The reaction sequence$(s)$ that would lead to $o$-xylene as the major product is (are)

Arrange the following compounds in the increasing order of their $pK_a$ values:
$I.$ Phenol
$II.$ $p$-Nitrophenol
$III.$ Ethanol
$IV.$ $p$-Nitrobenzoic acid

Draw the structures of the following compounds:
$(i)$ $3-$Methylbutanal
$(ii)$ $p-$Nitropropiophenone
$(iii)$ $p-$Methylbenzaldehyde
$(iv)$ $4-$Methylpent$-3-$en$-2-$one
$(v)$ $4-$Chloropentan$-2-$one
$(vi)$ $3-$Bromo$-4-$phenylpentanoic acid
$(vii)$ $p, p^{\prime}-$Dihydroxybenzophenone
$(viii)$ Hex$-2-$en$-4-$ynoic acid

Which of the following undergoes decarboxylation most readily on being heated?

At which value of $n$ does the formation of a six-membered ring take place in the following reaction?
$Br-(CH_2)_n-CH_2-Br + CH_2(CO_2Et)_2 \xrightarrow{NaOEt, EtOH} \text{cyclic product}$

An organic acid $P$ $(C_{11}H_{12}O_2)$ can easily be oxidized to a dibasic acid which reacts with ethylene glycol to produce a polymer,dacron. Upon ozonolysis,$P$ gives an aliphatic ketone as one of the products. $P$ undergoes the following reaction sequences to furnish $R$ via $Q$. The compound $P$ also undergoes another set of reactions to produce $S$.
$(1)$ The compound $R$ is
$(2)$ The compound $S$ is
Give the answer for questions $(1)$ and $(2)$.