JEE MAIN Differential Equation Previous Year Question Paper and Solution with PDF

Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations

JEE MAIN
Previous Year Questions

JEE MAIN
Previous Year Questions
JEE MAIN

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Differential Equation PYQ

Qus : 1 JEE MAIN PYQ

Let the population of rabbits surviving at time $t$ be governed by the differential equation $\dfrac{dp(t)}{dt}=\dfrac{1}{2}p(t)-200$. If $p(0)=100$, then $p(t)$ equals:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 2 JEE MAIN PYQ

The curve amongst the family of curves represented by the differential equation $(x^2 - y^2)dx + 2xy\,dy = 0$ which passes through $(1, 1)$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Evening Shift) PYQ

Solution

Qus : 3 JEE MAIN PYQ

The area enclosed by the closed curve $\mathcal{C}$ given by the differential equation $\dfrac{dy}{dx}+\dfrac{x+a}{\,y-2\,}=0,\quad y(1)=0$ is $4\pi$. Let $P$ and $Q$ be the points of intersection of the curve $\mathcal{C}$ with the $y$-axis. If the normals at $P$ and $Q$ on $\mathcal{C}$ intersect the $x$-axis at points $R$ and $S$ respectively, then the length of the line segment $RS$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Morning Shift) PYQ

Solution

Qus : 4 JEE MAIN PYQ

Let y = y(x) be the solution of the differential equation xdy = (y + x³ cosx)dx with y($\pi$) = 0, then $y\left( {{\pi \over 2}} \right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Evening Shift) PYQ

Solution

Qus : 5 JEE MAIN PYQ

If $y=y(x)$ is the solution curve of the differential equation $\dfrac{dy}{dx}+y\tan x=x\sec x,\ 0\le x\le \dfrac{\pi}{3},\ y(0)=1$, then $y\!\left(\dfrac{\pi}{6}\right)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Morning Shift) PYQ

Solution

Qus : 6 JEE MAIN PYQ

The general solution of the differential equation (y² – x³)dx – xydy = 0 (x $ \ne $ 0) is : (where c is a constant of integration)

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Evening Shift) PYQ

Solution

Qus : 7 JEE MAIN PYQ

If a curve $y=y(x)$ passes through the point $\left(1,\dfrac{\pi}{2}\right)$ and satisfies the differential equation $(7x^{4}\cot y-e^{x}\csc y),\dfrac{dx}{dy}=x^{5},\ x\ge1$, then at $x=2$, the value of $\cos y$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Evening Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

Let the solution curve $y=f(x)$ of the differential equation $\dfrac{dy}{dx}+\dfrac{xy}{x^{2}-1}=\dfrac{x^{4}+2x}{\sqrt{1-x^{2}}}$, $x\in(-1,1)$, pass through the origin. Then $\displaystyle \int_{-\sqrt{3}/2}^{\sqrt{3}/2} f(x)\,dx$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Evening Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $(x^{2}+4)^{2}\,dy+(2x^{3}y+8xy-2)\,dx=0.$ If $y(0)=0$, then $y(2)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Evening Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

Let y = y(x) be solution of the differential equation ${\log _{}}\left( {{{dy} \over {dx}}} \right) = 3x + 4y$, with y(0) = 0.If $y\left( { - {2 \over 3}{{\log }_e}2} \right) = \alpha {\log _e}2$, then the value of $\alpha$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (27 July Morning Shift) PYQ

Solution

Qus : 11 JEE MAIN PYQ

For all twice differentiable functions f : R $ \to $ R,with f(0) = f(1) = f'(0) = 0

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 6 September 2020 (Evening) PYQ

Solution

Qus : 12 JEE MAIN PYQ

Let $\alpha x = \exp(x^{\beta} y^{\gamma})$ be the solution of the differential equation $2x^{2}y\,dy - (1 - xy^{2})\,dx = 0,\ x>0,\ y(2)=\sqrt{\log_{e}2}.$ Then $\alpha + \beta - \gamma$ equals:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Evening Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

At present, a firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ w.r.t. additional number of workers $x$ is given by $\dfrac{dP}{dx}=100-12\sqrt{x}$. If the firm employs $25$ more workers, then the new level of production of items is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2013 (Offline) PYQ

Solution

Qus : 14 JEE MAIN PYQ

Let $x=x(y)$ be the solution of the differential equation $y=\left(x-y \frac{\mathrm{~d} x}{\mathrm{~d} y}\right) \sin \left(\frac{x}{y}\right), y>0$ and $x(1)=\frac{\pi}{2}$. Then $\cos (x(2))$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Evening Shift) PYQ

Solution

Qus : 15 JEE MAIN PYQ

Let $y = y_{1}(x)$ and $y = y_{2}(x)$ be two distinct solutions of the differential equation $\dfrac{dy}{dx} = x + y$, with $y_{1}(0) = 0$ and $y_{2}(0) = 1$ respectively. Then, the number of points of intersection of $y = y_{1}(x)$ and $y = y_{2}(x)$ is

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 July Morning Shift) PYQ

Solution

Qus : 16 JEE MAIN PYQ

If $y(x)$ is the solution of the differential equation $\dfrac{dy}{dx}+\left(\dfrac{2x+1}{x}\right)y=e^{-2x},\ x>0,$ where $y(1)=\dfrac{1}{2}e^{-2}$, then

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Morning Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

Let $y=y(x)$ be the solution curve of the differential equation $x(x^{2}+e^{x})^{2}dy+\big(e^{x}(x-2)y-x^{3}\big)dx=0, x>0,$ passing through the point $(1,0)$. Then $y(2)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Morning Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

Let y = y(x) be the solution of the differential equation ${{dy} \over {dx}} + 2y = f\left( x \right),$

where $f\left( x \right) = \left\{ {\matrix{ {1,} & {x \in \left[ {0,1} \right]} \cr {0,} & {otherwise} \cr } } \right.$

