JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 28 July 2022, Shift 2, Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30, Section A.

The sum of the absolute maximum and absolute minimum values of the function

f(x)=\tan^{-1}(\sin x-\cos x)

in the interval

[0,\ \pi]

is :

(1) $0$
(2) $\tan^{-1}\left(\frac{1}{\sqrt{2}}\right)-\frac{\pi}{4}$
(3) $\cos^{-1}\left(\frac{1}{\sqrt{3}}\right)-\frac{\pi}{4}$ Official answer
(4) $\frac{-\pi}{12}$

Official answer

Option 3

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Closed Interval Extrema

Same idea in other shifts

Asked 8× in all

4 Apr 2026, Shift 2 · Q12 $\max_{0\le x\le\pi}\left(16\sin\left(\frac x2\right)\cos^3\left(\frac x2\right)\right)$ is equal to:MediumSingle correct
7 Apr 2025, Shift 1 · Q17Let $x = -1$ and $x = 2$ be the critical points of the function $f(x) = x^3 + ax^2 + b\log_e|x| + 1$ , $x \neq 0$ . Let $m$ and $M$ …MediumSingle correct
30 Jan 2024, Shift 2 · Q9Let $f(x) = (x+3)^2 (x-2)^3$ , $x \in [-4, 4]$ . If $M$ and $m$ are the maximum and minimum values of $f$ , respectively in $[-4, 4]$ , then…MediumSingle correct
13 Apr 2023, Shift 1 · Q10 $\max_{0\leq x\leq\pi}\left\{x-2\sin x\cos x+\frac{1}{3}\sin 3x\right\}=$ HardSingle correct
25 Jul 2022, Shift 1 · Q6If the absolute maximum value of the function $f(x)=(x^2-2x+7)\,\mathrm{e}^{(4x^3-12x^2-180x+31)}$ in the interval $[-3,0]$ is…MediumSingle correct
24 Jun 2022, Shift 1 · Q12The sum of absolute maximum and absolute minimum values of the function $f(x)=|2x^2+3x-2|+\sin x\cos x$ in the interval $[0, 1]$ is :HardSingle correct
17 Mar 2021, Shift 2 · Q85Let $f:[-1, 1]\to\mathbf{R}$ be defined as $f(x)=ax^2+bx+c$ for all $x\in[-1, 1]$ , where $a, b, c\in\mathbf{R}$ such that $f(-1)=2$ ,…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.