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1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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
$${{\sqrt 3 } \over 4}$$
2
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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
$$y=0$$
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
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 $$x \in R$$

A
Statement - 1 is true, Statement -2 is true; Statement - 2 is not a correct explanation for Statement - 1.
B
Statement - 1 is true, Statement - 2 is false.
C
Statement - 1 is false, Statement - 2 is true.
D
Statement - 1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement - 1.
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