Which of the following is achiral?

  • A
    $2-$bromocyclohexanol
  • B
    $2-$chlorohexane
  • C
    $1,4-$dimethylcyclohexane
  • D
    $1-$chloro$-2-$deuterocyclohexane

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Optically active $(S)-2-$methoxypropanal on reaction with $MeMgX$ gives a mixture of alcohols. The major diastereomer $P$ on treatment with $MeI / K_2CO_3$ gives an optically inactive compound. $P$ is

The Fischer projection of $D$-erythrose is shown below.
$D$-Erythrose and its isomers are listed as $P$,$Q$,$R$,and $S$ in Column-$I$. Choose the correct relationship of $P$,$Q$,$R$,and $S$ with $D$-erythrose from Column-$II$.
Column-$I$:
$P$: $CHO-C(OH)(H)-C(OH)(H)-CH_2OH$ (rotated)
$Q$: $CHO-C(H)(OH)-C(OH)(H)-CH_2OH$
$R$: $CHO-C(OH)(H)-C(H)(OH)-CH_2OH$
$S$: $CHO-C(H)(OH)-C(H)(OH)-CH_2OH$ (enantiomer)
Column-$II$:
$1$. Diastereomer
$2$. Identical
$3$. Enantiomer

Which of the following is optically active?

Which of the following compounds are optically active?
$(I)$ $1,1-$dimethyl$-4-$chlorocyclohexane
$(II)$ $4-$chlorocyclohex$-1-$ene
$(III)$ penta$-2,3-$diene

Which of the following are enantiomers?

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