\(\text{(a) They can be differentiated by NaHCO}_3 \text{ test.} \) \(\text{(b) They both gives 2,4-DNP test.} \\ \text{(c) They both have same molecular mass.} \\ \text{(d) They both react with same rate with HCN.} \)
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The 2,4-DNP test is used to detect aldehydes and ketones. The molecular mass of similar products will remain the same if they are derivatives of the same parent compound.
In the given reaction, products \( X \) and \( Y \) are likely to be two different compounds formed via hydrolysis, with the potential of forming different derivatives that are tested differently.
Step 1: Statement (a) about NaHCO3 test.
NaHCO₃ test is typically used to differentiate between carboxylic acids and other compounds (e.g., alcohols or esters). However, since the reaction involves a hydrolysis process, it is not certain that both products react with NaHCO₃, thus statement (a) is not correct.
Step 2: Statement (b) about 2,4-DNP test.
The 2,4-DNP (2,4-dinitrophenylhydrazine) test is used to identify aldehydes and ketones. Given that the reaction likely involves products that are aldehydes or ketones, statement (b) is correct.
Step 3: Statement (c) about molecular mass.
Both products \( X \) and \( Y \) would have the same molecular mass if they are derivatives of the same compound and undergo similar types of reaction (like hydrolysis). Hence, statement (c) is correct.
Step 4: Statement (d) about reaction with HCN.
HCN reacts differently with different compounds, and it is unlikely that both products will react with the same rate. Thus, statement (d) is incorrect.
Step 5: Conclusion.
Therefore, the correct statements are (b) and (c), making the correct option (B).
Final Answer: (B) Statement b and c are correct
