JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 17th March Evening ShiftQuestion 6

Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=e^{-x}\sin x$. If $F:[0,1]\to\mathbf{R}$ is a differentiable function such that $F(x)=\int_{0}^{x}f(t)\,dt$, then the value of $\int_{0}^{1}\left(F'(x)+f(x)\right)e^{x}dx$ lies in the interval

Definite Integration

$\left[\frac{330}{360},\frac{331}{360}\right]$$\left[\frac{327}{360},\frac{329}{360}\right]$$\left[\frac{331}{360},\frac{334}{360}\right]$$\left[\frac{335}{360},\frac{336}{360}\right]$

JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 7

The value of $\int_{0}^{20\pi}(\sin^{4}x+\cos^{4}x)\,dx$ is equal to :

Definite Integration

$\frac{15\pi}{2}$$25\pi$$15\pi$$\frac{25\pi}{2}$

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

The integral $\int_{0}^{1}\cot^{-1}\left(1+x+x^{2}\right)dx$ is equal to:

Definite Integration

$2\tan^{-1}2+\frac{1}{2}\log_e\left(\frac{5}{4}\right)+\frac{\pi}{2}$$2\tan^{-1}2+\frac{1}{2}\log_e\left(\frac{5}{4}\right)-\frac{\pi}{2}$$2\tan^{-1}2-\frac{1}{2}\log_e\left(\frac{5}{4}\right)+\frac{\pi}{2}$$2\tan^{-1}2-\frac{1}{2}\log_e\left(\frac{5}{4}\right)-\frac{\pi}{2}$

JEE Main 2021 (Online) 26th February Morning ShiftQuestion 9

The value of $\int_{-\pi/2}^{\pi/2}\frac{\cos^{2}x}{1+3^{x}}dx$ is :

Definite Integration

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

JEE Main 2021 (Online) 26th February Morning ShiftQuestion 10

The value of $\sum_{n=1}^{100}\int_{n-1}^{n}e^{x-[x]}dx$, where $[x]$ is the greatest integer $\le x$, is :

Definite Integration

$100(1-e)$$100(1+e)$$100e$$100(e-1)$