$A$ cube has numerically equal volume and surface area. The volume of such a cube is ........... $units$.

Match the following physical quantities with their respective dimensional formulas:

$(A)$ Thermal conductivity	$(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant	(ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat	(iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat	(iv) $M^0L^2T^{-2}$

Identify the pair whose dimensions are equal.

Dimensions of the quantity $\frac{p}{\varepsilon_0 \mu_0}$,where $p$ is the pressure,$\varepsilon_0$ is the electric permittivity of free space,and $\mu_0$ is the permeability of free space,will be:

The density of a substance is $4 \, g/cc$ in a system in which the unit of length is $5 \, cm$ and the unit of mass is $20 \, g$. The density of the substance in the $CGS$ system is: (in $units$)

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$(A)$ Torque	$(I)$ $ML^{-2}T^{-2}$
$(B)$ Stress	$(II)$ $ML^2T^{-2}$
$(C)$ Pressure gradient	$(III)$ $ML^{-1}T^{-1}$
$(D)$ Coefficient of viscosity	$(IV)$ $ML^{-1}T^{-2}$

Choose the correct answer from the options given below: