See image — Hydrocarbons Chemistry Question

💡 Solution & Explanation

Concept: Catalytic hydrogenation of alkenes proceeds via syn addition of H2 to the double bond from the catalyst surface. Whether a mixture of cis and trans products forms depends on the geometry of the starting material and how hydrogen can be delivered to the prochiral centers. Option (a): 4-methylenecyclohexane with a CH3 at C4 (i.e., 4-methyl methylenecyclohexane). The exocyclic =CH2 at C1, upon hydrogenation, introduces a CH3 group at C1. The C4 already bears a CH3. Since C1 and C4 are not part of the double bond directly (it is exocyclic), the two faces of the ring are not equivalent and H2 can add from either face, giving both cis and trans-1,4-dimethylcyclohexane. Thus (a) gives a mixture. Option (b): 1,4-dimethylcyclohex-1-ene. The double bond is between C1 and C2, with a methyl at C1 and a methyl at C4. Upon hydrogenation, C1 and C2 receive H atoms. C1 already has a methyl group; after hydrogenation, C1 becomes a new stereocenter. C4 already bears a methyl. Syn addition from either face of the ring gives different relative stereochemistries at C1 and C4, producing a mixture of cis and trans-1,4-dimethylcyclohexane. Thus (b) also gives a mixture. Option (c): Cis-3,6-dimethylcyclohexene. The double bond is between C1 and C2, and the methyl groups are at C3 and C6 in a cis arrangement. After hydrogenation of the C1=C2 double bond, C1 and C2 become CH2 groups (no new stereocenters introduced there that relate to a 1,4-dimethyl product). The product would be cis-1,4-dimethylcyclohexane (renumbered), and since the existing stereocenters at C3 and C6 are fixed (cis), only the cis isomer results. Thus (c) does NOT give a mixture. Since both (a) and (b) give mixtures of cis and trans-1,4-dimethylcyclohexane upon catalytic hydrogenation, the answer is (d) both (a) & (b). Therefore, the correct answer is D.