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(B) The reaction of aryl halides with $HO^-$ ions follows the Nucleophilic Aromatic Substitution $(S_NAr)$ mechanism. The rate of $S_NAr$ reaction is

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$II > IV > III > I$

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(B) The reaction of aryl halides with $HO^-$ ions follows the Nucleophilic Aromatic Substitution $(S_NAr)$ mechanism. The rate of $S_NAr$ reaction is directly proportional to the number of electron-withdrawing groups $(-NO_2)$ present on the benzene ring,as they stabilize the Meisenheimer complex intermediate. The number of $-NO_2$ groups in the given compounds are: $(I)$ $meta$-nitro-bromobenzene: $1$ $-NO_2$ group. $(II)$ $2,4,6$-trinitro-bromobenzene: $3$ $-NO_2$ groups. $(III)$ $para$-nitro-bromobenzene: $1$ $-NO_2$ group. $(IV)$ $2,4$-dinitro-bromobenzene: $2$ $-NO_2$ groups. Comparing $(I)$ and $(III)$,the $-NO_2$ group at the $para$ position $(III)$ is more effective at stabilizing the negative charge via resonance than at the $meta$ position $(I)$. Thus,the order of reactivity is $II$ ($3$ $-NO_2$) > $IV$ ($2$ $-NO_2$) > $III$ ($1$ $-NO_2$ at $para$) > $I$ ($1$ $-NO_2$ at $meta$).

The decreasing order of reactivity of $meta$-nitro-bromobenzene $(I)$,$2,4,6$-trinitro-bromobenzene $(II)$,$para$-nitro-bromobenzene $(III)$,and $2,4$-dinitro-bromobenzene $(IV)$ towards $HO^-$ ions is:

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