NIT Surathkal - National Institute of Technology

For getting CSE branch at NITK, one should have more than 75 % marks in 12 and more than 95 percentile marks in JEE Mains.

It depends on the home state and category. If you belong to any respective NIT's home state, you can easily get a seat. But in other state case you can get mechanical and civil in NIT Puducherry and civil in NIT Surathkal.

Yes, it is considered one of the top three NITs. NITK is the only one, which has the funds for research area with top seven IITs. According to the place, it is better because it has a private beach. You can see the current in the sea from your class itself and professors are also well educated.

The selection for MBA program is done separately by the Institute during March and is based on the criteria specified.
Kindly wait for all the applicants to go through the selection process. Once done, selected candidature list will be put up in the website.

In general category, you might get admission in the top 3 NITs, that is Surathkal, Trichy and Warangal . You will get CE, ECE and EEE in most of the lower NITs.

I am sorry, but NIT-K cut-offs, as far as I know, reach the maximum of 5 digits. I think you should try for some other NIT or search some colleges where you could choose a branch in which you want to pursue your career.

Rather than focusing on such thing, you should also appear for JEE Mains, which is going to be conducted in April, because if you don't give the exam in April, then there are chances of falling down your rank, as competition is going to increase much this time.

Last date for receiving application form for admission to MBA Programme 2019-21 was 05.03.2019. Kindly visit
http://old1.nitk.ac.in/images/announcements/mba2019/Information_Bulletin_MBA_2019-21_.pdf.

I think, you can pursue mathematics in M.Tech and in B.Tech focus on your subjects only.

http://prism.nitk.ac.in/facilities.html
Visit the above link to get through the facilities offered by the campus.
http://prism.nitk.ac.in/
This link shall lead you to the required answers.