Step 1: Analyzing the hydrolysis reaction.
Given the structure of molecule \( (X) \), hydrolysis under mild acidic conditions will produce two compounds: \( (Y) \) and \( (Z) \). These two products are likely to be different forms of a functional group (e.g., an ester or amide) reacting under the same conditions.
Step 2: Identifying the properties of \( (Y) \) and \( (Z) \).
- (A) Both \( (Y) \) and \( (Z) \) having the same molar mass: This is unlikely as their functional groups and molecular structures could differ, resulting in different molar masses.
- (B) \( (Y) \) and \( (Z) \) can be distinguished from each other by NaHCO\(_3\): This is correct. Different functional groups such as acids and esters/amides will show different reactivity with NaHCO\(_3\).
- (C) \( (Y) \) and \( (Z) \) react with HCN with the same rates: This is likely correct, as both \( (Y) \) and \( (Z) \) are functionalized molecules with similar reactivity.
- (D) \( (Y) \) and \( (Z) \) undergo addition reaction with 2,4-DNP: This is also correct, as both \( (Y) \) and \( (Z) \) might be carbonyl compounds and thus react with 2,4-DNP.
Step 3: Conclusion.
The correct answers are \( (B) \) and \( (C) \) since they correctly describe the distinguishing properties of the compounds formed after hydrolysis.
Final Answer: (B) and (C) Only