Dear Aspirant

Eligibility criteria for Gate is as follows "Candidates must have passed graduation in engineering/technology or Master’s degree in any relevant science subject." so yes definitely you can do cse from IIT/NIT after doing IT in your bachelors but you should appear for computer science and IT paper of gate and that is it, even after doing mech in bachelors you can appear for cse in master only that you should appear for cse paper of gate.

Hope this helps you.