JEE Main · Maths · Trigonometric Functions
Properties of Triangles: JEE Main previous year questions
11 questions in the 108 JEE Main shifts Lumi analysed, in 4 of 8 years. Pattern: Comes in cycles. 3 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 11
- in 11 of 108 shifts
- Years asked
- 4/8
- last asked 2024
- Weighted estimate
- 0.1
- model; history: 0.1 a shift on average, typically 0.0–0.1
Key findings
- 01
Asked in 4 of 8 years with analysed shifts and in 11 of 108 shifts: 11 questions, #175 of 196 topics. Last asked in 2024.
- 02
55% of its questions since 2020 tested an idea no earlier year had asked; 3 repeated an idea from the year before.
- 03
The most repeated idea is Inradius and Circumradius, asked 6 times in 6 shifts (2021, 2022, 2024), most often as “circumradius area perimeter of coordinate triangle”.
- 04
JEE Main has asked 5 of the 63 ideas in this topic; 55 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (64%); 36% need a numerical answer, 0% are easy and 36% hard.
- 06
The skill tested most is multi-step (73%), then diagram reading (9%).
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: 3 in 24 shifts · 2023: 2 in 12 shifts · 2024: 3 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.
- Up to 2023
- 0.1
- a shift, of 25
- Since 2024
- 0.1
- 0.0
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 11/108
- 10% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 11 questions on Properties of Triangles since 2017.
Difficulty
QUESTIONS- Easy0 · 0%
- Medium7 · 64%
- Hard4 · 36%
Format
SHARE- Single correct · 7 Q64%
- Numerical value · 4 Q36%
Skill tested
SHARE- Multi-step · 8 Q73%
- Diagram reading · 1 Q9%
- Calculation · 1 Q9%
- Application · 1 Q9%
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 63 ideas in this topic. 55 have never been asked yet.
- Asked directly5 · 8%
- Touched inside another question3 · 5%
- Never asked55 · 87%
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; 2 came more than once.
circumradius area perimeter of coordinate triangle
Single correct · 6 shifts · 1 numericalmaximise angle ratio in right-angled figure
Numerical value · 2 shifts · 1 numericaltriangle sides from cosine rule then multiple angle
Numerical value · 1 shift · 1 numericalparameter difference from triangle centres
Numerical value · 1 shift · 1 numericalvalue from trigonometric condition in triangle
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Inradius and Circumradiuscircumradius area perimeter of coordinate triangle | 6 | 6 | Single correctMulti-step | 1 | |
| Sine Rule Applicationmaximise angle ratio in right-angled figure | 2 | 2 | Numerical valueDiagram reading | 1 | |
| Cosine Rule Applicationtriangle sides from cosine rule then multiple angle | 1 | 1 | Numerical valueMulti-step | 1 | |
| Euler Line Collinearity and Ratiosparameter difference from triangle centres | 1 | 1 | Numerical valueMulti-step | 1 | |
| Projection Rulevalue from trigonometric condition in triangle | 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
Properties of Triangles 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 20243 questions in 3 shifts
- 6 Apr, Shift 2Q30In a triangle , , , and . If , where…
Idea: Cosine Rule Application
New ideaMediumNumerical value - 8 Apr, Shift 1Q29If the orthocentre of the triangle formed by the lines , and , is the centroid of another triangle, whose…
Idea: Euler Line Collinearity and Ratios
New ideaHardNumerical value - 29 Jan, Shift 1Q14Let be the circumcenter of a triangle with vertices , and .…
Idea: Inradius and Circumradius
MediumSingle correct
JEE Main 20232 questions in 2 shifts
- 10 Apr, Shift 2Q30In the figure, and . If the area of is …
Idea: Sine Rule Application
HardNumerical value · figure - 12 Apr, Shift 1Q19In a triangle ABC, if and the lengths of the sides opposite to the angles A and C are and respectively,…
Idea: Projection Rule
New ideaHardSingle correct
JEE Main 20223 questions in 3 shifts
- 29 Jul, Shift 1Q13Let the circumcentre of a triangle with vertices , and , be . If the line AP intersects the…
Idea: Inradius and Circumradius
Asked the year beforeHardSingle correct - 29 Jul, Shift 2Q13Let A , B and C be vertices of a ABC. If…
Idea: Inradius and Circumradius
Asked the year beforeMediumSingle correct - 25 Jun, Shift 1Q3Let a, b and c be the length of sides of a triangle ABC such that If r and R are the radius of…
Idea: Inradius and Circumradius
Asked the year beforeMediumSingle correct
JEE Main 20213 questions in 3 shifts
- 27 Aug, Shift 1Q74Let , where A, B, C are angles of a triangle ABC. If the lengths of the sides opposite…
Idea: Sine Rule Application
New ideaMediumSingle correct - 16 Mar, Shift 2Q82In ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of ABC is 30 …
Idea: Inradius and Circumradius
New ideaMediumNumerical value - 18 Mar, Shift 2Q63A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be…
Idea: Inradius and Circumradius
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.