Match List $I$ with List $II$ :

List $I$ (Physical Quantity)	List $II$ (Dimensional Formula)
$(A)$ Pressure gradient	$(I)$ $\left[ M ^0 L ^2 T ^{-2}\right]$
$(B)$ Energy density	$(II)$ $\left[ M ^1 L ^{-1} T ^{-2}\right]$
$(C)$ Electric Field	$(III)$ $\left[ M ^1 L ^{-2} T ^{-2}\right]$
$(D)$ Latent heat	$(IV)$ $\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]$

Choose the correct answer from the options given below:

The dimensional formula of farad is

Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$, Planck's constant $h$ and the speed of light $c$, as $Y=c^\alpha h^\beta G^\gamma$. Which of the following is the correct option?

Given that $v$ is speed, $r$ is the radius and $g$ is the acceleration due to gravity. Which of the following is dimensionless

What is the dimensional formula of $a b^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning.

The dimensional formula for $r.m.s.$ (root mean square) velocity is