Answer is : (b) III < IV < I < II
As the size of alkyl group goes on increasing, the + I effect exerted by it becomes strong and, thus the carbocation will be more stable. So, among 1°, 2° and 3° carbocation, 3° will be most stable.
Although (CH3)2 \(\overset{+}{C}\)(OCH3) will be highly stable among the given carbocations due to resonance stabilisation.
Thus, the correct order of stability of carbocations will be