1. Cumene (C$_6$H$_5$CH(CH$_3$)$_2$) undergoes oxidation with KMnO$_4$/KOH/$\Delta$ to form benzoic acid (C$_6$H$_5$COOH, X) via cleavage of isopropyl group.
2. The side product is acetone (CH$_3$COCH$_3$, Y) after hydrolysis (H$^+$, H$_2$O).
3. Reaction: C$_6$H$_5$CH(CH$_3$)$_2$ $\to$ C$_6$H$_5$COOH + CH$_3$COCH$_3$.
4. Options (1), (2), (4) have incorrect products (e.g., isopropanol or acetophenone).
5. Thus, the answer is (3) COOH, CH$_3$COCH$_3$.