Dear Rahul,

For Mechanical Engineering you need to go through this syllabus I'm listing below, it is divided into 4 parts.

1. Engineering Mathematics

* Linear algebra

* Calculus

* Differential equation

* Complex variable

* Statistics and probability

* Numerical methods

2. Applied mechanics and design

* Engineering Mechanics

* Mechanics of Materials

* Theory of Machines

* Vibrations

* Machine Design

3. Fluid Mechanics and Thermal Sciences

* Fluid Mechanics

* Heat-Transfer

* Thermodynamics

* Applications

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

* Operations Research

For detailed explanation you can go with this link to know more

https://engineering.careers360.com/articles/gate-syllabus

And for books there is alot but its better if you follow some selective books only suggested by your faculty, you can refer with this link to find the best answer for yourself,

https://engineering.careers360.com/articles/what-are-best-books-for-gate-me

Best Of Luck!!!