NIT Surathkal - National Institute of Technology

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.

Total Fees INR 2.40 Lakh
Hostel Fees (Yearly) INR 35,700
Hostel fee includes:
Admission fee : Rs.100 (one time fee)
Establishment Charges (every semester) - Rs.4500
Maintenance Charges (every semester) - Rs. 900
Student Extra Curricular Charges (every semester) - Rs.200
Mess Charges (every semester) - Rs.12000
For extended details, kindly visit-
https://www.shiksha.com/b-tech/course/b-tech-in-mechanical-engineering-national-institute-of-technology-surathkal-mangalore-61468?rf=searchWidget&landing=clp

Your predicted rank is 142375 JEE Main Percentile 83.71, AIR, GEN)
Above is the possible rank you can get. The final rank will be based on the best of the scores of JEE-Mains January 2019 and April 2019 exam. The predicted rank may vary due to JEE Main tie breaker rules for same score. For information on the list of colleges eligible based on this prediction, follow the link below
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

With 5.9 CGPA in UG, it's a bit tricky. But with 75 percentile in CAT it's worth taking the risk.