1
AIEEE 2006
+4
-1
The function $$f\left( x \right) = {x \over 2} + {2 \over x}$$ has a local minimum at
A
$$x=2$$
B
$$x=-2$$
C
$$x=0$$
D
$$x=1$$
2
AIEEE 2006
+4
-1
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is
A
$${3 \over 2}{x^2}$$
B
$$\sqrt {{{{x^3}} \over 8}}$$
C
$${1 \over 2}{x^2}$$
D
$$\pi {x^2}$$
3
AIEEE 2005
+4
-1
Area of the greatest rectangle that can be inscribed in the
ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$
A
$$2ab$$
B
$$ab$$
C
$$\sqrt {ab}$$
D
$${a \over b}$$
4
AIEEE 2005
+4
-1
A spherical iron ball $$10$$ cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of $$50$$ cm$$^3$$ /min. When the thickness of ice is $$5$$ cm, then the rate at which the thickness of ice decreases is
A
$${1 \over {36\pi }}$$ cm/min
B
$${1 \over {18\pi }}$$ cm/min
C
$${1 \over {54\pi }}$$ cm/min
D
$${5 \over {6\pi }}$$ cm/min
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