Consider the following sequence of reactions
`underset((C_(4)H_(8)O_(3)))(A overset(CrO_(3))rarr B) overset("Warm")rarr CH_(3)overset(O) overset(||)C CH_(3)+CO_(2)`
The compound (A) is :

Options

A. `HOCH_(2)CH_(2)CH_(2)COOH`
B. `CH_(3)CH(OH)CH_(2)COOH`
C. `CH_(3)CH_(2)CH(OH)COOH`
D. `(CH_(3))_(2)C(OH)COOH`

Answer

To determine the compound (A) with the formula C₄H₈O₃, we need to analyze the sequence of reactions provided.

### Step-by-Step Solution:

1. **Identify the Reaction Type**:
The first reaction involves the treatment of compound A (C₄H₈O₃) with CrO₃, which is a mild oxidizing agent. The second part of the reaction indicates that upon warming, a product (B) is formed that leads to the release of CO₂ gas.

**Hint**: Recognize that the release of CO₂ suggests decarboxylation, which typically occurs with carboxylic acids.

2. **Analyze Product B**:
The product B, after warming, is indicated to be CH₃C(=O)CH₃ (acetone) plus CO₂. This suggests that B must contain a carboxylic acid group that can lose CO₂ upon heating.

**Hint**: The presence of CO₂ upon heating indicates that B likely has a carboxylic acid functional group.

3. **Determine Structure of B**:
Given that B leads to CH₃C(=O)CH₃ (acetone) after decarboxylation, we can deduce that B must be a carboxylic acid with the structure CH₃C(=O)CH₂COOH (butanoic acid). This structure allows for the loss of CO₂ when heated.

**Hint**: Consider the structure of B and how it can decarboxylate to yield acetone and CO₂.

4. **Identify Compound A**:
Since B is derived from A through oxidation, and B is a carboxylic acid, A must be a secondary alcohol that can be oxidized to form B. The structure of A can be deduced as CH₃CH(OH)CH₂COOH (2-hydroxybutanoic acid).

**Hint**: Remember that secondary alcohols oxidize to ketones, and since B is a carboxylic acid, A must be a secondary alcohol that can form a carboxylic acid upon oxidation.

5. **Final Structure of A**:
The final structure of A is CH₃CH(OH)CH₂COOH, which is 2-hydroxybutanoic acid.

### Conclusion:
The compound (A) is 2-hydroxybutanoic acid (C₄H₈O₃).