An experiment measures quantities $a, b,$ and $c$ and then $x$ is calculated from $x = \frac{a^{1/2} b^2}{c^3}.$ If the percentage errors in $a, b,$ and $c$ are $\pm 1\%, \pm 3\%,$ and $\pm 2\%$ respectively,then the percentage error in $x$ is:

$A$ calorie is a unit of heat or energy and it equals about $4.2 \; J$ where $1 \; J = 1 \; kg \; m^2 \; s^{-2}$. Suppose we employ a system of units in which the unit of mass equals $\alpha \; kg$, the unit of length equals $\beta \; m$, and the unit of time equals $\gamma \; s$. Show that a calorie has a magnitude $4.2 \; \alpha^{-1} \beta^{-2} \gamma^2$ in terms of the new units.

If the capacitance of a nanocapacitor is measured in terms of a unit $u$ made by combining the electric charge $e,$ Bohr radius $a_0,$ Planck's constant $h$ and speed of light $c,$ then

If force $(F)$,velocity $(V)$,and time $(T)$ are taken as fundamental units,then the dimensions of mass are:

If the velocity of light $c$,universal gravitational constant $G$,and Planck's constant $h$ are chosen as fundamental quantities,the dimensions of mass in the new system are:

Assertion $(A)$: Energy per unit volume and angular momentum can be added dimensionally.
Reason $(R)$: Physical quantities having same dimensions can be added or subtracted.