If y(0) = 0, then $y\left( {{3 \over 2}} \right)$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

Let y = y(x) be a solution curve of the differential equation $(y + 1){\tan ^2}x\,dx + \tan x\,dy + y\,dx = 0$, $x \in \left( {0,{\pi \over 2}} \right)$. If $\mathop {\lim }\limits_{x \to 0 + } xy(x) = 1$, then the value of $y\left( {{\pi \over 4}} \right)$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Morning Shift) PYQ

Solution

Qus : 20 JEE MAIN PYQ

Let $x=x(t)$ and $y=y(t)$ be solutions of the differential equations $\dfrac{dx}{dt}+ax=0$ and $\dfrac{dy}{dt}+by=0$ respectively, $a,b\in\mathbb{R}$. Given that $x(0)=2$, $y(0)=1$ and $3y(1)=2x(1)$, the value of $t$ for which $x(t)=y(t)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (27 January Morning Shift) PYQ

Solution

Qus : 21 JEE MAIN PYQ

Let $y = y(x)$ be the solution of the differential equation $\left(xy - 5x^2\sqrt{1 + x^2}\right)dx + (1 + x^2)dy = 0$, $y(0) = 0$. Then $y(\sqrt{3})$ is equal to

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (24 January Morning Shift) PYQ

Solution

Qus : 22 JEE MAIN PYQ

If the solution curve $f(x,y)=0$ of the differential equation $(1+\log_e x)\frac{dx}{dy}-x\log_e x=e^y,\; x>0,$ passes through the points $(1,0)$ and $(\alpha,2)$, then $\alpha^\alpha$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (6 April Evening Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

If $y=y(x)$ solves the differential equation $\dfrac{dy}{dx}+2y=\sin(2x)$ with $y(0)=\dfrac{3}{4}$, then $y!\left(\dfrac{\pi}{8}\right)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Morning Shift) PYQ

Solution

Qus : 24 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $(x^{2}+1),y'-2xy=(x^{4}+2x^{2}+1)\cos x$, with $y(0)=1$. Then $\displaystyle \int_{-3}^{3} y(x),dx$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Evening Shift) PYQ

Solution

Qus : 25 JEE MAIN PYQ

Let the solution curve of the differential equation $x,dy = \left(\sqrt{x^{2}+y^{2}}+y\right)dx,; x>0,$ intersect the line $x=1$ at $y=0$ and the line $x=2$ at $y=\alpha$. Then the value of $\alpha$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

Qus : 26 JEE MAIN PYQ

If x = x(y) is the solution of the differential equation $y{{dx} \over {dy}} = 2x + {y^3}(y + 1){e^y},\,x(1) = 0$; then x(e) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (24 June Morning Shift) PYQ

Solution

Qus : 27 JEE MAIN PYQ

Let y(x) be the solution of the differential equation 2x² dy + (e^y $-$ 2x)dx = 0, x > 0. If y(e) = 1, then y(1) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Evening Shift) PYQ

Solution

Qus : 28 JEE MAIN PYQ

. If $y(\theta)=\dfrac{2\cos\theta+\cos2\theta}{\cos3\theta+\cos2\theta+5\cos\theta+2}$, then at $\theta=\dfrac{\pi}{2}$, the value of $y''+y'+y$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Evening Shift) PYQ

Solution

Qus : 29 JEE MAIN PYQ

If $y=y(x),\; x\in(0,\pi/2)$ be the solution curve of the differential equation $$(\sin^{2}2x)\dfrac{dy}{dx}+(8\sin^{2}2x+2\sin 4x)y=2e^{-4x}(2\sin 2x+\cos 2x),$$ with $y(\pi/4)=e^{-\pi}$, then $y(\pi/6)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

Qus : 30 JEE MAIN PYQ

The curve satisfying the differential equation $(x^{2}-y^{2}),dx + 2xy,dy = 0$ and passing through the point $(1,1)$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

Qus : 31 JEE MAIN PYQ

$ \text{Let } C(\alpha,\beta) \text{ be the circumcenter of the triangle formed by the lines } 4x+3y=69,; 4y-3x=17,; x+7y=61. $ $ \text{Then } (\alpha-\beta)^2+\alpha+\beta \text{ is equal to:} $

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Morning Shift) PYQ

Solution

Qus : 32 JEE MAIN PYQ

The minimum value of the twice differentiable function $f(x)=\int_{0}^{x} e^{,x-t},f'(t),dt-(x^{2}-x+1)e^{x},; x\in\mathbb{R}$, is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

Qus : 33 JEE MAIN PYQ

he solution of the differential equation, $\dfrac{dy}{dx}=(x-y)^{2}$, when $y(1)=1$, is

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Evening Shift) PYQ

Solution

Qus : 34 JEE MAIN PYQ

The differential equation of the family of circles passing through the origin and having centre on the line $y=x$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Evening Shift) PYQ

Solution

Qus : 35 JEE MAIN PYQ

If $y=y(x)$ is the solution curve of the differential equation $(x^2-4)\,dy-(y^2-3y)\,dx=0,\ x>2,\ y(4)=\dfrac{3}{2}$ and the slope of the curve is never zero, then the value of $y(10)$ equals:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (27 January Evening Shift) PYQ

Solution

Qus : 36 JEE MAIN PYQ

$ \text{Let } y=y(x) \text{ be the solution curve of the differential equation } \dfrac{dy}{dx}+\dfrac{1}{x^{2}-1},y=\left(\dfrac{x-1}{x+1}\right)^{1/2},; x>1,\ \text{passing through the point } \left(2,\sqrt{\tfrac{1}{3}}\right). \text{ Then } \sqrt{7},y(8) \text{ is equal to:} $

