You can check the important topics below for mechanical engineering for GATE

Manufacturing- Orthogonal cutting, Tool life equation problems.

Thermal Sciences- Laws of TD, Properties.

Fluid Mechanics- Velocity potential, Flow through Pipes, Boundary layer theory.

Heat Transfer- Numbers in convection like Pr No, Gr No, Re No, etc.

Theory of Machines & Vibration- Pairs and its applications, Linkages, Inversions of single and double slider crank, Free damped vibrations

Industrial Engineering- Queuing theory, EOQ problems, Inventory control.

Engineering Mechanics- Structural analysis, Work and Energy, Law of Restitution

Engineering Materials- Effect of Alloying elements, Defects in the crystal structure.

Strength of materials- Joints, Design of gears, and bearings

Engineering Mathematics- Every topic is important. 

Good Luck!!