The length of a rod is measured by a meter scale having a least count of $0.1 \text{ cm}$ and the diameter is measured by vernier callipers having a least count of $0.01 \text{ cm}$. The length of the rod is $5.0 \text{ cm}$ and the radius is $2.0 \text{ cm}$. The percentage error in the calculated value of the volume is: (in $\%$)

The percentage error in the measurement of a physical quantity $m$ given by $m = \pi \tan \theta$ is minimum when $\theta = \dots \dots \dots \dots \dots ^\circ$ (Assume that the error in $\theta$ remains constant).

For $z = a^{2} x^{3} y^{1/2}$,where $a$ is a constant. If the percentage error in the measurement of $x$ and $y$ are $4\%$ and $12\%$,respectively,then the percentage error for $z$ will be $........... \%$.

The random error in the arithmetic mean of $100$ observations is $x$. What is the random error in the arithmetic mean of $400$ observations?

If $x = 10.0 \pm 0.1$ and $y = 10.0 \pm 0.1$,then $2x - 2y$ is equal to

Three students $S_{1}, S_{2}$ and $S_{3}$ perform an experiment for determining the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

Student No.	Length of pendulum $(cm)$	No. of oscillations $(n)$	Total time for oscillations $(s)$	Time period $(s)$
$1.$	$64.0$	$8$	$128.0$	$16.0$
$2.$	$64.0$	$4$	$64.0$	$16.0$
$3.$	$20.0$	$4$	$36.0$	$9.0$

(Least count of length $= 0.1 \, cm$,least count for time $= 0.1 \, s$)
If $E_{1}, E_{2}$ and $E_{3}$ are the percentage errors in $g$ for students $1, 2$ and $3$ respectively,then the minimum percentage error is obtained by student no. ....... .