JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 5 April 2024, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

Let

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

\frac{g(7)}{g'(7)}

is equal to :

(1) $1$
(2) $7$
(3) $14$ Official answer
(4) $42$

Official answer

Option 3

NTA final key.

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
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
9 Jan 2020, Shift 2 · Q60Let $f$ and $g$ be differentiable functions on $\mathbf{R}$ such that $f\circ g$ is the identity function. If for some $a,b\in\mathbf{R}$ ,…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.