Figure shows the $P-V$ diagram of a cyclic process. If $dQ$ is the heat energy supplied to the system, $dU$ is change in the internal energy of the system and $dW$ is the work done by the system, then which of the following relations is/are correct 

In a cylic process, the system returns to its initial state. Hence the change in the internal energy $dU = 0$. Therefore, choice $\left(2\right)$ is correct. From the first law of thermodynamics, $dQ = dU + dW = dW (dU = 0)$ Hence choice $\left(3\right)$ is also correct.