Question
For 1/3 < x < y < 2, which of the following statements is/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.
- (a)I only
- (b)II only
- (c)Both I and II
- (d)Neither I nor II
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f(t) = t + 1/t has a minimum at t = 1, so on (1/3, 2) it is not monotonic and I can fail. But g(t) = √(1+t²)/t = √(1 + 1/t²) is strictly decreasing, so x < y gives √(1+y²)/y < √(1+x²)/x. Only II is always correct.
UnlockIAS expert key, prepared 24 May 2026 and cross-verified by re-deriving the answer — this is our key, not the official UPSC provisional key (awaited).
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