A physical quantity $P$ is given by $P= \frac{{{A^3}{B^{\frac{1}{2}}}}}{{{C^{ - 4}}{D^{\frac{3}{2}}}}}$. The quantity which brings in the maximum percentage error in $P$ is

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

$Assertion$: In the measurement of physical quantities direct and indirect methods are used.

$Reason$ : The accuracy and precision of measuring instruments along with errors in measurements should be taken into account, while expressing the result.

Two resistors of resistances $R_{1}=100 \pm 3$ $ohm$ and $R_{2}=200 \pm 4$ $ohm$ are connected $(a)$ in series, $(b)$ in parallel. Find the equivalent resistance of the $(a)$ series combination, $(b)$ parallel combination. Use for $(a)$ the relation $R=R_{1}+R_{2}$ and for $(b)$ $\frac{1}{R^{\prime}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$ and $\frac{\Delta R^{\prime}}{R^{\prime 2}}=\frac{\Delta R_{1}}{R_{1}^{2}}+\frac{\Delta R_{2}}{R_{2}^{2}}$

If there is a positive error of $50\%$ in the measurement of velocity of a body, then the error in the measurement of kinetic energy is .............. $\%$