AIPMT PRELIMS 2003 Chemistry Equilibrium Constants MCQ Question

The following equilibria are given: $\text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3, \text{K}_1$ $\text{N}_2 + \text{O}_2 \rightleftharpoons 2\text{NO}, \text{K}_2$ $\text{H}_2 + \frac{1}{2}\text{O}_2 \rightleftharpoons \text{H}_2\text{O}, \text{K}_3$ The equilibrium constant of the reaction $2\text{NH}_3 + \frac{5}{2}\text{O}_2 \rightleftharpoons 2\text{NO} + 3\text{H}_2\text{O}$ in terms of $\text{K}_1, \text{K}_2$ and $\text{K}_3$ is: