JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2024, Shift 2, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

Suppose for a differentiable function

h

h(0)=0

h(1)=1

and

h'(0)=h'(1)=2

. If

g(x)=h(e^x)e^{h(x)}

, then

g'(0)

is equal to :

(1)3
(2)4Official answer
(3)5
(4)8

Official answer

Option 2

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Continuity and Differentiability of Composite Functions

Same idea in other shifts

Asked 7× in all

6 Apr 2026, Shift 2 · Q25Let $f(x)=\begin{cases}x^3+8;&x<0,\\x^2-4;&x\ge0,\end{cases}$ and $g(x)=\begin{cases}(x-8)^{1/3};&x<0,\\(x+4)^{1/2};&x\ge0.\end{cases}$ …HardNumerical value
11 Apr 2023, Shift 2 · Q10Let $f$ and $g$ be two functions defined by $f(x) = \begin{cases} x+1, & x<0 \\ |x-1|, & x \ge 0 \end{cases}$ and…MediumSingle correct
25 Jun 2022, Shift 2 · Q22Let $f(x) = \left[2x^2 + 1\right]$ and $g(x) = \begin{cases} 2x - 3, & x < 0 \\ 2x + 3, & x \geq 0 \end{cases}$ , where $[t]$ is the…HardNumerical value
26 Jun 2022, Shift 1 · Q7Let $f, g : \mathbf{R} \to \mathbf{R}$ be two real valued functions defined as…HardSingle correct
28 Jun 2022, Shift 2 · Q6Let $f, g : \mathbf{R} \to \mathbf{R}$ be functions defined by $f(x) = \begin{cases} [x] , & x < 0 \\ |1-x| , & x \geq 0 \end{cases}$ and…HardSingle correct
16 Mar 2021, Shift 2 · Q85Let $f:\mathbf R\to\mathbf R$ and $g:\mathbf R\to\mathbf R$ be defined as $f(x)=\begin{cases}x+a, & x<0\\ |x-1|, & x\ge0\end{cases}$ and…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.