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Evening Shift) PYQ

Solution

Qus : 37 JEE MAIN PYQ

Let $f:(0,\infty)\to\mathbb{R}$ be a function which is differentiable at all points of its domain and satisfies the condition $x^2 f'(x)=2x f(x)+3$, with $f(1)=4$. Then $2f(2)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (24 January Evening Shift) PYQ

Solution

Qus : 38 JEE MAIN PYQ

Let $g:(0,\infty ) \to R$ be a differentiable function such that $\int {\left( {{{x(\cos x - \sin x)} \over {{e^x} + 1}} + {{g(x)\left( {{e^x} + 1 - x{e^x}} \right)} \over {{{({e^x} + 1)}^2}}}} \right)dx = {{x\,g(x)} \over {{e^x} + 1}} + c} $, for all x > 0, where c is an arbitrary constant. Then :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Morning Shift) PYQ

Solution

Qus : 39 JEE MAIN PYQ

Let $y = y(x)$ be the solution of the differential equation $(x + 1)y' - y = {e^{3x}}{(x + 1)^2}$, with $y(0) = {1 \over 3}$. Then, the point $x = - {4 \over 3}$ for the curve $y = y(x)$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Morning Shift) PYQ

Solution

Qus : 40 JEE MAIN PYQ

Let $y = y(x)$ be the solution of the differential equation $\sin x \dfrac{dy}{dx} + y \cos x = 4x,\ x \in (0,\pi).$ If $y\left(\dfrac{\pi}{2}\right) = 0$, then $y\left(\dfrac{\pi}{6}\right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

Qus : 41 JEE MAIN PYQ

If the solution curve $y = y(x)$ of the differential equation ${y^2}dx + ({x^2} - xy + {y^2})dy = 0$, which passes through the point (1, 1) and intersects the line $y = \sqrt 3 x$ at the point $(\alpha ,\sqrt 3 \alpha )$, then value of ${\log _e}(\sqrt 3 \alpha )$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Morning Shift) PYQ

Solution

Qus : 42 JEE MAIN PYQ

Let the solution curve $y = y(x)$ of the differential equation $\left(1 + e^{2x}\right)\left(\dfrac{dy}{dx} + y\right) = 1$ pass through the point $\left(0, \dfrac{\pi}{2}\right)$. Then, $\lim_{x \to \infty} e^x y(x)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Morning Shift) PYQ

Solution

Qus : 43 JEE MAIN PYQ

$ \text{Let the solution curve } y=y(x) \text{ of the differential equation } (1+e^{2x})!\left(\dfrac{dy}{dx}+y\right)=1 \text{ pass through the point } \left(0,\dfrac{\pi}{2}\right). $ $ \text{Then } \lim_{x\to\infty} e^{x}y(x) \text{ is equal to:} $

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Morning Shift) PYQ

Solution

Qus : 44 JEE MAIN PYQ

Let $y=y(x)$ solve $(2x\log_e x),\dfrac{dy}{dx}+2y=\dfrac{3}{x}\log_e x$ for $x>0$ with $y(e^{-1})=0$. Then $y(e)$ equals:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

Qus : 45 JEE MAIN PYQ

If $y = y(x)$ is the solution of the differential equation $2{x^2}{{dy} \over {dx}} - 2xy + 3{y^2} = 0$ such that $y(e) = {e \over 3}$, then y(1) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Evening Shift) PYQ

Solution

Qus : 46 JEE MAIN PYQ

Let $y=y(x)$ solve the differential equation $(1+x^{2})\dfrac{dy}{dx}+y=e^{\tan^{-1}x}$ with $y(1)=0$. Then $y(0)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

Qus : 47 JEE MAIN PYQ

The function $f$ is differentiable and satisfies $x^{2}f(x)-x=4\displaystyle\int_{0}^{x} t f(t),dt$, with $f(1)=\dfrac{2}{3}$. Then $18f(3)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Morning Shift) PYQ

Solution

Qus : 48 JEE MAIN PYQ

If a curve passes through the point $(1, -2)$ and has slope of the tangent at any point $(x, y)$ on it as $\dfrac{x^2 - 2y}{x}$, then the curve also passes through the point:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Evening Shift) PYQ

Solution

Qus : 49 JEE MAIN PYQ

Let $f(x) = \int\limits_0^x {{e^t}f(t)dt + {e^x}} $ be a differentiable function for all x$\in$R. Then f(x) equals :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 February Evening Shift) PYQ

Solution

Qus : 50 JEE MAIN PYQ

A function $y=f(x)$ satisfies $f(x)\sin 2x+\sin x-(1+\cos^2x)\,f'(x)=0$ with condition $f(0)=0$. Then $f\!\left(\dfrac{\pi}{2}\right)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Morning Shift) PYQ

Solution

Qus : 51 JEE MAIN PYQ

If the solution curve of the differential equation $ \dfrac{dy}{dx}=\dfrac{x+y-2}{x-y} $ passes through the points $(2,1)$ and $(k+1,2)$, $k>0$, then

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Evening Shift) PYQ

Solution

Qus : 52 JEE MAIN PYQ

Let $y=y(x)$ be the solution curve of the differential equation $ \frac{dy}{dx}+\left(\frac{2x^{2}+11x+13}{x^{3}+6x^{2}+11x+6}\right)y=\frac{x+3}{x+1},\quad x>-1, $ which passes through the point $(0,1)$. Then $y(1)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Evening Shift) PYQ

Solution

Qus : 53 JEE MAIN PYQ

Suppose the solution of the differential equation $ \displaystyle \frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\alpha y-(\beta\gamma-4\alpha)} $ represents a circle passing through the origin. Then the radius of this circle is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Evening Shift) PYQ

