You need to cancel your admission in Bidhannagar College before getting admission through WBJEE. Just visit BNC with your guardian and reach their administrative section and gradually ask to cancel your admission. They will take back the ID card if they had given any during admission. After that they will ask you to show the mark sheet. Deliberately they put another stamp beside the previous one which will show something like ADMISSION CANCELLED.

Now you are all done with your problems.