JEE Main · Maths · Continuity and Differentiability
Continuity and Differentiability: JEE Main previous year questions
94 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 27 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 94
- in 76 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.7
- model; history: 0.6 a shift on average, typically 0.4–0.8
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 76 of 108 shifts: 94 questions, #9 of 196 topics.
- 02
29% of its questions since 2020 tested an idea no earlier year had asked; 50 repeated an idea from the year before.
- 03
The most repeated idea is Continuity involving GIF and Fractional Part, asked 17 times in 17 shifts (2020, 2021, 2022, 2023, 2024, 2026), most often as “count discontinuities of greatest integer function”.
- 04
JEE Main has asked 18 of the 62 ideas in this topic; 37 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (67%); 31% need a numerical answer, 4% are easy and 35% hard.
- 06
The skill tested most is multi-step (64%), then application (18%).
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: 10 in 12 shifts · 2021: 26 in 24 shifts · 2022: 24 in 24 shifts · 2023: 7 in 12 shifts · 2024: 17 in 18 shifts · 2025: 3 in 8 shifts · 2026: 7 in 9 shifts.
- Up to 2023
- 0.6
- a shift, of 25
- Since 2024
- 0.7
- 0.0
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 76/108
- 70% of analysed shifts
Recent framings
- statement I/II on differentiability and monotonicity
- find constant from continuity then integral
- count discontinuities of composite piecewise function
Revise first
- Continuity involving GIF and Fractional Part · asked 2020, 2021, 2022, 2023, 2024, 2026
- Differentiability via Functional Equations · asked 2020, 2021, 2022, 2024, 2025, 2026
- Differentiability of Modulus Functions · asked 2021, 2022, 2023, 2024, 2026
How it is asked
Difficulty, format and skill
Across all 94 questions on Continuity and Differentiability since 2017.
Difficulty
QUESTIONS- Easy4 · 4%
- Medium57 · 61%
- Hard33 · 35%
Format
SHARE- Single correct · 63 Q67%
- Numerical value · 29 Q31%
- Two statements · 2 Q2%
Skill tested
SHARE- Multi-step · 60 Q64%
- Application · 17 Q18%
- Calculation · 14 Q15%
- Conceptual · 2 Q2%
- Data or graph · 1 Q1%
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 62 ideas in this topic. 37 have never been asked yet.
- Asked directly18 · 29%
- Touched inside another question7 · 11%
- Never asked37 · 60%
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.
18 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; 13 came more than once.
count discontinuities of greatest integer function
Single correct · 17 shifts · 8 numericalderivative from functional equation
Single correct · 10 shifts · 3 numericalunknown constants from continuity of piecewise function
Single correct · 9 shifts · 1 numericalcount non-differentiable points of modulus function
Numerical value · 9 shifts · 4 numericalunknown constants from continuity of piecewise function
Single correct · 8 shifts · 1 numericalcount discontinuities of composite piecewise function
Single correct · 7 shifts · 3 numericalcontinuity and differentiability of piecewise function
Single correct · 7 shifts · 3 numericalcount non-differentiable points of composite function
Single correct · 6 shifts · 2 numericalvalue for continuity from trig limit
Numerical value · 4 shifts · 2 numericalfind constant from continuity then integral
Single correct · 3 shiftshigher-order derivative of oscillating piecewise function
Single correct · 3 shiftsunknown constants from differentiability then integrate
Single correct · 3 shifts · 1 numericalstatement i/ii on differentiability and monotonicity
Single correct · 2 shiftsunknown linear piece from continuity and derivative
Single correct · 1 shiftcontinuity of function defined by infinite limit
Single correct · 1 shiftcontinuity and differentiability of integral function
Single correct · 1 shiftunknown constants from continuity of piecewise function
Numerical value · 1 shift · 1 numericallimit recognised as derivative at a point
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Continuity involving GIF and Fractional Partcount discontinuities of greatest integer function | 17 | 17 | Single correctMulti-step | 8 | |
