Engineering Entrance Exam

Yes is the only way for undergraduate admission.

Check out the link below for details :
https://www.shiksha.com/b-tech/exams/jee-mains

Hello Vivek,
As the counselling for seat allotment has begun, I'm giving you the rank oriented answer. Your SC category rank should be below 4000 to get a good course at NIT Bhopal. You may refer the link below for closing and opening ranks:
http://josaa.nic.in/Result/result/OpeningClosingRank.aspx

Hello Tripti,
As per your rank, your chances are slim for getting any IIT's,however check here to know more:
https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx

Check the curriculum for BITSAT exam and match accordingly:
http://bitsadmission.com/bitsatmain.aspx check this link

You can appear for SAT Examination along with JEE provided you can prepare for both exams simultaneously.

My friend,
I don't think your marks and rank is in sync. Either rank or marks are wrong. try again after cross-checking and verifying.

The JEE score is valid in most of the colg. And is the creteria for the merit list and cutoffs. Do visit the official websites of the institutes for percise and bonafide information is my suggestion.

Now onwards, CET has been demolished and there is only 1 entrance i.e. JEE. So, focus only on your mains and advanced.