The correct option is B III < IV < II < I
Heat of hydrogenation∝1stability of alkene∝1Number of α−H
Hydrogenation of all of the above dienes involve the same bonding change, i.e. two pi-bonds are hydrogenated in each case.
Conjugated dienes are more stable, will evolve less heat in hydrogenation than the isolated diene. therefore III and IV will be less heat of hydrogenation than I and II.
Between III and IV, III evolves less heat as it is more stable than IV due presence of more α−H.
II has more α−H than I so it will be more stable than I and thus II would evolve least heat than I.
Hence, correct order of heat of hydrogenation is I > II > IV > III.