1
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
Let $$f:\left( {0,\infty } \right) \to R$$ be given by $$f\left( x \right) $$= $$\int\limits_{{1 \over x}}^x {{{{e^{ - \left( {t + {1 \over t}} \right)}}} \over t}} dt$$. Then
A
$$f(x)$$ is monotonically increasing on $$\left[ {1,\infty } \right)$$
B
$$f(x)$$ is monotonically decreasing on $$(0,1)$$
C
$$f(x)$$ $$ + f\left( {{1 \over x}} \right) = 0$$, for all $$x \in \left( {0,\infty } \right)$$
D
$$f\left( {{2^x}} \right)$$ is an odd function of $$x$$ on $$R$$
2
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
Let a $$\in$$ R and f : R $$\to$$ R be given by f(x) = x5 $$-$$ 5x + a. Then,
A
f(x) has three real roots , if a > 4
B
f(x) has only one real root, if a > 4
C
f(x) has three real roots, if a < $$-$$4
D
f(x) has three real roots, if $$-$$4 < a < 4
3
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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