Hello Shenbaga. Some of the top colleges in Chennai and Bangalore providing B.Des course are:

• NIFT Chennai- There are 6 streams under B.Des of which you will need to select one. The admission is through NIFT exam. It is a 4years duration course.
• MFT Chennai- It provides B.Sc degree in Design. It is a 3 year course.
• ICAT Design & Media College Chennai- Established in 2004. It is affiliated to Bharathiar University, Coimbatore.
• NIFT Bangalore
• Shrishti Institute of Art, Design & Technology, Bangalore- Admission is through SEAT followed by a personal interview.
• LISAA School of Design- Provides 3 year course in B.Des.

Hope this helps you. For further queries comment down below.

Good luck!