1
AIEEE 2011
+4
-1
Let $$I$$ be the purchase value of an equipment and $$V(t)$$ be the value after it has been used for $$t$$ years. The value $$V(t)$$ depreciates at a rate given by differential equation $${{dv\left( t \right)} \over {dt}} = - k\left( {T - t} \right),$$ where $$k>0$$ is a constant and $$T$$ is the total life in years of the equipment. Then the scrap value $$V(T)$$ of the equipment is
A
$$I - {{k{T^2}} \over 2}$$
B
$$I - {{k{{\left( {T - t} \right)}^2}} \over 2}$$
C
$${e^{ - kT}}$$
D
$${T^2} - {1 \over k}$$
2
AIEEE 2011
+4
-1
If $${{dy} \over {dx}} = y + 3 > 0\,\,$$ and $$y(0)=2,$$ then $$y\left( {\ln 2} \right)$$ is equal to :
A
$$5$$
B
$$13$$
C
$$-2$$
D
$$7$$
3
AIEEE 2010
+4
-1
Solution of the differential equation
$$\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x{\pi \over 2}$$ is
A
$$y\sec x = \tan x + c$$
B
$$y\tan x = \sec x + c$$
C
$$\tan x = \left( {\sec x + c} \right)y$$
D
$$\sec x = \left( {\tan x + c} \right)y$$
4
AIEEE 2009
+4
-1
The differential equation which represents the family of curves $$y = {c_1}{e^{{c_2}x}},$$ where $${c_1}$$ , and $${c_2}$$ are arbitrary constants, is
A
$$y'' = y'y$$
B
$$yy'' = y'$$
C
$$yy'' = {\left( {y'} \right)^2}$$
D
$$y' = {y^2}$$
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