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The pair of amphoteric hydroxides is :
A.$Be{(OH)_2}{\text{ and }}Zn{(OH)_2}$
B.$Al{(OH)_3}{\text{ and Li}}OH$
C.$B{(OH)_3}{\text{ and Be}}{(OH)_2}$
D.$Be{(OH)_2}{\text{ and Mg}}{(OH)_2}$

Answer
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Hint:
We can say that an amphoteric compound is a molecule or ion that can react both as an acid and as a base. Many metals (such as copper, zinc, tin, lead, aluminium, and beryllium) form amphoteric oxides or hydroxides. $Al_2O_3$ is an example of an amphoteric oxide.

Complete step by step answer:
An amphoteric compound is a type of molecule or an ion that is well capable on its own to react both as an acid and as a base. Many heavy metals such as zinc, copper, are an example of an amphoteric oxide.
Aluminium hydroxide is an amphoteric oxide as per its nature. It signifies that it has both the basic and the acidic properties when reacted.
Like many hydroxides of the various other metals, such as beryllium, tin, lead, aluminium and even chromium, zinc hydroxide (and zinc oxide), is amphoteric in nature in many reactions possible.
Therefore they will readily dissolve in a dilute solution of a strong acid, such as HCl, and also in a solution of an alkali such as sodium hydroxide.
Beryllium hydroxide, is an amphoteric hydroxide, dissolving in both acids and alkalis.
Therefore by the set of facts we can clearly get the list of amphoteric hydroxides.
Hence option D, $Be{(OH)_2}{\text{ and Mg}}{(OH)_2}$ is a correct answer.

Note:
Amphoteric hydroxides act as either Bronsted-Lowry bases (accepting protons) or Lewis acids (accepting an electron pair), depending on reaction conditions. This is because they are capable of performing both the ${H^ + }$ and $O{H^ - }$ giving reactions.