JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 3rd August Morning ShiftQuestion 1

$\int_{1}^{2}\left([x^{2}-1]+[x^{2}+1]\right)dx$ is equal to ($[t]$ denotes the greatest integer $\le t$)

Definite Integration

$\frac{14}{3}$$5-\sqrt{2}-\sqrt{3}$$1$$10-2\sqrt{2}-2\sqrt{3}$

JEE Main 2021 (Online) 24th February Evening ShiftQuestion 2

The value of the integral $\int_{1}^{3}\left[x^{2}-2x-2\right]dx$, where $[x]$ denotes the greatest integer less than or equal to $x$, is :

Definite Integration

$-5$$-4$$-\sqrt{2}-\sqrt{3}-1$$-\sqrt{2}-\sqrt{3}+1$

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 3

The value of $\int_{-1}^{1}x^{2}e^{[x^{3}]}dx$, where $[t]$ denotes the greatest integer $\le t$, is :

Definite Integration

$\frac{e+1}{3}$$\frac{1}{3e}$$\frac{e-1}{3e}$$\frac{e+1}{3e}$

JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 4

If $\int_{0}^{100\pi}\frac{\sin^{2}x}{e^{\left(\frac{x}{\pi}-\left[\frac{x}{\pi}\right]\right)}}dx=\frac{\alpha\pi^{3}}{1+4\pi^{2}}$, $\alpha\in\mathbf{R}$, where $[x]$ is the greatest integer less than or equal to $x$, then the value of $\alpha$ is :

Definite Integration

$150\left(e^{-1}-1\right)$$50(e-1)$$100(1-e)$$200\left(1-e^{-1}\right)$

JEE Main 2021 (Online) 18th March Evening ShiftQuestion 5

Let $g(x)=\int_{0}^{x}f(t)\,dt$, where $f$ is continuous function in $[0,3]$ such that $\frac{1}{3}\le f(t)\le1$ for all $t\in[0,1]$ and $0\le f(t)\le\frac{1}{2}$ for all $t\in(1,3]$. The largest possible interval in which $g(3)$ lies is :

Definite Integration

$\left[\frac{1}{3},2\right]$$\left[-1,-\frac{1}{2}\right]$$[1,3]$$\left[-\frac{3}{2},-1\right]$