Colleges in Pune

Yes, you are eligible for Fergusson College, Pune because it takes admissions into UG courses on merit basis. It conducts entrance tests only for PG level.
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Hello dear,
I think it is not mandatory that you must join the hostel. The total hostel fees for a year is between 80k to 1 lac. But it depends upon your choice.
After getting admission in this college, ask for all details like placements and also talk with the senior students of colleges what are their experience in that college.
Then take admission in that college.
Hope this will help you.
Best of luck for choosing the right college.

Game design is basically a part of programming which you will study better in CS or IT branch, but if you want to go ahead in game designing, you can look for online courses about programming languages.

It might be a little difficult but you should definitely try for offline admission process as well.

It is not possible with this rank. You should score maximum to get admission. They have various branches but every branch's cut-off is high and not below JEE Mains score of 240.
If you score 250+ then hope to get a branch but not CS.

You should apply for JEE NCHM-CT entrance exam for IHMs and score a good rank to choose great instituties.