Electrical and Electronics Engineering

Yes, you can get admission in either EEE or civil branch in Coimbatore, Bangalore or Chennai. Your rank is enough to get you a seat. You should participate in the counselling process.
Best of luck.

Yes, you can participate in JoSAA counselling. You can select the state, college and branch as per your interest and convenience. Many students of Bihar prefer West Bengal and Delhi. In West Bengal, you will complete your degree in the cheap and best way. Delhi is a little bit costly. If you don't have any financial problems, then go for Delhi.
Best of luck.

Go for KSOU. Regards.

I'll prefer you to opt for the EEE branch, as this branch has more scope and better placements in India.

Check out the college predictor below:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Please visit this link-
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/upsee-college-predictor&ved=2ahUKEwjEw_fS5IbiAhX_6nMBHRRfARgQFjAIegQIARAB&usg=AOvVaw35nIYCmB-o81pLl73rIIvk

Please visit this link. This is a college predictor by Shiksha and I hope this will help you to choose the right college-
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwie-7mvrITiAhWz73MBHYuID8oQFjAAegQIAxAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H.

Please visit this link. This is a college predictor by Shiksha and I hope this will help you to choose the right college-
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwie-7mvrITiAhWz73MBHYuID8oQFjAAegQIAxAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H.

Please use this link and I hope this will help you to choose the right college https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor