The physical quantities not having the same dimensions are

The physical quantities that do not have the same dimensions are momentum and Planck's constant.

Let us analyze the dimensions of each pair step-by-step to verify this:

1. Torque and Work:
Torque ($\tau$) is given by the formula:
$\tau =\text{Force}\times \text{perpendicular distance}$
Dimensions of Force = $\left[{\text{MLT}}^{-2}\right]$
Dimensions of distance = $\left[\text{L}\right]$
Therefore, dimensions of Torque = $\left[{\text{ML}}^2{\text{T}}^{-2}\right]$

Work ($W$) is given by the formula:
$W=\text{Force}\times \text{displacement}$
Therefore, dimensions of Work = $\left[{\text{MLT}}^{-2}\right]\times \left[\text{L}\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$
Since both have the dimensions $\left[{\text{ML}}^2{\text{T}}^{-2}\right]$, torque and work have the same dimensions.

2. Momentum and Planck's constant:
Linear Momentum ($p$) is given by:
$p=\text{mass}\times \text{velocity}$
Dimensions of Momentum = $\left[\text{M}\right]\times \left[{\text{LT}}^{-1}\right]=\left[{\text{MLT}}^{-1}\right]$

Planck's constant ($h$) is related to energy ($E$) and frequency ($\nu$) by the relation $E=h\nu$:
$h=\frac{E}{\nu }$
Dimensions of Energy = $\left[{\text{ML}}^2{\text{T}}^{-2}\right]$
Dimensions of frequency = $\left[{\text{T}}^{-1}\right]$
Therefore, dimensions of Planck's constant = $\frac{\left[{\text{ML}}^2{\text{T}}^{-2}\right]}{\left[{\text{T}}^{-1}\right]}=\left[{\text{ML}}^2{\text{T}}^{-1}\right]$
Comparing the two, we see that $\left[{\text{MLT}}^{-1}\right]\ne \left[{\text{ML}}^2{\text{T}}^{-1}\right]$. Thus, momentum and Planck's constant do not have the same dimensions.

3. Stress and Young's modulus:
Stress is given by:
$\text{Stress}=\frac{\text{Force}}{\text{Area}}$
Dimensions of Stress = $\frac{\left[{\text{MLT}}^{-2}\right]}{\left[{\text{L}}^2\right]}=\left[{\text{ML}}^{-1}{\text{T}}^{-2}\right]$

Young's modulus ($Y$) is given by:
$Y=\frac{\text{Stress}}{\text{Strain}}$
Since strain is a dimensionless quantity ($\left[{\text{M}}^0{\text{L}}^0{\text{T}}^0\right]$), the dimensions of Young's modulus are identical to those of stress:
Dimensions of Young's modulus = $\left[{\text{ML}}^{-1}{\text{T}}^{-2}\right]$
Thus, stress and Young's modulus have the same dimensions.

4. Speed and 1/√(ε₀μ₀):
From electromagnetic theory, the speed of light ($c$) in vacuum is given by:
$c=\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$
Where ${\epsilon }_0$ is the permittivity of free space and ${\mu }_0$ is the permeability of free space.
Since this expression represents the speed of light, its dimensions are identical to the dimensions of speed:
Dimensions = $\left[{\text{LT}}^{-1}\right]$
Thus, speed and $\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$ have the same dimensions.