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Differential Equations

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2021
Let $f$ be a twice differentiable function defined on $R$ such that $f(0)=1, f^{\prime}(0)=2$ and $f^{\prime}(x) \neq 0$ for all $x \in R$. If $...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
The differential equation satisfied by the system of parabolas $y^2=4 a(x+a)$ is :
JEE Main Mathematics Easy
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Q JEE-MAIN 2021
Let the curve $y=y(x)$ be the solution of the differential equation, $\frac{d y}{d x}=2(x+1)$. If the numerical value of area bounded by the curve $y=y(x)$...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
If $y=y(x)$ is the solution of the differential equation, $\frac{d y}{d x}+2 y \tan x=\sin x, y\left(\frac{\pi}{3}\right)=0$, then the maximum value of the function $y(x)$...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
If $y=y(x)$ is the solution of the equation $e^{\sin \mid y} \cos y \frac{d y}{d x}+e^{\sin y} \cos x=\cos x, y(0)=0$; then $...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
The difference between degree and order of a differential equation that represents the family of curves given by $y^2=a\left(x+\frac{\sqrt{a}}{2}\right), a>0$ is
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Q JEE MAIN 2021
If the tangent to the curve $y=x^3$ at the point $P\left(t, t^3\right)$ meets the curve again at $Q$, then the ordinate of the point which...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
The rate of growth of bacteria in a culture is proportional to the number of bacteris present and the bacteria count is 1000 at initial...
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Q JEE MAIN 2021
The population $P=P(t)$ at time ' $t$ ' of a certain species follows the differential equation $\frac{d P}{d t}=0.5 P-450$. If $P(0)=850$, then the time...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
If a curve passes through the origin and the slope of the tangent to it at any point $(x, y)$ is $\frac{x^2-4 x+y+8}{x-2}$, then this...
JEE Main Mathematics Medium
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