Civil Services Examination · Question 21
For 1/3 < x < y < 2, which of the following statements are always correct? I. x + 1/x < y + 1/y II. √(1 + y²)/y < √(1 + x²)/x Select the answer using the code given below.
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Answer: (B) II only
Explanation
t + 1/t decreases on (0, 1), so I fails (x = 0.5, y = 1 gives 2.5 > 2). √(1 + t²)/t = √(1/t² + 1) is strictly decreasing for t > 0, so II always holds.