Which of the following reduction reaction CANNOT be carried out with coke?

The reduction of a metal oxide by coke (carbon) depends on the relative positions of the metal and carbon on the Ellingham diagram. Carbon can reduce a metal oxide only if the Gibbs free energy line for the formation of $$CO/CO_2$$ lies below the line for the metal oxide at the operating temperature.

Aluminium oxide ($$Al_2O_3$$) is extremely stable with a very large negative $$\Delta G_f°$$. On the Ellingham diagram, the line for $$Al_2O_3$$ lies well below the line for $$CO$$ at all practical temperatures. This means carbon cannot reduce $$Al_2O_3$$ to aluminium. This is why aluminium is extracted industrially by electrolysis of molten alumina (Hall-Heroult process) rather than by carbon reduction.

In contrast, $$ZnO$$, $$Fe_2O_3$$, and $$Cu_2O$$ can all be reduced by coke at sufficiently high temperatures, as their Ellingham diagram lines cross above the carbon line. Zinc is extracted by carbon reduction at about 1400°C, iron is produced in blast furnaces using coke, and copper oxide is easily reduced by carbon.

Therefore, the reduction that cannot be carried out with coke is $$Al_2O_3 \to Al$$, which is option (1).