JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q85

Question 85 of 90 in this shift, Maths question 25 of 30, Section B.

Let

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

f'(-1)=1

and for

x\in(-1, 1)

the maximum value of

f''(x)

\frac{1}{2}

. If

f(x)\leq\alpha

x\in[-1, 1]

, then the least value of

\alpha

is equal to __________.

Official answer

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
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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
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

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.