What would happen if you put a nuclear bomb at the center of Mt. Everest

And you set it off. And it exploded?

Would the mountain contain the blast, or would it blow up? Would there be an earthquake?

You could pick up the blast on seismographs. Nothing else noticeable.

There have been underground nuclear tests. They went underground after atmospheric tests were banned by international treaty.

Earthquakes are very common in such an unstable region so another one would hardly make a difference.

If you dug from the Chinese side you would spend the rest of your time in a forced reeducation camp.

Other than that it would be just another underground test.
It would need to be quite close to the surface for it to have any external effects.

If it was close to the surface then radiation could escape.
The radiation fallout would contaminate the Ganges and Brahmaputra rivers so the Indians would also want to punish you too.

minor seismic activity. nothing much else. all depends on the yield of the bomb. most contries test nuclear weapons underground after the non-proliferation treaty.

-The People of Nepal would come after You... :)

the top might fall off

You will be the first one to die, so you would never find out.