| Differentiability via Functional Equationsderivative from functional equation | 10 | 10 | Single correctMulti-step | 3 | |
| Finding Unknown Constants for Continuityunknown constants from continuity of piecewise function | 10 | 9 | Single correctMulti-step | 1 | |
| Differentiability of Modulus Functionscount non-differentiable points of modulus function | 9 | 9 | Numerical valueApplication | 4 | |
| Continuity at a Pointunknown constants from continuity of piecewise function | 8 | 8 | Single correctMulti-step | 1 | |
| Continuity and Differentiability of Composite Functionscount discontinuities of composite piecewise function | 7 | 7 | Single correctMulti-step | 3 | |
| Piecewise Differentiabilitycontinuity and differentiability of piecewise function | 7 | 7 | Single correctMulti-step | 3 | |
| Differentiability of Max/Min Functionscount non-differentiable points of composite function | 6 | 6 | Single correctApplication | 2 | |
| Limits via Series Expansion for Continuityvalue for continuity from trig limit | 4 | 4 | Numerical valueCalculation | 2 | |
| Finding Unknowns using Continuityfind constant from continuity then integral | 3 | 3 | Single correctMulti-step | – | |
| Existence of Higher Order Derivativeshigher-order derivative of oscillating piecewise function | 3 | 3 | Single correctMulti-step | – | |
| Finding Unknowns using Differentiabilityunknown constants from differentiability then integrate | 3 | 3 | Single correctMulti-step | 1 | |
| Modulus Traps in Trigonometric Functionsstatement i/ii on differentiability and monotonicity | 2 | 2 | Single correctApplication | – | |
| Continuity of f(x)^g(x)unknown linear piece from continuity and derivative | 1 | 1 | Single correctMulti-step | – | |
| Functions Defined by Infinite Limitscontinuity of function defined by infinite limit | 1 | 1 | Single correctMulti-step | – | |
| Continuity and Differentiability of Integral Functionscontinuity and differentiability of integral function | 1 | 1 | Single correctConceptual | – | |
| Finding Unknown Constants via Continuityunknown constants from continuity of piecewise function | 1 | 1 | Numerical valueMulti-step | 1 | |
| LHD and RHD Calculationlimit recognised as derivative at a point | 1 | 1 | Single correctApplication | – |
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
Continuity and Differentiability 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 20267 questions in 6 shifts
- 2 Apr, Shift 2Q25The number of points in the interval , at which the function , where…
Idea: Continuity involving GIF and Fractional Part
MediumNumerical value - 4 Apr, Shift 1Q25The number of points, at which the function , , is not…
Idea: Differentiability of Max/Min Functions
HardNumerical value - 4 Apr, Shift 2Q22Let and . If the number of points where is not…
Idea: Differentiability of Modulus Functions
MediumNumerical value - 5 Apr, Shift 1Q19Let be a differentiable function such that for all…
Idea: Differentiability via Functional Equations
Asked the year beforeMediumSingle correct - 6 Apr, Shift 2Q25Let and …
Idea: Continuity and Differentiability of Composite Functions
HardNumerical value - 8 Apr, Shift 2Q13For the function , , consider the following statements : Statement I : is…
Idea: Modulus Traps in Trigonometric Functions
MediumTwo statements - 8 Apr, Shift 2Q19Let . If is continuous…
Idea: Finding Unknowns using Continuity
Asked the year beforeMediumSingle correct
JEE Main 20253 questions in 3 shifts
- 2 Apr, Shift 1Q14Let be a twice differentiable function such that…
Idea: Differentiability via Functional Equations
Asked the year beforeHardSingle correct - 3 Apr, Shift 1Q17Let be…
Idea: Finding Unknowns using Continuity
MediumSingle correct - 7 Apr, Shift 2Q25If the function is continuous at , then is equal to ________.
Idea: Limits via Series Expansion for Continuity
Asked the year beforeHardNumerical value
JEE Main 202417 questions in 15 shifts
- 4 Apr, Shift 1Q6Let be a function given by…
Idea: Continuity at a Point
MediumSingle correct - 4 Apr, Shift 2Q8If the function is…
Idea: Continuity at a Point
HardSingle correct - 5 Apr, Shift 1Q7If the function , , is continuous at , then is equal to :
Idea: Limits via Series Expansion for Continuity
MediumSingle correct - 5 Apr, Shift 2Q10Let be given by , where denotes the greatest integer less than or equal…
