JEE Maths PYQ Practice, chapter-wise

JEE Main 2026 (Online) 8th April Evening ShiftQuestion 1

For the function $f(x)=e^{\sin|x|}-|x|$, $x\in\mathbf{R}$, consider the following statements : Statement I : $f$ is differentiable for all $x\in\mathbf{R}$. Statement II : $f$ is increasing in $\left(-\pi,-\frac{\pi}{2}\right)$. In the light of the above statements, choose the correct answer from the options given below :

Differentiation and its Application

Both Statement I and Statement II are trueBoth Statement I and Statement II are falseStatement I is true but Statement II is falseStatement I is false but Statement II is true

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

Let $f:S\to S$ where $S=(0,\infty)$ be a twice differentiable function such that $f(x+1)=xf(x)$. If $g:S\to\mathbf{R}$ be defined as $g(x)=\log_ef(x)$, then the value of $|g''(5)-g''(1)|$ is equal to :

Differentiation and its Application

$\frac{205}{144}$$\frac{197}{144}$$\frac{187}{144}$$1$

JEE Main 2021 (Online) 27th August Morning ShiftQuestion 3

A wire of length $20$ m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the hexagon is minimum, is :

Differentiation and its Application

$\frac{5}{2+\sqrt{3}}$$\frac{5}{3+\sqrt{3}}$$\frac{10}{3+2\sqrt{3}}$$\frac{10}{2+3\sqrt{3}}$

JEE Main 2021 (Online) 4th August Morning ShiftQuestion 4

The equation of the tangent to the curve $y=\int_{x^{2}}^{x^{3}}\frac{dt}{\sqrt{1+t^{2}}}$ at the point whose abscissa is $1$, is

Differentiation and its Application

$x+\sqrt{2}y-1=0$$\sqrt{3}x-y-\sqrt{3}=0$$x-y-1=0$$x-\sqrt{2}y-1=0$

JEE Main 2021 (Online) 24th February Morning ShiftQuestion 5

If the tangent to the curve $y=x^{3}$ at the point $P(t,t^{3})$ meets the curve again at $Q$, then the ordinate of the point which divides $PQ$ internally in the ratio $1:2$ is :

Differentiation and its Application

$0$$2t^{3}$$-t^{3}$$-2t^{3}$