$A$ physical quantity $X$ is given by $X = \frac{2k^3l^2}{m\sqrt{n}}$. The percentage errors in the measurements of $k, l, m$ and $n$ are $1\%, 2\%, 3\%$ and $4\%$ respectively. The value of $X$ is uncertain by .......... $\%$

If the random error in the arithmetic mean of $50$ observations is $\alpha$,then the random error in the arithmetic mean of $150$ observations would be

The least count of a stop watch is $\frac{1}{5} \text{ s}$. The time of $20$ oscillations of a pendulum is measured to be $25 \text{ s}$. The maximum percentage error in the measurement of time will be .......... $\%$

$A$ student performs an experiment for the determination of $g = \frac{4 \pi^{2} \ell}{T^{2}}$. Given $\ell = 1 \, m$,the student commits an error of $\Delta \ell$. For $T$,the student measures the time of $n$ oscillations using a stopwatch with a least count of $\Delta T$ and commits a human error of $0.1 \, s$. For which of the following data will the measurement of $g$ be the most accurate?

Four persons measure the length of a rod as $20.00 \ cm$,$19.75 \ cm$,$17.01 \ cm$,and $18.25 \ cm$. The relative error in the measurement of the average length of the rod is:

The percentage error in the measurement of mass and velocity are $3 \%$ and $4 \%$ respectively. The percentage error in the measurement of kinetic energy is (in $\%$)