Each oxy-acid contains at least one X-OH unit (X is non-metal). The H-atom of X-OH unit is ionisable and the number of -OH groups directly attach to non-metal decides the basicity of oxy-acid.
Q. Which of the following oxy-acid does not have its peroxy form having two central atoms?

Options

A. `H_(2)N_(2)O_(2)`
B. `H_(4)P_(2)O_(6)`
C. `H_(2)S_(2)O_(6)`
D. `H_(3)PO_(3)`

Explanation

To solve the question regarding which oxy-acid does not have its peroxy form having two central atoms, we will analyze each of the given oxy-acids based on their central atoms and their ability to form peroxy linkages.

### Step-by-Step Solution:

1. **Understanding Oxy-Acids and Peroxy Forms**:
- Oxy-acids are acids that contain oxygen, hydrogen, and another element (non-metal).
- A peroxy form of an oxy-acid contains a peroxy linkage (-O-O-), which requires two central atoms.

2. **Analyzing the Given Oxy-Acids**:
- We have four oxy-acids to analyze:
- A) H₂N₂O₂
- B) H₄P₂O₆
- C) H₂S₂O₆
- D) H₃PO₃

3. **Examining Option A: H₂N₂O₂**:
- Central atom: Nitrogen (N).
- Nitrogen is in period 2 and cannot expand its octet.
- Therefore, H₂N₂O₂ cannot form a peroxy linkage and does not have two central atoms in its peroxy form.

4. **Examining Option B: H₄P₂O₆**:
- Central atom: Phosphorus (P).
- Phosphorus is in period 3 and can expand its octet.
- Thus, H₄P₂O₆ can form a peroxy linkage and has two central atoms in its peroxy form.

5. **Examining Option C: H₂S₂O₆**:
- Central atom: Sulfur (S).
- Sulfur is also in period 3 and can expand its octet.
- Therefore, H₂S₂O₆ can form a peroxy linkage and has two central atoms in its peroxy form.

6. **Examining Option D: H₃PO₃**:
- Central atom: Phosphorus (P).
- As previously noted, phosphorus can expand its octet.
- Thus, H₃PO₃ can also form a peroxy linkage and has two central atoms in its peroxy form.

7. **Conclusion**:
- Only H₂N₂O₂ (Option A) does not have a peroxy form with two central atoms because its central atom, nitrogen, cannot expand its octet.

### Final Answer:
The oxy-acid that does not have its peroxy form having two central atoms is **A) H₂N₂O₂**.