Hello, 

Yeah appear for the counselling if the people before you didn't choose any NIT you may be eligible for that seat. So appear for counselling. If you have luck you may get best NIT. And after if you attend the counselling and if you not get seat in NIT you can go for top private universities.

Here are the top private universities:

BITS Pilani.

VIT University.

Amrita University.

SRM University.

PSG college of engineering.

Sastra University.

Githam university.

KL University.

Thank you and all the best.