College of Technology and Engineering

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Please follow the above mentioned link.

You just need to give OJEE for lateral entry and as soon as you give OJEE le entrance exam you will be getting your score on the basis of your score. You have to do choice filling and you will be getting a preferred college.

Within the first 30000, you can ensure seats without any problem. If it is above 50k, its totally impossible.

If you think you can manage the preparations without losing concentration, then go for it. Your class 12th marks suggest that you have the calibre to score 100+ marks in JEE. So, if you can prepare without being frustrated, go for it.

Hello Aswin,
Colleges in TN admit students based on marks obtained in 12th exam. This Institute also falls in TN. In addition I am giving you a link to this college. For any doubts, you can give them a call.
http://www.psgtech.edu/

Don't opt for a branch based on the college. In fact, go for the branch in which you have interest, and are most passionate about. You should analyze the scope and future growth prospects before taking admission in a college to pursue the course of your choice.
You can also opt for psychometric test comprising of aptitude, personality, and career interest.