The chiral compounds among the following are:

  • A
    $IV$ and $VI$
  • B
    $II$ and $IV$
  • C
    $IV$ and $V$
  • D
    $I$ and $III$

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Optical isomerism arises due to the presence of

Identify the relationship between the given pair of molecules.

When does an organic molecule exhibit optical activity?

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

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