Cis-trans isomerism arises from differing groups on each carbon of a double bond, yielding non-superimposable mirror images. Analysis of each option:
- Option (1) 2-Methylhex-2-ene: The double bond is between C2 and C3. C2 has a methyl group and a hydrogen atom. C3 has a methyl group and an ethyl group. Since each carbon of the double bond has two different substituents, cis-trans isomerism is possible.
- Option (2) 1,1-Dimethylcyclopropane: Both methyl groups are attached to C1 of the cyclopropane ring. Due to the identical substituents on C1, cis-trans isomerism is not possible.
- Option (3) 1,2-Dimethylcyclohexane: This molecule is a saturated hydrocarbon and lacks a double bond. Therefore, cis-trans isomerism is not applicable.
- Option (4) Pent-1-ene: Although a double bond exists, C1 of the double bond is attached to two hydrogen atoms, and C2 is attached to a methyl group and an ethyl group. Since C1 has identical substituents, cis-trans isomerism is not possible.
Consequently, 2-Methylhex-2-ene is the only compound among the options that exhibits cis-trans isomerism.