JEE Main Maths · Application of Derivatives

Monotonicity in JEE Main

Name: Monotonicity: JEE Main previous year questions
Creator: Lumi

Monotonicity (Maths, Application of Derivatives) came 6 times in 6 of the 42 JEE Main shifts Lumi analysed, across 4 distinct ideas. 2 of them came in 2024–26; it was last asked in 2025.

Questions: 6; in 6 shifts
Ideas asked: 4; 1 asked more than once
Numerical answer: 0; 0% of its questions
Pattern: Asked most years; last asked 2025

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 1Medium 3Hard 2

Format

Single correct4 Q
Two statements2 Q

Ideas inside the topic

4 ideas

Finding Intervals3 Q
First Derivative Test1 Q
Proving Inequalities1 Q
Counting Roots using Monotonicity1 Q

Where it sits

Part of Application of Derivatives, which had 47 questions in all. Monotonicity accounts for 13% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Every question

All 6 Monotonicity questions

Newest first, each with its options and official answer.

8 Apr 2025, Shift 2 · Q17Let the function $f(x) = \frac{x}{3} + \frac{3}{x} + 3$ , $x \neq 0$ be strictly increasing in…EasySingle correct
8 Apr 2024, Shift 1 · Q7For the function $f(x)=(\cos x)-x+1$ , $x\in\mathbb{R}$ , between the following two statements (S1) $f(x)=0$ for only one value of $x$ in…MediumTwo statements
11 Apr 2023, Shift 1 · Q10Let $f : [2, 4] \to \mathbb{R}$ be a differentiable function such that $(x \log_e x) f'(x) + (\log_e x) f(x) + f(x) \ge 1,\ x \in [2, 4]$ …HardTwo statements
24 Jun 2022, Shift 1 · Q10For the function $f(x)=4\log_e(x-1)-2x^2+4x+5,\ x>1$ , which one of the following is NOT correct ?HardSingle 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