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Friday, 9 October

JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2025, Shift 1, Maths Q13

Question 13 of 75 in this shift, Maths question 13 of 25, Section A.

Let the vertices Q and R of the triangle PQR lie on the line x+35=y−12=z+43\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, QR=5\mathrm{QR}=5 and the coordinates of the point P be (0,2,3)(0, 2, 3). If the area of the triangle PQR is mn\frac{m}{n} then :
  1. (1)5m−212 n=05\mathrm{m}-21\sqrt{2}\,\mathrm{n}=0
  2. (2)5m−221 n=05\mathrm{m}-2\sqrt{21}\,\mathrm{n}=0
  3. (3)m−521 n=0\mathrm{m}-5\sqrt{21}\,\mathrm{n}=0
  4. (4)2m−521 n=02\mathrm{m}-5\sqrt{21}\,\mathrm{n}=0Official answer

Official answer

Option 4

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Lines in 3D
Idea tested
Perpendicular Distance from Point to Line

Same idea in other shifts

Asked 4× in all
  1. 5 Apr 2026, Shift 1 · Q13The square of the distance of the point P(5,6,7)P(5, 6, 7) from the line x−22=y−53=z−24\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4} is equal to:EasySingle correct
  2. 7 Apr 2025, Shift 2 · Q17Consider the lines L1:x−1=y−2=zL_1: x-1=y-2=z and L2:x−2=y=z−1L_2: x-2=y=z-1. Let the feet of the perpendiculars from the point P(5,1,−3)P(5,1,-3) on the lines L1L_1…MediumSingle correct
  3. 9 Apr 2024, Shift 2 · Q16Consider the line L passing through the points (1,2,3)(1, 2, 3) and (2,3,5)(2, 3, 5). The distance of the point…HardSingle 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.