See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Identify the compound: The structure shown is 1,1,2-trimethylcyclohexane. C1 bears two methyl groups (gem-dimethyl), and C2 bears one methyl group. Step 2 - Identify stereocenters for geometric (cis/trans) isomerism in cyclic compounds: Geometric isomerism in cycloalkanes arises when two different ring carbons each bear two different substituents, allowing for cis and trans arrangements relative to the ring plane. Step 3 - Analyze C1: C1 has two methyl groups attached to it. Because both substituents on C1 (the two methyls) are identical, C1 is NOT a stereocenter and cannot give rise to cis/trans isomerism. A carbon bearing two identical groups cannot show geometric isomerism. Step 4 - Analyze C2: C2 has one methyl group and one H. However, geometric isomerism requires BOTH ring carbons involved to have two different groups. Since C1 already fails this requirement (it has two identical methyl groups), there is no cis/trans relationship possible between C1 and C2. Step 5 - Conclusion: Because C1 is a quaternary carbon with two identical substituents (two CH3 groups), the molecule cannot exhibit geometric isomerism. There are 0 geometric isomers possible. Why other options fail: - (b) 2, (c) 3, (d) 4 all assume stereogenic centers exist, but C1 with two identical methyl groups disqualifies any cis/trans isomerism. Therefore, the correct answer is A.