Assertion (A): `pH` value of `HCN` solution decreases when `NaCN` is added to it.
Reason (R) : `NaCN` provides a common ion `CN^(Theta)`.

Options

A. If both (A) and (R) are correc, and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct but (R) is not the correct explanation of (A).
C. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect, but (R) is correct.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the pH value of an HCN solution decreases when NaCN is added to it.
- HCN (hydrocyanic acid) is a weak acid that partially dissociates in solution to produce H⁺ ions and CN⁻ ions.

2. **Analyzing the Effect of Adding NaCN**:
- NaCN (sodium cyanide) is a salt that completely dissociates in solution to provide Na⁺ ions and CN⁻ ions.
- The addition of NaCN increases the concentration of the CN⁻ ion in the solution.

3. **Common Ion Effect**:
- The presence of a common ion (in this case, CN⁻) will affect the dissociation of the weak acid (HCN).
- According to Le Chatelier's principle, if the concentration of one of the products (CN⁻) increases, the equilibrium of the dissociation of HCN will shift to the left to counteract this change, resulting in a decrease in the concentration of H⁺ ions.

4. **Impact on pH**:
- Since the concentration of H⁺ ions decreases when NaCN is added, the pH of the solution will actually increase (because pH is inversely related to the concentration of H⁺ ions).
- Therefore, the assertion that the pH decreases is incorrect.

5. **Understanding the Reason (R)**:
- The reason states that NaCN provides a common ion (CN⁻).
- This statement is correct; NaCN does indeed provide the common ion CN⁻.

6. **Conclusion**:
- The assertion (A) is incorrect because the pH of the solution increases, not decreases, when NaCN is added.
- The reason (R) is correct because NaCN does provide a common ion.
- Therefore, the correct answer is that assertion A is incorrect and reason R is correct.

### Final Answer:
The correct option is **4**: Assertion A is incorrect, but Reason R is correct.