Idea: Continuity involving GIF and Fractional Part
Asked the year beforeMediumSingle correct - 6 Apr, Shift 1Q8If , then
Idea: Existence of Higher Order Derivatives
MediumSingle correct - 6 Apr, Shift 2Q10Suppose for a differentiable function , , and . If , then is equal to :
Idea: Continuity and Differentiability of Composite Functions
Asked the year beforeMediumSingle correct - 6 Apr, Shift 2Q24Let denote the greatest integer less than or equal to . Let be a function defined by…
Idea: Continuity involving GIF and Fractional Part
Asked the year beforeMediumNumerical value - 8 Apr, Shift 2Q9For , let…
Idea: Finding Unknown Constants for Continuity
HardSingle correct - 9 Apr, Shift 1Q24Let be a function given by…
Idea: Finding Unknown Constants for Continuity
HardNumerical value - 1 Feb, Shift 1Q8Let be defined as :…
Idea: Finding Unknown Constants for Continuity
MediumSingle correct - 1 Feb, Shift 2Q8Let , . If and denote the number of points where is not continuous and not differentiable…
Idea: Differentiability of Modulus Functions
Asked the year beforeMediumSingle correct - 27 Jan, Shift 1Q8Consider the function.…
Idea: Continuity involving GIF and Fractional Part
Asked the year beforeHardSingle correct - 30 Jan, Shift 1Q30If the function is differentiable on , then…
Idea: Piecewise Differentiability
MediumNumerical value - 30 Jan, Shift 2Q7Let be a function satisfying for all…
Idea: Differentiability via Functional Equations
MediumSingle correct - 30 Jan, Shift 2Q8Let and be real constants such that the function defined by…
Idea: Finding Unknowns using Differentiability
Asked the year beforeMediumSingle correct - 31 Jan, Shift 1Q9Let be a linear funchion and is…
Idea: Continuity of f(x)^g(x)
New ideaHardSingle correct - 31 Jan, Shift 2Q8Consider the function defined by . If and be respectively the number of points…
Idea: Differentiability of Modulus Functions
Asked the year beforeMediumSingle correct
JEE Main 20237 questions in 7 shifts
- 6 Apr, Shift 1Q25Let and be the greatest integer . Then the number of points, where the function ,…
Idea: Continuity involving GIF and Fractional Part
Asked the year beforeHardNumerical value - 8 Apr, Shift 2Q25Let and be positive real numbers such that the function…
Idea: Finding Unknowns using Differentiability
MediumNumerical value - 10 Apr, Shift 1Q27Let be defined by where denotes the…
Idea: Differentiability of Modulus Functions
Asked the year beforeHardNumerical value - 11 Apr, Shift 1Q7Let , where and denotes the greatest integer less than or equal to . Then, is
Idea: Continuity involving GIF and Fractional Part
Asked the year beforeMediumSingle correct - 11 Apr, Shift 2Q10Let and be two functions defined by and…
Idea: Continuity and Differentiability of Composite Functions
Asked the year beforeMediumSingle correct - 12 Apr, Shift 1Q25Let be the greatest integer . Then the number of points in the interval , where the function…
Idea: Continuity involving GIF and Fractional Part
Asked the year beforeMediumNumerical value - 15 Apr, Shift 1Q9Let denote the greatest integer function and , . Let be the number of points in…
Idea: Differentiability of Max/Min Functions
Asked the year beforeHardSingle correct
JEE Main 202224 questions in 18 shifts
- 25 Jul, Shift 1Q26Let …
Idea: Piecewise Differentiability
Asked the year beforeHardNumerical value - 26 Jul, Shift 1Q1Let be a continuous function such that . If , then is…
Idea: Differentiability via Functional Equations
Asked the year beforeMediumSingle correct - 26 Jul, Shift 1Q7If the function…
Idea: Finding Unknown Constants for Continuity
Asked the year beforeMediumSingle correct - 26 Jul, Shift 1Q8If and…
Idea: Finding Unknown Constants for Continuity
Asked the year beforeMediumSingle correct - 27 Jul, Shift 1Q20Let a function be defined as :…
Idea: Piecewise Differentiability
Asked the year beforeHardSingle correct - 27 Jul, Shift 2Q5If for , the function is continuous at , then :
Idea: Continuity at a Point
Asked the year beforeMediumSingle correct - 27 Jul, Shift 2 · Q6Differentiability of Modulus FunctionsAsked the year beforeMedium
- 28 Jul, Shift 2 · Q65Functions Defined by Infinite LimitsNew ideaHard
- 29 Jul, Shift 1 · Q18Differentiability of Modulus FunctionsAsked the year beforeHard
