Hey there

Yes ofcourse you can give gate exam if you choose IT branch and you can get iits but generally PSUs don't have IT jobs except Bsnl etc. So less job options but you will have chances of studying higher.

Check about GATE

https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/articles/gate-cutoff/amp&ved=2ahUKEwi3lcTFu7HjAhVB7WEKHUaNAkIQFjALegQIBBAB&usg=AOvVaw0etbw7kEQj4iH6wMKrSqdL&ampcf=1

Good luck