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1

JEE Advanced 2015 Paper 1 Offline

MCQ (More than One Correct Answer)
Let $$y(x)$$ be a solution of the differential equation
$$\left( {1 + {e^x}} \right)y' + y{e^x} = 1.$$
If $$y(0)=2$$, then which of the following statement is (are) true?
A
$$y(-4)=0$$
B
$$y(-2)=0$$
C
$$y(x)$$ has a critical point in the interval $$(-1, 0)$$
D
$$y(x)$$ has no critical point in the interval $$(-1,0)$$
2

IIT-JEE 2012 Paper 1 Offline

MCQ (More than One Correct Answer)
If $$y(x)$$ satisfies the differential equation $$y' - y\,tan\,x = 2x\,secx$$ and $$y(0)=0,$$ then
A
$$y\left( {{\pi \over 4}} \right) = {{{\pi ^2}} \over {8\sqrt 2 }}$$
B
$$y'\left( {{\pi \over 4}} \right) = {{{\pi ^2}} \over {18}}$$
C
$$y\left( {{\pi \over 3}} \right) = {{{\pi ^2}} \over 9}$$
D
$$y'\left( {{\pi \over 3}} \right) = {{4\pi } \over 3} + {{2{\pi ^2}} \over {3\sqrt 3 }}$$
3

IIT-JEE 2006

MCQ (More than One Correct Answer)
A curve $$y=f(x)$$ passes through $$(1,1)$$ and at $$P(x,y),$$ tangent cuts the $$x$$-axis and $$y$$-axis at $$A$$ and $$B$$ respectively such that $$BP:AP=3:1,$$ then
A
equation of curve is $$xy'-3y=0$$
B
normal at $$(1,1)$$ is $$x+3y=4$$
C
curve passes through $$(2, 1/8)$$
D
equation of curve is $$xy'+3y=0$$
4

IIT-JEE 1999

MCQ (More than One Correct Answer)
The differential equation representing the family of curves
$${y^2} = 2c\left( {x + \sqrt c } \right),$$ where $$c$$ is a positive parameter, is of
A
order $$1$$
B
order $$2$$
C
degree $$3$$
D
degree $$4$$

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