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## IIT JEE 2008 Paper II

 Formats Worksheet / Test Paper Quiz Review
: Multiple choice

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