Yes, you can. The best colleges are IIIT, National Institute of design and others can be found by searching in this url: https://www.google.co.in/url?sa=t&source=web&rct=j&url=http://www.graphic-design-institute.com/blogs/top-10-design-colleges-and-institutes-india&ved=0ahUKEwiipJC1iNzZAhXKKY8KHal_DQAQFgg7MAI&usg=AOvVaw1wAZjhRkUl52NI_VltE3_z

yes, of course, one can apply for masters in product design engineering all you need is BE/BTECH in any engineering branch with 50% marks in graduation.

some of the reputed organization like IIT Delhi

Vivesvaraya institute of technology Belgaum

MNIT Allahabad offer a dynamic course on product design engineering they do conduct entrance examinations for the admission .

all the best !!

 

Well you can always opt for change in field for postgraduate after undergraduate.

I have a list of 4 foreign colleges which are best as under :

University of Glasgow, UK

Coventry University,UK

Centennial college, Canada

University of Technology Sydney, Australia

Changing your field of post graduation from that of the   under graduate course  is possible.
You need to write the exam conducted by the universities.
In my knowledge,   these are the institutes that are considered to be the best as per the quality knowledge imparted to the students and the opportunities after completion of the courses-

1) National institute of design

•       Location - Ahemadabad.

2)MIT Institute of design (MIT ID)
               location- pune.
3) DJ Academy of design.
 .             Location- coimbatore.
4) Department of design-IIT GUWAHATI.
5) Industrial design centre- IIT BOMBAY.
6) school of planning and architecture
               Location - Delhi.
7) University of petroleum and energy studies(UPES)
               Location- Dehradun.
Note- The above mentioned colleges are NOT arranged in priority wise order.

THANK YOU.

Yes u can...  According to me the best colleges in our India is IIT as u must be aware of that