The correct answer is: A. d.c. shunt motor.
A rotary converter is a device that converts alternating current (AC) to direct current (DC). It can also be run as a DC shunt motor. A DC shunt motor is a type of DC motor that has a field winding that is connected in parallel with the armature winding. The field winding creates a magnetic field that interacts with the current in the armature winding to produce torque. The torque produced by a DC shunt motor is proportional to the current in the armature winding and the field current.
A DC shunt motor can be run as a rotary converter by connecting the AC input to the armature winding and the DC output to the field winding. The AC input will cause the armature winding to produce current, which will create a magnetic field. The field current will be supplied by the DC output. The interaction of the armature field and the field current will produce torque, which will cause the motor to rotate.
The other options are incorrect because they are not types of DC motors. A DC series motor is a type of DC motor that has a field winding that is connected in series with the armature winding. A DC compound motor is a type of DC motor that has both a shunt field winding and a series field winding. An induction motor is an AC motor that has a stator winding and a rotor winding. A synchronous motor is an AC motor that has a stator winding and a rotor winding that are locked in step with each other.