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IIT JEE 2008
Paper II


Formats Worksheet / Test Paper Quiz Review
: Multiple choice

Your Performance  

1.

14. Which of the following is true ?

  (2 + a) 2 f″(1) (2 – a)2 f″(– 1) = 0

  (2 – a) 2 f″(1) – (2 + a)2 f″(– 1) = 0

  f′(1) f′(–1) = (2 – a)2

  f′(1) f′(–1) = – (2 + a)2

  Half-n-half Clue
 

2.

15. Which of the following is true ?

  f(x) is decreasing on (–1, 1) and has a local minimum at x = 1

  f(x) is increasing on (–1, 1) and has a local maximum at x = 1

  f(x) is increasing on (–1, 1) but has neither a local maximum nor a local minimum at x = 1

  f(x) is decreasing on (–1, 1) but has neither a local maximum nor a local minimum at x = 1

  Half-n-half Clue
 

3.

16. Let
g(x) = ex

0
f′(t)

1 + t2
dt

Which of the following is true ?

  g′(x) is positive on (–∞, 0) and negative on (0, ∞)

  g′(x) is negative on (–∞, 0) and positive on (0, ∞)

  g′(x) changes sign on both (–∞, 0) and (0, ∞)

  g′ (x) does not change sign on (–∞, ∞)

  Half-n-half Clue
 
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