Step 1: Understanding the Concept:
The reaction sequence involves hydroboration-oxidation, controlled oxidation of an alcohol, and Grignard addition to a carbonyl compound.
Step 2: Key Formula or Approach:
Map the reagents to their specific organic transformations: hydroboration-oxidation yields anti-Markovnikov alcohols, $CrO_3$ in anhydrous media stops at the aldehyde stage, and Grignard addition creates a higher-order alcohol. (Note: The starting material is indicated as $C_4H_{10}$ in OCR, but hydroboration applies to alkenes; we proceed based on the products derived from an implied terminal alkene like propene or butene. Based on the options, the starting alkene is propene $C_3H_6$ since the products have 3 carbon chains before Grignard.)
Step 3: Detailed Explanation:
Let's analyze the options. The options (B) and (C) suggest the chain "P" has 3 carbons ($CH_3-CH_2-CH_2-OH$). This implies the starting alkene was Propene ($CH_3-CH=CH_2$), not $C_4H_{10}$.
1. Reaction 1 (Hydroboration-Oxidation): $CH_{3}-CH=CH_{2}$ reacts with $(BH_{3})_{2}$ followed by $H_{2}O_{2}/NaOH$. This is an anti-Markovnikov addition of water.
Product P: $CH_{3}-CH_{2}-CH_{2}-OH$ (Propan-1-ol).
2. Reaction 2 (Mild Oxidation): P (Propan-1-ol) reacts with $CrO_{3}$ in anhydrous medium. Primary alcohols are oxidized to aldehydes.
Product Q: $CH_{3}-CH_{2}-CHO$ (Propanal).
3. Reaction 3 (Grignard Reaction): Q (Propanal) reacts with $CH_{3}MgBr$ followed by hydrolysis. The nucleophilic $CH_{3}^{-}$ attacks the carbonyl carbon of the aldehyde.
Product R: $CH_{3}-CH_{2}-CH(OH)-CH_{3}$ (Butan-2-ol).
Step 4: Final Answer:
Matching the derived structures with the options leads to choice (B).