WBJEE

Yes, you will get so many colleges I am mentioning top 5 colleges:
1- Jadavpur University
2- University Of Calcutta
3- Kalyani Government Engineering College
4- Heritage Institute Of Technology
5- Maulana Abul Kalam Azad University Of Technology.

No, the cutoff in Jadavpur is 200 for OBC.

Hello Santanu,
Your rank is quite good. I hope you get what you want. However, to help you, I am attaching a link that will predict the college for you:
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor

HITK is one of the autonomous private colleges in West Bengal. For admission in top branches like CSE, IT and ECE, you need to have a rank within the 7000 to 8000 range. For branches like mechanical and civil, you need to have a rank within 12000. Furthermore, sometimes it depends on the seat availability of college and counselling process. You can wait patiently and go through the counselling process.

HIT-K is an autonomous private college in West Bengal. It takes admission through WBJEE. For the top branches like CSE, IT and ECE rank needed is within 7000 to 8000 in WBJEE. For mechanical branch ranks needed is within 10000. There would be better chances of your admission in the mechanical branch at HIT-K if you have rank is within the specified range. Moreover sometimes it may go down to 12000 depending upon seat availability of college and counselling process. All the best and wait for counselling to start.

If you are not satisfied with your allotted college, you have to go for the upgradation option.
What is the use of upgradation option?
Once you have chosen this option, you have chances of getting a good college.

Go through the following link:
https://googleweblight.com/i?u=https://www.shiksha.com/b-tech/resources/wbjee-college-predictor&grqid=2ZTvkiwy&s=1&hl=en-IN&geid=1031

You don't have any chance if you are from general category. I would suggest you to explore your other possibilities through private colleges.

Go through the following link:
https://googleweblight.com/i?u=https://www.shiksha.com/b-tech/resources/wbjee-college-predictor&grqid=hzmQfxuL&s=1&hl=en-IN&geid=1031

You can get into Haldia or Techno India College.