AIEEE 2011 | Differential Equations Question 190 | Mathematics

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

$$I - {{k{T^2}} \over 2}$$

$$I - {{k{{\left( {T - t} \right)}^2}} \over 2}$$

$${e^{ - kT}}$$

$${T^2} - {1 \over k}$$

AIEEE 2011

MCQ (Single Correct Answer)

-1

If $${{dy} \over {dx}} = y + 3 > 0\,\,$$ and $$y(0)=2,$$ then $$y\left( {\ln 2} \right)$$ is equal to :

$$5$$

$$13$$

$$-2$$

$$7$$

AIEEE 2010

MCQ (Single Correct Answer)

-1

Solution of the differential equation

$$\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x <{\pi \over 2}$$ is :

$$y\sec x = \tan x + c$$

$$y\tan x = \sec x + c$$

$$\tan x = \left( {\sec x + c} \right)y$$

$$\sec x = \left( {\tan x + c} \right)y$$

AIEEE 2009

MCQ (Single Correct Answer)

-1

Out of Syllabus

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

$$y'' = y'y$$

$$yy'' = y'$$

$$yy'' = {\left( {y'} \right)^2}$$

$$y' = {y^2}$$

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