Game design

You can take any stream in 11th and 12th class. After that, you can join any game design courses in universities.

If you want to go for Punjab region, then give a try to explore about Lovely professional University in game design course. Being an LPU student, the culture is good here to study. For more information visit lpu.in.All the best.

Anil, you can opt any stream but it will be good for you if you opt computer Science as one of the subjects in 11th.

A degree, of course, is a better choice. It has more credibility in the market and is also a more elaborate course.

Find the eligibility criteria here:
https://www.icat.ac.in/admission-eligibility.asp

Here is the list of some top affordable colleges for game design in India. NID (National Institute of Design), Ahmedabad. IDC, IIT Bombay. Pearl Academy, (Delhi, Mumbai, Jaipur)
NIFT, Delhi. MAEER'S MIT Institute of Design, Pune. Srishti School of Art Design and Technology, (Bengaluru, Pune, Trivandrum)
Indian School of Design and Innovation, (Mumbai)
If you want more, then just visit: https://www.shiksha.com/it-software/game-design/colleges/colleges-india.

Yes, it is a good choice, there are many demands of game design developer in market, not only in India but abroad too. If you are doing Diploma in game design, then you can get a good job, or do freelance, but if you want to grow more than I would suggest you to do Masters in game design. Most of abroad companies require Master's degree for providing you jobs.

You don't need to get admission in Colleges for learning game development, there are lots of institute offering game development courses, here is list of some. Aiga - Institute for Gaming & Animation Bangalore India
Zee Institute of Creative Arts - Hyderabad
Animaster Academy
If you want more, just browse here. https://www.shiksha.com/it-software/game-design/colleges/colleges-india.

To get complete list please follow given link
https://www.shiksha.com/design/communication-design/colleges/game-design-colleges-Jaipur.