An example of a disproportionation reaction is

Disproportionation = same element simultaneously oxidised and reduced.

Step 1 — Check option (3): $\mathrm{2CuBr \rightarrow CuBr_2 + Cu}$

• Cu in $\mathrm{CuBr}$: $+1$ (reactant)
• Cu in $\mathrm{CuBr_2}$: $+2$ → oxidised
• Cu in $\mathrm{Cu}$: $0$ → reduced
• Same element (Cu) both oxidised and reduced → Disproportionation ✓

Step 2 — Eliminate others:

(1) $\mathrm{2KMnO_4 \rightarrow K_2MnO_4 + MnO_2 + O_2}$:

• Mn: $+7 \rightarrow +6$ (reduced) and $+7 \rightarrow +4$ (reduced)
• O: $-2 \rightarrow 0$ (oxidised in $\mathrm{O_2}$) Different elements change → this is a decomposition/redox but Mn only reduces; O is oxidised. Not a pure disproportionation.

(2) Two different elements (Mn reduced, I oxidised) → not disproportionation ✗

(4) $\mathrm{Br^-}$ oxidised, $\mathrm{Cl_2}$ reduced — two different elements → displacement, not disproportionation ✗

Answer: Option (3) — $\mathrm{2CuBr \rightarrow CuBr_2 + Cu}$