The maximum torque which a synchronous motor will develop at rest for any angular position of the rotor, at rated stator supply voltage and frequency, is known as

locked-rotor torque
synchronous torque
pull up torque
reluctance torque

The correct answer is A. locked-rotor torque.

Locked-rotor torque is the maximum torque that a synchronous motor will develop at rest for any angular position of the rotor, at rated stator supply voltage and frequency. It is the torque that the motor must develop to overcome the friction and windage losses in the motor and start rotating.

Synchronous torque is the torque that the motor develops when it is running at synchronous speed. It is the torque that the motor must develop to overcome the load on the shaft.

Pull-up torque is the torque that the motor develops when it is starting from rest and accelerating up to synchronous speed. It is the sum of the locked-rotor torque and the synchronous torque.

Reluctance torque is the torque that is developed in a reluctance motor due to the reluctance of the magnetic path. It is a secondary effect and is not as important as the locked-rotor torque, synchronous torque, or pull-up torque.