The correct option is C I < III < II < IV
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.
Also, more substituted alkene are more stable and evolve less heat. therefore, I would evolve least heat. Between II and III, III evolves less heat as it is more substituted followed by II. Between II and IV, II evolves less heat as it is more substituted than IV.
Hence, correct order is IV>II>III>I.