Engineering Entrance Exam

It depends upon sastra rank.

Yes, it is mandatory.

Yes, you will get CEG for B.E. in Computer Science and Engineering because yours marks are very good enough for CEG for B.E CSE.

The last year closing rank at SVNIT for Integrated M.Sc. (Mathematics) was 126745 in general category. So you can get the chances here for doing integrated M.Sc. (5 years) course. The following are the other options for you.
1. Auro University
2. P. T. Sarvajanik College of Science.

Hello Mithun, Presently Surathkal is one of the most sought after NIT by the students. Hense, invariably the cutoffs are quite stiff. How much percentile u need for admission is difficult to guess, but to help you I am attaching a link that will predict which college you can get based on your rankin

Hello Rahul. Your rank of 5800, even if for other state student, is quite good. I feel with this rank, you should get admission in your desired stream or branch. However to help you, I am attaching a link that can predict college for you based on your ranking. https://www.shiksha.com/engineering/wbj