Step 1: Understanding the Reaction Sequence
- The starting compound is tert-butanol \((CH_3)_3COH\).
- The first step involves reaction with Na, converting it into the sodium alkoxide \((CH_3)_3CO^-Na^+\) (P).
- The second step involves treatment with CH\(_3\)Br, leading to an alkylation reaction forming \((CH_3)_3CBr\) (Q).
- In the final step, hydrolysis with HI results in substitution of Br by Cl, giving \( (CH_3)_3Cl \), and an additional byproduct CH\(_3\)OH.
Step 2: Identifying the Products
- The final products obtained are \( (CH_3)_3Cl \) (tert-butyl chloride) and \( CH_3OH \) (methanol).
Step 3: Correct Answer
Thus, the correct answer is (CH\(_3\))\(_3\)Cl, CH\(_3\)OH.