Solution

Qus : 54 JEE MAIN PYQ

Let $y = y(x)$ be a solution curve of the differential equation \[ (1 - x^2 y^2)\,dx = y\,dx + x\,dy. \] If the line $x = 1$ intersects the curve $y = y(x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y(x)$ at $y = \alpha$, then a value of $\alpha$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (11 April Morning Shift) PYQ

Solution

Qus : 55 JEE MAIN PYQ

Let $f(x)=x-1$ and $g(x)=e^x$ for $x\in\mathbb{R}$. If $\dfrac{dy}{dx}=e^{-2\sqrt{x}}g\big(f(f(x))\big)-\dfrac{y}{\sqrt{x}}, y(0)=0$, then $y(1)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (8 April Evening Shift) PYQ

Solution

Qus : 56 JEE MAIN PYQ

Let $y = y(x)$ be the solution of the differential equation $\dfrac{2 + \sin x}{y+1} \cdot \dfrac{dy}{dx} = -\cos x,\; y > 0,\; y(0) = 1.$ If $y(\pi) = a$ and $\dfrac{dy}{dx}$ at $x = \pi$ is $b$, then the ordered pair $(a,b)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2 September 2020 (Morning) PYQ

Solution

Qus : 57 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $x^{3}\,dy+(xy-1)\,dx=0,\quad x>0,$ with $y\!\left(\dfrac{1}{2}\right)=3-e.$ Then $y(1)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (24 January Morning Shift) PYQ

Solution

Qus : 58 JEE MAIN PYQ

If $y = y(x)$ is the solution of the differential equation $x{{dy} \over {dx}} + 2y = x\,{e^x}$, $y(1) = 0$ then the local maximum value of the function $z(x) = {x^2}y(x) - {e^x},\,x \in R$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 June Evening Shift) PYQ

Solution

Qus : 59 JEE MAIN PYQ

If y = y(x) is the solution of the differential equation, ${{dy} \over {dx}} + 2y\tan x = \sin x,y\left( {{\pi \over 3}} \right) = 0$, then the maximum value of the function y(x) over R is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Morning Shift) PYQ

Solution

Qus : 60 JEE MAIN PYQ

f the solution of the differential equation ${{dy} \over {dx}} + {e^x}\left( {{x^2} - 2} \right)y = \left( {{x^2} - 2x} \right)\left( {{x^2} - 2} \right){e^{2x}}$ satisfies $y(0) = 0$, then the value of y(2) is _______________.

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 June Evening Shift) PYQ

Solution

Qus : 61 JEE MAIN PYQ

If y = y(x) is the solution of the differential equation ${{dy} \over {dx}}$ + (tan x) y = sin x, $0 \le x \le {\pi \over 3}$, with y(0) = 0, then $y\left( {{\pi \over 4}} \right)$ equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Evening Shift) PYQ

Solution

Qus : 62 JEE MAIN PYQ

Let $f(x)$ be a positive function such that the area bounded by $y=f(x)$, $y=0$ from $x=0$ to $x=a>0$ is $e^{-a}+4a^{2}+a-1$. Then the differential equation whose general solution is $y=c_1f(x)+c_2$, where $c_1$ and $c_2$ are arbitrary constants, is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Solution

Qus : 63 JEE MAIN PYQ

If $(2+\sin x)\dfrac{dy}{dx}+(y+1)\cos x=0$ and $y(0)=1$, then $y\left(\dfrac{\pi}{2}\right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (Offline) PYQ

Solution

Qus : 64 JEE MAIN PYQ

Consider the integral $I = \int_0^{10} {{{[x]{e^{[x]}}} \over {{e^{x - 1}}}}dx} $, where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Evening Shift) PYQ

Solution

Qus : 65 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $(1+y^{2})e^{\tan x},dx+\cos^{2}x,(1+e^{2\tan x}),dy=0$, $y(0)=1$. Then $y!\left(\tfrac{\pi}{4}\right)$ is equal to

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Solution

Qus : 66 JEE MAIN PYQ

If a curve y = f(x), passing through the point(1, 2), is the solution of the differential equation,
2x²dy= (2xy + y²)dx, then $f\left( {{1 \over 2}} \right)$ is equal to

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2 September 2020 (Evening) PYQ

Solution

Qus : 67 JEE MAIN PYQ

Let A = {2, 3, 4, 5, ....., 30} and '$ \simeq $' be an equivalence relation on A $\times$ A, defined by (a, b) $ \simeq $ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4, 3) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Evening Shift) PYQ

Solution

Qus : 68 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $(x^2+1)^2\dfrac{dy}{dx}+2x(x^2+1)y=1$ such that $y(0)=0$. If $\sqrt{a,y(1)}=\dfrac{\pi}{32}$, then the value of $a$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Morning Shift) PYQ

Solution

Qus : 69 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $(x^{2}-3y^{2})\,dx+3xy\,dy=0$, with $y(1)=1$. Then $6y^{2}(e)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (24 January Evening Shift) PYQ

Solution

Qus : 70 JEE MAIN PYQ

If ${{dy} \over {dx}} + {{{2^{x - y}}({2^y} - 1)} \over {{2^x} - 1}} = 0$, x, y > 0, y(1) = 1, then y(2) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 June Morning Shift) PYQ

Solution

Qus : 71 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $\sec x,dy+{2(1-x)\tan x+x(2-x)},dx=0$ with $y(0)=2$. Then $y(2)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (30 January Morning Shift) PYQ

Solution

Qus : 72 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation \[ \frac{dy}{dx}+\frac{5}{x(x^5+1)}\,y=\frac{(x^5+1)^2}{x^7},\quad x>0. \] If $y(1)=2$, then $y(2)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (11 April Evening Shift) PYQ

