JEE Main · Maths · Limits and Derivatives
L'Hopital's Rule: JEE Main previous year questions
61 questions in the 108 JEE Main shifts Lumi analysed, in 8 of 8 years. Pattern: Asked most years. 22 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 61
- in 59 of 108 shifts
- Years asked
- 8/8
- last asked 2026
- Weighted estimate
- 0.5
- model; history: 0.6 a shift on average, typically 0.4–0.8
Key findings
- 01
Asked in 8 of 8 years with analysed shifts and in 59 of 108 shifts: 61 questions, #39 of 196 topics. It came in every year with analysed shifts.
- 02
35% of its questions since 2020 tested an idea no earlier year had asked; 30 repeated an idea from the year before.
- 03
The most repeated idea is Simplifying with Standard Limits Before L'Hopital, asked 13 times in 13 shifts (2021, 2022, 2023, 2024, 2025, 2026), most often as “unknown constants from finite limit”.
- 04
JEE Main has asked 18 of the 64 ideas in this topic; 41 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (74%); 25% need a numerical answer, 8% are easy and 28% hard.
- 06
The skill tested most is calculation (54%), then multi-step (43%).
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: 1 in 1 shift · 2020: 8 in 12 shifts · 2021: 15 in 24 shifts · 2022: 12 in 24 shifts · 2023: 3 in 12 shifts · 2024: 12 in 18 shifts · 2025: 6 in 8 shifts · 2026: 4 in 9 shifts.
- Up to 2023
- 0.5
- a shift, of 25
- Since 2024
- 0.6
- 0.0
- Usual gap
- 1.3 yrs
- between years asking it
- Shifts with it
- 59/108
- 55% of analysed shifts
Revise first
- Simplifying with Standard Limits Before L'Hopital · asked 2021, 2022, 2023, 2024, 2025, 2026
- Choosing Series Expansion over L'Hopital · asked 2020, 2021, 2022, 2023, 2024, 2025, 2026
- Determining Unknown Constants from Finite Limits · asked 2021, 2022, 2025, 2026
How it is asked
Difficulty, format and skill
Across all 61 questions on L'Hopital's Rule since 2017.
Difficulty
QUESTIONS- Easy5 · 8%
- Medium39 · 64%
- Hard17 · 28%
Format
SHARE- Single correct · 45 Q74%
- Numerical value · 15 Q25%
- Two statements · 1 Q2%
Skill tested
SHARE- Calculation · 33 Q54%
- Multi-step · 26 Q43%
- Application · 2 Q3%
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 18 of the 64 ideas in this topic. 41 have never been asked yet.
- Asked directly18 · 28%
- Touched inside another question5 · 8%
- Never asked41 · 64%
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.
16 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
18 different ideas were tested; 9 came more than once.
unknown constants from finite limit
Single correct · 13 shifts · 4 numericalunknown constants from finite limit
Single correct · 10 shifts · 3 numericalunknown constants from finite limit
Single correct · 6 shifts · 1 numericallimit of one-to-infinity form
Single correct · 6 shifts · 1 numericallimit of one-to-infinity form
Single correct · 5 shifts · 1 numericalevaluate limits with nested radicals
Single correct · 4 shifts · 1 numericalleft-hand limit with greatest integer function
Single correct · 3 shiftslimit of integral function via l'hopital
Single correct · 3 shiftsleft and right limits with fractional part
Numerical value · 2 shifts · 1 numericallimit of polynomial quotient from derivative identity
Single correct · 1 shiftlimit of determinant function
Numerical value · 1 shift · 1 numericallimit of trigonometric expression at a point
Single correct · 1 shiftlimit using derivative of unknown function
Numerical value · 1 shift · 1 numericallimit of trig expression after simplification
Single correct · 1 shiftunknown constants from finite limit
Numerical value · 1 shift · 1 numericallimit of radical expressions
Single correct · 1 shiftone-sided limit with root of 1-cos
Single correct · 1 shiftlimit of trig expression at pi/2
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Simplifying with Standard Limits Before L'Hopitalunknown constants from finite limit | 13 | 13 | Single correctMulti-step | 4 | |
| Choosing Series Expansion over L'Hopitalunknown constants from finite limit | 10 | 10 | Single correctCalculation | 3 | |
| Determining Unknown Constants from Finite Limitsunknown constants from finite limit | 6 | 6 | Single correctMulti-step | 1 | |
| e-Power Shortcut for 1^infinity Formslimit of one-to-infinity form | 6 | 6 | Single correctCalculation | 1 | |
| Indeterminate Power Formslimit of one-to-infinity form | 5 | 5 | Single correctCalculation | 1 | |
