$A$ dimensionless quantity is constructed in terms of electronic charge $e$,permittivity of free space $\varepsilon_0$,Planck's constant $h$,and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0^\beta h^\gamma c^\delta$ and $n$ is a non-zero integer,then $(\alpha, \beta, \gamma, \delta)$ is given by

$A$ physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^2}{4\pi \varepsilon_0}$ is $[c$ is velocity of light,$G$ is the universal gravitational constant and $e$ is charge$]$.

The dimensions of the product $\mu_{0} \varepsilon_{0}$ are related to those of velocity as

$A$ force $F$ is given by $F = at + bt^2$,where $t$ is time. What are the dimensions of $a$ and $b$?

If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G, c$ and $h$ are the universal gravitational constant,speed of light,and Planck's constant respectively,then:

$A$ small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time,the velocity of the ball attains a constant value known as terminal velocity $v_T$. The terminal velocity depends on $(i)$ the mass of the ball $m$,$(ii)$ $\eta$,$(iii)$ $r$,and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct?