Tape recorders, also known as magnetic tape recorders, are electronic devices used for recording and playing back audio signals. They use a magnetic tape to store the recorded information. When it comes to the type of motors used in tape recorders, the correct answer is option 'C' - Hysteresis motor.

Explanation:
- Hysteresis Motor:
A hysteresis motor is a synchronous motor that operates based on the hysteresis loss of the magnetic material. It is a type of single-phase motor that is used in applications where precise control of speed and position is required, such as in tape recorders.
- Working Principle of Hysteresis Motor:
The hysteresis motor consists of a rotor and a stator. The rotor is made of a magnetic material with high hysteresis loss, such as cobalt steel. The stator consists of a set of electromagnets.
- When an alternating current is supplied to the stator windings, a rotating magnetic field is produced. This rotating magnetic field induces eddy currents in the rotor. These eddy currents cause the rotor to rotate in the direction of the rotating magnetic field.
- Since the rotor material has high hysteresis loss, there is a time lag between the magnetic field and the rotor rotation. This time lag causes a torque to be developed, which drives the rotor in synchronization with the rotating magnetic field.
- Advantages of Hysteresis Motor:
1. Smooth and silent operation.
2. High torque at low speeds.
3. No brushes or commutators, resulting in low maintenance.
4. Accurate speed control.
5. Good speed regulation.
- Other Motor Types:
a) Reluctance Motor: Reluctance motors are not commonly used in tape recorders. They operate based on the principle of reluctance torque and are typically used in applications like fans, blowers, and pumps.
b) Universal Motor: Universal motors are not typically used in tape recorders. They are called "universal" because they can operate on both AC and DC power sources. They are commonly used in appliances like vacuum cleaners and power tools.

In conclusion, the correct motor type used in tape recorders is the hysteresis motor. It provides smooth and silent operation, good speed control, and accurate speed regulation, making it suitable for the precise requirements of recording and playing back audio signals.