JEE Main · Maths · Application of Derivatives

Curve Sketching: JEE Main previous year questions

Name: Curve Sketching: JEE Main previous year questions
Creator: Lumi

5 questions in the 108 JEE Main shifts Lumi analysed, in 2 of 8 years. Pattern: Occasional. 3 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 5; in 4 of 108 shifts
Years asked: 2/8; last asked 2024
Chance in a shift: 9%; calibrated model, how we compute it
Weighted estimate: 0.0; model; history: 0.0 a shift on average, typically 0.0–0.1

Key findings

01
Asked in 2 of 8 years with analysed shifts and in 4 of 108 shifts: 5 questions, #191 of 196 topics. Last asked in 2024.
02
40% of its questions since 2020 tested an idea no earlier year had asked; 3 repeated an idea from the year before.
03
The most repeated idea is Graphical Root Counting, asked 3 times in 3 shifts (2023, 2024), most often as “count roots of function and its derivative”.
04
JEE Main has asked 2 of the 57 ideas in this topic; 53 have never been asked, directly or inside another question.
05
Mostly asked as numerical value (80%); 80% need a numerical answer, 0% are easy and 0% hard.
06
The skill tested most is multi-step (100%).

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: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 2 in 12 shifts · 2024: 3 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Up to 2023: 0.0; a shift, of 25
Since 2024: 0.1; 0.0
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 4/108; 4% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 5 questions on Curve Sketching since 2017.

Difficulty

QUESTIONS

Easy0 · 0%
Medium5 · 100%
Hard0 · 0%

Format

Numerical value · 4 Q80%
Two statements · 1 Q20%

Skill tested

Multi-step · 5 Q100%

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 2 of the 57 ideas in this topic. 53 have never been asked yet.

Asked directly2 · 4%
Touched inside another question2 · 4%
Never asked53 · 93%

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

Chapter, idea, question

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

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

Open4 · 80%80%2/822
2 ideas inside
- OpenRepeated2 · 50%50%2/8
- OpenRepeated2 · 50%50%2/8
Open1 · 20%20%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

2 different ideas were tested; 2 came more than once.

Graphical Root Counting3×
count roots of function and its derivative
Numerical value · 3 shifts · 3 numerical
Root Counting via Intersection Sketching2×
statements on roots of cubic on interval
Numerical value · 2 shifts · 1 numerical

Idea	Years asked	Times	Shifts	Format	Numerical
Graphical Root Countingcount roots of function and its derivative		3	3	Numerical valueMulti-step	3
Root Counting via Intersection Sketchingstatements on roots of cubic on interval		2	2	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

Curve Sketching 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.

JEE Main 20243 questions in 2 shifts

5 Apr, Shift 2Q30
The number of real solutions of the equation $x|x+5| + 2|x+7| - 2 = 0$ is ________.
Idea: Graphical Root Counting
Asked the year beforeMediumNumerical value
29 Jan, Shift 1Q10
Consider the function $f:\left[\frac{1}{2},1\right]\to\mathbb{R}$ defined by $f(x)=4\sqrt{2}x^3-3\sqrt{2}x-1$ . Consider the statements (I)…
Idea: Root Counting via Intersection Sketching
Asked the year beforeMediumTwo statements
29 Jan, Shift 1Q24
Let $f(x)=2^x-x^2$ , $x\in\mathbb{R}$ . If $m$ and $n$ are respectively the number of points at which the curves $y=f(x)$ and $y=f'(x)$ …
Idea: Graphical Root Counting
Asked the year beforeMediumNumerical value

JEE Main 20232 questions in 2 shifts

6 Apr, Shift 2Q24
The number of points, where the curve $y=x^5-20x^3+50x+2$ crosses the x-axis, is ________.
Idea: Graphical Root Counting
New ideaMediumNumerical value
11 Apr, Shift 2Q24
The number of points, where the curve $f(x) = e^{8x} - e^{6x} - 3e^{4x} - e^{2x} + 1$ , $x \in \mathbb{R}$ cuts $x$ -axis, is equal to…
Idea: Root Counting via Intersection Sketching
New ideaMediumNumerical value

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.