NIT

Regarding your JoSAA counseling, it totally depends on whether you belong to a category or not. Secondly, you might want to reassess what you want to do in graduation and after graduation. In case you are determined for B.Tech then a better option would be to try again next year. However, if that option is not available then a number of good private institutions are available for you. So, right now your main concern should be about the branch that you want to pursue. I hope that you applied for exams like AMU, WBJEE AKTU, IPU etc. (registered for Thapar). As they are good enough and have low fee structures (I think AMU engineering is the cheapest in India). To be frank with you I don't think your JEE rank is good enough to land you into a decent college through JoSAA. Don't lose hope, all the counselings will begin from June. It'd be better to weigh in your options then. For now, just keep looking for other registrations and prepare for any upcoming exams.