JEE Maths PYQ Practice, chapter-wise

JEE Main 2026 (Online) 5th April Evening ShiftQuestion 6

Let $f:[1,\infty)\to\mathbf{R}$ be a differentiable function defined as $f(x)=\int_{1}^{x}f(t)\,dt+(1-x)(\log_e x-1)+e$. Then the value of $f(f(1))$ is :

Differential Equation

$(1+e^{e})$$(1+e)$$(1+e+e^{e})$$1+2e$

JEE Main 2021 (Online) 24th February Evening ShiftQuestion 7

If a curve $y=f(x)$ passes through the point $(1,2)$ and satisfies $x\frac{dy}{dx}+y=bx^{4}$, then for what value of $b$, $\int_{1}^{2}f(x)dx=\frac{62}{5}$ ?

Differential Equation

$10$$\frac{31}{5}$$5$$\frac{62}{5}$

JEE Main 2021 (Online) 17th March Evening ShiftQuestion 8

If the curve $y=y(x)$ is the solution of the differential equation $2\left(x^{2}+x^{5/4}\right)dy-y\left(x+x^{1/4}\right)dx=2x^{9/4}dx$, $x>0$ which passes through the point $\left(1,1-\frac{4}{3}\log_e2\right)$, then the value of $y(16)$ is equal to :

Differential Equation

$4\left(\frac{31}{3}-\frac{8}{3}\log_e3\right)$$\frac{31}{3}-\frac{8}{3}\log_e3$$\frac{31}{3}+\frac{8}{3}\log_e3$$4\left(\frac{31}{3}+\frac{8}{3}\log_e3\right)$

JEE Main 2021 (Online) 17th March Evening ShiftQuestion 9

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

Differential Equation

$2\log_e\left(\frac{3\sqrt{3}-8}{4}\right)$$2\log_e\left(\frac{\sqrt{3}+7}{2}\right)$$2\log_e\left(\frac{2\sqrt{3}+9}{6}\right)$$2\log_e\left(\frac{2\sqrt{3}+10}{11}\right)$

JEE Main 2021 (Online) 16th March Evening ShiftQuestion 10

Let $C_1$ be the curve obtained by the solution of differential equation $2xy\frac{dy}{dx}=y^{2}-x^{2}$, $x>0$. Let the curve $C_2$ be the solution of $\frac{2xy}{x^{2}-y^{2}}=\frac{dy}{dx}$. If both the curves pass through $(1,1)$, then the area enclosed by the curves $C_1$ and $C_2$ is equal to :

Differential Equation

$\frac{\pi}{4}+1$$\pi-1$$\frac{\pi}{2}-1$$\pi+1$