Which of the following cannot function as an oxidising agent?

Oxidising agent = species that gets reduced (gains electrons). For a species to act as an oxidising agent, the central atom must be able to decrease its oxidation state.

Step 1 — Check each species:

(1) $\mathrm{N^{3-}}$: N is in its lowest possible oxidation state ($-3$). It cannot be further reduced → cannot act as oxidising agent ✗

(2) $\mathrm{SO_4^{2-}}$: S is $+6$, can be reduced to lower states (e.g., $\mathrm{SO_2}$, $\mathrm{S}$, $\mathrm{H_2S}$) → can act as oxidising agent ✓

(3) $\mathrm{BrO_3^{-}}$: Br is $+5$, can be reduced to $\mathrm{Br^-}$ ($-1$) → strong oxidising agent ✓

(4) $\mathrm{MnO_4^{-}}$: Mn is $+7$, can be reduced to $\mathrm{Mn^{2+}}$, $\mathrm{MnO_2}$, etc. → very strong oxidising agent ✓

Answer: Option (1) — $\mathrm{N^{3-}}$