Colleges in Mangalore

You can get the fee structure at shiksha.com platform
Please follow given link and search college, then you can get full details of college
https://www.shiksha.com/btech/resources/college-reviews/1

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.

There will be two JEE Main exam this year. First one was in January month and second one will be in the month of April. National Testing agency will release percentile score for both the exam. Better of them will be considered. According to this percentile score, NTA will release JEE Main rank for every students. Then, after counselling process will be started by Joint seat allocation authority(according to last year). Last year, there were 7 rounds and 2 special rounds in counselling process. After completing counselling process every student have to report their respective allocated college.

Kindly wait for the ranking cut off to be released, post JEE Mains April 2019, for the particular college of interest. Meanwhile, follow the link: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Your Predicted Rank is 32600 JEE Main Percentile 96.27, 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. Kindly visit the following page for additional details on the list of colleges. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.