JEE Main · Maths · Application of Derivatives

Monotonicity: JEE Main previous year questions

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

23 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Asked most years. 5 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 23; in 22 of 108 shifts
Years asked: 6/8; last asked 2025
Chance in a shift: 19%; calibrated model, how we compute it
Weighted estimate: 0.1; model; history: 0.1 a shift on average, typically 0.0–0.2

Key findings

01
Asked in 6 of 8 years with analysed shifts and in 22 of 108 shifts: 23 questions, #132 of 196 topics. Last asked in 2025.
02
57% of its questions since 2020 tested an idea no earlier year had asked; 8 repeated an idea from the year before.
03
The most repeated idea is Finding Intervals, asked 7 times in 7 shifts (2020, 2021, 2022, 2024, 2025), most often as “find intervals of monotonicity of rational function”.
04
JEE Main has asked 12 of the 62 ideas in this topic; 43 have never been asked, directly or inside another question.
05
Mostly asked as single correct (83%); 4% need a numerical answer, 17% are easy and 30% hard.
06
The skill tested most is multi-step (57%), then application (39%).

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 7 in 24 shifts · 2022: 7 in 24 shifts · 2023: 2 in 12 shifts · 2024: 4 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.

Up to 2023: 0.2; a shift, of 25
Since 2024: 0.1; -0.1
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 22/108; 20% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 23 questions on Monotonicity since 2017.

Difficulty

QUESTIONS

4127

Easy4 · 17%
Medium12 · 52%
Hard7 · 30%

Format

Single correct · 19 Q83%
Two statements · 3 Q13%
Numerical value · 1 Q4%

Skill tested

Multi-step · 13 Q57%
Application · 9 Q39%
Conceptual · 1 Q4%

Repeats

New idea, or one asked before?

Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 12 of the 62 ideas in this topic. 43 have never been asked yet.

12743

Asked directly12 · 19%
Touched inside another question7 · 11%
Never asked43 · 69%

Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.

Drill down

Idea, year, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

ideaAskedShareYears’17’20’21’22’23’24’25’26

OpenRepeated7 · 30%30%5/822
- 8 Apr ’25 S2 · Q17
  Let the function $f(x) = \frac{x}{3} + \frac{3}{x} + 3$ , $x \neq 0$ be strictly increasing in…
  easySingle correctAsked the year before
- 1 Feb ’24 S1 · Q7
  If $5f(x)+4f\left(\frac{1}{x}\right)=x^2-2,\ \forall\ x\neq0$ and $y=9x^2f(x)$ , then $y$ is strictly increasing in :
  hardSingle correct
- 28 Jul ’22 S2 · Q66
  The function $f(x)=xe^{x(1-x)},\ x\in\mathbb{R}$ , is :
  mediumSingle correctAsked the year before
- 30 Jun ’22 S1 · Q9
  Let $f(x) = 4x^3 - 11x^2 + 8x - 5$ , $x \in \mathbf{R}$ . Then $f$ :
  easySingle correctAsked the year before
- 25 Jul ’21 S1 · Q67
  Let $f(x)=3\sin^4x+10\sin^3x+6\sin^2x-3$ , $x\in\left[-\frac{\pi}{6},\frac{\pi}{2}\right]$ . Then, $f$ is :
  mediumSingle correctAsked the year before
- 16 Mar ’21 S2 · Q64
  Let $f$ 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 correctAsked the year before
- 3 Sep ’20 S1 · Q59
  The function, $f(x)=(3x-7)x^{2/3}$ , $x\in\mathbf{R}$ , is increasing for all $x$ lying in :
  mediumSingle correctNew idea
OpenRepeated4 · 17%17%3/82
OpenRepeated2 · 9%9%2/8
Open2 · 9%9%1/82
Open1 · 4%4%1/8
Open1 · 4%4%1/8
Open1 · 4%4%1/8
Open1 · 4%4%1/8
Open1 · 4%4%1/8
Open1 · 4%4%1/8
Open1 · 4%4%1/8
Open1 · 4%4%1/8

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

Every idea inside this topic

12 different ideas were tested; 4 came more than once.

Finding Intervals7×
find intervals of monotonicity of rational function
Single correct · 7 shifts
First Derivative Test4×
identify incorrect statement on function behaviour
Single correct · 4 shifts
Counting Roots using Monotonicity2×
statement i/ii on monotonicity and roots
Single correct · 2 shifts
Monotonicity in Piecewise Functions2×
increasing interval of piecewise function
Single correct · 2 shifts
Monotonicity of the Derivative Function1×
statement i/ii on monotonicity
Two statements · 1 shift
Monotonicity of Variable Exponent Functions1×
interval of monotonicity of a function
Single correct · 1 shift
Proving Inequalities1×
statement a/b on bounds of function from derivative inequality
Two statements · 1 shift
Strict Monotonicity1×
monotonicity of symmetric function sum
Single correct · 1 shift
Monotonicity of Composite Functions1×
inequality on composite of monotonic functions
Single correct · 1 shift
Parameter Range for Global Monotonicity1×
parameter range for increasing function
Single correct · 1 shift
Trigonometric Monotonicity by Quadrant1×
monotonicity of derived function combination
Single correct · 1 shift
Parameter Range for Localized Monotonicity1×
parameter range for monotonic on interval
Numerical value · 1 shift · 1 numerical

Idea	Times	Shifts	Format	Numerical
Finding Intervalsfind intervals of monotonicity of rational function	7	7	Single correctApplication	–
First Derivative Testidentify incorrect statement on function behaviour	4	4	Single correctMulti-step	–
Counting Roots using Monotonicitystatement i/ii on monotonicity and roots	2	2	Single correctApplication	–
Monotonicity in Piecewise Functionsincreasing interval of piecewise function	2	2	Single correctApplication	–
Monotonicity of the Derivative Functionstatement i/ii on monotonicity	1	1	Two statementsApplication	–
Monotonicity of Variable Exponent Functionsinterval of monotonicity of a function	1	1	Single correctApplication	–
Proving Inequalitiesstatement a/b on bounds of function from derivative inequality	1	1	Two statementsMulti-step	–
Strict Monotonicitymonotonicity of symmetric function sum	1	1	Single correctMulti-step	–
Monotonicity of Composite Functionsinequality on composite of monotonic functions	1	1	Single correctMulti-step	–
Parameter Range for Global Monotonicityparameter range for increasing function	1	1	Single correctMulti-step	–
Trigonometric Monotonicity by Quadrantmonotonicity of derived function combination	1	1	Single correctMulti-step	–
Parameter Range for Localized Monotonicityparameter range for monotonic on interval	1	1	Numerical valueMulti-step	1

Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas

Every question

Monotonicity questions, year by year

The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.

Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.

Key findings

Questions a shift, year by year

Difficulty, format and skill

Difficulty

Format

Skill tested

New idea, or one asked before?

Coverage of the topic

Idea, year, question

Every idea inside this topic

Monotonicity questions, year by year

JEE Main 20251 question in 1 shift

JEE Main 20244 questions in 4 shifts

JEE Main 20232 questions in 2 shifts

JEE Main 20227 questions in 6 shifts

JEE Main 20217 questions in 7 shifts

JEE Main 20202 questions in 2 shifts

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