For $z=a^{2} x^{3} y^{\frac{1}{2}}$, where $a$ is a constant. If percentage error in measurement of $x$ and $y$ are $4 \%$ and $12 \%$, respectively, then the percentage error for $z$ will be $........... \%$

The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be

A sliver wire has mass $(0.6 \pm 0.006) \; g$, radius $(0.5 \pm 0.005) \; mm$ and length $(4 \pm 0.04) \; cm$. The maximum percentage error in the measurement of its density will be $......\,\%$

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 .............. $\%$

Two resistors of resistances $R_1 = (300 \pm 3) \,\Omega $ and $R_2 = (500 \pm 4)$ are connected in series. The equivalent resistance of the series combination is