The most basic oxide among MnO, \[M{n_2}{O_3},{\text{ }}Mn{O_2}\]and \[M{n_2}{o_7}\] is :
  A.\;\;\;\;\;MnO \\
  B.\;\;\;\;\;Mn{O_2} \\
  C.\;\;\;\;\;M{n_2}{O_3} \\
  D.\;\;\;\;\;M{n_2}{O_7} \\

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For the transition metal oxides, the lowest oxidation state is the most basic, since it can donate lone pairs of electrons and function as a Lewis base.

Complete step by step answer:
-The basicity decreases with increasing oxidation state.
- In MnO, Mn has an oxidation state of +2 and its least acidic and hence more basic.
Further, in case on \[M{n_2}{O_7}\], Mn is +7 oxidation state so it is more acidic and hence least basic
-In general, the electropositive character of the oxide’s central atom will determine whether the oxide will be acidic or basic. The more electropositive the central atom, the more basic the oxide. The more electronegative the central atom, the more acidic the oxide.
-The most basic oxides include:
1.Sodium oxide, which reacts with water to produce sodium hydroxide
2.Magnesium oxide, which reacts with hydrochloric acid to form magnesium chloride
3.Copper (II) oxide, which reacts with nitric acid to form copper nitrate.

Hence, option A is correct.

 On going down the group, the atomic radius increases so ionization energy decreases, that means tendency of losing electron increases which implies increase in metallic character. The oxides and hydroxides of metals are basic in nature and thus basic character increases down the group.