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Saturday, 31 October

JEE Main 2025 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 3 April 2025, Shift 2, Maths Q7

Question 7 of 75 in this shift, Maths question 7 of 25, Section A.

Line 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, P1,P2,…,P12\mathrm{P_1, P_2, \ldots, P_{12}} are 12 points on line L1\mathrm{L_1} and Q1,Q2,…,Q9\mathrm{Q_1, Q_2, \ldots, Q_9} are 9 points on line L2\mathrm{L_2}. Then the total number of triangles, that can be formed having vertices at three of the 22 points O,P1,P2,…,P12,Q1,Q2,…,Q9\mathrm{O, P_1, P_2, \ldots, P_{12}, Q_1, Q_2, \ldots, Q_9}, is:
  1. (1)1026
  2. (2)1080
  3. (3)1134Official answer
  4. (4)1188

Official answer

Option 3

NTA final key.

Chapter
Permutations and Combinations
Topic
Permutations and Combinations
Idea tested
Triangles from Points with Collinearity

Same idea in other shifts

Asked 4× in all
  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. 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
  3. 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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.