You can complete your masters in design from the following colleges/ institutes in India-

National Institute of Fashion Technology (NIFT)

National Institute of Design (NID)

Indian Institute of Technology (IIT)

Pearl Academy delhi

UIID

The entrance exam for admission into the masters course can be GATE, NIFT entrance exam, etc

You can download the previous years question papers from here:

https://design.careers360.com/articles/ceed-sample-papers