Mechanical Engineering

Yes, we have 240 intake in mechanical engineering looking into number of seat and overall merit of JEE. It may be possible to get admission at Dr. D. Y. Patil Institute of Technology, Pimpri, Pune.

Make Use of Shiksha's TS EAMCET college predictor:
https://www.shiksha.com/b-tech/resources/ts-eamcet-college-predictor

The chances of a non-local getting a seat are less, but you may even attempt TS EAMCET for better chances for getting into CBIT. You need to get a good rank to ensure a free seat.

To secure a seat you need to have a rank below 5000. Further, the ranks are admitted according to the financial attraction of the course and the time of admission.

Andhra University
GMRIT
JNTUK
KITS
GPREC.

The definition of best varies from person to person and is influenced by personal inclinations and one's strength. For example, some people might go with a regular stream like CS mechanical, Electronics and some might go with not so common branches like robotics, petroleum, and mining. Opt for the engineering branch that you love the most and are most passionate about and analyze the future work conditions, scope and growth prospects before taking admission
You can also opt for psychometric test comprising of Aptitude, personality and career interest to clear confusion.

Top Engineering Colleges in India Offering B.Tech lateral entry are mentioned below:
1) Delhi Technological University
2) Manipal institute of Technology, Karnataka
3) Netaji Subhash Engineering College, Kolkata
4) Jamia Millia Islamia
Regards.