Graphic design

Graphic design is a creative process that reaches into everything we do these days. From websites to application interfaces to product packaging, the talented hand of a graphic designer is seen everywhere.
You need to choose an area of graphic design. For example, are you interested in advertising, web development, multimedia (ex. the TV industry), print design, or animation? These can all be considered different forms of graphic design. Learn about different tools like Adobe Photoshop and Adobe Illustrator. Focus on books that teach design fundamentals.

In India, graphic design is considered as a lucrative career option nowadays. Students can choose a wide range of programs in graphic design in India and they can also start their career as a graphic designer. Different job opportunities in this sector are:
Graphic Designer
Design Management Professional
Creative Directors
Brand identity designer
Logo Designer
Layout artist
Flash Designers
Art Workers

Not really sure if this course if offered by the university.
Request you to please visit the website for an idea: https://www.keralauniversity.ac.in/dept/d-list.

You must do 1 or 2-year degree programs in graphic designing.
B.Sc in design and animation.
Good luck!

The answer to your question solely depends on your rate of interest, if you are willing to do the course and if you are interested in it, it is surely good for you.
If you want to make career in this very field, then this course would act as a stepping stone in your career.

Yes, some private institutes allow you to do it.

You can look for this college:
LISAA School of Design, Bangalore (Interior Design | Fashion Design | Graphic and Web Design), Koramangala
https://www.shiksha.com/animation/graphic-web-design/colleges/colleges-bangalore

Some of the good institutes are as follows:
MAAC, LISAA School of Design, Graphic and Design Institute.

Product design has a vast scope. You should try for some private colleges.