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