When the $TLC$ solvent reaches a height of $10 \, cm$,compound $(A)$ reaches $8 \, cm$ and compound $(B)$ reaches $6 \, cm$. Calculate the $R_f$ values of $(A)$ and $(B)$.

Given below are two statements:
Statement $I$: $A$ mixture of $C_{12}H_{22}O_{11}$ (sugar) and $NaCl$ can be separated by dissolving sugar in alcohol, due to differential solubility.
Statement $II$: Rose essence from rose petals is separated by steam distillation due to its high volatility and insolubility in $H_2O$.

State True or False for the following statements:
$(i)$ The volatile liquid is purified by fractional distillation or simple distillation.
$(ii)$ Two liquids are separated by fractional distillation.
$(iii)$ Liquids with a small difference in boiling points are separated by fractional distillation.
$(iv)$ Liquids with a large difference in boiling points are separated by fractional distillation.

The correct match between items of List-$I$ and List-$II$ is

List-$I$	List-$II$
$A$. Coloured impurity	$(p)$. Steam distillation
$B$. Mixture of $o-$nitrophenol and $p-$nitrophenol	$(q)$. Fractional distillation
$C$. Crude naphtha	$(r)$. Charcoal treatment
$D$. Mixture of glycerol and sugars	$(s)$. Distillation under reduced pressure

Gasoline is obtained from crude petroleum oil by its

Which purification method is used to separate liquids that have a sufficient difference in their boiling points?