1. We are told that B reacts with hydroxylamine but does not give Tollens' test.

2. Reaction with hydroxylamine: Hydroxylamine, $NH_2OH$, reacts with carbonyl compounds to form oximes. So $B$ must be either:

   • an aldehyde, or
   • a ketone.

3. Tollens' test:

   • Aldehydes generally give a positive Tollens' test.
   • Ketones generally do not give Tollens' test.

   Therefore, since $B$ does not give Tollens' test, $B$ must be a ketone.

4. Among the given options:

   • Butanal = aldehyde
   • Butan-2-one / 2-butanone = ketone

   Hence, $B =$ Butan-2-one (2-butanone).

5. Now identify $A$. The question implies that $A$ on hydrolysis/related transformation gives $B$.

   • A gem-dihalide of type $R_2CCl_2$ on hydrolysis gives a ketone.
   • A gem-dihalide of type $RCHCl_2$ on hydrolysis gives an aldehyde.

6. Check the structures:

   • 1,1-Dichlorobutane has both Cl on terminal carbon: $CH_3CH_2CH_2CHCl_2$ On hydrolysis, this gives: $CH_3CH_2CH_2CHO$ which is butanal (aldehyde).

   • 2,2-Dichlorobutane has both Cl on second carbon: $CH_3CCl_2CH_2CH_3$ On hydrolysis, this gives: $CH_3COCH_2CH_3$ which is butan-2-one (ketone).

7. Since $B$ must be butan-2-one, the corresponding $A$ is 2,2-dichlorobutane.

8. Therefore the correct pair is: $A = 2,2\text{-Dichlorobutane}, \quad B = \text{Butan-2-one}$

9. Option check:

   • A: $1,1$-Dichlorobutane and Butanal ❌ (aldehyde gives Tollens' test)
   • B: $2,2$-Dichlorobutane and Butan-2-one ✅
   • C: $1,1$-Dichlorobutane and 2-Butanone ❌ (mismatch in conversion)
   • D: $2,2$-Dichlorobutane and Butanal ❌

So, the correct answer is B.