$\bullet$ (III) is the weakest base due to the presence of three $- NO _{2}$ group, which exert strong $- M$ effect.
$\bullet$ In compound (IV) group is thrown out of the plane of aromatic ring due to steric crowding by $- NO _{2}$ groups at ortho positions as a result of this lone pair of electron on $N$-atom does not participate in resonance with aromatic ring and hence it acts as an aliphatic amine. So, (IV) is the strongest base.
$\bullet$ Correct order of basicity is; III $< I < II < IV$ (in basic character).
$\bullet$ Difference of $pK_a$ values is highest between (III) and (IV).
$\bullet$ $pK _{ b } ;$ (I) $\rightarrow 9.42 ;$ (II) $\rightarrow 8.94$, (IV) $\rightarrow 4.60$