JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 31 January 2024, Shift 2, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

If the function

f:(-\infty,-1]\to(a,b]

defined by

f(x)=e^{x^3-3x+1}

is one - one and onto, then the distance of the point

P(2b+4,\,a+2)

from the line

x+e^{-3}y=4

is :

(1) $4\sqrt{1+e^6}$
(2) $3\sqrt{1+e^6}$
(3) $2\sqrt{1+e^6}$ Official answer
(4) $\sqrt{1+e^6}$

Official answer

Option 3

NTA final key.

Chapter: Application of Derivatives
Topic: Functions and Domain
Idea tested: Range via Monotonicity and Derivatives

Same topic in other shifts

All Functions and Domain questions

2 Apr 2026, Shift 1 · Q21If the domain of the function $f(x)=\sqrt{\log_{(0.6)}\left(\left|\frac{2x-5}{x^2-4}\right|\right)}$ is…HardNumerical value
4 Apr 2026, Shift 2 · Q1For the function $f:[1,\infty)\to[1,\infty)$ defined by $f(x)=(x-1)^4+1$ , among the two statements: (I) The set…HardOther
2 Apr 2025, Shift 2 · Q1If the domain of the function $f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}}$ is $(a, b)$ , then $(1+a)^2 + b^2$ is equal to :EasySingle correct
3 Apr 2025, Shift 1 · Q2If the domain of the function $f(x) = \log_e\left(\frac{2x-3}{5+4x}\right) + \sin^{-1}\left(\frac{4+3x}{2-x}\right)$ is $[\alpha, \beta)$ ,…MediumSingle correct
3 Apr 2025, Shift 2 · Q2If the domain of the function $f(x) = \log_7 (1 - \log_4 (x^2 - 9x + 18))$ is $(\alpha, \beta) \cup (\gamma, \delta)$ , then…MediumSingle correct
8 Apr 2025, Shift 2 · Q21Let the domain of the function $f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha, \beta]$ and the domain of…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 42 of the 174 JEE Main shifts held from 2017 to 2026.