JEE Main · Maths · Relations and Functions
Functions and Domain: JEE Main previous year questions
36 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 16 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 36
- in 35 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.3
- model; history: 0.3 a shift on average, typically 0.1–0.5
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 35 of 108 shifts: 36 questions, #92 of 196 topics.
- 02
64% of its questions since 2020 tested an idea no earlier year had asked; 7 repeated an idea from the year before.
- 03
The most repeated idea is Inverse Trig Function Domain, asked 6 times in 6 shifts (2022, 2023, 2024, 2025), most often as “domain endpoints of inverse trig and log”.
- 04
JEE Main has asked 20 of the 61 ideas in this topic; 32 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (75%); 19% need a numerical answer, 17% are easy and 17% hard.
- 06
The skill tested most is multi-step (61%), then application (31%).
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: 1 in 12 shifts · 2021: 9 in 24 shifts · 2022: 2 in 24 shifts · 2023: 8 in 12 shifts · 2024: 10 in 18 shifts · 2025: 4 in 8 shifts · 2026: 2 in 9 shifts.
- Up to 2023
- 0.2
- a shift, of 25
- Since 2024
- 0.4
- 0.2
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 35/108
- 32% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 36 questions on Functions and Domain since 2017.
Difficulty
QUESTIONS- Easy6 · 17%
- Medium24 · 67%
- Hard6 · 17%
Format
SHARE- Single correct · 27 Q75%
- Numerical value · 7 Q19%
- Other · 1 Q3%
- Two statements · 1 Q3%
Skill tested
SHARE- Multi-step · 22 Q61%
- Application · 11 Q31%
- Calculation · 2 Q6%
- Conceptual · 1 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 20 of the 61 ideas in this topic. 32 have never been asked yet.
- Asked directly20 · 33%
- Touched inside another question9 · 15%
- Never asked32 · 52%
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
20 different ideas were tested; 8 came more than once.
domain endpoints of inverse trig and log
Single correct · 6 shifts · 1 numericalstatement i/ii on inverse function
Single correct · 3 shiftsdomain of sum of log and inverse trig
Single correct · 3 shiftsrange of composition of piecewise functions
Single correct · 3 shiftsstatement i/ii on domain and range
Single correct · 3 shiftsdomain endpoints of log-modulus function
Numerical value · 2 shifts · 2 numericalrange of trig function then gp sum
Numerical value · 2 shifts · 1 numericaldomain of function with inverse trig and gif
Numerical value · 2 shifts · 1 numericaldomain of function with roots and modulus
Single correct · 1 shiftdomain of nested logarithmic function
Single correct · 1 shiftclassify function as one-one or onto
Single correct · 1 shiftrange of reciprocal of trig expression
Single correct · 1 shiftrange of function via monotonicity then point-line distance
Single correct · 1 shiftdomain of function with root, rational and log parts
Single correct · 1 shiftcount integral solutions of log inequality
Single correct · 1 shiftrange of inverse trig composite function
Single correct · 1 shiftdomain of inverse trig composite with removable gap
Single correct · 1 shiftcount solutions of logarithmic equation
Numerical value · 1 shift · 1 numericalminimum of sum of modulus functions
Numerical value · 1 shift · 1 numericalrange of function with greatest integer
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Inverse Trig Function Domaindomain endpoints of inverse trig and log | 6 | 6 | Single correctMulti-step | 1 | |
| Domain and Range of Inverse Functionsstatement i/ii on inverse function | 3 | 3 | Single correctMulti-step | – | |
| Intersection of Domainsdomain of sum of log and inverse trig | 3 | 3 | Single correctApplication | – | |
| Range of Composite Functionsrange of composition of piecewise functions | 3 | 3 | Single correctMulti-step | – | |
| Domain Constraints of Greatest Integer Functionstatement i/ii on domain and range | 3 | 3 | Single correctMulti-step | – | |
| Domain via Logarithmic Inequalitiesdomain endpoints of log-modulus function | 2 | 2 | Numerical valueMulti-step | 2 | |
| Range of Quadratic Rational Functionsrange of trig function then gp sum | 2 | 2 | Numerical valueApplication | 1 | |
| Domain of Inverse Secant and Cosecantdomain of function with inverse trig and gif | 2 | 2 | Numerical valueApplication | 1 | |
| Domain of 1/sqrt(f(x))domain of function with roots and modulus | 1 | 1 | Single correctApplication | – | |
| Domain of Nested Logarithmsdomain of nested logarithmic function | 1 | 1 | Single correctMulti-step | – | |
| Domain and Range of Piecewise Functionsclassify function as one-one or onto | 1 | 1 | Single correctMulti-step | – | |
| Range of a*sin(x) + b*cos(x) Formsrange of reciprocal of trig expression | 1 | 1 | Single correctApplication | – | |
| Range via Monotonicity and Derivativesrange of function via monotonicity then point-line distance | 1 | 1 | Single correctMulti-step | – | |
| Square Root Function Domaindomain of function with root, rational and log parts | 1 | 1 | Single correctApplication | – | |
| Domain of Variable Base Logarithmscount integral solutions of log inequality | 1 | 1 | Single correctMulti-step | – | |
| Range of Inverse Trigonometric Functionsrange of inverse trig composite function | 1 | 1 | Single correctApplication | – | |
| Domain of Composite Functionsdomain of inverse trig composite with removable gap | 1 | 1 | Single correctMulti-step | – | |
