Engineering Entrance Exam

HBTI Kanpur is a state government institute of Uttar Pradesh state.
The admission to B.Tech. courses at HBTI Kanpur is done on the basis of merit in
U.P. State Engineering Entrance Examination I.e. UPSEE.
The 10% of the total intake is filled on the basis of merit in AIEEE (students of UP only may apply).
There is no provision of admission in HBTI Kanpur, through IIT-JEE rank.
You can't appear the UPSEE counselling on the basis of IIT-JEE score.
If you are a UP domicile student and you have appeared AIEEE or UPSEE then only
you can apply for admission in HBTI Kanpur

Yes, with home state quota, you will most probably get a seat in NIT-Jamshedpur. Moreover, you can find the expected cut-off for NIT-Jamshedpur in the link below:
https://www.shiksha.com/b-tech/resources/jee-mains-cut-off-predictor

If you feel there was some good reason that you couldn't perform well in JEE, then only you should go for it. Because 2 years drop will make a big difference for your career as it will shift 2 years ahead. And there is no surety if you could perform well in the next year's attempt.

You are eligible for admission in college listed below:
Kalyani Government Engineering College
Jalpaiguri Government Engineering College
Haldia Institute of Technology
Heritage Institute of Technology

Counseling of WBJEE will start from June 12 for admission in various colleges under WB.
For more information, visit this site:
https://www.shiksha.com/b-tech/wbjee-exam-counselling

Counseling of WBJEE will start from June 12 for admission in various colleges under WB.
For more information, visit this site:
https://www.shiksha.com/b-tech/wbjee-exam-counselling

Counseling of WBJEE will start from June 12 for admission in various colleges under WB.

Yes, you will definitely get admission in Jadavpur University with 648 rank under SC category.
So, just wait for the counseling to start.
All the best for future.

Yes, he will definitely get admission in Government College.
The available college for him are:
Kalyani Government Engineering College
Jalpaiguri Government Engineering College

You are eligible for admission in various government and private colleges in West Bengal like:
Kalyani Government College
Jalpaiguri Government Engineering College
Heritage Institute of Technology
Haldia Institute of Technology
University Institute of Technology, Burdwan