Jharkhand

Both the colleges are good. NIT-Hamirpur was established in 1986 and converted into NIT in 2002. BIT Mesra was established in 1955. Both Colleges are one of the top Engineering Colleges in India. You can take any of two. Both are good.

Yes, you can get lateral entry after completing your diploma from Arka University. On the basis of last year's percentage of diploma, you will get admission.
Best of luck for your future and if there's any query, feel free to ask.

Haldia Institute of Technology
Heritage Institute of Technology
Kalyani Government Engineering
Academy of Technology, Adisaptagram, Hoogly
University Institute of Technology, Burdwan
Narula Institute of Technology, Kolkata
All the best!

Hi,
You can take admission in good private college as well, there is no harm in it. You can use the CLAT 2018 college predictor option available on shiksha.com. The College Predictor helps students to get an idea about the chances of admission in the college of their choice based on CLAT 2018 result. Please refer the link below for your reference:
https://www.shiksha.com/law/resources/clat-college-predictor

Usha Martin University, [UMU] Ranchi
Doranda College, Ranchi
Gossner College, Ranchi University, [RU] Ranchi
These are some of the colleges I could list.

The minimum academic qualification for admission through JEE is that a candidate must have passed in the final examination of 10+2 (Class XII), or its equivalent with an aggregate score of minimum 60% in PCM+English. Candidate must have appeared in JEE. Selection will be based on JEE score.

Kindly visit this link:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor