In a D.C. machine laboratory, the type of DC supply that will be used is an induction motor D.C. generator set (option C). This choice is based on several factors that make it the most suitable option for the laboratory.

1. Induction Motor and D.C. Generator Combination:
- The induction motor D.C. generator set consists of an induction motor and a D.C. generator connected together. This combination allows for efficient and reliable operation.
- The induction motor is used to drive the D.C. generator, providing the necessary mechanical power to generate electricity.
- This combination is commonly used in laboratories and industrial applications due to its simplicity, ease of operation, and low maintenance requirements.

2. Advantages of the Induction Motor D.C. Generator Set:
- The induction motor D.C. generator set offers several advantages over other types of DC supplies.
- It provides a stable and constant D.C. output voltage, which is essential for conducting accurate experiments in the laboratory.
- The induction motor D.C. generator set can handle both light and heavy loads, making it versatile for various laboratory experiments.
- It has a high efficiency, ensuring minimal power losses during the conversion process.
- The set-up is relatively simple and cost-effective compared to other options, making it suitable for laboratory environments.

3. Alternatives to Consider:
- Option A, the rotary converter, is a type of AC to DC converter. It is not commonly used in laboratory settings as it may be more complex and expensive compared to the induction motor D.C. generator set.
- Option B, the mercury arc rectifier, is another type of AC to DC converter. However, it is considered outdated and has been largely replaced by more modern and efficient rectifier technologies.
- Option D, the synchronous motor D.C. generator set, is another viable option. However, it requires precise synchronization between the motor and the generator, which may be more challenging to achieve in a laboratory setting.

In summary, the induction motor D.C. generator set is the most suitable choice for a D.C. machine laboratory due to its reliable performance, stability, versatility, and cost-effectiveness.