| Conjugation vs L'Hopital for Radicalsevaluate limits with nested radicals | 4 | 4 | Single correctCalculation | 1 | |
| Handling Greatest Integer Functionsleft-hand limit with greatest integer function | 3 | 3 | Single correctMulti-step | – | |
| L'Hopital with Leibniz Rulelimit of integral function via l'hopital | 3 | 3 | Single correctCalculation | – | |
| L'Hopital with Inverse Trigonometric Functionsleft and right limits with fractional part | 2 | 2 | Numerical valueCalculation | 1 | |
| Derivative Limit Existence Conditionlimit of polynomial quotient from derivative identity | 1 | 1 | Single correctMulti-step | – | |
| L'Hopital on Determinant Functionslimit of determinant function | 1 | 1 | Numerical valueMulti-step | 1 | |
| Single Application of L'Hopitallimit of trigonometric expression at a point | 1 | 1 | Single correctCalculation | – | |
| Recognizing the Derivative Definitionlimit using derivative of unknown function | 1 | 1 | Numerical valueCalculation | 1 | |
| Trigonometric Pre-Simplificationlimit of trig expression after simplification | 1 | 1 | Single correctCalculation | – | |
| First Principle Derivative Recognitionunknown constants from finite limit | 1 | 1 | Numerical valueMulti-step | 1 | |
| Fractional Power Substitutionlimit of radical expressions | 1 | 1 | Single correctCalculation | – | |
| Trigonometric Simplification Before Differentiationone-sided limit with root of 1-cos | 1 | 1 | Single correctMulti-step | – | |
| Repeated L'Hopital Applicationlimit of trig expression at pi/2 | 1 | 1 | Single correctCalculation | – |
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
L'Hopital's Rule questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20264 questions in 4 shifts
- 2 Apr, Shift 1Q16If , then is equal to :
Idea: Determining Unknown Constants from Finite Limits
Asked the year beforeHardSingle correct - 5 Apr, Shift 1Q17The product of all possible values of , for which…
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeHardSingle correct - 5 Apr, Shift 2Q17Let . Then the number of solutions of the equation , …
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeMediumSingle correct - 6 Apr, Shift 1Q17The value of is:
Idea: Choosing Series Expansion over L'Hopital
Asked the year beforeMediumSingle correct
JEE Main 20256 questions in 6 shifts
- 2 Apr, Shift 1Q7For , if , then…
Idea: Determining Unknown Constants from Finite Limits
MediumSingle correct - 2 Apr, Shift 2Q17If is finite, then is equal to :
Idea: Determining Unknown Constants from Finite Limits
MediumSingle correct - 3 Apr, Shift 2Q25If , then is equal to ___________.
Idea: Indeterminate Power Forms
Asked the year beforeMediumNumerical value - 7 Apr, Shift 1Q16…
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeMediumSingle correct - 7 Apr, Shift 2Q23For , let and be the roots of the equation…
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeHardNumerical value - 8 Apr, Shift 2Q16Given below are two statements: Statement I :…
Idea: Choosing Series Expansion over L'Hopital
Asked the year beforeMediumTwo statements
JEE Main 202412 questions in 12 shifts
- 4 Apr, Shift 1Q24If , where , then…
Idea: Conjugation vs L'Hopital for Radicals
HardNumerical value - 5 Apr, Shift 2Q23Let be a root of the equation . If…
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeHardNumerical value - 8 Apr, Shift 1Q26The value of is ____________.
Idea: Choosing Series Expansion over L'Hopital
Asked the year beforeMediumNumerical value - 8 Apr, Shift 2Q25If and…
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeHardNumerical value - 9 Apr, Shift 2Q5is equal to
Idea: Indeterminate Power Forms
HardSingle correct - 1 Feb, Shift 1Q26Let denote the fractional part of and , . If L and…
Idea: L'Hopital with Inverse Trigonometric Functions
HardNumerical value - 1 Feb, Shift 2Q9Let . If for some ,…
Idea: Handling Greatest Integer Functions
MediumSingle correct - 27 Jan, Shift 1Q9If and , then the…
Idea: Conjugation vs L'Hopital for Radicals
MediumSingle correct - 29 Jan, Shift 1Q8…
Idea: L'Hopital with Leibniz Rule
MediumSingle correct - 30 Jan, Shift 1Q8Let be a differentiable function such that . If…
Idea: L'Hopital with Leibniz Rule
MediumSingle correct - 31 Jan, Shift 1Q6Asked the year beforeMediumSingle correct
- 31 Jan, Shift 2Q25If , then is equal to ________.
