IIT-JEE 2009 Paper 2 Offline | Definite Integrals and Applications of Integrals Question 64 | Mathematics

IIT-JEE 2009 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

If $${I_n} = \int\limits_{ - \pi }^\pi {{{\sin nx} \over {(1 + {\pi ^x})\sin x}}dx,n = 0,1,2,} $$ .... then

$${I_n} = {I_{n + 2}}$$

$$\sum\limits_{m = 1}^{10} {{I_{2m + 1}}} = 10\pi $$

$$\sum\limits_{m = 1}^{10} {{I_{2m}}} = 0$$

$${I_n} = {I_{n + 1}}$$

IIT-JEE 2009 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Area of the region bounded by the curve $$y = {e^x}$$ and lines $$x=0$$ and $$y=e$$ is

$$e-1$$

$$\int\limits_1^e {\ln \left( {e + 1 - y} \right)dy} $$

$$e - \int\limits_0^1 {{e^x}dx} $$

$$\int\limits_1^e {\ln y\,dy} $$

IIT-JEE 1999

MCQ (More than One Correct Answer)

-0.75

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 $$9/2$$?

$$-4$$

$$-2$$

$$2$$

$$4$$

JEE Advanced Subjects