Which of the products is formed when acetone is reacted with barium hydroxide solution?

In the presence of peroxide,styrene reacts with $HBr$ to give $X$. When $X$ is reacted with magnesium in dry ether followed by $CO_2$ and hydrolysis,it gives $Y$. Treatment of $Y$ with $PCl_5$ and then with $H_2, Pd-BaSO_4$ gives $Z$. What is $Z$?

The compound formed by the reaction of ethanal with semicarbazide contains $.....................$ number of nitrogen atoms.

The major product formed in the following reaction is:
$CH_3CHO + PhCOCH_3 \xrightarrow{\text{dil. } NaOH}$

Compound $CH_3-CO-CH_2-OH$ reduces:

The reaction $R-C(=O)-R + HCN \xrightarrow{\text{catalyst}} R-C(OH)(CN)-R$ is a nucleophilic addition reaction. Which of the following can be used as a catalyst in the above reaction?