Explanation:
In a variable speed S.I. engine, the maximum torque occurs at the maximum indicated power.

- S.I. engine: Spark Ignition Engine, which is also known as a gasoline engine, works on the principle of the Otto cycle. In this engine, the fuel and the air mixture is ignited by an electric spark. It is widely used in automobiles, motorcycles, and other vehicles.
- Variable speed: The speed of the engine can be varied by changing the throttle opening, which controls the amount of air-fuel mixture entering the engine. This is done to optimize the engine performance at different operating conditions such as speed, load, and temperature.
- Torque: It is the twisting force that is produced by the engine, which is transmitted to the wheels through the transmission system. It is measured in Newton-meters(Nm) or pound-feet(lb-ft).
- Indicated power: It is the power developed by the engine inside the cylinder, which is indicated by the pressure-volume diagram. It is measured in kW or hp.
- Maximum torque: It is the maximum twisting force that the engine can produce at a particular speed and load condition. It is achieved when the air-fuel mixture is burnt efficiently, and the engine is operating at its peak efficiency.
- Maximum indicated power: It is the maximum power that the engine can produce inside the cylinder. It is achieved when the engine is operating at its highest efficiency.

Therefore, the maximum torque occurs at the maximum indicated power because:

- When the engine is operating at its highest efficiency, the combustion process is optimized, and the maximum amount of energy is released from the air-fuel mixture.
- This energy is converted into mechanical force by the engine, which produces the maximum torque at a particular speed and load condition.
- Thus, the maximum torque is directly proportional to the maximum indicated power, and they occur at the same operating condition.

Conclusion:
Hence, option C is the correct answer, i.e., the maximum torque occurs at the maximum indicated power in a variable speed S.I. engine.

I think max volumetric efficiency