Solution

Qus : 73 JEE MAIN PYQ

The solution curve of the differential equation, (1 + e^-x)(1 + y²)${{dy} \over {dx}}$ = y², which passes throughthe point (0, 1), is

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Morning) PYQ

Solution

Qus : 74 JEE MAIN PYQ

Let $y=y(x)$ be the solution curve of the differential equation $\sec y,\dfrac{dy}{dx}+2x\sin y=x^{3}\cos y$, with $y(1)=0$. Then $y(\sqrt{3})$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Evening Shift) PYQ

Solution

Qus : 75 JEE MAIN PYQ

Which of the following is true for y(x) that satisfies the differential equation ${{dy} \over {dx}}$ = xy $-$ 1 + x $-$ y; y(0) = 0 :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Morning Shift) PYQ

Solution

Qus : 76 JEE MAIN PYQ

Let $y=y(x),\ y>0$, be a solution curve of the differential equation \[ (1+x^2)\,dy = y(x-y)\,dx. \] If $y(0)=1$ and $y(2\sqrt{2})=\beta$, then

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (12 April Morning Shift) PYQ

Solution

Qus : 77 JEE MAIN PYQ

A function $y=f(x)$ satisfies $f(x) \sin 2 x+\sin x-\left(1+\cos ^2 x\right) f^{\prime}(x)=0$ with condition $f(0)=0$. Then, $f\left(\frac{\pi}{2}\right)$ is equal to

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Morning Shift) PYQ

Solution

Qus : 78 JEE MAIN PYQ

If the solution curve of the differential equation $(({\tan ^{ - 1}}y) - x)dy = (1 + {y^2})dx$ passes through the point (1, 0), then the abscissa of the point on the curve whose ordinate is tan(1), is

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 June Evening Shift) PYQ

Solution

Qus : 79 JEE MAIN PYQ

The curve satisfying the differential equation $y,dx-(x+3y^{2}),dy=0$ and passing through the point (1,1), also passes through the point :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (8 April Morning Shift) PYQ

Solution

Qus : 80 JEE MAIN PYQ

Let $y=y(x)$ be the solution curve of the differential equation $\displaystyle \frac{dy}{dx}=\frac{y}{x}\bigl(1+xy^{2}(1+\log_{e}x)\bigr),\ x>0,\ y(1)=3.$ Then $\displaystyle \frac{y^{2}(x)}{9}$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Morning Shift) PYQ

Solution

Qus : 81 JEE MAIN PYQ

The population P = P(t) at time 't' of a certain species follows the differential equation ${{dP} \over {dt}}$ = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (24 February Morning Shift) PYQ

Solution

Qus : 82 JEE MAIN PYQ

If the curve y = y(x) is the solution of the differential equation $2({x^2} + {x^{5/4}})dy - y(x + {x^{1/4}})dx = {2x^{9/4}}dx$, x > 0 which passes through the point $\left( {1,1 - {4 \over 3}{{\log }_e}2} \right)$, then the value of y(16) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Evening Shift) PYQ

Solution

Qus : 83 JEE MAIN PYQ

Let $y=y_1(x)$ and $y=y_2(x)$ be the solution curves of the differential equation $\dfrac{dy}{dx}=y+7$ with initial conditions $y_1(0)=0$ and $y_2(0)=1$ respectively. Then the curves $y=y_1(x)$ and $y=y_2(x)$ intersect at:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (13 April Morning Shift) PYQ

Solution

Qus : 84 JEE MAIN PYQ

If $\sin\left(\dfrac{y}{x}\right)=\log_e|x|+\dfrac{\alpha}{x}$ is a solution of the differential equation $x\cos\left(\dfrac{y}{x}\right)\dfrac{dy}{dx}=y\cos\left(\dfrac{y}{x}\right)+x$ with $y(1)=\dfrac{\pi}{3}$, then $\alpha^2$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Evening Shift) PYQ

Solution

Qus : 85 JEE MAIN PYQ

Let the solution curve $y = y(x)$ of the differential equation

$\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]x{{dy} \over {dx}} = x + \left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]y$

pass through the points (1, 0) and (2$\alpha$, $\alpha$), $\alpha$ > 0. Then $\alpha$ is equal to

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Morning Shift) PYQ

Solution

Qus : 86 JEE MAIN PYQ

Let y = y(x) be the solution of the differential equation $\cos x(3\sin x + \cos x + 3)dy = (1 + y\sin x(3\sin x + \cos x + 3))dx,0 \le x \le {\pi \over 2},y(0) = 0$. Then, $y\left( {{\pi \over 3}} \right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Evening Shift) PYQ

Solution

Qus : 87 JEE MAIN PYQ

Let y = y(x) be the solution of the differential equation $x(1 - {x^2}){{dy} \over {dx}} + (3{x^2}y - y - 4{x^3}) = 0$, $x > 1$, with $y(2) = - 2$. Then y(3) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Morning Shift) PYQ

Solution

Qus : 88 JEE MAIN PYQ

The solution of the differential equation $(x^{2}+y^{2}),dx-5xy,dy=0,; y(1)=0,$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Morning Shift) PYQ

Solution

Qus : 89 JEE MAIN PYQ

Let $y=y(t)$ be a solution of the differential equation $\dfrac{dy}{dt}+\alpha y=\gamma e^{-\beta t}$ where $\alpha>0$, $\beta>0$ and $\gamma>0$. Then $\displaystyle \lim_{t\to\infty} y(t)$

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Evening Shift) PYQ

Solution

Qus : 90 JEE MAIN PYQ

If $2x = y^{\tfrac{1}{5}} + y^{-\tfrac{1}{5}}$ and $(x^{2} - 1)\dfrac{d^{2}y}{dx^{2}} + \lambda x\dfrac{dy}{dx} + ky = 0$, then $\lambda + k$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (9 April Morning Shift) PYQ

