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1
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
A
local minimum at $$\pi $$ and $$2\pi $$
B
local minimum at $$\pi $$ and local maximum at $$2\pi $$
C
local maximum at $$\pi $$ and local minimum at $$2\pi $$
D
local maximum at $$\pi $$ and $$2\pi $$
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
The shortest distance between line $$y-x=1$$ and curve $$x = {y^2}$$ is
A
$${{3\sqrt 2 } \over 8}$$
B
$${8 \over {3\sqrt 2 }}$$
C
$${4 \over {\sqrt 3 }}$$
D
$${{\sqrt 3 } \over 4}$$
3
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

A
$$0$$
B
$$ - {1 \over 2}$$
C
$$-1$$
D
$$1$$
4
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
A
$$y=1$$
B
$$y=2$$
C
$$y=3$$
D
$$y=0$$
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