JEE Main 2020 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 6 September 2020, Shift 2, Maths Q57

Question 57 of 75 in this shift, Maths question 7 of 25.

For all twice differentiable functions

f:\mathbf{R}\to\mathbf{R}

, with

f(0)=f(1)=f'(0)=0

(1) $f''(x)\neq0$ at every point $x\in(0,1)$
(2) $f''(0)=0$
(3) $f''(x)=0$ , for some $x\in(0,1)$ Official answer
(4) $f''(x)=0$ , at every point $x\in(0,1)$

Official answer

Option 3

NTA final key (Sep 2020).

Chapter: Continuity and Differentiability
Topic: Mean Value Theorem
Idea tested: Rolle's Theorem for Second Derivative

Same topic in other shifts

All Mean Value Theorem questions

5 Apr 2026, Shift 2 · Q20Let $f(x)$ and $g(x)$ be twice differentiable functions satisfying $f''(x)=g''(x)$ for all $x \in \mathbf{R}$ , $f'(1)=2g'(1)=4$ and…MediumSingle correct
3 Aug 2021, Shift 2 · Q70Let $f : \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $f(0) = 2$ . If $\left|\frac{df}{dx}\right| \le 3$ , for all…MediumSingle correct
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

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.