The NIT Goa offers Under Graduate courses and Ph.D. degrees in five engineering departments - Computer Science and Engineering, Electronics and Communication Engineering, Electrical and Electronics Engineering, Civil Engineering and Mechanical Engineering. The Institute also offers Ph.D. degrees in Physics, Mathematics, Chemistry, Economics and English specialization. The Institute admits students into the B.Tech. degree courses on the basis of ranks obtained in the Joint Entrance Examination JEE (Main) and the scheme of Direct Admission to Students Abroad (DASA). The Institute also offers M.Tech. courses like Computer Science and Engineering (CSE), VLSI and Power Electronics and Power Systems (PEPS).

There is no fixed cut-off marks for IIT Goa. The cutoff varies drastically from year to year based on the paper level and steadily increasing competition. 

National Institute of Technology Goa is an Institute of National Importance and the placements here are much better than that of anywhere else. The Mechanical department is doing good, and the placements are also decent. Some of the stats are:

Highest package: 15LPA
Lowest Package: 6LPA
Average Package: 8 LPA

You can also use our college predictor to see your chances in all the colleges:
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Hope I have answered your question. All the best!