Which of the following compounds are opticall | vedclass

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(C) compound is optically active if it lacks a plane of symmetry and a center of inversion (i.e.,it is chiral).$(I)$ $1,1$-dimethyl-$4$-chlorocyclohex

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$II$ and $III$

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(C) compound is optically active if it lacks a plane of symmetry and a center of inversion (i.e.,it is chiral).$(I)$ $1,1$-dimethyl-$4$-chlorocyclohexane: This molecule has a plane of symmetry passing through the $C1$ and $C4$ atoms. Therefore,it is achiral and optically inactive.$(II)$ $4$-chlorocyclohex-$1$-ene: The $C4$ atom is bonded to four different groups ($-H$,$-Cl$,and two different paths around the ring). Thus,$C4$ is a chiral center. The molecule lacks a plane of symmetry and is optically active.$(III)$ Penta-$2,3$-diene: This is an allene with an even number of double bonds. The terminal carbons are substituted such that the molecule lacks a plane of symmetry and a center of inversion. It is axially chiral and optically active.Therefore,compounds $(II)$ and $(III)$ are 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

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