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Friday, 9 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 16 March 2021, Shift 2, Maths Q73

Question 73 of 90 in this shift, Maths question 13 of 30, Section A.

Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let α\alpha be the number of triangles having these points from different sides as vertices and β\beta be the number of quadrilaterals having these points from different sides as vertices. Then (β−α)(\beta-\alpha) is equal to :
  1. (1)1173
  2. (2)1890
  3. (3)717Official answer
  4. (4)795

Official answer

Option 3

NTA final key.

Chapter
Permutations and Combinations
Topic
Permutations and Combinations
Idea tested
Number of Triangles from Points

Same idea in other shifts

Asked 3× in all
  1. 2 Apr 2026, Shift 2 · Q7Let pnp_n denote the total number of triangles formed by joining the vertices of an nn-side regular polygon. If pn+1−pn=66p_{n+1} - p_n = 66,…EasySingle correct
  2. 7 Apr 2025, Shift 2 · Q8Let pp be the number of all triangles that can be formed by joining the vertices of a regular polygon PP of nn sides and qq be the…MediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.