yes, you can apply for M.Tech in IIT kharagpur based on your gate score as it is good for b.tech as well as M.Tech so getting a good score and applying for iitk is the best option.
All the iit and nit are the best options for doing the course because the level of study is good and also you will mates like that only who are really focussed on being studies.although college doesn't matter a lot we say but still upto some extent it matters bro.
Candidates can check B.Tech Cut off for Top IITs & NITs here.
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