If $x$  and $a$ stand for distance then for what value of $n$ is given equation dimensionally correct the eq. is  $\int {\frac{{dx}}{{\sqrt {{a^2}\, – \,{x^n}} \,}}\, = \,{{\sin }^{ – 1}}\,\frac{x}{a}} $

Consider following statements

$(A)$ Any physical quantity have more than one unit

$(B)$ Any physical quantity have only one dimensional formula

$(C)$ More than one physical quantities may have same dimension

$(D)$ We can add and subtract only those expression having same dimension

Number of correct statement is

An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is

The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be

A famous relation in physics relates 'moving mass' $m$ to the 'rest mass' $m_{0}$ of a particle in terms of its speed $v$ and the speed of light, $c .$ (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant $c$. He writes:

$m=\frac{m_{0}}{\left(1-v^{2}\right)^{1 / 2}}$

Guess where to put the missing $c$