Predict the major product of the following reaction sequence:

Two aliphatic aldehydes $P$ and $Q$ react in the presence of aqueous $K_2CO_3$ to give compound $R$,which upon treatment with $HCN$ provides compound $S$. On acidification and heating,$S$ gives the product shown below:
$1.$ The compounds $P$ and $Q$ respectively are:
$2.$ The compound $R$ is:
$3.$ The compound $S$ is:
Give the answer for questions $1$,$2$ and $3$.

For the conversion of cyclohexanone to $1-$hydroxy$-1-$methylcyclohexan$-2-$one,the correct order of reagents used is:
$(1)$ $CH_3MgBr / H^+$
$(2)$ $H^+ / \Delta$
$(3)$ $KMnO_4$ (cold dil.)
$(4)$ $CrO_3$

In the given reaction sequence,the percentage of oxygen in compound $(Q)$ is . . . . . . $\%$. (Nearest integer)

$A$ carbonyl compound $X$ $(C_3H_6O)$ on oxidation gives a carboxylic acid $Y$ $(C_3H_6O_2)$. The oxime of $X$ is:

The conversion shown in the image can be achieved by: