$$A\,(C_4H_8Cl_2) \xrightarrow[\;373\,K\;]{\text{Hydrolysis}} B\,(C_4H_8O)$$
B reacts with Hydroxyl amine but does not give Tollen's test. Identify A and B.

We are given compound A with molecular formula $$C_4H_8Cl_2$$ which on hydrolysis at 373 K gives compound B with molecular formula $$C_4H_8O$$.

Compound B reacts with hydroxylamine ($$NH_2OH$$), which means B contains a carbonyl group ($$C=O$$). However, B does not give Tollen's test, which means B is not an aldehyde. Therefore, B must be a ketone.

The only ketone with molecular formula $$C_4H_8O$$ is butan-2-one ($$CH_3COCH_2CH_3$$).

For the hydrolysis of a geminal dihalide (two halogen atoms on the same carbon) to give a ketone, the two chlorine atoms must be on the same carbon that is not a terminal carbon. In 2,2-dichlorobutane ($$CH_3CCl_2CH_2CH_3$$), hydrolysis gives:

$$CH_3CCl_2CH_2CH_3 + H_2O \xrightarrow{373K} CH_3COCH_2CH_3 + 2HCl$$

The geminal diol intermediate ($$CH_3C(OH)_2CH_2CH_3$$) loses water to form butan-2-one.

If A were 1,1-dichlorobutane ($$CH_3CH_2CH_2CHCl_2$$), hydrolysis would give butanal (an aldehyde), which would give a positive Tollen's test. This contradicts the given information.

Therefore, A is 2,2-dichlorobutane and B is butan-2-one.

The correct answer is Option 2.