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(B) Nucleophilic aromatic substitution $(S_NAr)$ reactions are facilitated by the presence of electron-withdrawing groups (like $-NO_2$) on the benzen

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$II > IV > III > I$

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(B) Nucleophilic aromatic substitution $(S_NAr)$ reactions are facilitated by the presence of electron-withdrawing groups (like $-NO_2$) on the benzene ring,especially at the ortho and para positions.$1$. Compound $(II)$ has three $-NO_2$ groups (at $2, 4, 6$ positions),making it the most reactive.$2$. Compound $(IV)$ has two $-NO_2$ groups (at $2, 4$ positions),making it the second most reactive.$3$. Compound $(III)$ has one $-NO_2$ group at the para position,which is more effective than the meta position.$4$. Compound $(I)$ has one $-NO_2$ group at the meta position,which is the least effective for stabilizing the intermediate carbanion.Thus,the decreasing order of reactivity is $(II) > (IV) > (III) > (I)$.

The decreasing order of reactivity of the given compounds towards nucleophilic substitution with aqueous $NaOH$ is:
$(I)$ $1$-bromo-$3$-nitrobenzene
$(II)$ $1$-bromo-$2,4,6$-trinitrobenzene
$(III)$ $1$-bromo-$4$-nitrobenzene
$(IV)$ $1$-bromo-$2,4$-dinitrobenzene

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The decreasing order of reactivity of the given compounds towards nucleophilic substitution with aqueous $NaOH$ is:$(I)$ $1$-bromo-$3$-nitrobenzene$(II)$ $1$-bromo-$2,4,6$-trinitrobenzene$(III)$ $1$-bromo-$4$-nitrobenzene$(IV)$ $1$-bromo-$2,4$-dinitrobenzene