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1

IIT-JEE 2009

MCQ (More than One Correct Answer)
Area of the region bounded by the curve $$y = {e^x}$$ and lines $$x=0$$ and $$y=e$$ is
A
$$e-1$$
B
$$\int\limits_1^e {\ln \left( {e + 1 - y} \right)dy} $$
C
$$e - \int\limits_0^1 {{e^x}dx} $$
D
$$\int\limits_1^e {\ln y\,dy} $$
2

IIT-JEE 2008

MCQ (More than One Correct Answer)
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
$$\int\limits_0^{1/2} {f\left( t \right){e^{\sin \,\pi t}}dt = } \int\limits_{1/2}^1 {f\left( {1 - t} \right){e^{\sin \,\pi t}}dt} $$
3

IIT-JEE 1999

MCQ (More than One Correct Answer)
For which of the following values of $$m$$, is the area of the region bounded by the curve $$y = x - {x^2}$$ and the line $$y=mx$$ equals $$9/2$$?
A
$$-4$$
B
$$-2$$
C
$$2$$
D
$$4$$

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