JEE Advanced 2014 Paper 1 Offline | Definite Integration Question 34 | Mathematics

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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

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

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

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