Question

which was the most recent group to invade northern india

Answer 1

Is there no multiple choice?
If you want to be technical, then you could say the British when they colonized pretty much the entire sub-continent.
If you want to be extremely technical, then you could argue that the Chinese were, given they invaded north India for a couple months in the 60's.

But realistically if you're talking about a group that invaded and stayed or assimilated then it would be the Mughals.