For getting into the best institute you need a rank under 1k. With your rank i suppose you can get the following:

Abacus institute of engineering and management, civil,cs, electrical,ece, mechanical

Academy of technology, ece,electrical,it, mechanical, instrumentation

Aryabhatta institute,eee,ece, it, Mechanical

Asansol engineering college, electrical,eee,ece,mech

These are some of the colleges that you might get. Not guaranteed about the branches. Hope it helps.