The compound $X- Cl$ (where $x=$ aryl, alkyl, or their derivatives on reaction with sodium methoxide (NaOMe) produces $X-$ OMe and NaCl in accordance with following chemical equation
The above reaction is a type of nucleophilic substitution reaction in which nucleophile [here OMe] replaces halogen atom of $X-C l$.
Reactivity of such organic halides in nucleophilic substitution reaction depends upon polarity of $C - Cl$ bond. Higher the polarity of $C - Cl$ bond easier will be the nucleophilic substitution reaction, hence, faster will be the reaction here $C - Cl$ bond in aryl halide has partially double bond character due to conjugation of lone pair of Cl with $\pi$ electrons of benzene ring as shown below
Due to partial double bond character breaking of $C - Cl$ bond aryl halide become impossible. Among the given four substrates the compound having most polar $C - Cl$ bond will undergo faster nucleophilic substitution reaction. Greater the number of electron withdrawing group higher will be polarity of $C - Cl$ bond.
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Number of withdrawing groups
(a) has two electron withdrawing groups hence, (a) has most polar C - Cl bond and (a) will undergo fastest reaction chemical reaction occurring in the above reaction is as follows
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