- 29 Jul, Shift 2 · Q4Finding Unknown Constants for ContinuityAsked the year beforeEasy
- 29 Jul, Shift 2 · Q26Continuity involving GIF and Fractional PartAsked the year beforeHard
- 30 Jul, Shift 2 · Q69Continuity at a PointAsked the year beforeHard
- 24 Jun, Shift 1 · Q25Continuity involving GIF and Fractional PartAsked the year beforeHard
- 24 Jun, Shift 2 · Q5Continuity involving GIF and Fractional PartAsked the year beforeHard
- 24 Jun, Shift 2 · Q17Existence of Higher Order DerivativesHard
- 25 Jun, Shift 2 · Q22Continuity and Differentiability of Composite FunctionsAsked the year beforeHard
- 26 Jun, Shift 1 · Q7Continuity and Differentiability of Composite FunctionsAsked the year beforeHard
- 26 Jun, Shift 2 · Q5Differentiability of Max/Min FunctionsAsked the year beforeMedium
- 26 Jun, Shift 2 · Q21Differentiability via Functional EquationsAsked the year beforeHard
- 27 Jun, Shift 1 · Q5Continuity involving GIF and Fractional PartAsked the year beforeMedium
- 27 Jun, Shift 2 · Q25Continuity involving GIF and Fractional PartAsked the year beforeMedium
- 28 Jun, Shift 1 · Q8Continuity involving GIF and Fractional PartAsked the year beforeHard
- 28 Jun, Shift 2 · Q6Continuity and Differentiability of Composite FunctionsAsked the year beforeHard
- 29 Jun, Shift 1 · Q4Piecewise DifferentiabilityAsked the year beforeHard
JEE Main 202126 questions in 19 shifts
- 3 Aug, Shift 1 · Q66Finding Unknowns using ContinuityNew ideaMedium
- 3 Aug, Shift 2 · Q69Finding Unknown Constants for ContinuityNew ideaMedium
- 4 Aug, Shift 1 · Q89Differentiability of Modulus FunctionsNew ideaMedium
- 4 Aug, Shift 2 · Q67Differentiability via Functional EquationsAsked the year beforeEasy
- 26 Aug, Shift 1 · Q82Continuity at a PointAsked the year beforeMedium
- 26 Aug, Shift 2 · Q76Differentiability of Max/Min FunctionsAsked the year beforeMedium
- 31 Aug, Shift 1 · Q68Finding Unknown Constants for ContinuityNew ideaMedium
- 31 Aug, Shift 1 · Q69Differentiability of Modulus FunctionsNew ideaMedium
- 24 Feb, Shift 1 · Q69Continuity involving GIF and Fractional PartAsked the year beforeMedium
- 25 Feb, Shift 1 · Q86Differentiability of Modulus FunctionsNew ideaMedium
- 25 Feb, Shift 2 · Q81Differentiability of Max/Min FunctionsAsked the year beforeHard
- 26 Feb, Shift 1 · Q74Differentiability via Functional EquationsAsked the year beforeMedium
- 26 Feb, Shift 2 · Q68LHD and RHD CalculationNew ideaEasy
- 26 Feb, Shift 2 · Q77Finding Unknown Constants for ContinuityNew ideaMedium
- 22 Jul, Shift 2 · Q65Limits via Series Expansion for ContinuityNew ideaHard
- 22 Jul, Shift 2 · Q85Piecewise DifferentiabilityAsked the year beforeHard
- 25 Jul, Shift 1 · Q64Continuity and Differentiability of Integral FunctionsNew ideaMedium
- 25 Jul, Shift 1 · Q65Continuity at a PointAsked the year beforeMedium
- 25 Jul, Shift 2 · Q72Piecewise DifferentiabilityAsked the year beforeMedium
- 25 Jul, Shift 2 · Q90Finding Unknown Constants via ContinuityNew ideaMedium
- 16 Mar, Shift 2 · Q69Continuity involving GIF and Fractional PartAsked the year beforeHard
- 16 Mar, Shift 2 · Q85Continuity and Differentiability of Composite FunctionsNew ideaMedium
- 17 Mar, Shift 1 · Q84Limits via Series Expansion for ContinuityNew ideaMedium
- 18 Mar, Shift 1 · Q70Finding Unknowns using DifferentiabilityNew ideaMedium
- 18 Mar, Shift 2 · Q72Finding Unknown Constants for ContinuityNew ideaMedium
- 18 Mar, Shift 2 · Q90Differentiability via Functional EquationsAsked the year beforeMedium
JEE Main 202010 questions in 8 shifts
- 8 Jan, Shift 1 · Q58Modulus Traps in Trigonometric FunctionsNew ideaHard
- 9 Jan, Shift 1 · Q58Continuity at a PointNew ideaMedium
- 9 Jan, Shift 2 · Q58Continuity involving GIF and Fractional PartNew ideaMedium
- 2 Sep, Shift 1 · Q59Continuity at a PointNew ideaMedium
- 4 Sep, Shift 1 · Q73Differentiability via Functional EquationsNew ideaMedium
- 4 Sep, Shift 2 · Q58Differentiability via Functional EquationsNew ideaHard
- 4 Sep, Shift 2 · Q59Piecewise DifferentiabilityNew ideaMedium
- 5 Sep, Shift 1 · Q59Existence of Higher Order DerivativesNew ideaMedium
- 5 Sep, Shift 1 · Q73Continuity involving GIF and Fractional PartNew ideaMedium
- 6 Sep, Shift 2 · Q58Differentiability of Max/Min FunctionsNew ideaEasy
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.