Solution

Qus : 91 JEE MAIN PYQ

Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable $x$ to be the number of rotten apples in a draw of two apples, the variance of $x$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Morning Shift) PYQ

Solution

Qus : 92 JEE MAIN PYQ

The solution curve of the differential equation $2y\dfrac{dy}{dx}+3=5\dfrac{dy}{dx}$, passing through the point $(0,1)$, is a conic whose vertex lies on the line:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Morning Shift) PYQ

Solution

Qus : 93 JEE MAIN PYQ

Let x = x(y) be the solution of the differential equation $2y\,{e^{x/{y^2}}}dx + \left( {{y^2} - 4x{e^{x/{y^2}}}} \right)dy = 0$ such that x(1) = 0. Then, x(e) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Evening Shift) PYQ

Solution

Qus : 94 JEE MAIN PYQ

The solution of the differential equation $x\dfrac{dy}{dx} + 2y = x^2 \ (x \ne 0)$ with $y(1) = 1$, is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Morning Shift) PYQ

Solution

Qus : 95 JEE MAIN PYQ

Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 $\tan x(\cos x - y)$. If the curve passes through the point $\left( {{\pi \over 4},0} \right)$, then the value of $\int\limits_0^{\pi /2} {y\,dx} $ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Evening Shift) PYQ

Solution

Qus : 96 JEE MAIN PYQ

The solution curve of the differential equation $y\dfrac{dx}{dy}=x(\log_e x-\log_e y+1),\ x>0,\ y>0,$ passing through the point $(e,1)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Morning Shift) PYQ

Solution

Qus : 97 JEE MAIN PYQ

Let $\displaystyle \int_{0}^{x}\sqrt{1-\big(y'(t)\big)^{2}},dt=\int_{0}^{x}y(t),dt,\ 0\le x\le 3,\ y\ge0,\ y(0)=0$. Then at $x=2$, $,y''+y+1$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Evening Shift) PYQ

Solution

Qus : 98 JEE MAIN PYQ

If $\cos x{{dy} \over {dx}} - y\sin x = 6x$, (0 < x < ${\pi \over 2}$)
and $y\left( {{\pi \over 3}} \right)$ = 0 then $y\left( {{\pi \over 6}} \right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Evening Shift) PYQ

Solution

Qus : 99 JEE MAIN PYQ

If a curve $y = f(x)$ passes through the point $(1,-1)$ and satisfies the differential equation $ y(1+xy),dx = x,dy $, then $ f\left(-\dfrac{1}{2}\right) $ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

Qus : 100 JEE MAIN PYQ

Let $x=x(y)$ be the solution of the differential equation $2(y+2)\log_e(y+2)\,dx+\big(x+4-2\log_e(y+2)\big)\,dy=0,\quad y>-1$ with $x\big(e^{4}-2\big)=1$. Then $x\big(e^{9}-2\big)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (15 April Morning Shift) PYQ

Solution

Qus : 101 JEE MAIN PYQ

If ${{dy} \over {dx}} = {{{2^{x + y}} - {2^x}} \over {{2^y}}}$, y(0) = 1, then y(1) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Morning Shift) PYQ

Solution

Qus : 102 JEE MAIN PYQ

Let the solution curve of the differential equation

$x{{dy} \over {dx}} - y = \sqrt {{y^2} + 16{x^2}} $, $y(1) = 3$ be $y = y(x)$. Then y(2) is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Morning Shift) PYQ

Solution

Qus : 103 JEE MAIN PYQ

If $\log_{e} y = 3\sin^{-1}x$, then $,(1-x^{2})y''-xy',$ at $x=\dfrac{1}{2}$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Evening Shift) PYQ

Solution

Qus : 104 JEE MAIN PYQ

Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function. If $10 \int_1^1 f(\mathrm{t}) \mathrm{dt}=5 x f(x)-x^5-9$ for all $x \geqslant 1$, then the value of $f(3)$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Evening Shift) PYQ

Solution

Qus : 105 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $$x\log_e x \,\frac{dy}{dx}+y=x^2\log_e x,\quad (x>1).$$ If $y(2)=2$, then $y(e)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (29 January Evening Shift) PYQ

Solution

Qus : 106 JEE MAIN PYQ

If x³dy + xy dx = x²dy + 2y dx; y(2) = e and x > 1, then y(4) is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Evening) PYQ

Solution

Qus : 107 JEE MAIN PYQ

If ${{dy} \over {dx}} = {{{2^x}y + {2^y}{{.2}^x}} \over {{2^x} + {2^{x + y}}{{\log }_e}2}}$, y(0) = 0, then for y = 1, the value of x lies in the interval :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Evening Shift) PYQ

Solution

Qus : 108 JEE MAIN PYQ

If $y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\phi '\left( {{{{y^2}} \over {{x^2}}}} \right)}}} \right]$, x > 0, $\phi$ > 0, and y(1) = $-$1, then $\phi \left( {{{{y^2}} \over 4}} \right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Evening Shift) PYQ

Solution

Qus : 109 JEE MAIN PYQ

The temperature $T(t)$ of a body at time $t=0$ is $160^\circ\!F$ and it decreases continuously as per the differential equation $\dfrac{dT}{dt}=-K(T-80)$, where $K$ is a positive constant. If $T(15)=120^\circ\!F$, then $T(45)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Evening Shift) PYQ

Solution

Qus : 110 JEE MAIN PYQ

Let y = y(x) be the solution of the differential equation $x\tan \left( {{y \over x}} \right)dy = \left( {y\tan \left( {{y \over x}} \right) - x} \right)dx$, $ - 1 \le x \le 1$, $y\left( {{1 \over 2}} \right) = {\pi \over 6}$. Then the area of the region bounded by the curves x = 0, $x = {1 \over {\sqrt 2 }}$ and y = y(x) in the upper half plane is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (20 July Morning Shift) PYQ

