Consider the following redox reaction :
`H_(2)O + AX + BY rarr HA + YO + BX_(2)` (unbalanced)
It is also known that oxidation number of `X` is `-2` and neither `X` nor water is involved in the redox process. (In compound `BY, B` is cation and consider its oxidation number `lt 4`).
Answer the following question based on the information given.
Select the correct option(s) :

Options

A. The element `A` is under going reduction.
B. The element `B` is under going reduction.
C. The element `B` is under going oxidation.
D. The element `Y` is under going oxidation.

Answer

To solve the given redox reaction problem step by step, we will analyze the oxidation states and the changes occurring in the reaction.

### Step 1: Identify the oxidation states
In the reaction:
\[ H_2O + AX + BY \rightarrow HA + YO + BX_2 \]

We are given that the oxidation number of \( X \) is \(-2\).

### Step 2: Determine the oxidation state of \( A \)
Since \( X \) has an oxidation state of \(-2\), we can deduce the oxidation state of \( A \) in the compound \( AX \). The overall charge of the compound \( AX \) must be neutral, so:
\[ \text{Oxidation state of } A + (-2) = 0 \]
This implies:
\[ \text{Oxidation state of } A = +2 \]

### Step 3: Analyze the change in oxidation state of \( A \)
In the product \( HA \), since \( H \) has an oxidation state of \( +1 \), the oxidation state of \( A \) must be:
\[ +1 + \text{Oxidation state of } A = 0 \]
This means:
\[ \text{Oxidation state of } A = -1 \]
Thus, \( A \) is reduced from \( +2 \) to \(-1\), indicating that \( A \) is undergoing reduction.

### Step 4: Determine the oxidation state of \( B \)
We know that \( B \) is a cation with an oxidation state less than \( +4 \). In the product \( BX_2 \), since \( X \) has an oxidation state of \(-2\):
\[ \text{Oxidation state of } B + 2(-2) = 0 \]
This leads to:
\[ \text{Oxidation state of } B - 4 = 0 \]
Thus:
\[ \text{Oxidation state of } B = +4 \]

### Step 5: Analyze the change in oxidation state of \( B \)
Since \( B \) started with an oxidation state less than \( +4 \) and increased to \( +4 \), it has lost electrons, which means \( B \) is undergoing oxidation.

### Step 6: Determine the oxidation state of \( Y \)
In the product \( YO \), where \( O \) has an oxidation state of \(-2\):
\[ \text{Oxidation state of } Y + (-2) = 0 \]
This implies:
\[ \text{Oxidation state of } Y = +2 \]

### Step 7: Analyze the change in oxidation state of \( Y \)
If \( Y \) was originally an anion (since \( B \) is a cation), it must have had a negative oxidation state. The change from a negative state to \( +2 \) indicates that \( Y \) has also lost electrons, meaning \( Y \) is undergoing oxidation.

### Conclusion
Based on the analysis:
- \( A \) is undergoing reduction.
- \( B \) is undergoing oxidation.
- \( Y \) is also undergoing oxidation.

Thus, the correct options based on the information provided are:
- A: \( A \) is undergoing reduction (Correct)
- B: \( B \) is undergoing reduction (Incorrect, \( B \) is oxidized)
- C: \( B \) is undergoing oxidation (Correct)
- D: \( Y \) is undergoing oxidation (Correct)

### Final Answer
The correct options are A, C, and D.