Hello student,
You have not mentioned which category you belong to or the state. With a score of 350, it becomes difficult to procure a seat in private colleges when comparing the results of previous years in your category is general. It also depends on the state you choose. For example, With this score you have chances of getting a seat in the colleges of Uttar Pradesh while it is not so in the case of states like Tamilnadu and Rajasthan. Also,  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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