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Which of the following is amphoteric oxide?
\[\text{M}{{\text{n}}_{\text{2}}}{{\text{O}}_{7}}\],$\text{Cr}{{\text{O}}_{\text{3}}}$, $\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{3}}}$,$\text{CrO}$, \[{{\text{V}}_{\text{2}}}{{\text{O}}_{\text{5}}}\], ${{\text{V}}_{\text{2}}}{{\text{O}}_{\text{4}}}$
(i)\[{{\text{V}}_{\text{2}}}{{\text{O}}_{\text{5}}}\], $\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{3}}}$
(ii)\[\text{M}{{\text{n}}_{\text{2}}}{{\text{O}}_{7}}\], $\text{Cr}{{\text{O}}_{\text{3}}}$
(iii)$\text{CrO}$, \[{{\text{V}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]
(iv)\[{{\text{V}}_{\text{2}}}{{\text{O}}_{\text{5}}}\], ${{\text{V}}_{\text{2}}}{{\text{O}}_{\text{4}}}$

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Hint Transition metals shows variable number of oxidation state, when the transition metal ion of a compound present in their middle oxidation state, it can increase its oxidation state by losing electrons(oxidation) or can decrease its oxidation state by accepting electron(reduction). They show reactivity in both acidic and basic medium.Are the examples of amphoteric oxide.

Complete Step by step solution –
An amphoteric oxide is an oxide that reacts (dissolve) with both acid as well as base. Normally transition metal oxides are basic in nature. There are many transition metals (like copper, zinc and iron) which form amphoteric oxides. Chemical nature of oxide will be determined by the oxidation state of the central metal ion of oxide. The more electropositive the central metal the more basic the oxide, and the more electronegative the central metal ion the more acidic the oxide. In lower oxidation state transition metal oxide is basic in nature, while in higher oxidation state they are acidic in nature.
In $M{{n}_{2}}{{O}_{7}}$, $\text{M}{{\text{n}}^{\text{7+}}}$ ion present in their maximum oxidation state. It can only gain electrons, so this metal oxide will be acidic in nature.
Chromium metal ions show variation in oxidation state from +2 to +6. In $\text{Cr}{{\text{O}}_{\text{3}}}$, $\text{C}{{\text{r}}^{\text{+6}}}$ ion present in maximum oxidation state, so this oxide will be acidic in nature. However in $\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{3}}}$, $\text{C}{{\text{r}}^{\text{3+}}}$ present in middle oxidation state. $\text{C}{{\text{r}}^{\text{3+}}}$ Ion is amphoteric in nature. $\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{3}}}$ is insoluble in water. It soluble in acid form ${{\text{ }\!\![\!\!\text{ Cr(}{{\text{H}}_{\text{2}}}\text{O}{{\text{)}}_{\text{6}}}\text{ }\!\!]\!\!\text{ }}^{\text{3-}}}$ salt and also reacts with base to form salt of ${{\text{ }\!\![\!\!\text{ Cr(OH}{{\text{)}}_{\text{6}}}\text{ }\!\!]\!\!\text{ }}^{\text{3-}}}$. In $\text{CrO}$, $\text{C}{{\text{r}}^{\text{2+}}}$ ion present in the lowest oxidation state. So, this is a basic metal oxide.
In\[{{\text{V}}_{\text{2}}}{{\text{O}}_{\text{5}}}\], ${{\text{V}}^{\text{+5}}}$ ion is present in its highest oxidation state. However \[{{\text{V}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] is amphoteric oxide but mainly acidic. \[{{\text{V}}_{\text{2}}}{{\text{O}}_{\text{5}}}\] Reacts with alkalis as well as acids gives $\text{VO}_{\text{4}}^{\text{3-}}$ and$\text{VO}_{\text{2}}^{\text{+}}$.

So, option (i) will be the correct option.

Note– nature of metal oxide is basic in nature because when they are dissolved in water they form metallic hydroxide. However, non-metal oxides are acidic in nature, after dissolving in water they form oxyacid.