JEE Main · Maths · Integrals
Leibniz Rule: JEE Main previous year questions
18 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Asked most years. 7 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 18
- in 16 of 108 shifts
- Years asked
- 6/8
- last asked 2026
- Weighted estimate
- 0.2
- 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 16 of 108 shifts: 18 questions, #147 of 196 topics.
- 02
33% of its questions since 2020 tested an idea no earlier year had asked; 10 repeated an idea from the year before.
- 03
The most repeated idea is Solving Integral Equations, asked 11 times in 11 shifts (2021, 2022, 2023, 2024, 2025, 2026), most often as “integral equation to differential equation”.
- 04
JEE Main has asked 5 of the 61 ideas in this topic; 49 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (67%); 33% need a numerical answer, 0% are easy and 56% hard.
- 06
The skill tested most is multi-step (78%), then application (17%).
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: 3 in 24 shifts · 2022: 6 in 24 shifts · 2023: 2 in 12 shifts · 2024: 4 in 18 shifts · 2025: 1 in 8 shifts · 2026: 2 in 9 shifts.
- Up to 2023
- 0.1
- a shift, of 25
- Since 2024
- 0.2
- 0.1
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 16/108
- 15% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 18 questions on Leibniz Rule since 2017.
Difficulty
QUESTIONS- Easy0 · 0%
- Medium8 · 44%
- Hard10 · 56%
Format
SHARE- Single correct · 12 Q67%
- Numerical value · 6 Q33%
Skill tested
SHARE- Multi-step · 14 Q78%
- Application · 3 Q17%
- Calculation · 1 Q6%
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.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 5 of the 61 ideas in this topic. 49 have never been asked yet.
- Asked directly5 · 8%
- Touched inside another question7 · 11%
- Never asked49 · 80%
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.
4 ideas inside
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
5 different ideas were tested; 3 came more than once.
integral equation to differential equation
Single correct · 11 shifts · 5 numericallimit of integral function by leibniz and l'hopital
Single correct · 3 shiftsvalue from integral function and its derivative
Numerical value · 2 shifts · 1 numericalhigher derivatives of function with integral term
Single correct · 1 shiftlimit of integral from integral equation
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Solving Integral Equationsintegral equation to differential equation | 11 | 11 | Single correctMulti-step | 5 | |
| Limit Evaluationlimit of integral function by leibniz and l'hopital | 3 | 3 | Single correctMulti-step | – | |
| Variable Limit Leibnizvalue from integral function and its derivative | 2 | 2 | Numerical valueMulti-step | 1 | |
| Higher Order Derivativeshigher derivatives of function with integral term | 1 | 1 | Single correctMulti-step | – | |
| Constant Limit Leibnizlimit of integral from integral equation | 1 | 1 | Single correctMulti-step | – |
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
Leibniz Rule 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 20262 questions in 2 shifts
- 4 Apr, Shift 2Q25Let be a twice differentiable function such that ,…
Idea: Solving Integral Equations
Asked the year beforeHardNumerical value - 5 Apr, Shift 2Q19Let be a differentiable function defined as . Then the value of…
Idea: Solving Integral Equations
Asked the year beforeHardSingle correct
JEE Main 20251 question in 1 shift
- 2 Apr, Shift 2Q20Let be a differentiable function. If for all…
Idea: Solving Integral Equations
Asked the year beforeMediumSingle correct
JEE Main 20244 questions in 3 shifts
- 4 Apr, Shift 2Q9Let . Then, is equal to
Idea: Limit Evaluation
HardSingle correct - 9 Apr, Shift 2Q9…
Idea: Limit Evaluation
HardSingle correct - 9 Apr, Shift 2Q13Let . Then at , is equal to
Idea: Solving Integral Equations
Asked the year beforeHardSingle correct - 1 Feb, Shift 2Q24Let and . If , then is equal to ________.
Idea: Solving Integral Equations
Asked the year beforeMediumNumerical value
JEE Main 20232 questions in 2 shifts
- 10 Apr, Shift 1Q9Let be a differentiable function such that , . Then is equal to
Idea: Solving Integral Equations
Asked the year beforeMediumSingle correct - 10 Apr, Shift 2Q11Let be a continuous function satisfying . Then…
Idea: Solving Integral Equations
Asked the year beforeMediumSingle correct
JEE Main 20226 questions in 6 shifts
- 25 Jul, Shift 2Q26Let be a twice differentiable function on . If and…
Idea: Solving Integral Equations
Asked the year beforeHardNumerical value - 27 Jul, Shift 2Q28Let f be a differentiable function satisfying ,…
Idea: Solving Integral Equations
Asked the year beforeHardNumerical value - 30 Jul, Shift 2Q70If , then at , the value of is equal to
Idea: Higher Order Derivatives
New ideaHardSingle correct - 27 Jun, Shift 2Q8Let be a differentiable function in . If , then…
Idea: Variable Limit Leibniz
New ideaMediumSingle correct - 29 Jun, Shift 2Q7Let be a real valued continuous function on and . Then, which of the following points…
Idea: Solving Integral Equations
Asked the year beforeMediumSingle correct - 30 Jun, Shift 1Q25Let . If , then the value of…
Idea: Variable Limit Leibniz
New ideaHardNumerical value
JEE Main 20213 questions in 2 shifts
- 31 Aug, Shift 1Q72Let be a non-negative function in and twice differentiable in . If…
Idea: Constant Limit Leibniz
New ideaHardSingle correct - 31 Aug, Shift 1Q85If , , and , then is __________.
Idea: Solving Integral Equations
New ideaMediumNumerical value - 24 Feb, Shift 1Q66is equal to :
Idea: Limit Evaluation
New ideaMediumSingle correct
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.