1
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
For the function $$$f\left( x \right) = x\cos \,{1 \over x},x \ge 1,$$$
A
for at least one $$x$$ in the interval $$\left[ {1,\infty } \right)$$, $$f\left( {x + 2} \right) - f\left( x \right) < 2$$
B
$$\mathop {\lim }\limits_{x \to \infty } f'\left( x \right) = 1$$
C
for all $$x$$ in the interval $$\left[ {1,\infty } \right)f\left( {x + 2} \right) - f\left( x \right) > 2$$
D
$$f'(x)$$ is strictly decreasing in the interval $$\left[ {1,\infty } \right)$$
2
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

Your input ____
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 __________.

Your input ____
4
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
$${I_n} = {I_{n + 1}}$$
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