If p, 1, q are in AP and p, 2, q are in GP, then which of the following statements is/are correct?
I. p, 4, q are in HP.
II. (1/p), 1/4, (1/q) are in AP.
Select the answer using the code given below.
A.I only
B.II only
C.Both I and II✓ Correct
D.Neither I nor II
Explanation
From AP: p + q = 2. From GP: pq = 4. For HP, we need 1/p, 1/4, 1/q in AP, i.e., 2/4 = 1/p + 1/q = (p+q)/(pq) = 2/4 = 1/2. ✓ So 1/p, 1/4, 1/q are in AP, which means p, 4, q are in HP. Both statements are correct.
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