1
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1

Let $$f:R \to R$$ be a continuous function which satisfies $$f(x) = \int\limits_0^x {f(t)dt} $$. Then, the value of $$f(\ln 5)$$ is ____________.

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2
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

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

A
$${I_n} = {I_{n + 2}}$$
B
$$\sum\limits_{m = 1}^{10} {{I_{2m + 1}}} = 10\pi $$
C
$$\sum\limits_{m = 1}^{10} {{I_{2m}}} = 0$$
D
$${I_n} = {I_{n + 1}}$$
3
IIT-JEE 2009 Paper 2 Offline
Numerical
+4
-0

The maximum value of the function $$f(x) = 2{x^3} - 15{x^2} + 36x - 48$$ on the set $$A = \{ x|{x^2} + 20 \le 9x|\} $$ is __________.

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4
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1
Let $$p(x)$$ be a polynomial of degree $$4$$ having extremum at

$$x = 1,2$$ and $$\mathop {\lim }\limits_{x \to 0} \left( {1 + {{p\left( x \right)} \over {{x^2}}}} \right) = 2$$.

Then the value of $$p (2)$$ is

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