Engineering Entrance Exam

I think it is not possible to get a seat in CBIT.

The West Bengal Joint Entrance Examinations Board conducts mock counselling before the original e-counselling for the awareness of the aspiring WBJEE2018/JEE (Mains)-2018 candidates. WBJEE 2018 mock counselling is set to be held from May 28 to June 2 across 33 centres. It will be conducted in offline mode. Regards.

I think not possible to get a seat in CBIT, may be you can try for chemical or bio-tech.

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.

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.

It depends on the rank you get, go through this link for colleges accepting Mains marks.
Link: https://www.shiksha.com/b-tech/colleges/b-tech-colleges-accepting-jee-mains-Hyderabad.

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
Please refer to the link provided below for details regarding WBJEE counselling following the entrance exam:
https://www.shiksha.com/b-tech/exams/wbjee/counselling.

It is not possible with this rank. You should score maximum to get admission. They have various branches but every branch's cut-off is high and not below JEE Mains score of 240.
If you score 250+ then hope to get a branch but not CS.

All government colleges take admissions on the basis of the entrance exams result. Since you didn't give one it is highly unlikely now. One thing that you can do and don't place your hope on it. You can wait and later contact the colleges to see if they have any seats vacant or they are conducting spot counselling.

You have good marks in JEE. You can get government colleges of your state it's better to try once in the state-level counselling. Taking drop is not a good option because to get NIT, you must have 75 percentage in 12th so if you take a drop, then also you will not get any NIT software scoring good marks so if you take a drop, you should also try for improvement in board exam, then it will be beneficial.