JEE Maths PYQ Practice, chapter-wise

JEE Main 2026 (Online) 5th April Evening ShiftQuestion 16

Let $\left(2^{1-a}+2^{1+a}\right)$, $f(a)$, $\left(3^{a}+3^{-a}\right)$ be in A.P. and $\alpha$ be the minimum value of $f(a)$. Then the value of the integral $\int_{\log_e(\alpha-1)}^{\log_e(\alpha)}\frac{dx}{\left(e^{2x}-e^{-2x}\right)}$ is :

Definite Integration

$\frac{1}{2}\log_e\left(\frac{4}{3}\right)$$\frac{1}{4}\log_e\left(\frac{4}{3}\right)$$\frac{1}{2}\log_e\left(\frac{8}{5}\right)$$\frac{1}{4}\log_e\left(\frac{8}{5}\right)$

JEE Main 2021 (Online) 16th March Evening ShiftQuestion 17

Consider the integral $I=\int_{0}^{10}\frac{[x]e^{[x]}}{e^{x-1}}dx$, where $[x]$ denotes the greatest integer less than or equal to $x$. Then the value of $I$ is equal to :

Definite Integration

$45(e+1)$$9(e+1)$$45(e-1)$$9(e-1)$

JEE Main 2021 (Online) 26th August Evening ShiftQuestion 18

The value of $\int_{-\pi/2}^{\pi/2}\left(\frac{1+\sin^{2}x}{1+\pi^{\sin x}}\right)dx$ is :

Definite Integration

$\frac{3\pi}{2}$$\frac{3\pi}{4}$$\frac{\pi}{2}$$\frac{5\pi}{4}$

JEE Main 2021 (Online) 25th February Evening ShiftQuestion 19

If $I_n=\int_{\pi/4}^{\pi/2}\cot^{n}x\,dx$, then :

Definite Integration

$\frac{1}{I_2+I_4},\frac{1}{I_3+I_5},\frac{1}{I_4+I_6}$ are in A.P.$I_2+I_4,\ I_3+I_5,\ I_4+I_6$ are in A.P.$\frac{1}{I_2+I_4},\frac{1}{I_3+I_5},\frac{1}{I_4+I_6}$ are in G.P.$I_2+I_4,\ (I_3+I_5)^{2},\ I_4+I_6$ are in G.P.

JEE Main 2021 (Online) 4th August Morning ShiftQuestion 20

If $I_1=\int_{0}^{\pi}xe^{\operatorname{cosec}x}dx$ and $I_2=\int_{0}^{\pi}e^{\operatorname{cosec}x}dx$, then the ratio $I_1:I_2$ is equal to

Definite Integration

$\pi:2$$2:\pi$$\pi:3$$3:\pi$