$A$ compound having molecular formula $C_3H_6O$,on reaction with $NH_2NHCONH_2$ produces mainly $P$ (which shows stereoisomerism). $P$ on reaction with $KOH$ / ethylene glycol,$\Delta$ produces propane. Identify $(P)$.

What is the product formed when a ketone reacts with $Mg-Hg$ in the presence of water?

Which of the following gives a positive iodoform test? The reaction is shown below:
$2,3,5-\text{trimethylhepta-2,4-diene} \xrightarrow[(2) H_2O/Zn]{(1) O_3} X (C_3H_6O) + Y (C_3H_4O_2) + Z (C_2H_4O)$

$4$-formylbenzoic acid on treatment with one equivalent of hydrazine followed by heating with alc. $KOH$ gives the major product:

The major product in the following transformation is

An organic compound $P$ having molecular formula $C_6H_6O_3$ gives a ferric chloride test and does not have an intramolecular hydrogen bond. The compound $P$ reacts with $3$ equivalents of $NH_2OH$ to produce oxime $Q$. Treatment of $P$ with excess methyl iodide in the presence of $KOH$ produces compound $R$ as the major product. Reaction of $R$ with excess iso-butylmagnesium bromide followed by treatment with $H_3O^{+}$ gives compound $S$ as the major product. The total number of methyl $(-CH_3)$ groups in compound $S$ is . . . .