1
AIEEE 2012
+4
-1
A spherical balloon is filled with $$4500\pi$$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $$72\pi$$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases $$49$$ minutes after the leakage began is :
A
$${{9 \over 7}}$$
B
$${{7 \over 9}}$$
C
$${{2 \over 9}}$$
D
$${{9 \over 2}}$$
2
AIEEE 2012
+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 $$b = {-1 \over 4}$$

A
Statement - 1 is false, Statement - 2 is true.
B
Statement - 1 is true , Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.
C
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
D
Statement - 1 is true, Statement - 2 is false.
3
AIEEE 2012
+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 :
A
$$-{1 \over 4}$$
B
$$-4$$
C
$$-2$$
D
$$-{1 \over 2}$$
4
AIEEE 2011
+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 $$2\pi$$
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