Staements I: `._zX^4` undergoes `2 alpha`-decays, `2 beta`-decays (negative `beta`) and `2 gamma`-decays. As a result, the daughter product is `._z._-2X^(A-B)`.
Staements II: In `alpha`-decay, the mass number decreases by 4 unit and atomic number decreases by `2` unit. In `beta`-decay (negative `beta`), the mass number remains unchanged and atomic number increases by `1` unit. In `gamma`-decay, mass number and atomic number remain unchanged.

Options

A. Statement-1 is true, Statement-2: is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is true, Statement-2: is true, Statement-2 is NOT a correct explanation for Statement-1.
C. Statement-1 is true but statement-2 is false
D. Statement-1 is false, Statement-2 is true

Explanation

To solve the problem, we need to analyze the changes in the atomic and mass numbers of the parent atom \( _zX^A \) after it undergoes the specified decays.

### Step-by-Step Solution

1. **Identify the Initial Values**:
- We start with a parent atom \( _zX^A \) where \( A \) is the mass number and \( z \) is the atomic number.

2. **Alpha Decay**:
- In alpha decay, the mass number decreases by 4 and the atomic number decreases by 2.
- Since there are 2 alpha decays:
- Mass number after 2 alpha decays: \( A - 2 \times 4 = A - 8 \)
- Atomic number after 2 alpha decays: \( z - 2 \times 2 = z - 4 \)

3. **Beta Decay**:
- In beta decay (negative beta), the mass number remains unchanged, while the atomic number increases by 1.
- Since there are 2 beta decays:
- Mass number remains: \( A - 8 \)
- Atomic number after 2 beta decays: \( (z - 4) + 2 = z - 2 \)

4. **Gamma Decay**:
- In gamma decay, there is no change in either the mass number or the atomic number.
- Therefore, after 2 gamma decays:
- Mass number remains: \( A - 8 \)
- Atomic number remains: \( z - 2 \)

5. **Final Daughter Product**:
- After all the decays, the daughter product can be represented as \( _{z-2}X^{A-8} \).

### Conclusion
The final daughter product after the specified decays is \( _{z-2}X^{A-8} \), which confirms that Statement I is incorrect as it states the daughter product should be \( _{z}X^{(A-B)} \) instead of \( _{z-2}X^{(A-8)} \).

Statement II is correct as it accurately describes the changes in atomic and mass numbers during alpha, beta, and gamma decays.

### Final Answer
- Statement I: False
- Statement II: True

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