Dear student, 

As per your request, The syllabus for GATE mechanical engineering is as follows.

Section 1: Engineering Mathematics-Linear Algebra,Calculus,Differential equations,Complex variables,Probability and Statistics,Numerical Methods:

Section 2: Applied Mechanics and Design- Engineering Mechanics,Mechanics of Materials,Theory of Machines,Vibrations,Machine Design.

Section 3: Fluid Mechanics and Thermal Sciences- Fluid Mechanics,Heat-Transfer,Thermodynamics,Applications.

Section 4: Materials, Manufacturing and Industrial Engineering- Engineering Materials,Casting, Forming and Joining Processes,Machining and Machine Tool Operations,Metrology and Inspection,Computer Integrated Manufacturing,Production Planning and Control,Inventory Control.

 Also, check  this link :- https://engineering.careers360.com/articles/gate-syllabus-for-mechanical-engineering

Good luck