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

Explain the principle of paper chromatography.

Which one of the following methods is suitable to separate a mixture of $n$-pentane and toluene?

The most suitable method of separation of a $1:1$ mixture of $ortho$- and $para$-nitrophenols is:

When is distillation under reduced pressure used?

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?