The equation of state for some gases is given by $(P + \frac{a}{V^2})(V - b) = RT$,where $P$ is pressure,$V$ is volume,$T$ is absolute temperature,and $a, b, R$ are constants. What are the dimensions of '$a$'?

In the $CGS$ system, the magnitude of the force is $100 \ dynes$. In another system where the fundamental physical quantities are $kilogram$, $meter$, and $minute$, the magnitude of the force is:

If the dimensional formula of $(\text{Energy} \times \text{speed})$ is $[M^{a} L^{b} T^{c}]$,then $a, b,$ and $c$ are:

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A\sqrt{x}}{x + B}$, where $A$ and $B$ are constants with appropriate dimensions. The dimensions of $AB$ are . . . . . . .

Given below are two statements: One is labelled as Assertion $(A)$ and other is labelled as Reason $(R)$.
Assertion $(A)$: Time period of oscillation of a liquid drop depends on surface tension $(S)$,if density of the liquid is $\rho$ and radius of the drop is $r$,then $T = k \sqrt{\rho r^{3} / S}$ is dimensionally correct,where $k$ is dimensionless.
Reason $(R)$: Using dimensional analysis,we find that the $R.H.S.$ has different dimensions than that of the time period.

The position of a particle moving on the $x-$axis is given by $x(t) = A \sin t + B \cos^2 t + Ct^2 + D$,where $t$ is time. The dimension of $\frac{ABC}{D}$ is $-$