Product Design

Hello Anurag,
The best colleges for product design I know of include Georgia Institute of Technology, Carnegie Mellon University, Arizona State University, University of Cincinnati, Ohio State University, University of Illinois at Urbana-Champaign and Rhode Island School of Design to name a few. These are best known in terms of research and internship.
Now, product design is also called industrial design and will include components of arts, mathematics, engineering and other aspects of designing. You must therefore check the syllabus carefully before applying and if it fits with your interests and requirements. I am not in a position to comment on colleges in India unfortunately, but I am pretty sure you will find your answers.
All the best.

Design is a very good field and has plethora of opportunities. As you are interested in Auto Design and Product design you can pursue post graduate course that is M.Design in Transporation Design and product design. These design courses will arm you with understanding and identification of the transportation and mobility sectors and finding creative solutions. As of product design you will learn how to create a new product to be sold by a business to its customers Few colleges that offers B. Des and M.Des courses are UPES, National Institute of Design, M.S Ramaiyah, AD-The design school. as far as placement is concerned, UPES fared a better placement last year. All the best