$A$ physical quantity $x$ is related as $x = \frac{\sqrt{a}b^3}{c^4d^{-4}}$. Relative errors in the quantities $a, b, c$ and $d$ are $2\%, 1\%, 3\%$ and $4\%$ respectively. The relative error in $x$ will be: (in $\%$)

$A$ force $F$ is applied on a square plate of length $L$. If the percentage error in the determination of $L$ is $3 \%$ and in $F$ is $4 \%$, then the permissible error in the calculation of pressure is (in $\%$)

What is error in measurement? What is mistake in measurement?

During Searle's experiment,the zero of the Vernier scale lies between $3.20 \times 10^{-2} \text{ m}$ and $3.25 \times 10^{-2} \text{ m}$ of the main scale. The $20^{\text{th}}$ division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of $2 \text{ kg}$ is applied to the wire,the zero of the Vernier scale still lies between $3.20 \times 10^{-2} \text{ m}$ and $3.25 \times 10^{-2} \text{ m}$ of the main scale,but now the $45^{\text{th}}$ division of the Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is $2 \text{ m}$ and its cross-sectional area is $8 \times 10^{-7} \text{ m}^2$. The least count of the Vernier scale is $1.0 \times 10^{-5} \text{ m}$. The maximum percentage error in the Young's modulus of the wire is:

In an experiment to measure the height of a bridge by dropping a stone into water underneath,if the error in the measurement of time is $0.1\;s$ at the end of $2\;s$,then the error in the estimation of the height of the bridge will be (in $;m$)

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $\left(\frac{x}{100}\right) \%$. If the relative errors in measuring the mass and the diameter are $6.0 \%$ and $1.5 \%$ respectively,the value of $x$ is