Birla Institute of Technology, Mesra

Hello KVS,
Since you have 108748 (31564 obc ncl) in JEE Mains at all India level. Then on the basis your rank you can use the Shiksha JEE Main College Predictor 2021. The link has been attached below. It is updated with Closing rank from 2020, 2019 and 2018. Also you can get Colleges Based on your Gender, Category and Home State. The link will help you to know about Fees, Cut Off, Admission and Placement Reviews for 600+ Colleges. This is the link of the website where you can check the college as per you rank also. https://www.shiksha.com/engineering/jee-main-college-predictor
Best Wishes!!

Though BIT M is better, I wouldn't join anyone. Only top 25 B schools are worth joining. You should study hard to score 90 + percentile in CAT to get in a decent college
You can think about Lexicon MILE too.

If interested in doing CSE or ECE courses, than you can get the following options also during the JEE Main counselling.
1. IIIT Guwahati (CSE)
2. IIITM Gwalior (IT)
3. NIT Hamirpur (Integrated M.Tech ECE)
4. BIT Mesra (ECE)
5. NIT Uttarakhand (ECE)
6. NIT Patna (ECE)
7. IIIT Raichur (CSE)
8. IIIT Kotak (CSE)
So from above, wait for colleges and participate in JOSSA for JEE Main counselling.