Why does 1,2-dichloro-4-nitrobenzene undergo SNAr para and not meta to the nitro group?
You can obtain an answer by looking at the electronic structure.  $\ce{NO2}$ is a meta director for electrophilic aromatic substitution (EAS).  The question asks about nucleophilic aromatic substitution (NAS). Aromatic substitutions involve a free pair of electrons resonating around a structure. Electrophiles may add at any resonance site where the pair of electrons are. Nucleophiles may inversely add to any site where electrons are not present shown in the picture below. Therefore if a functional group is meta directing for EAS it will be ortho/para directing for NAS and vice versa.