Which substance is used in the purification of bone charcoal?

Give the information of the following in short.
$(i)$ Fractional column $(ii)$ Theoretical plate $(iii)$ Mechanism of fractional column.

Which are the methods of purification of organic compounds?

Which purification technique is used for high boiling organic liquid compounds that decompose near their boiling point?

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 | $12.5$ |

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 $(B)$.