Hello student,
Yes,  With a score of 416 ,you have chances of getting Indira Gandhi institute of medical sciences in Patna when comparing the results of previous years. Last year, a score of 406 was required to fetch one a seat in that college in SC category under the state quota. 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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