The pair of amphoteric hydroxides is:
(A) $Al{(OH)_3},LiOH$
(B) $Be{(OH)_2},Mg{(OH)_2}$
(C) $B{(OH)_3},Be{(OH)_2}$
(D) $Be{(OH)_2},Zn{(OH)_2}$

Hint: Amphoteric hydroxides are the compounds that can act as both an acid as well as a base. It has been found that they are generally hydroxides of metals which can exist in multiple oxidation states.

Complete step by step solution:
Here, we will check which of the given pairs of hydroxides are amphoteric in nature.
- Amphoteric compounds are the ones which can act as both acid as well as bases. So, they can give reactions of acids as well as base.
- The electropositive nature of the metal atom involved in the hydroxide holds the key for the amphoteric nature of its hydroxide.
- There are many metals like Aluminum, Copper, Lead, Zinc, Tin, Beryllium which forms oxides and hydroxides which are amphoteric in nature.
- The amphoteric hydroxides will behave as an acid or base depending upon the reaction conditions. Let’s see the given options one by one to find which pair is of amphoteric oxides.
- $Al{(OH)_3}$ is amphoteric in nature but LiOH which is a hydroxide of Lithium is basic in nature.
- $Be{(OH)_2}$ is amphoteric in nature but hydroxide of manganese $Mg{(OH)_2}$ is basic in nature.
- $B{(OH)_3}$ is a hydroxide which is acidic in nature and it is named as boric acid as well. As we have seen earlier, $Be{(OH)_2}$ is an amphoteric hydroxide.
- The pair of hydroxides shown in option (D) is amphoteric. Both $Be{(OH)_2}$ and $Zn{(OH)_2}$ are amphoteric in nature. They can act as both acid as well as base.

Therefore, the correct answer is (D).

Note: Note that $Zn{(OH)_2}$ is an amphoteric oxide which is used in the manufacture of oral drugs and baby powder. $Be{(OH)_2}$ has its use in the manufacture of some important beryllium metal alloys.