Which of the following is amphoteric oxide?
$\text{M}{{\text{n}}_{2}}{{\text{O}}_{7}}\text{, Cr}{{\text{O}}_{3}}\text{, C}{{\text{r}}_{2}}{{\text{O}}_{3}}\text{, CrO, }{{\text{V}}_{2}}{{\text{O}}_{5}}\text{, }{{\text{V}}_{2}}{{\text{O}}_{4}}$
  & \text{A}\text{. }{{\text{V}}_{2}}{{\text{O}}_{5}}\text{, C}{{\text{r}}_{2}}{{\text{O}}_{3}} \\
 & \text{B}\text{. M}{{\text{n}}_{2}}{{\text{O}}_{7}}\text{, Cr}{{\text{O}}_{3}} \\
 & \text{C}\text{. CrO, }{{\text{V}}_{2}}{{\text{O}}_{5}}\text{ } \\
 & \text{D}\text{. }{{\text{V}}_{2}}{{\text{O}}_{5}}\text{, }{{\text{V}}_{2}}{{\text{O}}_{4}} \\

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Hint: Amphoteric oxides are those species which can react with both acid as well as with base. Mostly the metallic oxides come under the category of amphoteric oxides. Such as zinc oxide and aluminium oxide.

Complete Answer:
-As we know that the amphoteric oxides react with both acid as well as a base.
-So, from the above-given compounds, only vanadium pentoxide and chromium (III) oxide are the amphoteric oxides.
-This is so because vanadium pentoxide can react with both acid and base.
-The vanadium pentoxide reacts with base and acid to yield $\text{VO}_{4}^{-3}\text{ and VO}_{4}^{+}$ respectively.
-Similarly, chromium (III) oxide can also react with both acid and base.
-It gives both acid as well as a base to give \[{{\left[ \text{Cr}{{\left( {{\text{H}}_{2}}\text{O} \right)}_{6}} \right]}^{3+}}\text{ and }{{\left[ \text{Cr}{{\left( \text{OH} \right)}_{6}} \right]}^{3-}}\]respectively.
-Manganese heptoxide is an acid in which manganese has the oxidation state of +7 it means that manganese tends to accept the pair of electrons that's why they cannot react with a base to give a pair of electrons and are considered as Lewis acid.
-So, option B. is an incorrect answer.
-In option C, chromium oxide is present which is basic and because it has an oxidation state of +2 and we know that the compound having low oxidation state is basic.
-So, option C is an incorrect answer.
-In ${{\text{V}}_{2}}{{\text{O}}_{4}}$, the oxidation state of vanadium is +4 which shows that it tends to donate a pair of the electron that's why it is as basic only and not amphoteric.
-So, option D is an incorrect answer.

Therefore, option A ${{\text{V}}_{2}}{{\text{O}}_{5}}\text{, C}{{\text{r}}_{2}}{{\text{O}}_{3}}$ is the correct answer.

Note: Chromium (III) oxide is insoluble in water. It can also react with concentrated alkali to form the chromite ions. One can identify the amphoteric oxide by its property that if it is dissolved in a solution and then if the oxide can donate or when needed, it can also accept a pair of electrons.