Hello,hope you are doing well.First of all I want to tell you that there is very less chance to get government Colleges in rajasthan.Yes, that will be a better option to think of the private colleges. The private colleges that you can go for are-

• Tilak Ayurved Mahavidyalaya, Pune

•K G Mittal Ayurvedic College, Mumbai

•Sumatibhai Shah Ayurved Mahavidyalaya Malwadi, Pune

Cut offs change every year depending on various factors such as no.of Candidates appearing for the exam, no.of Candidates qualified, top NEET score and difficulty of the exam.This year all India quota the cutoffs may be higher than the other years, that is why any score less than 590 or 600 out of 720 is less.

For more information you can go through the article on  previous year's cut off-

https://medicine.careers360.com/articles/neet-cutoff-up

For more information-

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

Hope you will be benifited

Thank you