Amongst the following, the total number of compounds soluble in aqueous $NaOH$ at room temperature is:
$(I)$ Benzaldehyde
$(II)$ $1$-Naphthol
$(III)$ $4$-(Dimethylamino)phenol
$(IV)$ $4$-Methylphenol
$(V)$ Benzoic acid
$(VI)$ $N,N$-Dimethylcyclohexanamine
$(VII)$ $1$-Naphthoic acid
$(VIII)$ $1,4$-Di-tert-butylbenzene
$(IX)$ $1$-Naphthylmethanol

Choose the correct option$(s)$ for the following reaction sequence. Consider $Q$,$R$ and $S$ as major products.

What are $\underline{A}, \underline{B}, \underline{C}$ in the following reactions?
$(I)$ $(CH_3 CO_2)_2 Ca \stackrel{\Delta}{\longrightarrow} \underline{A}$
$(II)$ $CH_3 CO_2 H \underset{\text{Red P}}{\stackrel{HI}{\longrightarrow}} \underline{B}$
$(III)$ $2 CH_3 CO_2 H \stackrel{P_4 O_{10}}{\longrightarrow} \underline{C}$
$\underline{A} \quad \underline{B} \quad \underline{C}$

Ethanol on reaction with alkaline $KMnO_4$ gives $X$,which when reacted with methanol in the presence of an acid gives a sweet-smelling compound $Y$. $X$ and $Y$ respectively are:

Ethanol $(C_2H_5OH)$ and formic acid $(HCO_2H)$ cannot be distinguished by:

The number of methoxy groups in a compound can be determined by treating it with