Correct option is C
A is incorrect: The auxiliary motor's purpose is to accelerate the synchronous motor to near synchronous speed, not run it below it.
D is incorrect: Auxiliary motor starting is still a widely used method for starting synchronous motors.
B is correct: The auxiliary motor is much smaller in size and rating compared to the main synchronous motor because it only needs to bring the rotor close to synchronous speed.
C is incorrect: Auxiliary motor starting can be used for both loaded and unloaded synchronous motors.