Dear student.
Greetings.
Yes, NIT Karnataka, SURATKAL offers Computer science engineering as a course. The admissions are taken according to the marks of JEE main examination. Visit this link to know more about the cutoff, fee structure of NITK, SURATKAL. https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.careers360.com/university/national-institute-of-technology-karnataka-surathkal&ved=2ahUKEwj6jpKp9pHeAhWLRY8KHdrwBJEQFjAAegQIARAB&usg=AOvVaw3TFIBZT0BAfOFQTH3QORxK&cshid=1539932315828
Thank you.
All the best.

Hello,
Yes CSE BRANCH is available in NIT SURATHKAL.You can take admission in this college only through your jee mains score.As it is one of the top NITs , so try to score around 225 above in jee mains to get admission there.
Good luck.