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JEE Advanced levelSingle correct optionDifficulty 3 of 3st315

The compound shown is bicyclo[4.3.0]nonane (hydrindane), in which a cyclohexane ring and a cyclopentane ring share the C-C bond between the two bridgehead carbons. Considering configuration only, the number of stereoisomers is

  1. A2
  2. B3
  3. C4
  4. D1

Answer: B

The two bridgehead carbons are stereocentres. The two bridgehead hydrogens can be on the same side (cis-fused) or opposite sides (trans-fused) of the ring system. In the cis isomer a mirror plane passes through the midpoint of the shared bond and perpendicular to it, exchanging the two bridgeheads, so cis-hydrindane is achiral. In the trans isomer that plane is lost and the compound is chiral, existing as a pair of enantiomers. Total = 1 + 2 = 3. (Decalin is different: both its cis and trans isomers are achiral by configuration, giving 2.)
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