Study the following sequence of reaction and identify the product (Y).
`CH_(3)CHO +HCHO overset("dil."NaOH)underset("heat") to X overset(HCN) underset(H_(3)O^(+)) to Y`

Options

A. `CH_(2)=CH-underset(OH)underset(|)(CH)-COOH`
B. `CH_(3)-overset(CN)overset(|)underset(OH)underset(|)C-COOH`
C. `CH_(3)CH_(2)-underset(OH) underset(|)CH-COOH`
D. `CH_(2)=CH-underset(CN)underset(|)(CH)-COOH`

Explanation

To solve the problem, we need to analyze the given reactions step by step.

### Step 1: Identify the first reaction
The first reaction involves acetaldehyde (CH₃CHO) reacting with formaldehyde (HCHO) in the presence of dilute NaOH and heat. This reaction is known as aldol condensation.

1. **Write the reactants:**
- Acetaldehyde (CH₃CHO)
- Formaldehyde (HCHO)

2. **Identify the aldol condensation:**
- Aldol condensation requires at least one of the reactants to have an alpha-hydrogen. Acetaldehyde has an alpha-hydrogen (the hydrogen on the carbon adjacent to the carbonyl group).

3. **Mechanism of aldol condensation:**
- The hydroxide ion (OH⁻) from NaOH will deprotonate the alpha-hydrogen of acetaldehyde, forming an enolate ion.
- The enolate ion will then attack the carbonyl carbon of formaldehyde, leading to the formation of a β-hydroxy aldehyde (the aldol product).

4. **Formulate the product (X):**
- The product (X) after aldol condensation will be 3-hydroxybutanal (CH₃CH(OH)CH₂CHO).

### Step 2: Identify the second reaction
The second reaction involves the product (X) reacting with HCN in the presence of H₃O⁺.

1. **Write the reactant:**
- The product from the first reaction: 3-hydroxybutanal (CH₃CH(OH)CH₂CHO).

2. **Mechanism of cyanohydrin formation:**
- The carbonyl group (CHO) of 3-hydroxybutanal can react with HCN to form a cyanohydrin.
- The hydroxyl group (OH) will remain, and the CN group will add to the carbonyl carbon.

3. **Formulate the product (Y):**
- The product (Y) after this reaction will be 3-hydroxybutyronitrile (CH₃CH(OH)CH₂CN).

### Final Product
The final product (Y) is 3-hydroxybutyronitrile.

### Conclusion
Thus, the product (Y) is **3-hydroxybutyronitrile**.