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(D) Catalytic hydrogenation of alkenes involves the syn-addition of $H_2$ across the double bond. $(a)$ $4-$methylmethylenecyclohexane: The hydrogenat

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(D) Catalytic hydrogenation of alkenes involves the syn-addition of $H_2$ across the double bond. $(a)$ $4-$methylmethylenecyclohexane: The hydrogenation of the exocyclic double bond results in the formation of $1,4-$dimethylcyclohexane. Since the methyl group at position $4$ is already present,the addition of $H_2$ can occur from either face of the ring,leading to a mixture of $cis$ and $trans$ isomers. $(b)$ $1,4-$dimethylcyclohex$-1-$ene: The hydrogenation of the endocyclic double bond also leads to the formation of $1,4-$dimethylcyclohexane. Due to the presence of the methyl group at position $4$,the approach of the catalyst can result in both $cis$ and $trans$ configurations. $(c)$ $cis-3,6-$dimethylcyclohexene: Similarly,hydrogenation here leads to $1,4-$dimethylcyclohexane (due to symmetry,$3,6-$dimethylcyclohexene is equivalent to $1,4-$dimethylcyclohexene). The addition of $H_2$ to the double bond will yield a mixture of $cis$ and $trans$ isomers. Therefore,all the given compounds will yield a mixture of $cis$ and $trans-1,4-$dimethylcyclohexane.

Which of the following will give a mixture of $cis$ and $trans-1,4-$dimethylcyclohexane upon catalytic hydrogenation?

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