Bihar

See eligibility, admissions process, fees, course details, reviews and other details. please go through the link given below:
https://www.shiksha.com/bba/colleges/bba-colleges-patna

Hi Dear,
Kindly use the JEE Mains college predictor app to get more insights about the shortlisted colleges for your JEE Mains score. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

As of now, you don't need to think about problems. Just plan your area of interest and go ahead.

Yes, you can take admission in various Government College. Here are some links, please go through it.
https://www.shiksha.com/b-tech/course/b-tech-lateral-entry-government-college-of-engineering-amravati-gcoea-239643
https://www.shiksha.com/b-tech/course/b-tech-lateral-entry-institute-of-engineering-and-management-salt-lake-city-kolkata-235244

You need to obtain a domicile certificate for getting this benefit. You can go back to Bihar and apply if you need a state quota. To get domicile from Madhya Pradesh, you need following document and you may apply for the position of a Tehsildar or a citizen service centre:
The proof of the continuous resident of the state for a minimum period of 15 years.
Deed of Land in the state
Valid identification proof
School certificates
Copy of Ration/Voter ID card
Tehsil Enquiry report
Parents/Guardian domicile certificate which states that they are permanent resident of the state in case you are a minor.

You may use the college and rank predictor for COMEDK examination that gives you the colleges that you can get with your rank in COMEDK examination:
1) https://www.shiksha.com/b-tech/resources/comedk-college-predictor
2) https://www.shiksha.com/b-tech/resources/comedk-rank-predictor

Hi Dear,
Here is an article by Shiksha authors about top engineering colleges along with their rankings, fee structure and total seats. Just apply the filter to get desired results.
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india/44-2-0-0-0

Try to solve as many problems as you can as they improve your skills in solving the problems with speed and accuracy. Then have a strong knowledge of the concepts so that you can easily answer nearly 40% of the paper in physics and chemistry. The previous years papers help you in getting an idea of how the questions are being asked.
If you haven't joined any coaching centre then you are advised to join as they may guide you in a proper manner and also efficiently than self-study.
All the best.