Yes you can apply for GATE Exam after completion of MSc course in streams through distance education mode .. here I am giving you information about required criteria to apply for Graduate Aptitude Test in Engineering

GATE Eligibility
You have to pass Bachelor’s degree in Engineering/ Technology/Architecture/Pharmacy (4 years after 10+2)

Or
You must complete master degree in any branch of Science/ Mathematics/ Statistics/ Computer Applications or equivalent
Or
You have to pass Four-year Integrated Master's degree programme (Post-B.Sc.) in Engineering/Technology or in the third or higher year of Five-year Integrated Master's degree programme and Dual Degree programme in Engineering/Technology.

Age limit :
There is no age limit for GATE exam