There are several topics covered in the Mechanical Engineering optional subject for the UPSC exam. These topics are designed to test the candidate's understanding and knowledge of the various aspects of mechanical engineering. Some of the key topics covered in this subject are:

1. Mechanics of Materials:
This topic deals with the behavior of materials under different types of loading and stress conditions. It includes the study of concepts like stress, strain, elasticity, plasticity, and failure of materials.

2. Theory of Machines:
This topic focuses on the study of mechanisms and machines. It includes the analysis and design of various types of machines, such as gears, cams, linkages, and flywheels. Candidates are expected to have a thorough understanding of concepts like kinematics, dynamics, and mechanisms.

3. Thermodynamics and Heat Transfer:
This topic covers the fundamental principles of thermodynamics, including the laws of thermodynamics, thermodynamic cycles, and energy conversion. It also includes the study of heat transfer mechanisms, such as conduction, convection, and radiation.

4. Fluid Mechanics and Hydraulic Machines:
This topic deals with the behavior of fluids under different flow conditions. It includes the study of fluid properties, fluid statics, fluid dynamics, and flow measurement. Candidates are also expected to have knowledge of hydraulic machines, such as turbines and pumps.

5. Manufacturing Science:
This topic covers the various manufacturing processes used in the industry. It includes the study of casting, machining, welding, forming, and joining processes. Candidates are expected to have knowledge of different manufacturing techniques and their applications.

6. Industrial Engineering and Operations Research:
This topic focuses on the principles and techniques used in industrial engineering and operations research. It includes the study of production planning and control, work study, facility layout, inventory control, and optimization techniques.

7. Engineering Mechanics:
This topic deals with the study of forces and their effects on bodies in motion or at rest. It includes the study of concepts like equilibrium, motion, and deformation of rigid bodies.

8. Machine Design:
This topic covers the principles and techniques used in the design of machine elements. It includes the study of topics like stress analysis, fatigue, failure theories, and design of various machine components.

Overall, the Mechanical Engineering optional subject for the UPSC exam covers a wide range of topics that are relevant to the field of mechanical engineering. Candidates are expected to have a deep understanding of these topics to effectively answer the questions in the exam.