1

AIEEE 2010

MCQ (Single Correct Answer)

+4

-1

Let $$f:R \to R$$ be a continuous function defined by
$$$f\left( x \right) = {1 \over {{e^x} + 2{e^{ - x}}}}$$$

**Statement - 1 :** $$f\left( c \right) = {1 \over 3},$$ for some $$c \in R$$.

**Statement - 2 :** $$0 < f\left( x \right) \le {1 \over {2\sqrt 2 }},$$ for all $$x \in R$$

2

AIEEE 2009

MCQ (Single Correct Answer)

+4

-1

Given $$P\left( x \right) = {x^4} + a{x^3} + b{x^2} + cx + d$$ such that $$x=0$$ is the only

real root of $$P'\,\left( x \right) = 0.$$ If $$P\left( { - 1} \right) < P\left( 1 \right),$$ then in the interval $$\left[ { - 1,1} \right]:$$

real root of $$P'\,\left( x \right) = 0.$$ If $$P\left( { - 1} \right) < P\left( 1 \right),$$ then in the interval $$\left[ { - 1,1} \right]:$$

3

AIEEE 2008

MCQ (Single Correct Answer)

+4

-1

Suppose the cubic $${x^3} - px + q$$ has three distinct real roots

where $$p>0$$ and $$q>0$$. Then which one of the following holds?

where $$p>0$$ and $$q>0$$. Then which one of the following holds?

4

AIEEE 2008

MCQ (Single Correct Answer)

+4

-1

How many real solutions does the equation

$${x^7} + 14{x^5} + 16{x^3} + 30x - 560 = 0$$ have?

$${x^7} + 14{x^5} + 16{x^3} + 30x - 560 = 0$$ have?

Questions Asked from Application of Derivatives (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

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