Solution

Qus : 111 JEE MAIN PYQ

If $y=y(x)$ is the solution of the differential equation $x\dfrac{dy}{dx}+2y=x^{2}$, satisfying $y(1)=1$, then $y\!\left(\dfrac{1}{2}\right)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Morning Shift) PYQ

Solution

Qus : 112 JEE MAIN PYQ

Let y = y(x) be the solution of the differential equation ${e^x}\sqrt {1 - {y^2}} dx + \left( {{y \over x}} \right)dy = 0$, y(1) = $-$1. Then the value of (y(3))² is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (20 July Morning Shift) PYQ

Solution

Qus : 113 JEE MAIN PYQ

Let the solution curve $y=y(x)$ of the differential equation \[ \frac{dy}{dx}=\frac{3x^5\tan^{-1}(x^3)}{(1+x^6)^{3/2}}\, y = 2x \exp\left\{\frac{x^3-\tan^{-1}(x^3)}{\sqrt{1+x^6}}\right\} \] pass through the origin. Then $y(1)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (30 January Morning Shift) PYQ

Solution

Qus : 114 JEE MAIN PYQ

If $y=y(x)$ is the solution of the differential equation $\dfrac{dy}{dx}=(\tan x-y)\sec^{2}x,\ x\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$, such that $y(0)=0$, then $y!\left(-\dfrac{\pi}{4}\right)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Morning Shift) PYQ

Solution

Qus : 115 JEE MAIN PYQ

If y = y(x) is the solution of the differential equation $\left( {1 + {e^{2x}}} \right){{dy} \over {dx}} + 2\left( {1 + {y^2}} \right){e^x} = 0$ and y (0) = 0, then $6\left( {y'(0) + {{\left( {y\left( {{{\log }_e}\sqrt 3 } \right)} \right)}^2}} \right)$ is equal to

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Evening Shift) PYQ

Solution

Qus : 116 JEE MAIN PYQ

If y = y(x) is the solution curve of the differential equation ${x^2}dy + \left( {y - {1 \over x}} \right)dx = 0$ ; x > 0 and y(1) = 1, then $y\left( {{1 \over 2}} \right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (1 September Evening Shift) PYQ

Solution

Qus : 117 JEE MAIN PYQ

Let y = y(x) be the solution of the differential equation,
xy'- y = x²(xcosx + sinx), x > 0. if y ($\pi $) = $\pi $ then
$y''\left( {{\pi \over 2}} \right) + y\left( {{\pi \over 2}} \right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 4 September 2020 (Morning) PYQ

Solution

Qus : 118 JEE MAIN PYQ

Let $x=x(y)$ be the solution of the differential equation $y^2\,dx+\left(x-\dfrac{1}{y}\right)dy=0$. If $x(1)=1$, then $x\!\left(\dfrac{1}{2}\right)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

Qus : 119 JEE MAIN PYQ

Let $g$ be a differentiable function such that $\displaystyle \int_0^x g(t),dt = x - \int_0^x t g(t),dt,; x \ge 0$ and let $y = y(x)$ satisfy the differential equation $\dfrac{dy}{dx} - y \tan x = 2(x + 1)\sec x, g(x),; x \in \left[0, \dfrac{\pi}{2}\right).$ If $y(0) = 0$, then $y\left(\dfrac{\pi}{3}\right)$ is equal to

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Morning Shift) PYQ

Solution

Qus : 120 JEE MAIN PYQ

Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} = 2x(x+y)^3 - x(x+y) - 1, \quad y(0) = 1.$ Then, $\left(\dfrac{1}{\sqrt{2}} + y\!\left(\dfrac{1}{\sqrt{2}}\right)\right)^2$ equals :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Morning Shift) PYQ

Solution

Qus : 121 JEE MAIN PYQ

Let y = y(x) be the solution of the differential equation $\cos e{c^2}xdy + 2dx = (1 + y\cos 2x)\cos e{c^2}xdx$, with $y\left( {{\pi \over 4}} \right) = 0$. Then, the value of ${(y(0) + 1)^2}$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (22 July Evening Shift) PYQ

Solution

Qus : 122 JEE MAIN PYQ

The solution of the differential equation $\dfrac{dy}{dx}=-\left(\dfrac{x^{2}+3y^{2}}{3x^{2}+y^{2}}\right),\ y(1)=0$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (30 January Evening Shift) PYQ

Solution

Qus : 123 JEE MAIN PYQ

For $x \in \mathbb{R},\ x \ne 0$, if $y(x)$ is a differentiable function such that $x \int_{1}^{x} y(t)\,dt = (x+1) \int_{1}^{x} t\,y(t)\,dt,$ then $y(x)$ equals: (where $C$ is a constant.)

