To solve this problem, we need to determine the reagents A and B for the given reactions involving \(\text{C}_6\text{H}_5\text{CN}\):
- \(\text{C}_6\text{H}_5\text{CN} \xrightarrow{\text{B}} \text{Y} \xrightarrow{\text{A}} \text{X} \, (\text{reacts with } 2,4\text{-DNP})\)
- \(\text{C}_6\text{H}_5\text{CN} \xrightarrow{\text{A}} \text{X} \, (\text{dissolves in dil. } \text{HCl})\)
Let's evaluate the reactions step-by-step:
Step 1: Understanding the reaction conditions and product behavior
The compound \(\text{X}\) reacts with 2,4-DNP and dissolves in dilute HCl, indicating that it is likely a carbonyl compound (could be an aldehyde or ketone).
Step 2: Identify A and B
- Reagent B should convert the cyanide group \((\text{CN})\) into a primary imine, which subsequently can be reduced to an aldehyde.
- Reagent A should convert the imine to a carbonyl compound, which also dissolves in dilute HCl.
Analysis of Reagents:
- Option 1: \(\text{LiAlH}_4, \text{H}_2\text{O}; \text{H}_2/\text{Ni}\)
- \(\text{LiAlH}_4\) reduces nitriles directly to amines, which do not react with 2,4-DNP.
- \(\text{H}_2/\text{Ni}\) is a catalytic hydrogenation reagent not suitable for selective reductions required here.
- Option 2: \(\text{Na}/\text{Hg}, \text{C}_2\text{H}_5\text{OH}; \text{DIBAL-H}, \text{H}_2\text{O}\)
- \(\text{Na}/\text{Hg}, \text{C}_2\text{H}_5\text{OH}\) selectively reduces nitriles to imines, which DIBAL-H can then reduce to aldehydes.
- \(\text{DIBAL-H}\) reduces the nitrile to an aldehyde, which reacts with 2,4-DNP and dissolves in dilute HCl.
- Option 3: \(\text{DIBAL-H}, \text{H}_2\text{O}; \text{LiAlH}_4, \text{H}_2\text{O}\)
- \(\text{DIBAL-H}\) first does work, but \(\text{LiAlH}_4\) will further reduce any product to an alcohol, not suitable.
- Option 4: \(\text{Na}/\text{Hg}, \text{C}_2\text{H}_5\text{OH}; \text{H}_2/\text{Ni}\)
- Similar selective reduction issues as Option 1.
Conclusion:
The correct option is Option 2, where B is \(\text{Na}/\text{Hg}, \text{C}_2\text{H}_5\text{OH}\) and A is \(\text{DIBAL-H}, \text{H}_2\text{O}\).