JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 September 2020, Shift 2, Maths Q58

Question 58 of 75 in this shift, Maths question 8 of 25.

Let

f : (0, \infty) \to (0, \infty)

be a differentiable function such that

f(1) = e

and

\lim_{t \to x} \frac{t^2 f^2(x) - x^2 f^2(t)}{t - x} = 0

. If

f(x) = 1

, then

x

is equal to :

(1) $e$
(2) $\frac{1}{e}$ Official answer
(3) $2e$
(4) $\frac{1}{2e}$

Official answer

Option 2

NTA final key (Sep 2020).

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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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
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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

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.