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.

Hi Anuj,
Germany has many outstanding schools for automotive design. However, four schools with representative automotive design programs are Hochschule Esslingen and Hochschule Pforzheim, both near Stuttgart; Westsächsiche Hochschule Zwickau, near Leipzig; and RWTH-Aachen University, near Cologne. They are commonly referred to as Esslingen, Pforzheim, Zwickau and Aachen.
Also, Umea Institute of Design (Sweden) has Masters in Transportation Design.
Below mentioned links will give you an idea about it:
https://www.hs-pforzheim.de/en-US/School-of-Design/Bachelor/Transportation-Design/Seiten/Inhaltseite.aspx
http://www.dh.umu.se/en/education/programmes/mfa-in-transportation-design/
You can explore the website of all of the above institutes to know more about course content.
About Job prospect, I have heard about some designers who have done the same courses from above institute and working in Design Studio of Audi and BMW. These are one of the best schools of design.
I hope it helps.
All the best.