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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3st199

For 1,2,3-trimethylcyclohexane (configuration only; the ring is treated as planar and time-averaged), which statements are correct?

  1. AThe isomer in which the C1 and C3 methyls are cis to each other and the C2 methyl is trans to both is achiral
  2. BThe all-cis isomer is chiral
  3. CExactly two of its stereoisomers are optically active
  4. DIt has four stereoisomers

Answer: A, C, D

Writing the three methyls as up/down, the arrangements uuu (all-cis) and udu have a mirror plane through C2 and C5, so they are achiral, while uud and its mirror image ddu form the only enantiomeric pair. Total 4 stereoisomers, 2 of them optically active (the pair). The all-cis isomer is meso-like (achiral), so the last statement is false (confirmed by enumeration).
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