Step 1: Identify functional group of [X].
Compound gives alcohol and acid on hydrolysis with dil. \( H_2SO_4 \).
So, \( [X] \) must be an ester.
Step 2: General reaction of ester hydrolysis.
\[
R-COO-R' \xrightarrow{H^+} R-COOH + R'-OH
\]
So:
\[
[B] = \text{alcohol}, \quad [C] = \text{carboxylic acid}
\]
Step 3: Use Jones reagent condition.
Jones reagent oxidizes primary alcohol to carboxylic acid.
Since \( [B] \rightarrow [C] \), alcohol must be primary alcohol.
Step 4: Use anhydride formation.
Heating \( [C] \) with \( P_2O_5 \) forms anhydride.
This confirms \( [C] \) is a carboxylic acid.
Step 5: Match molecular formula.
Given formula: \( C_6H_{12}O_2 \) corresponds to ester.
Step 6: Check correct structure.
Option (A):
\[
C_2H_5COO(CH_2)_2CH_3
\]
On hydrolysis:
\[
C_2H_5COOH + CH_3CH_2CH_2OH
\]
Alcohol is primary → can oxidize to acid.
Step 7: Final conclusion.
\[
\boxed{C_2H_5 - COO - (CH_2)_2 - CH_3}
\]