Electric field in a certain region is given by $\overrightarrow{ E }=\left(\frac{ A }{ x ^2} \hat{ i }+\frac{ B }{ y ^3} \hat{ j }\right)$. The $SI$ unit of $A$ and $B$ are
$Nm ^3\,C ^{-1} ; Nm ^2 \,C ^{-1}$
$Nm ^2\, C ^{-1} ; Nm ^3 \,C ^{-1}$
$Nm ^3 \,C ; Nm ^2 \,C$
$Nm ^2 \,C ; Nm ^3\, C$
The dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$, its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,
If force $[F],$ acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities. Find the dimensions of energy.
If the speed of light $(c)$, acceleration due to gravity $(g)$ and pressure $(p)$ are taken as the fundamental quantities, then the dimension of gravitational constant is
If $\varepsilon_0$ is permittivity of free space, $e$ is charge of proton, $G$ is universal gravitational constant and $m_p$ is mass of a proton then the dimensional formula for $\frac{e^2}{4 \pi \varepsilon_0 G m_p{ }^2}$ is