JEE Main 2020 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 9 January 2020, Shift 2, Maths Q60

Question 60 of 75 in this shift, Maths question 10 of 25, Section A.

Let

f

and

g

be differentiable functions on

\mathbf{R}

such that

f\circ g

is the identity function. If for some

a,b\in\mathbf{R}

g'(a)=5

and

g(a)=b

, then

f'(b)

is equal to :

(1) $\frac{1}{5}$ Official answer
(2) $\frac{2}{5}$
(3) $1$
(4) $5$

Official answer

Option 1

NTA final key (Jan 2020).

Chapter: Continuity and Differentiability
Topic: Chain Rule
Idea tested: Derivative of Inverse Functions via Chain Rule

Same idea in other shifts

Asked 4× in all

4 Apr 2024, Shift 1 · Q11Let $f(x)=x^5+2e^{x/4}$ for all $x \in \mathbf{R}$ . Consider a function $g(x)$ such that $(g\circ f)(x)=x$ for all $x \in \mathbf{R}$ .…MediumSingle correct
5 Apr 2024, Shift 1 · Q8Let $f(x)=x^5+2x^3+3x+1$ , $x\in\mathbb{R}$ , and $g(x)$ be a function such that $g(f(x))=x$ for all $x\in\mathbb{R}$ . Then…MediumSingle correct
25 Jun 2022, Shift 1 · Q6Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=x^3+x-5$ If $g(x)$ is a function such that $f(g(x))=x$ , $\forall$ 'x'…EasySingle 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.