Hi

It's quite difficult to predict because cut off  depends upon various factors like

------------) number of students that appeared in the neet exam,

------------) kind of marks obtained by them ,

------------)  toughness level of the neet examination

------------)  number of seats available etc

But yes,

As per 2020 cut off,

>>>>>>> with  4600  st rank

Yes, you have chances for BIT Mesra

For example,

In 6th round of josaa counselling 2020,

----------) Under other state,  4881 st  rank got production engineering in Birla Institute of Technology, Mesra, Ranchi

You can check the same at

https://josaa.nic.in/Result/Result/currentorcr.aspx

This prediction is on the past year data basis but  cut closing rank for colleges changes every year depending upon factors like number of candidates that write jee main examination, difficulty level of the question paper for different shifts of jee main etc so

To have a personalised report on your chances of getting a college you can go through our college predictor, it will give you complete list of colleges which you can get on the basis of the category you belong to,  your home state, your gender etc, the link for  jee main college predictor is provided below

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

To help you  further,

Minimum percentile in jee main 2021 to qualify it to  be eligible for jee advanced 2021 is given below :-

--------) general :-87.8992241 percentile

--------) EWS:- 66.2214845 percentile

--------) OBC-NCL :- 68.0234447 percentile

--------) SC :- 46.8825338 percentile

--------) ST:- 34.6728999 percentile

--------) PH :- 0.0096375 percentile

Thank you