According to Google Terms of Services, can I put adsense ads in .org and .edu domain? I did't find it.
As long as you carefully follow all the Adsense program policies I don't think there would be an issue.
I didn't see anything in the TOS that says you can't. Try looking at other .gov sites and see if they have them to make sure.
In the eyes of Adsense, All TLDs are created equal. However, for .gov/.edu domains, make sure you make it clear to the institution how the Adsense program operates and who benefits from it. Peace,
no problem to show adsense in .edu or .gov website. but normally those TLDs do not show any Commercial ads or adsense to maintain their status/rank.