Which of the following is an appropriate set of reactants for the preparation of 1-methoxy-4-nitrobenzene and why?
In principle, both reactions will work.

(a) is a nucleophilic aromatic substitution, in which is $\ce{Br-}$ is displaced by $\ce{CH3O-}$

(b) is a methylation of a phenoxide

I'd probably go for (a) for two reasons:


The nitro group in para position decreases the charge density on the oxygen atom of the phenol. As a result, this anion will be less reactive than an unsubstituted phenoxide.
Methyl bromide with a boiling point of just 4 °C is difficult to handle and a poor choice for a methylation reagent. I'd rather try dimethyl sulfate if I had to.