The resistance $R =\frac{ V }{ I },$ where $V =(50 \pm 2) \;V$ and $I=(20 \pm 0.2)\;A.$ The percentage error in $R$ is $x\%$. The value of $x$ to the nearest integer is .........

A student uses a simple pendulum of exactly $1 \mathrm{~m}$ length to determine $\mathrm{g}$, the acceleration due to gravity. He uses a stop watch with the least count of $1 \mathrm{sec}$ for this and records $40$ seconds for $20$ oscillations. For this observation, which of the following statement$(s)$ is (are) true?

$(A)$ Error $\Delta T$ in measuring $T$, the time period, is $0.05$ seconds

$(B)$ Error $\Delta \mathrm{T}$ in measuring $\mathrm{T}$, the time period, is $1$ second

$(C)$ Percentage error in the determination of $g$ is $5 \%$

$(D)$ Percentage error in the determination of $g$ is $2.5 \%$

Find the relative error in $Z,$ if $Z=\frac{A^{4} B^{1 / 3}}{ C D^{3 / 2}}$

A physical quantity $z$ depends on four observables $a,$ $b,$ $c$ and $d ,$ as $z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .$ The percentage of error in the measurement of $a, b, c$ and $d$ are $2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $z$ is$......\%$

The period of oscillation of a simple pendulum in the experiment is recorded as $2.63\, s, 2.56 s, 2.42\, s, 2.71\, s$ and $2.80 \,s$ respectively. The average absolute error is ......... $s$

A simple pendulum is being used to determine the value of gravitational acceleration $\mathrm{g}$ at a certain place. The length of the pendulum is $25.0\; \mathrm{cm}$ and a stop watch with $1\; \mathrm{s}$ resolution measures the time taken for $40$ oscillations to be $50\; s$. The accuracy in $g$ is  ....... $\%$