The dimensions of physical quantity X in the equation Force $=\frac{X}{\text{Density}}$ is given by 

(1) $M^1{L}^4{T}^{-2}$

(2) $M^2{L}^{-2}{T}^{-1}$

(3) $M^2{L}^{-2}{T}^{-2}$

(4) $M^1{L}^{-2}{T}^{-1}$

The dimensions of CV² matches with the dimensions of 

(1) L²I

(2) L²I ²

(3) LI²

(4) $\frac{1}{LI}$

The Martians use force (F), acceleration (A) and time (T) as their fundamental physical quantities. The dimensions of length on Martians system are 

(1) [FT²]

(2) [${\mathrm{F}}^{-1}{\mathrm{T}}^2$]

(3) [${\mathrm{F}}^{-1}{\mathrm{A}}^2{\mathrm{T}}^{-1}$]

(4) [AT²]

The dimension of $\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$ is that of 

(1) Velocity

(2) Time

(3) Capacitance

(4) Distance

An athletic coach told his team that muscle times speed equals power. What dimensions does he view for muscle?

(1) $ML{T}^{-2}$

(2) $M{L}^2{T}^{-2}$

(3) MLT²

(4) L

The dimensional formula of wave number is

(1) $M^0{L}^0{T}^{-1}$

(2) $M^0{L}^{-1}{T}^0$

(3) $M^{-1}{L}^{-1}{T}^0$

(4) $M^0{L}^0{T}^0$

The dimensions of stress are equal to 

(1) Force

(2) Pressure

(3) Work

(4) $\frac{1}{\text{Pressure}}$

Dimensional formula of magnetic flux is 

(1) $M{L}^2{T}^{-2}{A}^{-1}$

(2) $M{L}^0{T}^{-2}{A}^{-2}$

(3) $M^0{L}^{-2}{T}^{-2}{A}^{-3}$

(4) $M{L}^2{T}^{-2}{A}^3$

If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, then non-zero integers x, y and z such that $P^x{Q}^y{c}^z$ is dimensionless, are 

(1) $x=1,y=1,z=-1$

(2) $x=1,y=-1,z=1$

(3) $x=-1,y=1,z=1$

(4) $x=1,y=1,z=1$

Inductance L can be dimensionally represented as 

(1) $M{L}^2{T}^{-2}{A}^{-2}$

(2) $M{L}^2{T}^{-4}{A}^{-3}$

(3) $M{L}^{-2}{T}^{-2}{A}^{-2}$

(4) $M{L}^2{T}^4{A}^3$