B.E.

No, you cannot get admission in Sathyabama just with your class 12th and class 10th mark. You will have to write the Satyabhama entrance exam to get admission here at Satyabhama University .
You can apply for the entrance exam using our college website: http://sathyabama.ac.in/engineering-entrance-exam
This is the official website of our college. You can also get the other details like college fees etc. in this website.

Thiagarajar College of Engineering, [TCE] Madurai Fee Structure and List of Courses Summary:
BE (4-year)-42,005
Bachelor of Technology [B.Tech], 4-year: 3,08,650
Master of Engineering [ME], 2-year: 1,83,250
Master of Technology [M.Tech] 2-year: 1,61,625
Bachelor of Architecture [B.Arch] 5-year: 3,76,650.

Eligibility Criteria for Lateral Entry:
Candidate must have passed Diploma in Engineering/Technology from a recognized board.
https://www.shiksha.com/b-tech/course/b-tech-lateral-entry-mepco-schlenk-engineering-college-tamil-nadu-other-243401

Whatever the college you choose, firstly it depends on the rank you get in the entrance exam of that particular college. Based on the rank they decide the fee structure of the selected branch.

Hello Akshay,
BC quota is around 23% in most of the cases. The answer to your question is to be found using empirical and approximations. In IIT's, there are about 10000 seats and 1000 are for CSE. By the same logic, there are approximately 15 Lacs seats on all India basis and there should be about 1.5 Lacs seats for CSE. Out of these, approximately 23% would be under OBC. Best wishes to you.

Total fees of B.Tech. In Aerospace Engineering in Karunya Institute of Technology and Sciences, Coimbatore is INR 7.84 Lacs
https://www.shiksha.com/b-tech/course/b-tech-in-aerospace-engineering-karunya-institute-of-technology-and-sciences-Coimbatore-164341.

I'll tell you the whole admission procedure in detail.
So, first of all, you'll have to register yourself on cu FastTrack and one unique I'd will be generated to you.
After that you'll have to register yourself for the admission test and if you clear that test then you're eligible for the admission and you can also avail scholarship from the University that will be compensated to your academic fee only.

Use Jee Mains College Predictor to know the same:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor