The least count of a stopwatch is $0.2\, s$. The time for $20\, oscillations$ of a pendulum is measured to be $25\, s$. The percentage error in the measurement of time will be ........ $\%$

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).

$A$ metal wire has mass $(0.4 \pm 0.002) \, g$,radius $(0.3 \pm 0.001) \, mm$ and length $(5 \pm 0.02) \, cm$. The maximum possible percentage error in the measurement of density will nearly be $.......\%$

$A$ physical quantity is $A = P^2/Q^3$. The percentage error in the measurement of $P$ and $Q$ is $x$ and $y$ respectively. The maximum percentage error in the measurement of $A$ is:

While measuring the acceleration due to gravity by a simple pendulum,a student makes a positive error of $1\%$ in the length of the pendulum and a negative error of $3\%$ in the value of time period. His percentage error in the measurement of $g$ by the relation $g = 4{\pi ^2}(l/T^2)$ will be ........ $\%$

The random error in the arithmetic mean of $100$ observations is $x$; then the random error in the arithmetic mean of $400$ observations would be