What is a substance called that can rotate the plane of plane-polarized light?

The relationship between the pair of compounds shown below is respectively:

If $n$ represents the total number of asymmetric carbon atoms in a compound,the possible number of optical isomers of the compound is-

Which of the following compounds is an optically active substance with a low molecular weight?

Which one of the following compounds is optically active?

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 $2$.