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(A) The reactivity of $C-X$ bond towards nucleophilic substitution depends on the mechanism ($S_N1$ or $S_N2$).$1$. Alkyl halides ($III$ and $IV$) are

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$I < II < IV < III$

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(A) The reactivity of $C-X$ bond towards nucleophilic substitution depends on the mechanism ($S_N1$ or $S_N2$).$1$. Alkyl halides ($III$ and $IV$) are generally more reactive than aryl halides ($I$ and $II$) towards nucleophilic substitution because the $C-X$ bond in aryl halides has partial double bond character due to resonance.$2$. Among alkyl halides,the $3^o$ halide $(III)$ is more reactive than the $2^o$ halide $(IV)$ in $S_N1$ reactions due to the formation of a more stable carbocation.$3$. Among aryl halides,the presence of electron-withdrawing groups $(-NO_2)$ increases the reactivity towards nucleophilic aromatic substitution. Thus,$II$ is significantly more reactive than $I$.$4$. Comparing all,the order of reactivity is $I < II < IV < III$.

The correct order of increasing reactivity of $C-X$ bond towards nucleophile in the following compounds is:
$I$: Chlorobenzene (or aryl halide)
$II$: $2,4$-Dinitrochlorobenzene
$III$: $(CH_3)_3C-X$ ($3^o$ alkyl halide)
$IV$: $(CH_3)_2CH-X$ ($2^o$ alkyl halide)

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The correct order of increasing reactivity of $C-X$ bond towards nucleophile in the following compounds is:$I$: Chlorobenzene (or aryl halide)$II$: $2,4$-Dinitrochlorobenzene$III$: $(CH_3)_3C-X$ ($3^o$ alkyl halide)$IV$: $(CH_3)_2CH-X$ ($2^o$ alkyl halide)