Consider the following unbalanced redox reaction:
`H_(2)O+AX+BYrarrHA+OY+X_(2)B`
The oxidation number of `X` is `-2` and niether `X` nor water is involved in the redox process.
The positive oxidation states of `B` and `Y` in `BY` are respectively,

Options

A. `+1, -1`
B. `+2,-2`
C. `+3,-3`
D. All of these

Explanation

To solve the problem, we need to determine the positive oxidation states of elements B and Y in the compound BY, given the unbalanced redox reaction:

\[ H_2O + AX + BY \rightarrow HA + OY + X_2B \]

### Step-by-Step Solution:

1. **Identify the Oxidation States**:
- The oxidation state of \( X \) is given as \(-2\).
- Water (\( H_2O \)) is not involved in the redox process, so its oxidation states remain unchanged: \( H \) is \( +1 \) and \( O \) is \( -2 \).

2. **Write the Reaction**:
- The unbalanced reaction is:
\[ H_2O + AX + BY \rightarrow HA + OY + X_2B \]

3. **Determine the Oxidation State of A**:
- In the compound \( AX \), since \( X \) has an oxidation state of \(-2\), the oxidation state of \( A \) must be \( +2 \) to balance the charge.

4. **Determine the Oxidation State of HA**:
- In \( HA \), \( H \) is \( +1 \) and the total charge must balance to zero. Therefore, the oxidation state of \( A \) in \( HA \) must be \(-1\) (since \( +1 + (-1) = 0 \)).
- This indicates that \( A \) is reduced from \( +2 \) to \(-1\).

5. **Determine the Oxidation State of Y in OY**:
- In \( OY \), since \( O \) is \(-2\), to balance the charge, \( Y \) must be \( +2 \) (because \(-2 + 2 = 0\)).

6. **Determine the Oxidation State of B in X2B**:
- In \( X_2B \), since \( X \) has an oxidation state of \(-2\) and there are two \( X \) atoms, the total contribution from \( X \) is \(-4\).
- To balance this, \( B \) must have an oxidation state of \( +4 \) (because \(-4 + 4 = 0\)).

7. **Conclusion**:
- The positive oxidation states of \( B \) and \( Y \) in \( BY \) are \( +4 \) and \( +2 \) respectively.

### Final Answer:
- The positive oxidation states of \( B \) and \( Y \) in \( BY \) are \( +4 \) and \( +2 \).