You can check the list of top colleges below

Guru Gobind Singh Indraprastha University, Delhi

Indira Gandhi Delhi Technical University for Women, Delhi

SRM University, Chennai

Manipal Institute of Technology, Manipal

Amrita School of Engineering, Coimbatore

Good luck!!

Yes Why not? There is no hard fast rule that you cant. This more or less will depend upon the institute where you pursue the course. However I think you should have a good base in CS as that would be mostly the advantage to study the course. 

In order to make your career in artificial intelligence you can choose the branches like Mechanical Engineering, Electronics & Communication Engineering or Computer Science Engineering in your UG engineering program.

Below are the best universities in which you can take your admission for this course

IIIT Hyderabad

Osmania University

University

Assuming you are asking for B.Tech in Automation and Robotics so below I am providing a link which you can go through to check the list of colleges which offer the same -

List of B.E/ Btech in Automation And Robotics Colleges in India

Good Luck!!!

No.

B.Tech in automation and robotics is not there is VIT as Mechanical with specialization in Automotive Engineering is there.

Also, you can go through the below link to check what all courses VIT offers -

http://www.vit.ac.in/admissions/ug

Good Luck!!!

Some of the top colleges for Automation and Robotics are in India are:

MIT
SRM

Amrita School of Engineering

These are top private institutes and outstanding colleges for engineering studies.

Good Luck.

Hey
Eligibility for robotics at PSG college of technology, Coimbatore -: 50% aggregate marks in 12th with Physics, Chemistry, and Mathematics as mandatory subjects. 
Test needed -: TNPCEE (Tamil Nadu Professional Courses Entrance Examination)
Admission is through Tamil Nadu Engineering Admissions (TNEA) counseling guidelines based on marks obtained in class

Assuming you are asking for the colleges which offer B.E/B.Tech in Automation and Robotics so you can consider below link to check the list -

List of Be Btech in Automation And Robotics Colleges in India

Good Luck!!!

Choosing a branch totally depends on your interest.

There are good job opprountities in this field and it will increase in the future. Placements are also there in this field but if we compare it with CSE branch then CSE has better scope in terms of job and placements and

Kindly share which particular state you are focusing as there are many colleges available. Few decent colleges are mentioned below -

Indian Institute of Technology, Delhi

Institute of Technology, Nirma University

PS College of Techology, Coimbatore

Osmania University etc.

Good Luck!!!