The increasing order of the basicity of amines is p-nitro aniline < aniline < p-methoxy aniline < methylamine. Methylamine is most basic as the lone pair of electrons on the N atom is not involved in resonance with the phenyl group. Also, the +I effect of the methyl group increases the ease with which the lone pair of electrons can be donated. p-nitroaniline is least basic as the electron-withdrawing effect of the nitro group significantly decreases the ease with which N can donate the lone pair of electrons. p-methoxy aniline is more basic than aniline as the electron-releasing effect of the methoxy group increases the ease with which N can donate the lone pair of electrons. Hence, the correct option is A