In which of the following arrangements the order is NOT according to the property indicated against it?

We check every set one by one and compare it with the correct periodic trend.

Case 1: $$\text{Al}^{3+} \lt \text{Mg}^{2+} \lt \text{Na}^+ \lt \text{F}^-$$ (claimed: increasing ionic size)
All four ions are isoelectronic with $$10$$ electrons. Within an isoelectronic series, the ionic radius decreases as nuclear charge ($$Z$$) increases because the same electron cloud is attracted more strongly.
$$Z(\text F^-)=9,\;Z(\text{Na}^+)=11,\;Z(\text{Mg}^{2+})=12,\;Z(\text{Al}^{3+})=13$$
Hence radius order is $$\text{Al}^{3+} \lt \text{Mg}^{2+} \lt \text{Na}^+ \lt \text{F}^-$$, exactly as given. Therefore Case 1 is CORRECT.

Case 2: $$\text B \lt \text C \lt \text N \lt \text O$$ (claimed: increasing first-ionisation enthalpy)
Across a period, first ionisation enthalpy generally rises because of increasing nuclear charge, but there are two well-known exceptions: $$\text{Be} \gt \text{B}$$ and $$\text{N} \gt \text{O}$$ owing to the extra stability of the completely filled $$2s$$ subshell in Be and the half-filled $$2p^3$$ configuration in N.
Thus the actual order should be
$$\text B \lt \text C \lt \text O \lt \text N$$
The sequence given places $$\text N$$ before $$\text O$$, so it violates the real trend. Hence Case 2 is INCORRECT.

Case 3: $$\text I \lt \text{Br} \lt \text F \lt \text{Cl}$$ (claimed: increasing electron-gain enthalpy, i.e. becoming more negative)
Among the halogens the magnitude of electron-gain enthalpy follows
$$\text{Cl} \gt \text F \gt \text{Br} \gt \text I$$
Therefore, in terms of algebraic value (more negative means “larger”), the ascending order is indeed
$$\text I \lt \text{Br} \lt \text F \lt \text{Cl}$$. Case 3 is CORRECT.

Case 4: $$\text{Li} \lt \text{Na} \lt \text K \lt \text{Rb}$$ (claimed: increasing metallic radius)
Metallic/atomic radius grows down any group owing to the addition of new shells. The given order matches this. Case 4 is CORRECT.

The only arrangement that does not follow the stated property is Case 2.

Option B which is: $$\text{B} \lt \text{C} \lt \text{N} \lt \text{O}$$ — Increasing first ionisation enthalpy