The dimensional formula for Boltzmann's constant is 

(1) $\left[M{L}^2{T}^{-2}{\theta }^{-1}\right]$

(2) $\left[M{L}^2{T}^{-2}\right]$

(3) $\left[M{L}^0{T}^{-2}{\theta }^{-1}\right]$

(4) $\left[M{L}^{-2}{T}^{-1}{\theta }^{-1}\right]$

The dimensions of K in the equation $W=\frac{1}{2}K{x}^2$ is 

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

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

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

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

The physical quantities not having the same dimensions are: 

(1) Speed and ${\left({\mu }_0{\epsilon }_0\right)}^{-1/2}$

(2) Torque and work

(3) Momentum and Planck's constant

(4) Stress and Young's modules

The dimensional formula of relative density is: 

(1) ML^–3

(2) LT^–1

(3) MLT^–2

(4) Dimensionless

The dimensional formula for young's modulus is 

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

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

(3) MLT^–2

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

Frequency is the function of density $\left(\rho \right)$, length (a) and surface tension (T). Then its value is 

1. k.$\frac{\sqrt{\mathrm{T}}}{{\rho }^{1/2}{\mathrm{a}}^{3/2}}$

2. $k{\rho }^{3/2}{a}^{3/2}/\sqrt{T}$

3. $\frac{{\mathrm{T}}^{3/2}}{{\mathrm{k\rho }}^{1/2}{\mathrm{a}}^{3/2}}$

4. $\frac{T^{3/2}}{{\mathrm{k\rho }}^{1/2}{\mathrm{a}}^{1/2}}$

The dimensions of electric potential are:

(1) $\left[M{L}^2{T}^{-2}{Q}^{-1}\right]$

(2) $\left[ML{T}^{-2}{Q}^{-1}\right]$

(3) $\left[M{L}^2{T}^{-1}Q\right]$

(4) $\left[M{L}^2{T}^{-2}Q\right]$

The dimension of $\frac{R}{L}$ are

(1) T²

(2) T

(3) T^–1

(4) T^–2

The dimensions of shear modulus are

(1) MLT^–1

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

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

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

Pressure gradient has the same dimensions as that of:

(1) Velocity gradient

(2) Potential gradient

(3) Energy gradient

(4) None of these