A force defined by $F=\alpha t^2+\beta t$ acts on a particle at a given time $t$. The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:
$\alpha t / \beta$
$\alpha \beta t$
$\alpha \beta / t$
$\beta t / \alpha$
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}} $
In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is