JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 24th February Morning ShiftQuestion 1

If $f:\mathbf{R}\to\mathbf{R}$ is a function defined by $f(x)=[x-1]\cos\left(\frac{2x-1}{2}\right)\pi$, where $[\cdot]$ denotes the greatest integer function, then $f$ is :

Limits & Continuity

discontinuous only at $x=1$discontinuous at all integral values of $x$ except at $x=1$continuous only at $x=1$continuous for every real $x$

JEE Main 2026 (Online) 6th April Evening ShiftQuestion 2

Let $\lim_{x\to2}\frac{(\tan(x-2))\left(rx^{2}+(p-2)x-2p\right)}{(x-2)^{2}}=5$ for some $r,p\in\mathbf{R}$. If the set of all possible values of $q$, such that the roots of the equation $rx^{2}-px+q=0$ lie in $(0,2)$, be the interval $(\alpha,\beta]$, then $4(\alpha+\beta)$ equals :

Limits & Continuity

$11$$13$$17$$21$

JEE Main 2026 (Online) 5th April Evening ShiftQuestion 3

Let $f(x)=\lim_{y\to0}\frac{(1-\cos(xy))\tan(xy)}{y^{3}}$. Then the number of solutions of the equation $f(x)=\sin x$, $x\in\mathbf{R}$ is :

Limits & Continuity

$0$$2$$3$$1$

JEE Main 2026 (Online) 8th April Evening ShiftQuestion 4

Let $f(x)=\begin{cases}\frac{1}{3}, & x\le\frac{\pi}{2}\\ \frac{b(1-\sin x)}{(\pi-2x)^{2}}, & x>\frac{\pi}{2}\end{cases}$. If $f$ is continuous at $x=\pi/2$, then the value of $\int_{0}^{3b-6}\left|x^{2}+2x-3\right|dx$ is :

Limits & Continuity

$5$$2$$3$$4$

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

$\lim_{x\to0}\frac{\int_{0}^{x^{2}}\left(\sin\sqrt{t}\right)dt}{x^{3}}$ is equal to :

Limits & Continuity

$\frac{2}{3}$$\frac{3}{2}$$\frac{1}{15}$$0$