1

AIEEE 2010

MCQ (Single Correct Answer)

+4

-1

Let $$f:R \to R$$ be defined by
$$$f\left( x \right) = \left\{ {\matrix{
{k - 2x,\,\,if} & {x \le - 1} \cr
{2x + 3,\,\,if} & {x > - 1} \cr
} } \right.$$$

If $$f$$has a local minimum at $$x=-1$$, then a possible value of $$k$$ is

2

AIEEE 2010

MCQ (Single Correct Answer)

+4

-1

The equation of the tangent to the curve $$y = x + {4 \over {{x^2}}}$$, that

is parallel to the $$x$$-axis, is

is parallel to the $$x$$-axis, is

3

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 $$x \in R$$

4

AIEEE 2009

MCQ (Single Correct Answer)

+4

-1

Let $$f\left( x \right) = x\left| x \right|$$ and $$g\left( x \right) = \sin x.$$

**Statement-1:**gof is differentiable at $$x=0$$ and its derivative is continuous at that point.**Statement-2:**gof is twice differentiable at $$x=0$$.Questions Asked from Application of Derivatives (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

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