Which of the following reactions are disproportionation reaction ?

Options

A. `2Cu^(+)toCu^(2+)+Cu^(0)`
B. `3KMnO_(4)^(2-)4H^(+)to2MnO_(4)^(-)+MnO_(2)+2H_(2)O`
C. `2KMnO_(4)overset(triangle)toK_(2)MnO_(4)+MnO_(2)+O_(2)`
D. `2MnO_(4)^(-)+3Mn^(2+)+2H_(2)Oto5MnO_(2)+4H^(+)`

Explanation

To determine which of the following reactions are disproportionation reactions, we need to identify if the same element in a reaction is both oxidized and reduced. Let's analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Disproportionation Reaction**:
- A disproportionation reaction involves a single element undergoing both oxidation (loss of electrons) and reduction (gain of electrons) simultaneously, resulting in two different products with different oxidation states.

2. **Analyzing Option A**:
- Reaction: \( \text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu}^0 \)
- In this reaction, copper in the +1 oxidation state is oxidized to +2 (losing an electron) and reduced to 0 (gaining an electron).
- **Conclusion**: This is a disproportionation reaction.

3. **Analyzing Option B**:
- Reaction: \( \text{MnO}_4^- + 8 \text{H}^+ \rightarrow 2 \text{MnO}_4^{2-} + \text{MnO}_2 \)
- Here, manganese in \( \text{MnO}_4^- \) is in the +7 oxidation state and is reduced to +4 in \( \text{MnO}_2 \) (gaining electrons) while another manganese is oxidized from +6 to +7 (losing electrons).
- **Conclusion**: This is also a disproportionation reaction.

4. **Analyzing Option C**:
- Reaction: \( \text{KMnO}_4 \rightarrow \text{K}_2\text{MnO}_4 + \text{MnO}_2 \)
- In this case, manganese goes from +7 in \( \text{KMnO}_4 \) to +6 in \( \text{K}_2\text{MnO}_4 \) (reduction) and to +4 in \( \text{MnO}_2 \) (also reduction).
- **Conclusion**: This is not a disproportionation reaction since both transformations are reductions.

5. **Analyzing Option D**:
- Reaction: \( \text{MnO}_4^- \rightarrow \text{Mn}^{2+} + \text{MnO}_2 \)
- Here, manganese goes from +7 in \( \text{MnO}_4^- \) to +2 (reduction) and +4 in \( \text{MnO}_2 \) (also reduction).
- **Conclusion**: This is also not a disproportionation reaction as there is no oxidation occurring.

### Final Answer:
The correct options that represent disproportionation reactions are **A and B**.