The correct option is
B I>IV>II>IIIThe stability order is explained on the basis of Meromeric effect, Inductive effect and Hyperconjugation.
In these effects, we have to follow following order for stabler.
MeromericEffect>Hyperconjugation>InductiveEffect.
−OCH3 is ′+M′ group.
The cation which is in resonance with −OCH3 is more stable.
So (I) and (IV) are more stable than (II) and (III).
Between (I) and (IV), ′I′ is more stable because of Inductive effect as carbon atoms are more in I.
Between (II) and (III), II is more stable because of 9 hyper conjugative structure of II than ′4′ hyper conjugative structure of III.
So stability order is I>IV>II>III