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

Qus : 124 JEE MAIN PYQ

The general solution of the differential equation $(x - y^2),dx + y(5x + y^2),dy = 0$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 July Morning Shift) PYQ

Solution

Qus : 125 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $\dfrac{dy}{dx}+y\tan x=2x+x^{2}\tan x,\ x\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$, such that $y(0)=1$. Then:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Evening Shift) PYQ

Solution

Qus : 126 JEE MAIN PYQ

If $x=f(y)$ is the solution of the differential equation $(1+y^{2})+\big(x-2e^{\tan^{-1}y}\big)\dfrac{dy}{dx}=0,\ y\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$ with $f(0)=1$, then $f\!\left(\dfrac{1}{\sqrt{3}}\right)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Evening Shift) PYQ

Solution

Qus : 127 JEE MAIN PYQ

Let $\alpha$ be a non-zero real number. Suppose $f:\mathbf{R}\to\mathbf{R}$ is a differentiable function such that $f(0)=2$ and $\displaystyle \lim_{x\to -\infty} f(x)=1$. If $f'(x)=\alpha f(x)+3$, for all $x\in\mathbf{R}$, then $f(-\log_{e}2)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Evening Shift) PYQ

Solution

Qus : 128 JEE MAIN PYQ

If y = y(x) is the solution of the differential equation ${{5 + {e^x}} \over {2 + y}}.{{dy} \over {dx}} + {e^x} = 0$ satisfyingy(0) = 1, then a value of y(log_e13) is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Morning) PYQ

Solution

Qus : 129 JEE MAIN PYQ

Let $f:[0,1]\to\mathbb{R}$ be such that $f(xy)=f(x)\,f(y)$ for all $x,y\in[0,1]$, and $f(0)\ne 0$. If $y=v(x)$ satisfies the differential equation $\dfrac{dy}{dx}=f(x)$ with $y(0)=1$, then $y\!\left(\dfrac{1}{4}\right)+y\!\left(\dfrac{3}{4}\right)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Evening Shift) PYQ

Solution

Qus : 130 JEE MAIN PYQ

Let y = y(x) be the solution of the differential equation ${{dy} \over {dx}} = 1 + x{e^{y - x}}, - \sqrt 2 < x < \sqrt 2 ,y(0) = 0$ then, the minimum value of $y(x),x \in \left( { - \sqrt 2 ,\sqrt 2 } \right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Morning Shift) PYQ

Solution

Qus : 131 JEE MAIN PYQ

Let y = y(x) be the solution of the differentialequationcosx${{dy} \over {dx}}$ + 2ysinx = sin2x, x $ \in $ $\left( {0,{\pi \over 2}} \right)$.Ify$\left( {{\pi \over 3}} \right)$ = 0, then y$\left( {{\pi \over 4}} \right)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Evening) PYQ

Solution

Qus : 132 JEE MAIN PYQ

Let $y(x)$ be the solution of the differential equation $(x\log x)\dfrac{dy}{dx}+y=2x\log x,\;(x\ge 1).$ Then $y(e)$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2015 (Offline) PYQ

Solution

Qus : 133 JEE MAIN PYQ

Let a curve $y=f(x)$ pass through the points $(0,5)$ and $(\log_e 2,\,k)$. If the curve satisfies the differential equation $2(3+y)e^{2x}\,dx-(7+e^{2x})\,dy=0$, then $k$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Morning Shift) PYQ

Solution

Qus : 134 JEE MAIN PYQ

Let $y=y(x)$ be the solution of the differential equation $(3y^{2}-5x^{2})\,y\,dx+2x\,(x^{2}-y^{2})\,dy=0$ such that $y(1)=1$. Then $\left|(y(2))^{3}-12y(2)\right|$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (31 January Evening Shift) PYQ

Solution

Qus : 135 JEE MAIN PYQ

Let $f:[0,\infty)\to\mathbb{R}$ be a differentiable function such that $f(x)=1-2x+\displaystyle\int_{0}^{x}e^{,x-t}f(t),dt$ for all $x\in[0,\infty)$. Then the area of the region bounded by $y=f(x)$ and the coordinate axes is

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Morning Shift) PYQ

Solution

Qus : 136 JEE MAIN PYQ

If the solution $y = y(x)$ of the differential equation $(x^{4}+2x^{3}+3x^{2}+2x+2)\,dy-(2x^{2}+2x+3)\,dx=0$ satisfies $y(-1)=-\dfrac{\pi}{4}$, then $y(0)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Morning Shift) PYQ

Solution

Qus : 137 JEE MAIN PYQ

If $\dfrac{dy}{dx}+\dfrac{3}{\cos^2 x}\,y=\dfrac{1}{\cos^2 x},\ x\in\left(-\dfrac{\pi}{3},\dfrac{\pi}{3}\right)$ and $y\!\left(\dfrac{\pi}{4}\right)=\dfrac{4}{3}$, then $y\!\left(-\dfrac{\pi}{4}\right)$ equals:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Morning Shift) PYQ

Solution

Qus : 138 JEE MAIN PYQ

Let $f(x)= \begin{cases} x^{3}-x^{2}+10x-7, & x\le 1,\\ -2x+\log_{2}(b^{2}-4), & x>1. \end{cases}$ Then the set of all values of $b$ for which $f(x)$ has maximum value at $x=1$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Morning Shift) PYQ

Solution

Qus : 139 JEE MAIN PYQ

The general solution of the differential equation$\sqrt {1 + {x^2} + {y^2} + {x^2}{y^2}} $ + xy${{dy} \over {dx}}$ = 0 is : (where C is a constant of integration)

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 6 September 2020 (Morning) PYQ

Solution

Qus : 140 JEE MAIN PYQ

Let $f$ be a differentiable function such that $f'(x) = 7 - \dfrac{3}{4}\,\dfrac{f(x)}{x}$, for $x>0$, and $f(1)\neq 4$. Then $\displaystyle \lim_{x\to 0} x\,f\!\left(\dfrac{1}{x}\right)$ equals:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Evening Shift) PYQ

Solution

Qus : 141 JEE MAIN PYQ

Consider the differential equation $y^{2},dx+\left(x-\dfrac{1}{y}\right)dy=0.$ If $y=1$ when $x=1$, then the value of $x$ for which $y=2$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Morning Shift) PYQ

Solution

JEE MAIN

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

JEE MAIN

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

Ask Your Question or Put Your Review.

Please provide more information - at least 10 characters

Feedback

Info.

Information

Aspire's Library

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Differential Equation PYQ

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution