ICAR doesn't actually display the marks of students and it provides no analysis of the marks vs rank comparison. So it's a little difficult to say. But yes a rank under 2000 can surely give you a government college. I'll enlist down the cutoffs of some of the top colleges through ICAR with their cutoff rank -

1. PAU LUDHIANA - cutoff rank 385
2. CCSHAU, Hisar (Haryana) - rank 292
3. Banaras Hindu Univ., Varanasi (U.P.) - cutoff rank 148
4. GBPUA&T, Pantnagar - 379 rank

Best wishes. Thank you.