Colleges in Arunachal Pradesh

You better visit the link for better confirmation. https://www.ugc.ac.in/privateuniversitylist.aspx?id=2&Unitype=3

The last date was July 12.

Yes, there is an entrance exam for the admissions. Eligibility for the same is that the candidate must have done graduation.

Reference Books for NERIST Entrance Exam are:
Fundamentals of Physics and Inorganic Chemistry
Objective Mathematics by RD Sharma
Organic Chemistry Study Guide

Hi, your admission to NIT will be done by Central Seat Allocation Board which gives score by that 40% boards + 60% JEE Mains. They will give rank list based on this scores according to which you'll be asked to fill up your choices (NIT's plus some additional Pvt. Universities). I think you have some chance to get admission here but due to less marks in boards, you loose these chances. Don't worry and try to apply for these. I hope you understand.
Thanks.

Of course, you can apply JEE Mains.