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
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
$$-{1 \over 2}$$
3
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 $$2\pi$$
4
AIEEE 2011
+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
$${{\sqrt 3 } \over 4}$$
EXAM MAP
Medical
NEET