Jadavpur University

Jadavpur University is a State University of West Bengal and thus the admission is done through WBJEE, Jadavpur University doesn't take admissions through JEE Mains.
So, if you want to get into Jadavpur University, first sit for WBJEE.
To get into JU, you need to get a rank under 1500, if you are going for Electronics, CSE, Mechanical, Civil, Instrumentation etc., then you need a very decent score, your rank should be under 600700. But, if you want to get in IT, Power, Printing, Construction –etc, then scoring under 12001500 will be enough.

No, the cutoff in Jadavpur is 200 for OBC.

If you see the placement records of Jadavpur University, you will find that higher packages are provided to JU as compared to IIEST Shibpur. Though both are very prestigious college and if you have got CSE in both the colleges then I will recommend you to go for JU.

No, just JEE rank can't be the base for admission in this university.

https://www.shiksha.com/b-tech/resources/wbjee-college-predictor.
Check the college you can get with your rank.
All the best.

https://www.shiksha.com/b-tech/resources/wbjee-college-predictor
Check the colleges you can get with your rank.

Please specify the entrance exam in which you secured this rank, so that I may be able to populate relevant details. If you are talking about the WBJEE please refer to the link provided below which can be used to predict the colleges to which you qualify with this rank. Regards.
WBJEE 2018 College Predictor: https://www.shiksha.com/b-tech/resources/wbjee-college-predictor
Regards.

WBJEE 2018 College Predictor
Use your WBJEE 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of WBJEE 2017
Get resources & insights on colleges & courses
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor

Hey Suman,
It is really very tough to qualify for the entrance exam, to be least, with such marks.
You can definitely try some other colleges, which would give you an immense knowledge of your selection of course.
Good luck.