Idea: An oxidising agent is a species that gets reduced itself, i.e. it should be able to accept electrons.

So we check the oxidation state of the central atom in each species:

• A. $\mathrm{SO_4^{2-}}$

  Let oxidation state of S be $x$: $x + 4(-2) = -2$ $x - 8 = -2$ $x = +6$ Sulfur is in a high oxidation state, so it can be reduced and hence can act as an oxidising agent.

• B. $\mathrm{MnO_4^-}$

  Let oxidation state of Mn be $x$: $x + 4(-2) = -1$ $x - 8 = -1$ $x = +7$ Manganese is in its maximum/common highest oxidation state, so permanganate is a strong oxidising agent.

• C. $\mathrm{N^{3-}}$

  Oxidation state of nitrogen is $-3$. This is the lowest possible oxidation state of nitrogen, so it cannot be reduced further. Therefore it cannot accept electrons and hence cannot act as an oxidising agent.

• D. $\mathrm{BrO_3^-}$

  Let oxidation state of Br be $x$: $x + 3(-2) = -1$ $x - 6 = -1$ $x = +5$ Bromine in $+5$ oxidation state can still be reduced, so bromate can act as an oxidising agent.

Conclusion: The species that cannot function as an oxidising agent is: $\boxed{\mathrm{N^{3-}}}$

Option check:

• A: Can act as oxidising agent
• B: Can act as oxidising agent
• C: Cannot act as oxidising agent
• D: Can act as oxidising agent