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Saturday, 31 October

JEE Main · Maths · Permutations and Combinations

Triangles from Points with Collinearity

JEE Main asked Triangles from Points with Collinearity 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2024 and 2025. It belongs to Permutations and Combinations (Maths). The longest wait between two years asking it was 3 years. In 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
3 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.03’210’220’230.05’240.25’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 2 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20252 of 8
  • 20241 of 18
  • 20230 of 12
  • 20220 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: application.

  • Count triangles from collinear point sets
  • Count triangles from points with collinear subset

Difficulty

Easy 3Medium 1Hard 0

Every question was multiple choice.

Every question

All 4 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 8 Apr 2025, Shift 2 · Q7There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total…EasySingle correct
  2. 3 Apr 2025, Shift 2 · Q7Line L1\mathrm{L_1} of slope 2 and line L2\mathrm{L_2} of slope 12\frac{1}{2} intersect at the origin O. In the first quadrant,…EasySingle correct
  3. 4 Apr 2024, Shift 1 · Q7There are 5 points P1,P2,P3,P4,P5P_1, P_2, P_3, P_4, P_5 on the side AB, excluding A and B, of a triangle ABC. Similarly there are 6 points…MediumSingle correct
  4. 17 Mar 2021, Shift 2 · Q72If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be…EasySingle correct

Shifts: 17 Mar 2021, Shift 2, 4 Apr 2024, Shift 1, 3 Apr 2025, Shift 2, 8 Apr 2025, Shift 2.

Same topic

Other ideas in Permutations and Combinations

Permutations and Combinations has 33 ideas JEE Main has asked; 20 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas