Students who are outsiders which don't have domicile certificate are eligible only for private colleges.
You can check below top colleges in WB through WBJEE
Jadavpur University, Kolkata
Heritage Institute of Technology, Kolkata
Institute of Engineering and Management, Kolkata
Maulana Abul Kalam Azad University of Technology, Kolkata
Haldia Institute of Technology, Haldia
To check the complete list you can refer below link
List of top engineering colleges through WBJEE
To check the cut off you can refer below link
WBJEE Cut Off
Good Luck!!
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