Hello,
.
Some of the government colleges for BBA in Pune are mentioned below,
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• Brihan Maharashtra college
• Savitribai phule
• Tilak Maharashtra university
• Bharati vidyapeet University
• Indira college of commerce and science
• Balaji college of arts (BCACS)

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Some of them are here if not satisfied you can even go for others but government colleges are very few you should choose accordingly. If you can go for private then you have Many of them.