$\left( X \right)\,\xrightarrow{\Delta }\,\left( Y \right)$ amphoteric $ + \left( R \right) \uparrow \, + \,\left( S \right) \uparrow $
$P$ and $X$ are respectively
$\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \stackrel{\Delta}{\longrightarrow} \underset{\text { Amphoteric }}{\mathrm{PbO}}+2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2} \uparrow$
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$N_{2(g)} + 3H_{2(g)} \rightarrow 2NH_{3(g)}$ The equality relationship between $\frac{d[NH_3]}{dt}$ and $\frac{d[H_2]}{dt}$ is
| $column 1$ | $column 2$ | $column 3$ |
| $(I)$ Toluene | $(i)$ $\mathrm{NaOH} / \mathrm{Br}_2$ | $(P)$ Condensation |
| $(II)$ Acetophenone | $(ii)$ $\mathrm{Br}_2 / \mathrm{h} v$ | $(Q)$ Carboxylation |
| $(III)$ Benzaldehyde | $(iii)$ $\left(\mathrm{CH}_3 \mathrm{CO}\right)_2 \mathrm{O} / \mathrm{CH}_3 \mathrm{COOK}$ | $(R)$ Substion |
| $(IV)$ Phenol | $(iv)$ $\mathrm{NaOH} / \mathrm{CO}_2$ | $(S)$ Haloform |
($1$) For the synthesis of benzoic acid, the only $CORRECT$ combination is
$[A] (III) (iv) (R)$ $[B] (IV)(ii) (P)$ $[C] (I) (iv) (Q)$ $[D] (II) (i) (S)$
($2$) The only CORRECT combination in which the reaction proceeds through radical mechanism is
$[A] (I)$ $(ii) (R)$ $[B] (II) (iii) (R)$ $[C] (III) (ii) (P)$ $[D] (IV) (i) (Q)$
($3$) The only CORRECT combination that gives two different carboxylic acids is
$[A] (IV) (iii) (Q)$ $[B] (III) (iii) (P)$ $[C] (II) (iv) (R)$ $[D] (I) (i) (S)$
Given the answer quetion ($1$) ($2$) and ($3$)
$A ( g )+ B ( g ) \rightleftharpoons AB ( g ) \text {. }$
The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$ (in $J mol ^{-1}$ ). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction, the absolute value of $\Delta G ^{\ominus}$ (in $J mol ^{-1}$ ) for the reaction at $300 K$ is. . . . . (Given; $\ln (2)=0.7, RT =2500 J mol ^{-1}$ at $300 K$ and $G$ is the Gibbs energy)
$\begin{array}{*{20}{c}}
{\,\,O} \\
{\,\,||} \\
{C{H_3} - C - OH}
\end{array}$ $\xrightarrow[\Delta ]{{N{H_3}}}A\,\xrightarrow[\Delta ]{{{P_2}{O_5}'}}B$
(image) $\xrightarrow[(273-278\,K)]{NaN{{O}_{2}}/HCl}X$ ${\mkern 1mu} \xrightarrow{{N,N\, - \,\dim ethyl\,\,aniline}}Y$
The structure of $'Y'$ would be