I want to know about Maximum Number of attempts for Graduate aptitude test in engineering Exam

There is no Restriction for attempts of GATE Exam. You can appear for GATE as many as times as you wishes.

Eligibility for GATE Exam
You have to pass a Bachelor’s degree in Engineering/ Technology/Architecture stream from a well recognized university ..
OR
Master’s degree in any branch of Science / Mathematics / Statistics / Computer Applications or equivalent (Final year or Completed)
OR
Integrated Master’s degree programs or Dual Degree programs in Engineering / Technology (Five year programme)
(4th/5th Year or Completed)

Age limit :
There is not age limit for GATE exam ..