The species given below that does NOT show disproportionation reaction is:

Disproportionation requires the element to have an intermediate oxidation state — it must be able to both increase and decrease its oxidation state.

Step 1 — Oxidation states of Br in each species:

| Species | Oxidation state of Br | |---|---| | $\mathrm{BrO_4^{-}}$ | $x + 4(-2) = -1 \Rightarrow x = +7$ (highest possible) | | $\mathrm{BrO^{-}}$ | $x + (-2) = -1 \Rightarrow x = +1$ | | $\mathrm{BrO_2^{-}}$ | $x + 2(-2) = -1 \Rightarrow x = +3$ | | $\mathrm{BrO_3^{-}}$ | $x + 3(-2) = -1 \Rightarrow x = +5$ |

Step 2 — Identify which cannot disproportionate:

$\mathrm{BrO_4^{-}}$ has Br in the highest oxidation state (+7). It cannot be further oxidised, so it cannot undergo disproportionation (which requires simultaneous oxidation AND reduction of the same element).

$\mathrm{BrO^{-}}$, $\mathrm{BrO_2^{-}}$, and $\mathrm{BrO_3^{-}}$ all have intermediate oxidation states and can disproportionate.

Answer: Option (1) — $\mathrm{BrO_4^{-}}$