WBJEE

Yes, you will get the JADAVPUR UNIVERSITY But you have to get top rank like under 500 Because of the state quota.

I am sending you an authentic link from where you get all information about WBJEE exam. But It seems Exam already held of WBJEE. Please check it out the link. link-https://wbjeeb.nic.in/wbjeecms/public/home.aspx.

Please use this college predictor tool by Shiksha. It will help you to predict the college according to your rank or percentile:. .
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https://www.shiksha.com/college-predictor

Well there's no way to do that without giving WBJEE. JU does not take admission outside WBJEE counselling.

As per an official of WBJEEB, results for West Bengal Joint Entrance Examination WBJEE 2020) will now be declared in the month of May after lifting of extended lockdown. The students who have been waiting for the results can now expect it in third or fourth week of April 2020. The exam was successfully conducted on February 2, 2020. However, due to the outbreak of COVID-19 nationwide, a delay in release of results is observed. The result will be published in the form of Rank Card, having all relevant ranks, total score and component score in Paper I and Paper II on the official website.

You may refer the Shiksha college predictor.

For the time being you need to wait till the time the situation is not under control and then onky the further processes will be followed accordingly for the admissions.

Refer the link to know about the admission criteria of IEM Kolkata the best one in West Bengal for pursuing CSE https://www.shiksha.com/college/iem-kolkata-institute-of-engineering-and-management-salt-lake-city-23742/admission.