JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 26th August Morning ShiftQuestion 1

Let $f(x)=\cos\left(2\tan^{-1}\sin\left(\cot^{-1}\sqrt{\frac{1-x}{x}}\right)\right)$, $0<x<1$. Then :

Inverse Trigonometric Functions

$(1-x)^{2}f'(x)-2\left(f(x)\right)^{2}=0$$(1+x)^{2}f'(x)+2\left(f(x)\right)^{2}=0$$(1-x)^{2}f'(x)+2\left(f(x)\right)^{2}=0$$(1+x)^{2}f'(x)-2\left(f(x)\right)^{2}=0$

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

A possible value of $\tan\left(\frac{1}{4}\sin^{-1}\frac{\sqrt{63}}{8}\right)$ is :

Inverse Trigonometric Functions

$\frac{1}{\sqrt{7}}$$\frac{1}{2\sqrt{2}}$$\sqrt{7}-1$$2\sqrt{2}-1$

JEE Main 2021 (Online) 17th March Evening ShiftQuestion 3

The number of solutions of the equation $\sin^{-1}\left[x^{2}+\frac{1}{3}\right]+\cos^{-1}\left[x^{2}-\frac{2}{3}\right]=x^{2}$, for $x\in[-1,1]$, and $[x]$ denotes the greatest integer less than or equal to $x$, is :

Inverse Trigonometric Functions

$0$$2$$4$Infinite

JEE Main 2026 (Online) 6th April Evening ShiftQuestion 4

If $\sin\left(\tan^{-1}(x\sqrt{2})\right)=\cot\left(\sin^{-1}\sqrt{1-x^{2}}\right)$, $x\in(0,1)$, then the value of $x$ is :

Inverse Trigonometric Functions

$\frac{1}{2}$$\frac{1}{3}$$\frac{2}{3}$$\frac{5}{8}$

JEE Main 2021 (Online) 17th March Morning ShiftQuestion 5

The sum of possible values of $x$ for $\tan^{-1}(x+1)+\cot^{-1}\left(\frac{1}{x-1}\right)=\tan^{-1}\left(\frac{8}{31}\right)$ is :

Inverse Trigonometric Functions

$-\frac{33}{4}$$-\frac{32}{4}$$-\frac{31}{4}$$-\frac{30}{4}$