1
IIT-JEE 2008 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$f(x)$$ be a non-constant twice differentiable function defined on $$\left( { - \infty ,\infty } \right)$$


such that $$f\left( x \right) = f\left( {1 - x} \right)$$ and $$f'\left( {{1 \over 4}} \right) = 0.$$ Then,
A
$$f''\left( x \right)$$ vanishes at least twice on $$\left[ {0,1} \right]$$
B
$$f'\left( {{1 \over 2}} \right) = 0$$
C
$$\int\limits_{ - 1/2}^{1/2} {f\left( {x + {1 \over 2}} \right)\sin x\,dx} = 0$$
D
$$\int\limits_0^{1/2} {f\left( t \right){e^{\sin \,\pi t}}dt = } \int\limits_{1/2}^1 {f\left( {1 - t} \right){e^{\sin \,\pi t}}dt} $$
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