Exam

Sorry, but you cannot appear for the JEE Mains exam as it needs 75% or above, but you can appear for NDA exam.

Probably you may fetch a seat as some colleges have their closing rank near the rank you have secured.
All the best.

As you are in last month of admission session for B.Tech so there is approximately no entrance exam left all are over almost. so your 12th score is good so you try in counseling of college through your 12th marks.

You are advised to start your self preparation now and then opt for one year duration coaching for CAT 2018 starting in Nov Dec 17. This will give you sufficient CAT preparation time without impacting your B.Sc studies.

It looks a little difficult. Which colleges are you targeting? If you are trying for premium institutions, then you need to spend more time on improving your English and maths.

Most students apply in Chetana's Ramprasad Khandelwal Institute of Management & Research using their CET or MAT scores. I am not sure about the acceptability of ATMA scores. You can get in touch with the college office on the following number: 022 26513346.
All the best to you.

Sorry to say, but without clearing your class 12th, you cannot get admission in a college. The minimum eligibility is +2.

1000 for general and OBC boy students and 500 for all category girl students and 600 for SC, ST, and PWD Students for only paper 1 or paper 2. If you want to give both papers, then you have to pay Rs. 1800.

Yes, you can pursue B.Sc in nursing.