Acetone ($CH_3COCH_3$) is a ketone that contains $\alpha$-hydrogen atoms. When treated with a dilute alkali such as $Ba(OH)_2$, it undergoes an aldol condensation reaction. Two molecules of acetone undergo self-condensation to form a $\beta$-hydroxy ketone (a ketol) as the initial product 'X' before heating. The structure of 'X' is $CH_3-C(OH)(CH_3)-CH_2-CO-CH_3$ (4-hydroxy-4-methylpentan-2-one). Thus, the functional groups present in compound 'X' are an alcohol ($-OH$) and a ketone ($>C=O$).