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

The relative error in resistivity of a material where

resistance $= 1.05 \pm 0.01\, \Omega$

diameter $= 0.60 \pm 0.01\, mm$

length $= 75.3 \pm 0.1 \,cm$ is

What is error in measurement, done by any instrument ?

If there is an error of $1\%$ in calculation of mass of disc and $1.5\%$ error in radius, then $\%$ error in moment of inertia about an axis tangent to disc is  .......... $\%$

A physical quantity $P$ is related to four observables $a, b, c$ and $d$ as follows: $P=\frac{a^{2} b^{2}}{(\sqrt{c} d)}$ The percentage errors of measurement in $a, b, c$ and $d$ are $1 \%, 3 \%, 4 \%$ and $2 \%$ respectively. What is the percentage error in the quantity $P$ ? If the value of $P$ calculated using the above relation turns out to be $3.763,$ to what value should you round off the result?

A students measures the distance traversed in free fall of a body, the initially at rest, in a given time. He uses this data to estimate $g$ , the acceleration due to gravity . If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage error in the estimation of $g$ is