Which of the following quantities can be written in $SI$ units as $kg \cdot m^2 \cdot A^{-2} \cdot s^{-3}$?

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

Dimensions of $\frac{1}{{\mu _0 \varepsilon _0}}$,where symbols have their usual meaning,are:

The position of a particle at time $t$ is given by the equation $x(t) = \frac{v_0}{A}(1 - e^{-At})$, where $v_0$ is a constant and $A > 0$. The dimensions of $v_0$ and $A$ respectively are:

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Angular momentum	$(I)$ $[ML^2T^{-1}]$
$(B)$ Torque	$(II)$ $[ML^2T^{-2}]$
$(C)$ Stress	$(III)$ $[ML^{-1}T^{-2}]$
$(D)$ Pressure gradient	$(IV)$ $[ML^{-2}T^{-2}]$

Choose the correct answer from the options given below:

$A$ dimensionless quantity