If p^x = q^y = r^z, where x, y and z are in GP, then consider the following statements: I. p, q and r are in AP. II. p, q and r are in GP. Which of the statements given above is/are correct?

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Correct answer: B. II only

Let p^x = q^y = r^z = k Taking natural logarithm on all sides: x p = y q = z r = k x = k p , y = k q , z = k r Since x, y, and z are in GP, y^2 = xz Substituting the values of x, y, and z: ( k q )^2 = ( k p ) ( k r ) 1 ( q)^2 = 1 p r ( q)^2 = p r This implies that p, q, and r are in GP. Statement II is correct, while Statement I is not necessarily true. Answer: II only

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