1

AIEEE 2012

MCQ (Single Correct Answer)

+4

-1

Let $$a,b \in R$$ be such that the function $$f$$ given by $$f\left( x \right) = In\left| x \right| + b{x^2} + ax,\,x \ne 0$$ has extreme values at $$x=-1$$ and $$x=2$$

**Statement-1 :** $$f$$ has local maximum at $$x=-1$$ and at $$x=2$$.

**Statement-2 :** $$a = {1 \over 2}$$ and $$b = {-1 \over 4}$$

2

AIEEE 2012

MCQ (Single Correct Answer)

+4

-1

A line is drawn through the point $$(1, 2)$$ to meet the coordinate axes at $$P$$ and $$Q$$ such that it forms a triangle $$OPQ,$$ where $$O$$ is the origin. If the area of the triangle $$OPQ$$ is least, then the slope of the line $$PQ$$ is :

3

AIEEE 2011

MCQ (Single Correct Answer)

+4

-1

For $$x \in \left( {0,{{5\pi } \over 2}} \right),$$ define $$f\left( x \right) = \int\limits_0^x {\sqrt t \sin t\,dt.} $$ Then $$f$$ has

4

AIEEE 2011

MCQ (Single Correct Answer)

+4

-1

The shortest distance between line $$y-x=1$$ and curve $$x = {y^2}$$ is

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

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