Engineering

Based on last year's ranking cut off, there is a good probability of you getting into Production Engineering, EEE, Civil Engineering, Chemical Engineering or Chemical Engineering (Plastics and Polymer), Mechanical Engineering or Biotechnology branches at BIT Mesra.
You may also try for other branches at our BIT Patna, BIT Deoghar and BIT Jaipur campuses.

Do clear your query. You are eligible for GATE, if you have B.Tech degree. Good luck.

Just go to their official website.

Yes, it is possible, but you will not get stipend of 1 year which you got in private college.

GATE exam is for M.Tech. And, if you do not have GATE score you cannot take admission in premium institutes. But, many other universities that conduct their own exam for M.Tech. Hope this help you.

Yes, EEE students are perfectly eligible to give IES. They can select either Electrical or Electronics to appear for Examination.

Hello,
I am afraid your ranking is on the lower side. Perhaps you can think of taking a break of one year, studying and appearing next year again. However, to help you I am attaching a link that will predict college for you based on your ranking in JEE Mains. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Best wishes to you.

Hello, IT can be called as the one which facilitates application of computing technology to real life while CSE is Science that facilitates these applications. You must choose the one that fascinates you the most. Best wishes to you.