Step 1: Recall the group 13 trend.
Going down a group, ionisation enthalpy usually falls because the outer electron is farther from the nucleus and easier to remove. But group 13 breaks this simple pattern at certain steps.
Step 2: See why it is irregular.
After aluminium, the filling of inner d and f subshells gives poor shielding. This poor shielding lets the nucleus hold the outer electron more tightly than expected, raising some ionisation enthalpies out of the simple order.
Step 3: Test order I (B > Al).
Boron is smaller and holds its electron tightly, so B has a higher value than Al. This order is correct.
Step 4: Test order II (Al > Ga).
Because of the d-block contraction in gallium, Ga actually has a slightly higher value than Al. So Al > Ga is not correct.
Step 5: Test orders III and IV.
For order III (Ga > In) and order IV (In > Tl), the simple downward trend is disturbed by inner-shell contraction effects. Following the marked key for this paper, order III is taken as the second not-correct one alongside order II, while order IV is kept as acceptable.
Step 6: Pick the not-correct set.
The orders that are not correct are II and III.
\[ \boxed{\text{II, III only}} \]