An organic compound [A], molecular formula `C_(10)H_(20)O_(2)` was hydrolyzed with dilute sulphuric acid to
give a carboxylic acid [B] and an alcohol [C]. Oxidation of [C] with `CrO_(3) - H_(2)SO_(4)` produced [B].
Which of the following strucutres are not possible for [A]?

Options

A. `(CH_(3))_(3)-C-COOCH_(2)C(CH_(3))_(3)`
B. `CH_(3)-CH_(2)-underset(CH_(3))underset("| ")"CH"-OCOCH_(2)overset(CH_(3))overset("| ")"CH"-CH_(2)CH_(3)`
C. `CH_(3)CH_(2)CH_(2)COOCH_(2)CH_(2)CH_(2)CH_(3)`
D. `CH_(3)-CH_(2)-underset(CH_(3))underset("| ")"CH"-COOCH_(2)-overset(CH_(3))overset("| ")"CH"-CH_(2)CH_(3)`

Explanation

To solve the problem, we need to analyze the given organic compound [A] with the molecular formula \( C_{10}H_{20}O_{2} \). The compound undergoes hydrolysis to produce a carboxylic acid [B] and an alcohol [C]. Furthermore, oxidation of [C] with \( CrO_{3} - H_{2}SO_{4} \) regenerates [B]. We need to identify which structures are not possible for [A].

### Step-by-Step Solution:

1. **Understanding the Hydrolysis Reaction**:
- The hydrolysis of [A] produces a carboxylic acid [B] and an alcohol [C]. The general reaction can be represented as:
\[ \text{[A]} + H_2O \xrightarrow{\text{dilute } H_2SO_4} \text{[B]} + \text{[C]} \]
- Since [A] has the formula \( C_{10}H_{20}O_{2} \), it suggests that [A] could be an ester or a related compound.

2. **Identifying the Functional Groups**:
- The presence of \( O_2 \) in the molecular formula indicates that [A] is likely an ester or a compound that can yield both a carboxylic acid and an alcohol upon hydrolysis.

3. **Analyzing the Structures**:
- We will analyze each option provided to determine if they can yield the required products upon hydrolysis and subsequent oxidation.

4. **Option 1**:
- Draw the structure based on the given molecular formula.
- Perform hydrolysis and check if it produces a carboxylic acid and an alcohol.
- Check if the alcohol can be oxidized to regenerate the carboxylic acid.
- **Conclusion**: This structure is possible.

5. **Option 2**:
- Repeat the drawing and analysis as in Option 1.
- Perform hydrolysis and check the products.
- Check the oxidation of the alcohol.
- **Conclusion**: This structure is also possible.

6. **Option 3**:
- Draw the structure and analyze it similarly.
- Perform hydrolysis and check the products.
- Check the oxidation of the alcohol.
- **Conclusion**: If this structure does not yield the required products, it is not possible.

7. **Final Evaluation**:
- After analyzing all options, identify which structures do not conform to the requirement of producing [B] and [C] as specified.