JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 26th February Evening ShiftQuestion 1

Let $f(x)=\int_{0}^{x}e^{t}f(t)\,dt+e^{x}$ be a differentiable function for all $x\in\mathbf{R}$. Then $f(x)$ equals :

Differential Equation

$2e^{(e^{x}-1)}-1$$e^{(e^{x}-1)}$$2e^{e^{x}}-1$$e^{e^{x}}-1$

JEE Main 2021 (Online) 16th March Evening ShiftQuestion 2

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

Differential Equation

$\left(\frac{1}{2\sqrt{2}}\right)\log_e2$$\frac{1}{2}\log_e2$$\log_e2$$\frac{1}{4}\log_e2$

JEE Main 2021 (Online) 26th February Evening ShiftQuestion 3

Let slope of the tangent line to a curve at any point $P(x,y)$ be given by $\frac{xy^{2}+y}{x}$. If the curve intersects the line $x+2y=4$ at $x=-2$, then the value of $y$, for which the point $(3,y)$ lies on the curve, is :

Differential Equation

$-\frac{4}{3}$$-\frac{18}{19}$$\frac{18}{35}$$-\frac{18}{11}$

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 4

If a curve passes through the origin and the slope of the tangent to it at any point $(x,y)$ is $\frac{x^{2}-4x+y+8}{x-2}$, then this curve also passes through the point :

Differential Equation

$(4,5)$$(5,5)$$(5,4)$$(4,4)$

JEE Main 2026 (Online) 8th April Evening ShiftQuestion 5

Let $y=y(x)$ be the solution of the differential equation $x\sqrt{1-x^{2}}\,dy+\left(y\sqrt{1-x^{2}}-x\cos^{-1}x\right)dx=0$, $x\in(0,1)$, $\lim_{x\to1^{-}}y(x)=1$. Then $y\left(\frac{1}{2}\right)$ equals :

Differential Equation

$3-\frac{\pi}{\sqrt{3}}$$4-\sqrt{3}\,\pi$$4-\frac{2\pi}{\sqrt{3}}$$3-\frac{\pi}{2\sqrt{3}}$