Question

why only Mg and Mn reacts with nitric acid to produce hydrogen, not any other metal ?

Answer 1

Heya friend!!!
Mn and Mg lies above the Hydrogen in reactivity or activity series. Metals that lie above the hydrogen produces hydrogen gas when reacted with water but metals like Fe or Au do not as they lie below the hydrogen in table.
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Answer 2

because nitric acid is a strong oxidizing agent