JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 31st August Evening ShiftQuestion 26

If $[x]$ is the greatest integer $\le x$, then $\pi^{2}\int_{0}^{2}\left(\sin\frac{\pi x}{2}\right)(x-[x])^{[x]}dx$ is equal to :

Definite Integration

$2(\pi+1)$$2(\pi-1)$$4(\pi+1)$$4(\pi-1)$

JEE Main 2022 (Online) 24th June Evening ShiftQuestion 27

The value of the integral $\int_{-\pi/2}^{\pi/2}\frac{dx}{(1+e^{x})(\sin^{6}x+\cos^{6}x)}$ is equal to

Definite Integration

$2\pi$$0$$\pi$$\frac{\pi}{2}$

JEE Main 2022 (Online) 25th June Morning ShiftQuestion 28

The value of $\int_{0}^{\pi}\frac{e^{\cos x}\sin x}{\left(1+\cos^{2}x\right)\left(e^{\cos x}+e^{-\cos x}\right)}dx$ is equal to :

Definite Integration

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

JEE Main 2023 (Online) 11th April Morning ShiftQuestion 29

The value of the integral $\int_{-\log_e2}^{\log_e2}e^{x}\left(\log_e\left(e^{x}+\sqrt{1+e^{2x}}\right)\right)dx$ is equal to

Definite Integration

$\log_e\left(\frac{\left(2+\sqrt{5}\right)^{2}}{\sqrt{1+\sqrt{5}}}\right)-\frac{\sqrt{5}}{2}$$\log_e\left(\frac{\sqrt{2}\left(2+\sqrt{5}\right)^{2}}{\sqrt{1+\sqrt{5}}}\right)-\frac{\sqrt{5}}{2}$$\log_e\left(\frac{2\left(2+\sqrt{5}\right)}{\sqrt{1+\sqrt{5}}}\right)-\frac{\sqrt{5}}{2}$$\log_e\left(\frac{\sqrt{2}\left(3-\sqrt{5}\right)^{2}}{\sqrt{1+\sqrt{5}}}\right)+\frac{\sqrt{5}}{2}$

JEE Main 2025 (Online) 2nd April Evening ShiftQuestion 30

$4\int_{0}^{1}\left(\frac{1}{\sqrt{3+x^{2}}+\sqrt{1+x^{2}}}\right)dx-3\log_e(\sqrt{3})$ is equal to :

Definite Integration

$2+\sqrt{2}-\log_e\left(1+\sqrt{2}\right)$$2-\sqrt{2}-\log_e\left(1+\sqrt{2}\right)$$2+\sqrt{2}+\log_e\left(1+\sqrt{2}\right)$$2-\sqrt{2}+\log_e\left(1+\sqrt{2}\right)$