If you are a General category, Goa origin student then 70,000 should be enough to get you a seat. With your rank, you can get a seat for Mech or Civil. You have a good chance to get EEE or ECE too.
Here is the recent cutoff for the branches.
Specialization | Home State | Other State |
Civil Engineering | 87610 | 31362 - 35494 |
Computer Science & Engineering | 14581 | 7420 - 10323 |
Electrical & Electronics Engineering | 73349 | 19728 - 21121 |
Electronics and Communication Engineering | 34058 - 53405 | 14553 - 16711 |
Mechanical Engineering | 82553 - 83783 | 23542 - 26295 |
This should give you an idea about the cutoff required for NIT Goa.