Dear Student,

Only direct admissions are started and the some private university also started taking admission according to their own entrance exam but the admissions in IIT/NIT/IIIT will only be started once they complete their every. So if you are thinking to take admission in NI/IIIT then you need to wait till JEE mains ends and for IIT you need to wait for JEE advance.

I don't think you need to worry about the admissions as the exams are still going, they will start the admission process only when they complete the entrance part.

And if you want to take admission in private colleges without JEE then definitely you can take through direct admission as they are running.

Good Luck :)