1
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Let $$f:\left( { - 1,1} \right) \to R$$ be a differentiable function with $$f\left( 0 \right) = - 1$$ and $$f'\left( 0 \right) = 1$$. Let $$g\left( x \right) = {\left[ {f\left( {2f\left( x \right) + 2} \right)} \right]^2}$$. Then $$g'\left( 0 \right) = $$
A
$$-4$$
B
$$0$$
C
$$-2$$
D
$$4$$
2
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
For a regular polygon, let $$r$$ and $$R$$ be the radii of the inscribed and the circumscribed circles. A $$false$$ statement among the following is :
A
There is a regular polygon with $${r \over R} = {1 \over {\sqrt 2 }}$$
B
There is a regular polygon with $${r \over R} = {2 \over 3}$$
C
There is a regular polygon with $${r \over R} = {{\sqrt 3 } \over 2}$$
D
There is a regular polygon with $${r \over R} = {1 \over 2}$$
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
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
$$y=0$$
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