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IIT JEE Advanced 2012 Paper 2

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Paragraph for Questions 51 and 52:
Let f (x) = (1−x)2sin2x+x2 for all x ∊ R, and let g (x) =

x

∫

1

(

2(t−1)

t+1

−ln‌t) f (t) dt for all x ∊ (1 , ∞).

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Question : 52

Total: 60

Which of the following is true?

[JEE Adv 2012 P2]

g is increasing on (1, ∞).
g is decreasing on (1, ∞).
g is increasing on (1, 2) and decreasing on (2, ∞).
g is decreasing on (1, 2) and increasing on (2, ∞).

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