To determine the correct matches between List I and List II, we need to consider the dimensional formulas of the given physical quantities.

1. Torque (τ) is defined as the product of force (F) and distance (d):

$ \tau = F \cdot d $

The dimensional formula for torque is:

$ [\tau] = [M^1 L^2 T^{-2}] $

Thus, Torque corresponds to IV.

1. Magnetic field (B) is derived from the relation involving force (F), charge (q), and velocity (V):

$ F = qVB $

The dimensional formula for the magnetic field is:

$ [B] = [M^1 T^{-2} A^{-1}] $

Thus, Magnetic field corresponds to III.

1. Magnetic moment (M) is the product of current (I) and area (A):

$ M = I \cdot A $

The dimensional formula for the magnetic moment is:

$ [M] = [L^2 A^1] $

Thus, Magnetic moment corresponds to II.

1. Permeability of free space (μ₀) has the dimensional formula:

$ [μ₀] = [M^1 L^1 T^{-2} A^{-2}] $

Thus, Permeability of free space corresponds to I.

Based on the above analysis, the correct matches are:

• A. Torque – IV


• B. Magnetic Field – III


• C. Magnetic Moment – II


• D. Permeability of free space – I

Therefore, the correct option is Option D:

A-IV, B-III, C-II, D-I.