The correct order of basicity of the following amines 

$\mathrm{I}$ is most basic, because the lone pair of nitrogen is not delocalised by resonance in that, but in all others, there is resonance with benzene ring. 

$\mathrm{III}$ is more basic than $\mathrm{II}$ due to $+\mathrm{R}$ (or $+\mathrm{M}$) effect of $-{\mathrm{CH}}_3$, and $\mathrm{IV}$ is less basic than $\mathrm{II}$ because of $-\mathrm{R}$ (or $- \mathrm{M}$) effect of $-{\mathrm{NO}}_2$, i.e. correct order is $\mathrm{I}>\mathrm{III}>\mathrm{II}>\mathrm{IV}$.