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\( K_{1}, K_{2} \) and \( K_{3} \) are the equilibrium constants of the following reactions (I), (II) and (III) respectively:
(I) \( \mathrm{N}_{2}+2 \mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}_{2} \)
(II) \( 2 \mathrm{NO}_{2} \rightleftharpoons \mathrm{N}_{2}+2 \mathrm{O}_{2} \)
(III) \( \mathrm{NO}_{2} \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}+\mathrm{O}_{2} \)
The correct relation from the following is
(a) \( K_{1}=\frac{1}{K_{2}}=\frac{1}{K_{3}} \)
(b) \( K_{1}=\frac{1}{K_{2}}=\frac{1}{\left(K_{3}\right)^{2}} \)
(c) \( K_{1}=\sqrt{K_{2}}=K_{3} \)
(d) \( K_{1}=\frac{1}{K_{2}}=K_{3} \)
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