In acidic medium, \( \text{KMnO}_4 \) acts as an oxidizing agent. The reaction of \( \text{KMnO}_4 \) with \( \text{H}_2\text{S} \) leads to the precipitation of sulphur. This reaction occurs in acidic medium, where \( \text{KMnO}_4 \) oxidizes \( \text{H}_2\text{S} \) to sulphur. The other reactions do not occur in acidic medium or are not typical reactions for \( \text{KMnO}_4 \).
Therefore, the correct answer is Precipitation of sulphur from \( \text{H}_2\text{S} \).