$A$ physical quantity $X$ is given by $X = \frac{2 k^3 l^2}{m \sqrt{n}}$. The percentage errors in the measurements of $k, l, m,$ and $n$ are $1 \%, 2 \%, 3 \%,$ and $4 \%$ respectively. The percentage uncertainty in the value of $X$ is: (in $\%$)

If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$,radius $(r)$ of the drop,and density $(\rho)$ of the liquid,then the expression for $T$ is:

Force $(F)$ and density $(d)$ are related as $F = \frac{\alpha}{\beta + \sqrt{d}}$. The dimensions of $\alpha$ and $\beta$ are:

$L$, $C$, and $R$ represent the physical quantities inductance, capacitance, and resistance, respectively. The dimensional formula $ML^2T^{-4}A^{-2}$ corresponds to . . . . . . .

The dimensions of $\frac{\alpha}{\beta}$ in the equation $F = \frac{\alpha - t^2}{\beta v^2}$,where $F$ is force,$v$ is velocity,and $t$ is time,are ..........

To find the distance $d$ over which a signal can be seen clearly in foggy conditions,a railway engineer uses dimensional analysis and assumes that the distance depends on the mass density $\rho$ of the fog,intensity (power/area) $S$ of the light from the signal,and its frequency $f$. The engineer finds that $d$ is proportional to $S^{1/n}$. The value of $n$ is: