Hi Praveen,
I'd be happy to understand your current stage of progress including academics, courses, hobbies and other interests to help you understand what in you can lead to game design and also what aspect of game design can suit you better. You may also like to read this about the kind of preparation the best students put into this
http://bit.ly/1ddUSi8. Also, in most cases a broader learning like a combination of graphics, multimedia, web design, vfx, 2d and 3d animation, can lead to a better preparation towards launching oneself into a gaming career. A specialization in Game Design is a useful addon afterwards. And just to state the facts, none of the famous game designers in the world today have done anything remotely linked to game design. That said, do not take it as a bar to entry, but to elucidate the fact that a broad learning is always necessary to get into a challenging career such as game design. Now let's go into the nitty gritty on Game Design. To become a Game Designer, you must get a good knowledge of 3D software as well as preproduction. Usually in Games the environment is created in 3DSMax and Character animations in Maya, Only the models are made with less polygons and more textures. So choose a program that teaches you these software. It would not matter whether the programme is called game design programme or not. Rest, to become a level designer you must have a passion for game design. Also you must have passion for playing all kinds of games including card games, dice games, sports etc. The 3rd option is Game Design (it's different from Game Designer), where you design the game itself, i.e. what happens on each level, and how things go about as well as the base story of the game. It is a stage that you reach due to your vast knowledge and passion and even exceptional technical skills cannot help you reach. This is usually the story designer. May I ask, have you ever designed a game? Finally, to do game programming you would require knowledge of programming in which usually a BCA/ MCA would help. Typically game programmers usually would be knowing C, C+, Java, Android besides at least a Game Engine. Arena offers a very good Course in this regard namely AAIP where you can learn enough 3D Art and Effects for Gaming.
Hope this helps.
Wish you luck.
Hi Praveen,