Hello student,
Yes, With a score of 350, you have chances of procuring a seat in the private medical colleges when comparing the results of previous years. Last year, a minimum score of 202 got a seat in the Teerthankar Mahaveer medical college and research centre, Moradabad. But one thing to keep in mind is that scores and ranks vary each year with difficulty level of the question paper and availability of seats. However you can predict the colleges which you are likely to get using the given link
http://medicine.careers360.com/neet-college-predictor
Good luck

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