JEE Main · Maths · Inverse Trigonometric Functions
Inverse Trig Domains: JEE Main previous year questions
13 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Asked most years. 4 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 13
- in 13 of 108 shifts
- Years asked
- 6/8
- last asked 2026
- Weighted estimate
- 0.1
- model; history: 0.1 a shift on average, typically 0.0–0.1
Key findings
- 01
Asked in 6 of 8 years with analysed shifts and in 13 of 108 shifts: 13 questions, #167 of 196 topics. The years that asked it were 1.2 apart on average.
- 02
85% of its questions since 2020 tested an idea no earlier year had asked; none repeated an idea from the year before.
- 03
The most repeated idea is Inverse Trig with GIF and Fractional Part, asked 3 times in 3 shifts (2021, 2026), most often as “domain of inverse trig with greatest integer”.
- 04
JEE Main has asked 8 of the 61 ideas in this topic; 45 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (100%); 0% need a numerical answer, 23% are easy and 15% hard.
- 06
The skill tested most is multi-step (54%), 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: 4 in 24 shifts · 2022: 4 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 1 in 8 shifts · 2026: 2 in 9 shifts.
- Up to 2023
- 0.1
- a shift, of 25
- Since 2024
- 0.1
- 0.1
- Usual gap
- 1.2 yrs
- between years asking it
- Shifts with it
- 13/108
- 12% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 13 questions on Inverse Trig Domains since 2017.
Difficulty
QUESTIONS- Easy3 · 23%
- Medium8 · 62%
- Hard2 · 15%
Format
SHARE- Single correct · 13 Q100%
Skill tested
SHARE- Multi-step · 7 Q54%
- Application · 4 Q31%
- Calculation · 2 Q15%
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 8 of the 61 ideas in this topic. 45 have never been asked yet.
- Asked directly8 · 13%
- Touched inside another question8 · 13%
- Never asked45 · 74%
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.
7 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
8 different ideas were tested; 3 came more than once.
domain of inverse trig with greatest integer
Single correct · 3 shiftsdomain of composite inverse trig function
Single correct · 3 shiftsdomain of inverse trig with rational argument
Single correct · 2 shiftsdomains of nested log and inverse trig functions
Single correct · 1 shiftdomain of inverse trig with rational argument
Single correct · 1 shiftevaluate inverse trig of trig outside principal branch
Single correct · 1 shiftdomain of inverse trigonometric function
Single correct · 1 shiftdomain of inverse trig with modulus rational argument
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Inverse Trig with GIF and Fractional Partdomain of inverse trig with greatest integer | 3 | 3 | Single correctMulti-step | – | |
| Domain of Rational Composite Inverse Trigdomain of composite inverse trig function | 3 | 3 | Single correctApplication | – | |
| Domain Intersection of Multiple Inverse Trig Functionsdomain of inverse trig with rational argument | 2 | 2 | Single correctMulti-step | – | |
| Domain of Inverse Trig with Log/Exp Argumentsdomains of nested log and inverse trig functions | 1 | 1 | Single correctMulti-step | – | |
| Domain of Inverse Trig with Rational Argumentsdomain of inverse trig with rational argument | 1 | 1 | Single correctMulti-step | – | |
| Evaluating arcsin(sin x) Outside Principal Branchevaluate inverse trig of trig outside principal branch | 1 | 1 | Single correctCalculation | – | |
| Sec-1 and Csc-1 Domainsdomain of inverse trigonometric function | 1 | 1 | Single correctApplication | – | |
| Domain of Inverse Trig with Modulus Argumentsdomain of inverse trig with modulus rational argument | 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
Inverse Trig Domains 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 1Q1Let denote the greatest integer function. If the domain of the function is…
Idea: Inverse Trig with GIF and Fractional Part
MediumSingle correct - 6 Apr, Shift 1Q1Let denote the greatest integer function. If the domain of the function is…
Idea: Inverse Trig with GIF and Fractional Part
MediumSingle correct
JEE Main 20251 question in 1 shift
- 4 Apr, Shift 2Q1Let the domains of the functions and be…
Idea: Domain of Inverse Trig with Log/Exp Arguments
New ideaMediumSingle correct
JEE Main 20241 question in 1 shift
- 9 Apr, Shift 1Q1If the domain of the function is , then is equal…
Idea: Domain of Inverse Trig with Rational Arguments
New ideaMediumSingle correct
JEE Main 20224 questions in 4 shifts
- 28 Jul, Shift 1Q2Considering only the principal values of the inverse trigonometric functions, the domain of the function…
Idea: Domain of Rational Composite Inverse Trig
New ideaEasySingle correct - 29 Jul, Shift 2Q19The domain of the function is :
Idea: Domain of Rational Composite Inverse Trig
New ideaMediumSingle correct - 27 Jun, Shift 1Q19is equal to :
Idea: Evaluating arcsin(sin x) Outside Principal Branch
New ideaEasySingle correct - 29 Jun, Shift 1Q15The domain of the function is :
Idea: Domain of Rational Composite Inverse Trig
New ideaMediumSingle correct
JEE Main 20214 questions in 4 shifts
- 26 Aug, Shift 2Q61The domain of the function is :
Idea: Sec-1 and Csc-1 Domains
New ideaEasySingle correct - 31 Aug, Shift 2Q79The domain of the function is :
Idea: Domain Intersection of Multiple Inverse Trig Functions
New ideaHardSingle correct - 22 Jul, Shift 2Q61If the domain of the function is the interval…
Idea: Domain Intersection of Multiple Inverse Trig Functions
New ideaMediumSingle correct - 17 Mar, Shift 2Q61The number of solutions of the equation , for…
Idea: Inverse Trig with GIF and Fractional Part
New ideaHardSingle correct
JEE Main 20201 question in 1 shift
- 2 Sep, Shift 1Q69The domain of the function is . Then a is equal to :
Idea: Domain of Inverse Trig with Modulus Arguments
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.