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Differential Equations
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Previous Years Questions
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MCQ (More than One Correct Answer)
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Let $$\Gamma $$ denote a curve y = y(x) which is in the first quadrant and let the point (1, 0) lie on it. Let the tange...
JEE Advanced 2019 Paper 1 Offline
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If $$g(x) = \int_{\sin x}^{\sin (2x)} {{{\sin }^{ - 1}}} (t)\,dt$$, then
JEE Advanced 2017 Paper 2 Offline
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Let $$f:(0,\infty ) \to R$$ be a differentiable function such that $$f'(x) = 2 - {{f(x)} \over x}$$ for all $$x \in (0,\...
JEE Advanced 2016 Paper 1 Offline
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A solution curve of the differential equation $$\left( {{x^2} + xy + 4x + 2y + 4} \right){{dy} \over {dx}} - {y^2} = 0,...
JEE Advanced 2016 Paper 1 Offline
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Consider the family of all circles whose centres lie on the straight line $$y=x,$$ If this family of circle is represent...
JEE Advanced 2015 Paper 1 Offline
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Let $$y(x)$$ be a solution of the differential equation $$\left( {1 + {e^x}} \right)y' + y{e^x} = 1.$$ If $$y(0)=2$$, t...
JEE Advanced 2015 Paper 1 Offline
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If $$y(x)$$ satisfies the differential equation $$y' - y\,tan\,x = 2x\,secx$$ and $$y(0)=0,$$ then
IIT-JEE 2012 Paper 1 Offline
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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 ...
IIT-JEE 2006
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The differential equation representing the family of curves $${y^2} = 2c\left( {x + \sqrt c } \right),$$ where $$c$$ is...
IIT-JEE 1999
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Numerical
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Let f : R $$ \to $$ R be a differentiable function with f(0) = 0. If y = f(x) satisfies the differential equation $${{dy...
JEE Advanced 2018 Paper 2 Offline
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Let $$f:[1,\infty ) \to [2,\infty )$$ be a differentiable function such that $$f(1) = 2$$. If $$6\int\limits_1^x {f(t)dt...
IIT-JEE 2011 Paper 1 Offline
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Let $$y'\left( x \right) + y\left( x \right)g'\left( x \right) = g\left( x \right),g'\left( x \right),y\left( 0 \right) ...
IIT-JEE 2011 Paper 2 Offline
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MCQ (Single Correct Answer)
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If y = y(x) satisfies the differential equation$${8\sqrt x \left( {\sqrt {9 + \sqrt x } } \right)dy = {{\left( {\sqrt {4...
JEE Advanced 2017 Paper 2 Offline
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The function $$y=f(x)$$ is the solution of the differential equation $${{dy} \over {dx}} + {{xy} \over {{x^2} - 1}} = {{...
JEE Advanced 2014 Paper 2 Offline
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A curve passes through the point $$\left( {1,{\pi \over 6}} \right)$$. Let the slope of the curve at each point $$(x,y...
JEE Advanced 2013 Paper 1 Offline
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Let a solution $$y=y(x)$$ of the differential equation $$x\sqrt {{x^2} - 1} \,\,dy - y\sqrt {{y^2} - 1} \,dx = 0$$ satif...
IIT-JEE 2008
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The differential equation $${{dy} \over {dx}} = {{\sqrt {1 - {y^2}} } \over y}$$ determines a family of circles with
IIT-JEE 2005 Screening
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The solution of primitive integral equation $$\left( {{x^2} + {y^2}} \right)dy = xy$$ $$dx$$ is $$y=y(x),$$ If $$y(1)=1$...
IIT-JEE 2005 Screening
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For the primitive integral equation $$ydx + {y^2}dy = x\,dy;$$ $$x \in R,\,\,y > 0,y = y\left( x \right),\,y\left( 1...
IIT-JEE 2005 Screening
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If $$y=y(x)$$ and it follows the relation $$x\cos \,y + y\,cos\,x = \pi $$ then $$y''(0)=$$
IIT-JEE 2005 Screening
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If $$y=y(x)$$ and $${{2 + \sin x} \over {y + 1}}\left( {{{dy} \over {dx}}} \right) = - \cos x,y\left( 0 \right) = 1,$$ ...
IIT-JEE 2004 Screening
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If $$y(t)$$ is a solution of $$\left( {1 + t} \right){{dy} \over {dt}} - ty = 1$$ and $$y\left( 0 \right) = - 1,$$ then...
IIT-JEE 2003 Screening
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If $${x^2} + {y^2} = 1,$$ then
IIT-JEE 2000 Screening
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A solution of the differential equation $${\left( {{{dy} \over {dx}}} \right)^2} - x{{dy} \over {dx}} + y = 0$$ is
IIT-JEE 1999
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The order of the differential equation whose general solution is given by $$y = \left( {{C_1} + {C_2}} \right)\cos \left...
IIT-JEE 1998
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Subjective
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Match the statements/expressions in Column $$I$$ with the open intervals in Column $$II$$. Column $$I$$ (A)$$\,\,\,$$ I...
IIT-JEE 2009
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If length of tangent at any point on the curve $$y=f(x)$$ intecepted between the point and the $$x$$-axis is length $$1....
IIT-JEE 2005
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A curve $$'C''$$ passes through $$(2,0)$$ and the slope at $$(x,y|)$$ as $$\,{{{{\left( {x + 1} \right)}^2} + \left( {y ...
IIT-JEE 2004
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A right circular cone with radius $$R$$ and height $$H$$ contains a liquid which eveporates at a rate proportional to it...
IIT-JEE 2003
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A hemispherical tank of radius $$2$$ metres is initially full of water and has an outlet of $$12$$ cm2 cross-sectional a...
IIT-JEE 2001
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Let $$u(x)$$ and $$v(x)$$ satisfy the differential equation $${{du} \over {dx}} + p\left( x \right)u = f\left( x \right)...
IIT-JEE 1997
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Determine the equation of the curve passing through the origin, in the form $$y=f(x),$$ which satisfies the differential...
IIT-JEE 1996
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Let $$y=f(x)$$ be a curve passing through $$(1,1)$$ such that the triangle formed by the coordinate axes and the tangent...
IIT-JEE 1995
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A normal is drawn at a point $$P(x,y)$$ of a curve. It meets the $$x$$-axis at $$Q.$$ If $$PQ$$ is of constant length $$...
IIT-JEE 1994
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If $$\left( {a + bx} \right){e^{y/x}} = x,$$ then prove that $${x^3}{{{d^2}y} \over {d{x^2}}} = {\left( {x{{dy} \over {d...
IIT-JEE 1983
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