Is it possible that an object is in the state of accelerated motion due to external force acting on it, but no work is being done by the force. Explain it with an example.

Yes, it is possible that an object is in the state of accelerated motion due to external force acting on it, but no work is being done by the force. Since W = F.s where S is the displacement. So if the body is moving in a circular path then W=0.