Hello,
Yes she can opt for a private college as private college does not take jee main marks as the criteria fir admission.
Most colleges  has its own qualify in paper and many uthay are not too good also take admission without taking paper(i.e money).
So she can take cst in any of them

Definitely yes your sister can take admission in a private college even she can try for government college too as her performance was very good in JEE Mains 2019. She can use careers360 college predictor tool to predict her college on the basis of her rank in the JEE Mains 2019. 

https://engineering.careers360.com/jee-main-college-predictor

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