The percentage errors in quantities $P, Q, R$ and $S$ are $0.5\%, 1\%, 3\%$ and $1.5\%$ respectively in the measurement of a physical quantity $A = \frac{P^3 Q^2}{\sqrt{R} S}$. The maximum percentage error in the value of $A$ will be ........... $\%$.

The percentage error in the measurement of mass and speed are $3\%$ and $2\%$ respectively. Then,the percentage error in kinetic energy will be .......... $\%$

Using the expression $2 d \sin \theta = \lambda$,one calculates the values of $d$ by measuring the corresponding angles $\theta$ in the range $0^{\circ}$ to $90^{\circ}$. The wavelength $\lambda$ is exactly known and the error in $\theta$ is constant for all values of $\theta$. As $\theta$ increases from $0^{\circ}$:

$A$ wire has a mass $0.3 \pm 0.003 \, g$,radius $0.5 \pm 0.005 \, mm$ and length $6 \pm 0.06 \, cm$. The maximum percentage error in the measurement of its density is .......... $\%$

Calculate the mean percentage error in five observations: $80.0, 80.5, 81.0, 81.5, 82.0$. (in $\%$)

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