Identify chiral molecules from the following:

The correct statement$(s)$ about the compound $H_3C-CH(OH)-CH=CH-CH(OH)-CH_3$ $(X)$ is(are):
$(A)$ The total number of stereoisomers possible for $X$ is $6$.
$(B)$ The total number of diastereomers possible for $X$ is $3$.
$(C)$ If the stereochemistry about the double bond in $X$ is trans,the number of enantiomers possible for $X$ is $4$.
$(D)$ If the stereochemistry about the double bond in $X$ is cis,the number of enantiomers possible for $X$ is $2$.

The compound$(s)$ showing optical activity is/are:

Which of the following molecules can exhibit optical activity?

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

How many chiral isomers can be drawn from $2-$bromo,$3-$chloro butane?