B.Sc Game design

Yeah because it's a Diploma course. Any institution which has this course in their curriculum will offer you to pursue this course. If you have interested in game designing then I strongly recommended you to go for it, because in recent times the game design industry is seeing tremendous demand for their products because of the entry of the android system into the mobile industry.

Yes of course, you should know vector theory, basic trigonometry, and some more basics of maths. But you should know it. It will help you alot while programming games. Trust me.

For the clarification, you need to complete that first.

Hello Sravan, Definitely, you are eligible. As per the eligiblity criteria, HSC passed with a minimum of 55% in any stream are eligible. Only English is a mandatory subject. All the best for your future.

No there is no entrance exam there is a scholarship exam

Refer this link:
http://www.vit.ac.in/academics/schools/site/courses
but placement wise, I can say that B.Tech CSE is far better. Additional Information: Predict engineering colleges you can get on the basis of your JEE Rank: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_campaign=8321427.