A.C. servomotor is a type of motor that is widely used in various applications where precise control of speed and position is required. It is commonly used in robotics, CNC machines, and automation systems. The correct answer to this question is option 'C', which is a two-phase induction motor. Let's understand why this is the correct answer.

Two-phase induction motor:
- A two-phase induction motor is a type of motor that operates on a two-phase power supply. It is similar to a three-phase induction motor, but with two phases instead of three.
- In a two-phase induction motor, the stator windings are divided into two groups, each connected to a separate phase of the power supply.
- The two-phase stator windings produce a rotating magnetic field, which interacts with the rotor to create torque and rotation.
- The speed and direction of the motor can be controlled by varying the frequency and magnitude of the voltage applied to the stator windings.

Advantages of two-phase induction motors:
- Two-phase induction motors have several advantages, which make them suitable for servo applications:
- Precise control: Two-phase induction motors provide better control of speed and position compared to other types of motors. This is essential in applications that require high precision, such as robotics and CNC machines.
- Smooth operation: Two-phase induction motors operate smoothly and provide constant torque over a wide speed range. This allows for precise and smooth movement in servo applications.
- High efficiency: Two-phase induction motors are highly efficient and can convert a high percentage of electrical energy into mechanical energy. This helps in reducing power consumption and improving overall system efficiency.
- Compact size: Two-phase induction motors are relatively compact in size, making them suitable for applications with limited space.

In conclusion, A.C. servomotors are two-phase induction motors. They provide precise control of speed and position, making them suitable for various servo applications.