| Logarithmic Function Domaincount solutions of logarithmic equation | 1 | 1 | Numerical valueApplication | 1 | |
| Range of Sum of Modulus Functionsminimum of sum of modulus functions | 1 | 1 | Numerical valueCalculation | 1 | |
| Range Involving Mixed GIF and Fractional Partrange of function with greatest integer | 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
Functions and Domain 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
- 2 Apr, Shift 1Q21If the domain of the function is…
Idea: Domain via Logarithmic Inequalities
HardNumerical value - 4 Apr, Shift 2Q1For the function defined by , among the two statements: (I) The set…
Idea: Domain and Range of Inverse Functions
HardOther
JEE Main 20254 questions in 4 shifts
- 2 Apr, Shift 2Q1If the domain of the function is , then is equal to :
Idea: Domain of 1/sqrt(f(x))
New ideaEasySingle correct - 3 Apr, Shift 1Q2If the domain of the function is ,…
Idea: Inverse Trig Function Domain
Asked the year beforeMediumSingle correct - 3 Apr, Shift 2Q2If the domain of the function is , then…
Idea: Domain of Nested Logarithms
New ideaMediumSingle correct - 8 Apr, Shift 2Q21Let the domain of the function be and the domain of…
Idea: Inverse Trig Function Domain
Asked the year beforeMediumNumerical value
JEE Main 202410 questions in 10 shifts
- 4 Apr, Shift 1Q1If the domain of the function is…
Idea: Inverse Trig Function Domain
Asked the year beforeMediumSingle correct - 6 Apr, Shift 1Q2The function , is
Idea: Range of Quadratic Rational Functions
New ideaMediumSingle correct - 6 Apr, Shift 2Q1Let be a function defined on . Then the range of the function is equal to :
Idea: Range of a*sin(x) + b*cos(x) Forms
New ideaEasySingle correct - 8 Apr, Shift 1Q21If the range of , is , then…
Idea: Range of Quadratic Rational Functions
New ideaMediumNumerical value - 8 Apr, Shift 2Q2Let where and…
Idea: Domain and Range of Piecewise Functions
New ideaMediumSingle correct - 1 Feb, Shift 2Q1If the domain of the function is , then…
Idea: Square Root Function Domain
New ideaMediumSingle correct - 29 Jan, Shift 1Q1If ;…
Idea: Range of Composite Functions
Asked the year beforeMediumSingle correct - 30 Jan, Shift 1Q1If the domain of the function is , then…
Idea: Inverse Trig Function Domain
Asked the year beforeMediumSingle correct - 30 Jan, Shift 2Q1If the domain of the function is…
Idea: Intersection of Domains
MediumSingle correct - 31 Jan, Shift 2Q1If the function defined by is one - one and onto, then the distance of the point…
Idea: Range via Monotonicity and Derivatives
New ideaMediumSingle correct
JEE Main 20238 questions in 8 shifts
- 6 Apr, Shift 2Q1[English stem not rendered in the PDF; reconstructed from the Hindi copy] Let the function , where…
Idea: Domain Constraints of Greatest Integer Function
MediumTwo statements - 8 Apr, Shift 2Q21If domain of the function is…
Idea: Domain via Logarithmic Inequalities
New ideaHardNumerical value - 10 Apr, Shift 1Q1If , , then the least value of…
Idea: Range of Composite Functions
Asked the year beforeHardSingle correct - 10 Apr, Shift 2Q21If the domain of the function is , then…
Idea: Domain of Inverse Secant and Cosecant
MediumNumerical value - 11 Apr, Shift 1Q5The number of integral solutions of is
Idea: Domain of Variable Base Logarithms
New ideaHardSingle correct - 11 Apr, Shift 2Q2The domain of the function is (where denotes the greatest integer less than or equal to…
Idea: Domain Constraints of Greatest Integer Function
MediumSingle correct - 13 Apr, Shift 2Q1The range of is
Idea: Range of Inverse Trigonometric Functions
New ideaMediumSingle correct - 15 Apr, Shift 1Q1If the domain of the function is…
Idea: Inverse Trig Function Domain
Asked the year beforeMediumSingle correct
JEE Main 20222 questions in 2 shifts
- 27 Jul, Shift 2Q1The domain of the function , where [t] is the greatest…
Idea: Inverse Trig Function Domain
New ideaHardSingle correct - 26 Jun, Shift 2Q1Let be defined as and be…
Idea: Range of Composite Functions
New ideaMediumSingle correct
JEE Main 20219 questions in 8 shifts
- 4 Aug, Shift 1Q84If , , then the minimum value of is ______.
Idea: Range of Sum of Modulus Functions
New ideaEasyNumerical value - 4 Aug, Shift 2Q61The domain of the function is
Idea: Intersection of Domains
New ideaEasySingle correct - 26 Feb, Shift 1Q85The number of solutions of the equation is _________.
Idea: Logarithmic Function Domain
New ideaMediumNumerical value - 26 Feb, Shift 2Q69Let and . If , then the domain of the function is :
Idea: Domain of Composite Functions
New ideaMediumSingle correct - 22 Jul, Shift 2Q79Let denote the greatest integer less than or equal to . Then, the values of satisfying the equation…
Idea: Domain Constraints of Greatest Integer Function
New ideaMediumSingle correct - 17 Mar, Shift 1Q69The inverse of is :
Idea: Domain and Range of Inverse Functions
New ideaEasySingle correct - 18 Mar, Shift 1Q61If the functions are defined as and , then what is the common domain of the following functions :…
Idea: Intersection of Domains
New ideaEasySingle correct - 18 Mar, Shift 1Q71The real valued function , where denotes the greatest integer less than or equal to…
Idea: Domain of Inverse Secant and Cosecant
New ideaMediumSingle correct - 18 Mar, Shift 2Q76Let be defined by . Let be given as .…
Idea: Domain and Range of Inverse Functions
New ideaMediumSingle correct
JEE Main 20201 question in 1 shift
- 8 Jan, Shift 2Q51Let be a function defined by , where denotes the greatest integer .…
Idea: Range Involving Mixed GIF and Fractional Part
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.