Explanation:

In a DC machine, the armature terminal voltage is the voltage measured at the terminals of the armature winding. It is the voltage that is available for external use or for supplying power to the load. The induced EMF, on the other hand, is the voltage generated in the armature winding due to the rotation of the armature in the magnetic field.

Armature Terminal Voltage vs Induced EMF:
- When the armature terminal voltage is greater than the induced EMF, it means that the external voltage applied to the machine is higher than the voltage generated by the machine itself. This situation occurs when the machine is operating as a generator and is supplying power to the external load.
- In generating mode, the machine converts mechanical energy into electrical energy and delivers power to the load. The armature terminal voltage is higher than the induced EMF because the machine needs to generate a higher voltage to overcome the voltage drop and losses in the armature winding and to deliver the desired voltage to the load.

Other Modes:
- Regenerative mode refers to the operation of the machine as a motor where the mechanical energy is converted into electrical energy and returned back to the power supply. In this mode, the armature terminal voltage is lower than the induced EMF as the machine acts as a load on the power supply.
- None of the mentioned is incorrect because the question specifically asks for the correct option, which is "motoring mode". The other options are not applicable in this context.

Conclusion:
Therefore, when the armature terminal voltage is more than its induced EMF, the DC machine is in the motoring mode where it converts electrical energy into mechanical energy and operates as a motor.