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If a d.c. motor is disconnected from the source and armature circuit is short circuited through a suitable resistance, the process is called (a) regenerative breaking (b) rheostatic breaking (c) dynamic breaking (d) no breaking is possible

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If a d.c. motor is disconnected from the source and armature circuit is short circuited through a suitable resistance, the process is called rheostatic breaking because the kinetic energy of the rotor is dissipated in terms of heat and it is not utilized anywhere else. Since the kinetic energy tends to become zero, breaking action occurs.

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Heat is also an output in the thermal point of view
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Any motor using its stored energy to slow down or braking called Dynamic braking.

If in this process motor is transferring energy to source called as Regenerative braking.If motor is converting it's energy to heat by flowing current through resistor called as rheostatic braking.

In given case it is rheostatic braking.
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rheostatic breaking
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Answer is Dynamic breaking(rheostatic breaking).

In this supply is disconnected from the motor,and breaking resistor Rb is connected immediately.now the motor acts as a generator and produce a breaking torque.

It is not efficient method because it will dissipated heat in the resistor.
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b) rheostatic breaking

Because rheostat is connected to chang the power dissipated into heat.

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