-1}$
$(B)$ Pressure	$(II)$ $kg m s^{-1}$
$(C)$ Viscosity	$(III)$ $kg m^{-1} s^{-2}$
$(D)$ Impulse	$(IV)$ $kg s^{-2}$

Choose the correct answer from the options given below:

Match the following?

Column-$I$	Column-$II$
$(a)$ Ratio of change in time period of a simple pendulum with temperature to its original time period	$(i) \, \alpha \Delta T$
$(b)$ Ratio of the value of a length to its scale reading	$(ii) \, T$
$(c)$ Reciprocal of coefficient of volume expansion for an ideal gas of constant pressure	$(iii) \, (1 + \alpha \Delta T)$
$(d) \, \frac{F}{YA} =$	$(iv) \, \frac{1}{2} \alpha \Delta T$

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge,whose pitch is $0.5 \ mm$ and there are $50$ divisions on the circular scale. The reading on the main scale is $2.5 \ mm$ and that on the circular scale is $20$ divisions. If the measured mass of the ball has a relative error of $2 \%$,the relative percentage error in the density is (in $\%$)

Some physical constants are given in List-$I$ and their dimensional formulae are given in List-$II$. Match the following:

List-$I$	List-$II$
$(1)$ Planck's constant	$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant	(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus	(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity	(iv) $[M^{-1} L^3 T^{-2}]$

The correct answer is:

If the percentage errors in measuring the length and the diameter of a wire are $0.1 \%$ each,the percentage error in measuring its resistance will be: (in $\%$)