(a)
For $n = 4,\ l = 1;\ 4p$
For$\ n = 4,\ l = 0;\ 4s$
For $n = 3,l\ = 2;3d$
For $n = 2,\ l = 1;2p$
The order of increasing energy is as
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2p < 4s < 3d < 4p$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ i.e.,\ (IV) < (II) < (III) < (I)$