The measured value of the length of a simple pendulum is $20 \mathrm{~cm}$ with $2 \mathrm{~mm}$ accuracy. The time for $50$ oscillations was measured to be $40$ seconds with $1$ second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is $\mathrm{N} \%$. The value of $\mathrm{N}$ is:

The amount of heat produced in an electric circuit depends upon the current $(I),$ resistance $(R)$ and time $(t).$ If the error made in the measurements of the above quantities are $2\%, 1\%$ and $1\%$ respectively then the maximum possible error in the total heat produced will be  ........... $\%$

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$......\%$

A student performs an experiment to determine the Young's modulus of a wire, exactly $2 \mathrm{~m}$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \mathrm{~mm}$ with an uncertainty of $\pm 0.05 \mathrm{~mm}$ at a load of exactly $1.0 \mathrm{~kg}$. The student also measures the diameter of the wire to be $0.4 \mathrm{~mm}$ with an uncertainty of $\pm 0.01 \mathrm{~mm}$. Take $g=9.8 \mathrm{~m} / \mathrm{s}^2$ (exact). The Young's modulus obtained from the reading is

If $Z=\frac{A^{2} B^{3}}{C^{4}}$, then the relative error in $Z$ will be

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