Hi Mayank you need not worry for it.You can give competitive exams for private colleges like AMRITA,VIT.These are really very good institutes where you can get your dreams come true and also 

with a very good infrastructure .So I prefer you with these institutes.

Hello Dear

See entering into an any engineering institute for doing a b.tech is not a difficult task but for doing from the good College is the difficult one. Since you are lagging from the major eligibility factor i.e nit having the percentage more than 60 because of which you will directly cuttoff from the good private institutions inorder to take the admission in it, but anyways you can try to other colleges like LPU, Amity , SHARDA etc. which will intake the candidate's via management seats or through the entrance exam.

All the best