A physical quantity $y$ is represented by the formula $y=m^{2}\, r^{-4}\, g^{x}\,l^{-\frac{3}{2}}$. If the percentage error found in $y, m, r, l$ and $g$ are $18,1,0.5,4$ and $p$ respectively, then find the value of $x$ and $p$.

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are :

Error in the measurement of radius of a sphere is $1\%$. The error in the calculated value of its volume is  ......... $\%$

The radius of a sphere is $(5.3 \pm 0.1) \,cm$. The percentage error in its volume is

While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of $1\%$ in the length of the pendulum and a negative error of $3\%$ in the value of time period. His percentage error in the measurement of $g$ by the relation $g = 4{\pi ^2}\left( {l/{T^2}} \right)$ will be  ........ $\%$

Two resistances are given as $R _1=(10 \pm 0.5)\,\Omega$ and $R_2=(15 \pm 0.5)\, \Omega$. The percentage error in the measurement of equivalent resistance when they are connected in parallel is