Chromatographic technique/s based on the principle of differential adsorption is/are:
$A$. Column chromatography
$B$. Thin layer chromatography
$C$. Paper chromatography
Choose the most appropriate answer from the options given below:

The distillation technique most suited for separating glycerol from spent-lye in the soap industry is:

Using the given figure,the ratio of $R_f$ values of sample $A$ and sample $C$ is $x \times 10^{-2}$. The value of $x$ is . . . . . . . .
Table: Paper chromatography of Samples
| Component | Distance from base line (cm) |
| :--- | :--- |
| Sample $A$ | $5.0$ |
| Sample $B$ | $6.5$ |
| Sample $C$ | $10.0$ |
| Solvent front | $12.5$ |

What is the purification method based on the principle that the compound and the impurities have different solubilities in a given solvent?

If a liquid compound decomposes at its boiling point,which method$(s)$ can you choose for its purification? It is known that the compound is stable at low pressure,steam volatile,and insoluble in water.

Give the answer of the following questions in short:
$(i)$ When is simple distillation used?
$(ii)$ When is fractional distillation used?
$(iii)$ Which liquid is obtained first in fractional distillation?
$(iv)$ Which liquid is cooled first in fractional distillation?
$(v)$ What happens in the fractional column?