Jadavpur admits to multiple faculties:-

Engineering Faculty
This faculty offers Bachelors in Engineering and Architecture. You will need a WBJEE rank (within 1500 for most departments) for admissions which happens via counselling ( Page on wbjeeb.nic.in (http://wbjeeb.nic.in/counsinfo/CounsellingProcess.aspx) ). For B. Arch you will need marks in a national level architecture (drawing) exam for admission qualification (WBJEE rank generally required is lower here).

Science Faculty
The science faculty offers Bachelors in many science subjects and admissions is based on the marks you obtained in you class 12 board examinations (officially termed as merit). Form collection and cut-off selection happens mostly after the publication of the most popular board exams in Calcutta (namely, ICSE, CBSE and WB board).

Arts Faculty
Admission to this faculty is a combinations of merit (+2 marks for screening purposes) followed by and entrance examinations for most subjects in this faculty.

Lastly, there are entries to all departments via sports quota as well. Cut-offs in WBJEE rank or exams or +2 marks are a little lower in this case.