India

The scenario of asking for changes however is not as easy as it seems, precisely because the forms have information submitted when they took the JEE Main Exam. Post that candidates have qualified for Advanced on the basis of the same forms.
Still you can try change your category. Enter your Registration details on JEE Advanced portal and check the Category Confirmation pop-up. Choose the required option.
Prof KV Krishna, Chairman, JEE Advanced 2016, said, Wherever the conversions are possible, as per the JEE Mains remarks, we will be able to take care of it. We will accept the documents as per the declarations given on Advanced official website.

Hi Denilson,
The best among private universities in Tamil Nadu is VIT as it offers good placements and exposure. Both the branches Chennai and Vellore are good.
Prefer VIT, Vellore because that is main campus and also considered the best.
After that in terms of placements SRM University main campus is good.
Sastra University also is good in terms of faculty and placements.
These are good as per rankings also.
Then, if you want to go for some good university but with average rankings and placements you can see the following:
BS Abdur Rahman Crescent University
VelTech University
Sathyabama University
Rajalakshmi College Of Engineering
These universities are average when compared to the above three universities.
So, select the ones with good rankings and placements and make a wise decision.
All the best!