Assertion (A): Due to common ion effect, the solubility of `HgI_(2)` is expected to be less in an aqueous solution of `KI` than in water. But `HgI_(2)` dissolves in an aqueous solution of `KI` to form a clear solution.
Reason (R) : `I^(Theta)` ions is highly polarisable.

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 the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the solubility of `HgI₂` is expected to be less in an aqueous solution of `KI` than in pure water due to the common ion effect.
- The common ion effect indicates that the presence of a common ion (in this case, `I⁻` from `KI`) will suppress the solubility of a salt (here, `HgI₂`).

2. **Analyzing the Reaction**:
- The dissolution of `HgI₂` in water can be represented as:
\[ HgI₂ (s) \rightleftharpoons Hg^{2+} (aq) + 2I^{-} (aq) \]
- When `KI` is added, it dissociates into `K⁺` and `I⁻` ions. The increased concentration of `I⁻` ions shifts the equilibrium to the left, reducing the solubility of `HgI₂`.

3. **Formation of Soluble Complex**:
- Despite the common ion effect, `HgI₂` can still dissolve in `KI` to form a soluble complex:
\[ HgI₂ + 2KI \rightarrow K_2HgI_4 (aq) \]
- This complex formation explains why a clear solution is observed even in the presence of `KI`.

4. **Conclusion on Assertion**:
- The assertion is correct: the solubility of `HgI₂` is expected to be less in `KI` due to the common ion effect, but it still dissolves to form a soluble complex.

5. **Understanding the Reason (R)**:
- The reason states that `I⁻` ions are highly polarizable. This is true because `I⁻` is a larger ion, which makes it more polarizable.
- However, the polarizability of `I⁻` does not directly explain the solubility behavior of `HgI₂` in `KI`.

6. **Conclusion on Reason**:
- The reason is also correct, but it does not provide the correct explanation for the assertion. The solubility of `HgI₂` in `KI` is primarily due to the formation of the soluble complex rather than the polarizability of `I⁻`.

7. **Final Evaluation**:
- Both the assertion and the reason are correct, but the reason is not the correct explanation for the assertion. Therefore, the correct answer is that both A and R are correct, but R is not the correct explanation of A.

### Final Answer:
- The correct option is: **Both A and R are correct, but R is not the correct explanation of A.**