Staements I: `._zX^A` undergoes `2 alpha`-decays, `2 beta`-decays (negative `beta`) and `2 gamma`-decays. As a result, the daughter product is `._z._-2X^(A-8)`.
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

Answer

To solve the problem, we need to analyze the decay processes step by step based on the information provided in the statements.

### Step-by-Step Solution:

1. **Initial Nucleus**: We start with a nucleus represented as \( _zX^A \), 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.
- After 2 alpha decays:
- Mass number: \( A - 4 - 4 = A - 8 \)
- Atomic number: \( z - 2 - 2 = z - 4 \)
- Thus, after 2 alpha decays, the nucleus becomes \( _{z-4}X^{A-8} \).

3. **Beta Decay**:
- In negative beta decay, the mass number remains unchanged, but the atomic number increases by 1.
- After 2 beta decays:
- Mass number: \( A - 8 \) (remains the same)
- Atomic number: \( z - 4 + 2 = z - 2 \)
- Thus, after 2 beta decays, the nucleus becomes \( _{z-2}X^{A-8} \).

4. **Gamma Decay**:
- In gamma decay, both the mass number and atomic number remain unchanged.
- Therefore, after 2 gamma decays, the nucleus remains \( _{z-2}X^{A-8} \).

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

### Conclusion:
- Statement I is true as the daughter product is indeed \( _{z-2}X^{A-8} \).
- Statement II is also true as it accurately describes the changes in mass number and atomic number during alpha, beta, and gamma decays.

### Final Answer:
Both statements are true, and Statement II provides the correct explanation for Statement I.