Hey dear, cutoff varies every year if you see the last year's cutoff which went very high that even students getting 500 marks were unable to get a govt. Mbbs college. This, year, cutoff has gone higher than previous year, so you can understand the competition now. So, with this score being general candidate you won't get a govt. Mbbs college, but will surely get a bams or bhms college and since you asked about private colleges, so you will definitely get private colleges with this score. You can aslo use college predictor through this link:

https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer