Manipal

I have completed my engineering from JECRC. Don't go with the brand name of JECRC as it is no longer the way it was. You should try for government colleges. I am talking about only for study orientation purpose.

Manipal University is one of the topmost universities in India. I have heard that it has good placements for mechanical engineering.

For JEE Mains rank of 61000 if you are a government category candidate then you might get admission in north-east state colleges. Other institutes you have mentioned are private.

Manipal Institute of Technology has a really good department of engineering as compared to most colleges in India that offer the same course. The facilities and infrastructure are better and well maintained. The faculty members are very helpful and knowledgeable and enthusiastic about their subjects. We have good instrumentation for practical knowledge too.

Degrees awarded by deemed Universitirs are valid for all Government & Private jobs and Higher studies in India or abroad. These institutions degree are far superior to majority of central or state governments Universities. BITS Pilani is the most recognized and accepted Institute in International market after legacy IITs.

Yes, it offers this course and the fee for Indian students is 1,411,000.
For more detail you may visit this link:
https://manipal.edu/mit/programs/program-list/btech/btech-aeronautical-engineering.html

Brother, to get admission in Manipal University, first you will have to give an online entrance exam conducted by them. Go to their's web portal and fill your required branch and give that entrance exam. They will select you if you will get qualifying marks.