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Hello Aspirant,
With 339456 general rank and 24256 SC rank in JEE mains, it is very difficult or quite impossible to get any Government college in West Bengal.
Cutoff varies every year depending on various factors. Keep in mind that your chances to grab a seat will vary on the following basis:
Number of seats available
Number of students applied for the same branch
Performance of the students
The category you belong to etc.
You can check out rank vs marks vs percentile from the below link:
https://engineering.careers360.com/articles/jee-main-marks-vs-percentile
Use this JEE college predictor to get list of colleges based on your score:
https://engineering.careers360.com/jee-main-college-predictor?utm_source=qna&utm_medium=jee_cp
Visit this page to get more information about previous year's college wise, branch wise cutoff:
https://engineering.careers360.com/colleges/list-of-government-engineering-colleges-in-west-bengal-accepting-jee-main
Hope this information will help you.
Best wishes!
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