JEE Main 2021 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 26 February 2021, Shift 1, Maths Q74

Question 74 of 90 in this shift, Maths question 14 of 30, Section A.

Let

f

be any function defined on

\mathbf{R}

and let it satisfy the condition :

|f(x)-f(y)|\le|(x-y)^2|,\ \forall\,(x, y)\in\mathbf{R}

f(0)=1

, then :

(1) $f(x)>0,\ \forall\,x\in\mathbf{R}$ Official answer
(2) $f(x)<0,\ \forall\,x\in\mathbf{R}$
(3) $f(x)=0,\ \forall\,x\in\mathbf{R}$
(4) $f(x)$ can take any value in $\mathbf{R}$

Official answer

Option 1

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Differentiability via Functional Equations

Same idea in other shifts

Asked 10× in all

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26 Jun 2022, Shift 2 · Q21Let $f : \mathbb{R} \rightarrow \mathbb{R}$ satisfy $f(x + y) = 2^x f(y) + 4^y f(x)$ , $\forall x, y \in \mathbb{R}$ . If $f(2) = 3$ , then…HardNumerical value
4 Aug 2021, Shift 2 · Q67Let $f:\mathbb{R}\to\mathbb{R}$ be twice differentiable and satisfy $f(x+y)=f(x)+f(y)$ . If $f'(0)=1$ , then which of the following is true?EasySingle correct
18 Mar 2021, Shift 2 · Q90Let $f:\mathbb{R}\to\mathbb{R}$ satisfy the equation $f(x+y)=f(x)\cdot f(y)$ for all $x, y\in\mathbb{R}$ and $f(x)\neq0$ for any…MediumNumerical value
4 Sep 2020, Shift 1 · Q73Suppose a differentiable function $f(x)$ satisfies the identity $f(x+y) = f(x) + f(y) + xy^2 + x^2y$ , for all real $x$ and $y$ . If…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.