JEE Main 2025 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 8 April 2025, Shift 2, Maths Q17

Question 17 of 75 in this shift, Maths question 17 of 25, Section A.

Let the function

f(x) = \frac{x}{3} + \frac{3}{x} + 3

x \neq 0

be strictly increasing in

(-\infty, \alpha_1) \cup (\alpha_2, \infty)

and strictly decreasing in

(\alpha_3, \alpha_4) \cup (\alpha_4, \alpha_5)

. Then

\sum_{i=1}^{5} \alpha_i^2

is equal to

(1)28
(2)36Official answer
(3)40
(4)48

Official answer

Option 2

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: Finding Intervals

Same idea in other shifts

Asked 7× in all

1 Feb 2024, Shift 1 · Q7If $5f(x)+4f\left(\frac{1}{x}\right)=x^2-2,\ \forall\ x\neq0$ and $y=9x^2f(x)$ , then $y$ is strictly increasing in :HardSingle correct
28 Jul 2022, Shift 2 · Q66The function $f(x)=xe^{x(1-x)},\ x\in\mathbb{R}$ , is :MediumSingle correct
30 Jun 2022, Shift 1 · Q9Let $f(x) = 4x^3 - 11x^2 + 8x - 5$ , $x \in \mathbf{R}$ . Then $f$ :EasySingle correct
25 Jul 2021, Shift 1 · Q67Let $f(x)=3\sin^4x+10\sin^3x+6\sin^2x-3$ , $x\in\left[-\frac{\pi}{6},\frac{\pi}{2}\right]$ . Then, $f$ is :MediumSingle correct
16 Mar 2021, Shift 2 · Q64Let $f$ be a real valued function, defined on $\mathbf R-\{-1,1\}$ and given by $f(x)=3\log_e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}$ .…MediumSingle correct
3 Sep 2020, Shift 1 · Q59The function, $f(x)=(3x-7)x^{2/3}$ , $x\in\mathbf{R}$ , is increasing for all $x$ lying in :MediumSingle 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.