In neutral or mild alkaline solutions, potassium permanganate oxidizes manganous salt ($Mn^{2+}$) to.

$MnO_2$

The correct answer is Option (1) → $MnO_2$

Potassium permanganate (KMnO₄) is a strong oxidizing agent, but its oxidizing behaviour depends on the medium in which the reaction takes place.

The reduction product of permanganate ion MnO₄⁻ varies as follows:

In acidic medium MnO₄⁻ is reduced to Mn²⁺

In neutral or mildly alkaline medium MnO₄⁻ is reduced to MnO₂

In strongly alkaline medium MnO₄⁻ is reduced to MnO₄²⁻ (manganate ion)

Since the question specifies neutral or mildly alkaline solution, MnO₄⁻ will be reduced to MnO₂. During this process, KMnO₄ acts as an oxidizing agent and oxidizes Mn²⁺ (manganous ion) to MnO₂.

Oxidation state change of manganese: Mn²⁺ → MnO₂

In Mn²⁺, oxidation state of Mn = +2

In MnO₂, oxidation state of Mn = +4

Thus, Mn²⁺ undergoes oxidation.

Relevant half reactions in neutral/mild alkaline medium:

Reduction of permanganate:

MnO₄⁻ + 2H₂O + 3e⁻ → MnO₂ + 4OH⁻

Oxidation of manganous ion:

Mn²⁺ + 2H₂O → MnO₂ + 4H⁺ + 2e⁻

Overall, manganous ion is oxidized to MnO₂, which appears as a brown precipitate.

Why other options are incorrect:

Option 2 Mn²⁺

No oxidation occurs. This is the starting species.

Option 3 MnO₄²⁻

This forms only in strongly alkaline medium, not in neutral or mildly alkaline medium.

Option 4 MnO₄⁻

This is permanganate itself, not the oxidation product of Mn²⁺.