Which of the following statements is correct about $A$ and $B$?

Identify the total number of compounds containing at least one chiral carbon atom from the following list:
$1$. $2-$methylcyclohexanone
$2$. Cyclopentane$-1,3-$dione
$3$. $CH_3-CH_2-CH(NO_2)-COOH$
$4$. $CH_3-CH(I)-CH_2-NO_2$
$5$. $CH_3-CH_2-CH(OH)-CH_2OH$
$6$. $CH_3-CH_2-CH(I)-C_2H_5$

Identify the correct sequence for True and False.
$(I)$ Only compounds with chiral centers can be optically active.
$(II)$ Absence of elements of symmetry is the reason for a molecule's optical activity.
$(III)$ All organic compounds contain carbon $\&$ hydrogen.
$(IV)$ Different canonical forms of a molecule represent the actual structures of a molecule which has resonance in it.

Which of the following compounds is chiral?

Identify the pair of isomers $A$ and $B$ from the given options.

The urea molecule $\left[ H_2N-C(=O)-NH_2 \right]$ exhibits which type of isomerism?