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Saturday, 31 October

JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 1, Maths Q13

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

Let the line L pass through (1,1,1)(1, 1, 1) and intersect the lines x−12=y+13=z−14\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4} and x−31=y−42=z1\frac{x-3}{1} = \frac{y-4}{2} = \frac{z}{1}. Then, which of the following points lies on the line L?
  1. (1)(4,22,7)(4, 22, 7)
  2. (2)(7,15,13)(7, 15, 13)Official answer
  3. (3)(10,−29,−50)(10, -29, -50)
  4. (4)(5,4,3)(5, 4, 3)

Official answer

Option 2

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Lines in 3D
Idea tested
Condition for Intersection of Two Lines

Same idea in other shifts

Asked 3× in all
  1. 5 Apr 2026, Shift 1 · Q15The square of the distance of the point of intersection of the lines…MediumSingle correct
  2. 3 Sep 2020, Shift 1 · Q66The lines r⃗=(i^−j^)+l(2i^+k^)\vec{r}=(\hat{i}-\hat{j})+l(2\hat{i}+\hat{k}) and r⃗=(2i^−j^)+m(i^+j^−k^)\vec{r}=(2\hat{i}-\hat{j})+\mathrm{m}(\hat{i}+\hat{j}-\hat{k})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.