Step 1: Use the Tollens clue.
Ammoniacal $AgNO_3$ (Tollens reagent) oxidises aldehydes but not plain hydrocarbons. Since X is oxidised and Y is not, X must contain a $-CHO$ group while Y must not.
Step 2: Find the reaction that makes an aldehyde on benzene.
The Gattermann-Koch reaction adds a formyl group: $C_6H_6 \xrightarrow{CO+HCl,\ AlCl_3/CuCl} C_6H_5CHO$. So reaction A is Gattermann-Koch and X is benzaldehyde.
Step 3: Confirm X reacts with Tollens.
Benzaldehyde has $-CHO$, so it is oxidised by ammoniacal $AgNO_3$ (silver mirror), consistent with the clue.
Step 4: Find the reaction giving the unreactive Y.
Friedel-Crafts alkylation adds an alkyl group: $C_6H_6 \xrightarrow{RCl/AlCl_3} C_6H_5R$. Alkylbenzene has no $-CHO$, so it is not oxidised by Tollens. Reaction B is Friedel-Crafts.
Step 5: Pair the reactions.
Thus $A=$ Gattermann-Koch and $B=$ Friedel-Crafts.
Step 6: Choose the option.
This pairing matches option (3).
\[ \boxed{A=\text{Gattermann-Koch},\ B=\text{Friedel-Crafts (Option 3)}} \]