We need to identify which quantity is not dimensionless.

A quantity is dimensionless if it has no physical dimensions, i.e. its dimensional formula is $M^0L^0T^0$.

Check each option:

A) Relative magnetic permeability $(\mu_r)$

Relative permeability is defined as $\mu_r = \frac{\mu}{\mu_0}$ Since it is a ratio of two quantities having the same dimensions, it is dimensionless.

B) Power factor

Power factor is $\text{Power factor} = \cos\phi$ where $\phi$ is the phase difference. Since cosine of an angle is a pure number, power factor is dimensionless.

C) Permeability of free space $(\mu_0)$

From electromagnetic relations, $F = \frac{\mu_0 I_1 I_2 \ell}{2\pi r}$ so $\mu_0$ has physical dimensions.

Also, its SI unit is $\text{N A}^{-2}$ Hence it is not dimensionless.

D) Quality factor

Quality factor is generally defined as a ratio such as $Q = 2\pi \times \frac{\text{energy stored}}{\text{energy lost per cycle}}$ This is a ratio of same-dimensional quantities, so it is dimensionless.

Conclusion

The only quantity that is not dimensionless is: $\boxed{\text{C) Permeability of free space } (\mu_0)}$