JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 3 August 2021, Shift 2, Maths Q70

Question 70 of 90 in this shift, Maths question 10 of 30, Section A.

Let

f : \mathbb{R} \to \mathbb{R}

be a differentiable function such that

f(0) = 2

. If

\left|\frac{df}{dx}\right| \le 3

, for all

x \in \mathbb{R}

, then

f(1)

lies in the interval

(1) $[5, \infty)$
(2) $(-\infty, -1]$
(3) $[-1, 5]$ Official answer
(4) $(-\infty, -1) \cup (5, \infty)$

Official answer

Option 3

NTA final key.

Chapter: Application of Derivatives
Topic: Mean Value Theorem
Idea tested: Proving Lipschitz Condition via LMVT

Same topic in other shifts

All Mean Value Theorem questions

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8 Jan 2020, Shift 2 · Q59Let S be the set of all functions $f : [0, 1] \to \mathbf{R}$ , which are continuous on $[0, 1]$ and differentiable on $(0, 1)$ . Then for…HardSingle correct
9 Jan 2020, Shift 1 · Q60Let $f$ be any function continuous on [a, b] and twice differentiable on (a, b). If for all $x\in(\mathrm{a, b})$ , $f'(x)>0$ and…HardSingle correct
4 Sep 2020, Shift 1 · Q58Let $f$ be a twice differentiable function on $(1, 6)$ . If $f(2) = 8$ , $f'(2) = 5$ , $f'(x) \ge 1$ and $f''(x) \ge 4$ , for all…HardSingle correct
6 Sep 2020, Shift 2 · Q57For all twice differentiable functions $f:\mathbf{R}\to\mathbf{R}$ , with $f(0)=f(1)=f'(0)=0$ ,MediumSingle correct
6 Sep 2020, Shift 2 · Q59If the tangent to the curve, $y=f(x)=x\log_e x$ , $(x>0)$ at a point $(c, f(c))$ is parallel to the line - segment joining the points…MediumSingle 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.