WBJEE

Hello Akshay,
Please refer to this link to get more insights of the colleges and branches.
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor
However, as per your rank, NSIT will be the best find for you.

The government is considering conducting a single entrance examination for admission to all engineering colleges, including private institutions, across the country.
It is aimed at bringing transparency to the admission procedure, including checking the practice in some private institutions of extracting a heavy capitation fee from students.

If you are from Bihar state, you are eligible to take admission in a private college through WBJEE as you have other state quota.
Following are the colleges you can prefer:
Heritage Institute of Technology, Kolkata
Haldia Institute of Technology
Academy of Technology ?
Narula Institute of Technology

Sorry to say but with just 34 marks in WBJEE, you will not get admission in any Govt. college even if you belong to SC category. But still, your rank is too high and is out of the cut-off for Govt. colleges.
So, go for a private college.

Heritage is slightly better but it would matter only if you are amongst the brighter ones in your batch.

Hello Akshay,
Please refer to this link to get more insights of the colleges based on your rank:
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor
However, for more exposure opt for CSE.

Hi,
You may refer the links below that gives the college predictor for WBJEE which may give you the list of colleges that you can get with your rank in WBJEE examination:
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor

I think you should go through college predictor app or opening and closing rank of that college. It will help you.

Yes, you have fair chances of getting admission in Jalpaiguri govt. engineering college as you have an advantage of having ST category.
Your ST quota will help you to get that college.
All the best.