In the reaction sequence
`CH_(3)-overset(O)overset(||)(C)-H-underset(.^(Θ)OH)overset(HCN)rarr(A) underset(Delta)overset(H_(2)O //overset(o+)(H))rarr` Product is/are :

Options

A. Diasteromers
B. Racemic mixture of hydroxy acid
C. Product is racemic mixture of cyanohydrin
D. Products is optically inactive

Explanation

To solve the given question, we will follow the reaction sequence step by step.

### Step 1: Identify the Reactants
The reactant given is acetaldehyde (CH₃CHO) and it is reacted with HCN in a basic medium.

### Step 2: Understand the Reaction Type
The reaction between acetaldehyde and HCN is an example of a nucleophilic addition reaction. In this reaction, the nucleophile (CN⁻) attacks the electrophilic carbon of the carbonyl group.

### Step 3: Mechanism of the Reaction
1. The carbonyl carbon (C=O) is electrophilic due to the partial positive charge on it. The nucleophile (CN⁻) attacks this carbon.
2. The oxygen atom of the carbonyl group becomes negatively charged as a result of the nucleophilic attack.
3. The intermediate formed is a cyanohydrin, which has the structure:
\[ \text{C(OH)(CH₃)(CN)} \]
This is referred to as product A.

### Step 4: Hydrolysis of Cyanohydrin
The cyanohydrin undergoes hydrolysis when treated with water (H₂O) and heat. The hydrolysis reaction can be represented as follows:
1. The cyanohydrin reacts with water, leading to the formation of a hydroxy acid.
2. The product formed after hydrolysis is lactic acid (C₃H₆O₃), which can be represented as:
\[ \text{CH₃CHOHCOOH} \]

### Step 5: Determine the Optical Activity
Lactic acid exists in two forms: L-lactic acid and D-lactic acid, which are enantiomers (non-superimposable mirror images). Since both forms are produced in equal amounts during the reaction, the final product is a racemic mixture.

### Conclusion
The final product of the reaction sequence is a racemic mixture of lactic acid.

### Answer
The correct answer is: **A racemic mixture of lactic acid.**

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