JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

The 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 :

(1) $3+\frac{\sin(1)\cos^2(1/2)}{2}$
(2) $3+\frac{1}{2}(1+2\cos(1))\sin(1)$ Official answer
(3) $5+\frac{1}{2}(\sin(1)+\sin(2))$
(4) $2+\sin\left(\frac{1}{2}\right)\cos\left(\frac{1}{2}\right)$

Official answer

Option 2

NTA final key (2022 Session 1).

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
28 Jul 2022, Shift 2 · Q67The 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 :MediumSingle 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.