Idea: Choosing Series Expansion over L'Hopital
Asked the year beforeHardNumerical value
JEE Main 20233 questions in 3 shifts
- 8 Apr, Shift 1Q10is…
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeMediumSingle correct - 8 Apr, Shift 2Q9If are the roots of the equation , and…
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeHardSingle correct - 13 Apr, Shift 2Q9If , then is equal to
Idea: Choosing Series Expansion over L'Hopital
Asked the year beforeHardSingle correct
JEE Main 202212 questions in 12 shifts
- 25 Jul, Shift 1Q5If , then is equal to :
Idea: Determining Unknown Constants from Finite Limits
Asked the year beforeMediumSingle correct - 25 Jul, Shift 2Q6is equal to
Idea: Single Application of L'Hopital
New ideaMediumSingle correct - 26 Jul, Shift 2Q7Let for some . Then the value of …
Idea: Choosing Series Expansion over L'Hopital
Asked the year beforeMediumSingle correct - 28 Jul, Shift 1Q29is equal to…
Idea: e-Power Shortcut for 1^infinity Forms
Asked the year beforeHardNumerical value - 29 Jul, Shift 1Q5If , where…
Idea: Determining Unknown Constants from Finite Limits
Asked the year beforeMediumSingle correct - 25 Jun, Shift 1Q9Let be a polynomial function such that . Then, the value of is equal to :
Idea: Derivative Limit Existence Condition
New ideaHardSingle correct - 25 Jun, Shift 2Q5…
Idea: Conjugation vs L'Hopital for Radicals
Asked the year beforeHardSingle correct - 26 Jun, Shift 1Q6is equal to :
Idea: L'Hopital with Inverse Trigonometric Functions
New ideaMediumSingle correct - 26 Jun, Shift 2Q4is equal to :
Idea: Choosing Series Expansion over L'Hopital
Asked the year beforeMediumSingle correct - 28 Jun, Shift 2Q24If , then the value of is equal to __________.
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeMediumNumerical value - 29 Jun, Shift 2Q5The value of is equal to:
Idea: Simplifying with Standard Limits Before L'Hopital
Asked the year beforeMediumSingle correct - 30 Jun, Shift 1Q23Suppose exists and is equal to L, where…
Idea: L'Hopital on Determinant Functions
New ideaHardNumerical value
JEE Main 202115 questions in 14 shifts
- 3 Aug, Shift 1Q65The value of the limit : is equal to
Idea: Indeterminate Power Forms
New ideaHardSingle correct - 3 Aug, Shift 1Q89If be a differentiable function such that and , then …
Idea: Recognizing the Derivative Definition
New ideaEasyNumerical value - 3 Aug, Shift 2Q68is equal to
Idea: Indeterminate Power Forms
New ideaEasySingle correct - 4 Aug, Shift 1 · Q67e-Power Shortcut for 1^infinity FormsAsked the year beforeMedium
- 4 Aug, Shift 2 · Q66e-Power Shortcut for 1^infinity FormsAsked the year beforeMedium
- 27 Aug, Shift 1 · Q65Choosing Series Expansion over L'HopitalAsked the year beforeMedium
- 27 Aug, Shift 2 · Q66Conjugation vs L'Hopital for RadicalsNew ideaMedium
- 31 Aug, Shift 1 · Q67Simplifying with Standard Limits Before L'HopitalNew ideaMedium
- 31 Aug, Shift 2 · Q67Indeterminate Power FormsNew ideaMedium
- 25 Feb, Shift 1 · Q66e-Power Shortcut for 1^infinity FormsAsked the year beforeMedium
- 25 Feb, Shift 2 · Q84Determining Unknown Constants from Finite LimitsNew ideaMedium
- 26 Feb, Shift 1 · Q67Trigonometric Pre-SimplificationNew ideaMedium
- 17 Mar, Shift 1 · Q70Handling Greatest Integer FunctionsAsked the year beforeMedium
- 17 Mar, Shift 2 · Q65Simplifying with Standard Limits Before L'HopitalNew ideaMedium
- 18 Mar, Shift 1 · Q72Choosing Series Expansion over L'HopitalAsked the year beforeMedium
JEE Main 20208 questions in 7 shifts
- 8 Jan, Shift 1 · Q57e-Power Shortcut for 1^infinity FormsNew ideaEasy
- 8 Jan, Shift 2 · Q58L'Hopital with Leibniz RuleNew ideaEasy
- 2 Sep, Shift 1 · Q72First Principle Derivative RecognitionNew ideaMedium
- 2 Sep, Shift 2 · Q59e-Power Shortcut for 1^infinity FormsNew ideaEasy
- 3 Sep, Shift 1 · Q58Handling Greatest Integer FunctionsNew ideaMedium
- 3 Sep, Shift 1 · Q74Choosing Series Expansion over L'HopitalNew ideaMedium
- 3 Sep, Shift 2 · Q57Fractional Power SubstitutionNew ideaMedium
- 5 Sep, Shift 1 · Q58Trigonometric Simplification Before DifferentiationNew ideaMedium
JEE Main 20171 question in 1 shift
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.
More topics in Limits and Derivatives
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