Engineering Entrance Exam

It's hard to get admission in JK Institute of Applied Physics with such a rank. CSE branch closes at around 7000.

Yes, you are eligible for JEE Mains provided you have 75% in class 12th. It doesn't matter that you have appeared for any other examination or not.

Chandigarh College of Architecture is a prestigious college and there are only a couple of seats there for outside quota.
You have to score something above 265 to secure a seat there through JEE B.Arch paper. This may not be possible for you to take admission in this college.

Follow the following links:
https://www.shiksha.com/b-tech/course/b-tech-in-civil-engineering-national-institute-of-technology-surathkal-Bangalore-61474
https://www.shiksha.com/b-tech/course/b-tech-in-mechanical-engineering-national-institute-of-technology-surathkal-Bangalore-61468
https://www.shiksha.com/b-tech/course/b-tech-in-electronics-and-communication-engineering-national-institute-of-technology-surathkal-Bangalore-61501
https://www.shiksha.com/b-tech/course/b-tech-in-chemical-engineering-national-institute-of-technology-surathkal-Bangalore-61489

No, don't drop a year just for JEE Mains. Drop only if you are targeting JEE Advance and if you want IITs. Still if you are confident enough that you can do very well in JEE Mains next year and are sure to get top NITs, then only drop the year otherwise it's a waste of time.

Yes, you are eligible for both JEE Mains and Advance.

Surely you are eligible to give the exam. But you will be disqualified in the document verification round at the time when you report to the college. Hence you should not give JEE Mains.

The only criteria is that you have to fill the form for counseling as per the notification by JOSAA and pay the required fee. Yes, OBC candidates get benefit of their category. Hence there are two ranks - general rank and category rank.

Hi,
It's not a very good idea for you that you repeat one more year. It will be wastage of time. Generally, what happens is students whose ranks are within 2000-5000 they want to improve their ranks so they repeat the year. You must sit in JEE Mains counseling if you want a college. Enroll yourself for REAP counseling. You can get some good colleges in Rajasthan. You should even enroll for the state counseling. Don't go for VIT or SRM.