The incorrect statements from the following is:
A. The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy.
B. $$E^\circ_{cell}$$ is dependent on the pressure.
C. $$\frac{dE_{cell}}{dT} = \frac{\Delta_r S}{nF}$$
D. A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

The problem asks us to find which of the four given statements are incorrect. For each statement we compare it with the accepted thermodynamic relations for electrochemical cells.

Statement A
“The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy.”

For an electrochemical cell operating reversibly at constant $$T$$ and $$P$$, the maximum non-expansion (electrical) work is related to the reaction Gibbs energy by the equation $$w_{\text{elec,max}} = -\Delta_r G$$. Thus electrical work is equal in magnitude but opposite in sign to $$\Delta_r G$$. Because Statement A omits the minus sign, it is incorrect.

Statement B
“$$E^\circ_{cell}$$ is dependent on the pressure.”

The standard cell potential $$E^\circ_{cell}$$ is defined for standard conditions: temperature $$T = 298\,\text{K}$$ (unless specified otherwise), all solute activities $$a = 1$$, and gases at a partial pressure of $$1\,\text{bar}$$. Since the pressure is fixed by definition (1 bar), $$E^\circ_{cell}$$ itself does not vary with pressure. Hence Statement B is incorrect.

Statement C
“$$\dfrac{dE_{cell}}{dT} = \dfrac{\Delta_r S}{nF}$$”

At constant pressure the temperature-dependence of the cell potential is given by $$\left(\dfrac{\partial E_{cell}}{\partial T}\right)_P = \dfrac{\Delta_r S}{nF}$$, where $$\Delta_r S$$ is the entropy change of the cell reaction, $$n$$ is the number of electrons transferred, and $$F$$ is the Faraday constant. Therefore Statement C is correct.

Statement D
“A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.”

For truly reversible operation the external (opposing) potential must equal the cell’s own emf so that an infinitesimal change will reverse the direction of current. Thus Statement D is correct.

To summarise, the incorrect statements are A and B.

If the option code “3” in the original question corresponds to the pair (A, B), then the given answer key is validated.