Can A Transformer work at D.C supply ? Give Reason ?

NO.

For a transformer to work, the current in one coil has to somehow make current flow in the other coil and the circuit it's connected to. A DC current in one coil will make a magnetic field on the other coil, but a magnetic field by itself won't drive any electrons around. A CHANGING magnetic field, however, does create an electric force which will accelerate those electrons in the other coil into carrying a current.