The correct increasing order of basic strength for the following compounds is
II < I < III
The methyl group present in 4-methylaniline is an electron releasing group (via hyperconjugation). Hence, we could make a case for a greater-than-normal availability nitrogen lone pair to be donated. Hence, the third structure - 4-methylaniline is more basic than just plain aniline. In structure (II), the nitro group is strongly electron-withdrawing via conjugation and to a smaller extent even via (negative) inductive effect. Hence, in 4-nitroaniline, the availability of nitrogen's lone in the −NH2 group is significantly diminished. Hence, (II) is less basic than (I), which is further less basic than (III). Hence the order of basic strength is (II) < (I) < (III)