Learn

Saturday, 10 October

JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 April 2025, Shift 1, Maths Q14

Question 14 of 75 in this shift, Maths question 14 of 25, Section A.

Line L1\mathrm{L}_1 passes through the point (1,2,3)(1, 2, 3) and is parallel to zz-axis. Line L2\mathrm{L}_2 passes through the point (λ,5,6)(\lambda, 5, 6) and is parallel to yy-axis. Let for λ=λ1,λ2\lambda = \lambda_1, \lambda_2, λ2<λ1\lambda_2 < \lambda_1, the shortest distance between the two lines be 3. Then the square of the distance of the point (λ1,λ2,7)(\lambda_1, \lambda_2, 7) from the line L1\mathrm{L}_1 is
  1. (1)25Official answer
  2. (2)32
  3. (3)37
  4. (4)40

Official answer

Option 1

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Skew Lines
Idea tested
Solve for Parameter Given Shortest Distance

Same topic in other shifts

All Skew Lines questions
  1. 4 Apr 2026, Shift 2 · Q13The shortest distance between the lines…EasySingle correct
  2. 6 Apr 2026, Shift 2 · Q14The shortest distance between the lines x−41=y−32=z−2−3\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3} and x+22=y−64=z−5−5\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5} is :EasySingle correct
  3. 2 Apr 2025, Shift 2 · Q15The line L1L_1 is parallel to the vector a⃗=−3i^+2j^+4k^\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k} and passes through the point (7,6,2)(7, 6, 2) and the line…EasySingle correct
  4. 4 Apr 2025, Shift 2 · Q14Let the values of p, for which the shortest distance between the lines x+13=y4=z5\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5} and…MediumSingle correct
  5. 7 Apr 2025, Shift 1 · Q14If the shortest distance between the lines x−12=y−23=z−34\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} and…MediumSingle correct
  6. 8 Apr 2025, Shift 2 · Q15Let the values of λ\lambda for which the shortest distance between the lines x−12=y−23=z−34\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} and…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.