hello nitu,

yes you can do M.des after BE. you have appear in GATE.

• Candidates must have passed a recognized Bachelor’s degree in Engineering (B.E/ B.Tech) / Design  (B.Des) / Architecture (B.Arch).

•  Candidates must have a valid score in CEED 2015/ CEED 2016 or GATE.

 B.Des candidates must have a valid score in CEED 2016 or CEED 2017.

check here all details about admission criteria

https://engineering.careers360.com/articles/mdes-admissions

thank you.