Synchronous motors are a type of AC motor that operates at a constant speed called the synchronous speed. This speed is determined by the frequency of the power supply and the number of poles in the motor. The synchronous speed can be calculated using the formula:

Synchronous Speed = (120 * Frequency) / Number of Poles

Now, let's discuss each option and understand why option 'C' is correct:

a) Increases as the load increases:
If the load on a synchronous motor increases, the motor will start to slow down. This is because the increased load will require more torque to be produced by the motor, and as a result, the motor speed will decrease. However, the synchronous speed of the motor will remain constant regardless of the load. So, this option is incorrect.

b) Decreases as the load decreases:
Similarly, if the load on a synchronous motor decreases, the motor will start to speed up. This is because the reduced load will require less torque to be produced by the motor, and as a result, the motor speed will increase. However, the synchronous speed of the motor will remain constant regardless of the load. So, this option is also incorrect.

c) Always remains constant:
The correct answer is option 'C'. The speed of a synchronous motor always remains constant irrespective of the load. This is because a synchronous motor operates at its synchronous speed, which is determined by the power supply frequency and the number of poles in the motor. The rotor of a synchronous motor rotates at the same speed as the rotating magnetic field produced by the stator, thus ensuring a constant speed.

d) None of the above:
Option 'D' is incorrect as the correct answer is option 'C'.

In summary, the speed of a synchronous motor always remains constant regardless of the load. This is because the motor operates at its synchronous speed, which is determined by the power supply frequency and the number of poles in the motor.