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In order to get admission in private colleges, you need to have cleared the NEET examination. That's the basic criteria. So, yes you will get admission in private colleges but the choice of college is yours. You can try Karpagam Faculty of Medical Sciences and Research, Coimbatore or PSG institute of Medical Sciences, Coimbatore. Check out the link below:

https://www.google.com/amp/s/medicine.careers360.com/articles/neet-cutoff-tamil-nadu/amp