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

Which of the following expressions can be deduced on the basis of dimensional analysis? (All symbols have their usual meanings)

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 body with acceleration '$a$' is given by $x = K{a^m}{t^n}$,where $t$ is time. Find the dimensions of $m$ and $n$.

Let force $F = A \sin(Ct) + B \cos(Dx)$,where $x$ and $t$ are displacement and time respectively. The dimensions of $\frac{C}{D}$ are the same as the dimensions of

If $C$ (the velocity of light), $h$ (Planck's constant), and $G$ (gravitational constant) are taken as fundamental quantities, then the dimensional formula of mass is