Which of the following will show optical isomerism?

Which of the following will show optical activity?

How many chiral carbon atoms are present in the following compound?

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 $2$.

Given below are two statements.
Statement $I$: The compound shown below is optically active.
[Image of compound $A$]
Statement $II$: The compound shown below is the mirror image of the above compound $A$.
[Image of compound $B$]
In the light of the above statements,choose the most appropriate answer from the options given below.

Which of the following is expected to be optically active?