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

What is called as relative error ? Define fractional error.

A physical parameter a can be determined by measuring the parameters $b, c, d $ and $e $ using the relation $a =$ ${b^\alpha }{c^\beta }/{d^\gamma }{e^\delta }$. If the maximum errors in the measurement of $b, c, d$ and e are ${b_1}\%$, ${c_1}\%$, ${d_1}\%$ and ${e_1}\%$, then the maximum error in the value of a determined by the experiment is

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$

Assertion $A$ : A spherical body of radius $(5 \pm 0.1)$ $mm$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4\,\%$.

Reason $R$ : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.

In the light of the above statements, choose the correct answer from the options given below on :

The percentage errors in the measurement of mass and speed are $2\%$ and $3\%$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed  ......... $\%$

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