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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Cartesian Shortest Distance

JEE Main asked Cartesian Shortest Distance 15 times in 15 of the 108 shifts Lumi analysed, in 2020, 2022, 2023, 2024, 2025 and 2026. It belongs to Skew Lines, in Three Dimensional Geometry (Maths). The longest wait between two years asking it was 2 years. In 2022, 2023 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
15
in 15 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.08’200’210.14’220.14’230.28’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 4 in 24 shifts · 2023: 2 in 12 shifts · 2024: 6 in 18 shifts · 2025: 1 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20251 of 8
  • 20246 of 18
  • 20232 of 12
  • 20224 of 24
  • 20210 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Shortest distance between skew lines
  • Parameter from shortest distance between skew lines

Difficulty

Easy 3Medium 11Hard 1

2 of the 15 questions had a numerical answer.

Every question

All 15 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 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
  2. 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
  3. 31 Jan 2024, Shift 2 · Q17The shortest distance, between lines L1L_1 and L2L_2, where L1:x−12=y+1−3=z+42L_1:\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2} and L2L_2 is the line,…MediumSingle correct
  4. 30 Jan 2024, Shift 1 · Q28If d1d_1 is the shortest distance between the lines x+1=2y=−12zx+1=2y=-12z, x=y+2=6z−6x=y+2=6z-6 and d2d_2 is the shortest distance between the lines…MediumNumerical value
  5. 27 Jan 2024, Shift 1 · Q18If the shortest distance between the lines x−41=y+12=z−3\dfrac{x-4}{1}=\dfrac{y+1}{2}=\dfrac{z}{-3} and…MediumSingle correct
  6. 1 Feb 2024, Shift 1 · Q16If the shortest distance between the lines x−λ−2=y−21=z−11\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1} and…MediumSingle correct
  7. 9 Apr 2024, Shift 1 · Q16The shortest distance between the lines x−34=y+7−11=z−15\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5} and x−53=y−9−6=z+21\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1} is :EasySingle correct
  8. 8 Apr 2024, Shift 2 · Q16If the shortest distance between the lines x−λ2=y−43=z−34\frac{x-\lambda}{2} = \frac{y-4}{3} = \frac{z-3}{4} and…MediumSingle correct
  9. 15 Apr 2023, Shift 1 · Q15Let S be the set of all values of λ\lambda, for which the shortest distance between the lines…MediumSingle correct
  10. 10 Apr 2023, Shift 1 · Q15The shortest distance between the lines x+21=y−2=z−52\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2} and x−41=y−12=z+30\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0} isEasySingle correct
  11. 27 Jun 2022, Shift 2 · Q14The shortest distance between the lines x−32=y−23=z−1−1\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{-1} and x+32=y−61=z−53\frac{x+3}{2}=\frac{y-6}{1}=\frac{z-5}{3}, isMediumSingle correct
  12. 24 Jun 2022, Shift 2 · Q14If the shortest distance between the lines x−12=y−23=z−3λ\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{\lambda} and…MediumSingle correct
  13. 30 Jul 2022, Shift 2 · Q87Let L1L_1 be a line in the yzyz - plane with yy and zz intercepts 14\frac{1}{4} and 1C\frac{1}{C} (C>0)(C > 0) respectively. Let L2L_2 be…HardNumerical value
  14. 25 Jul 2022, Shift 2 · Q16The shortest distance between the lines x+7−6=y−67=z\frac{x+7}{-6}=\frac{y-6}{7}=z and 7−x2=y−2=z−6\frac{7-x}{2}=y-2=z-6 isMediumSingle correct
  15. 8 Jan 2020, Shift 1 · Q65The shortest distance between the lines x−33=y−8−1=z−31\dfrac{x-3}{3}=\dfrac{y-8}{-1}=\dfrac{z-3}{1} and…MediumSingle correct

Shifts: 8 Jan 2020, Shift 1, 24 Jun 2022, Shift 2, 27 Jun 2022, Shift 2, 25 Jul 2022, Shift 2, 30 Jul 2022, Shift 2, 10 Apr 2023, Shift 1, 15 Apr 2023, Shift 1, 27 Jan 2024, Shift 1, 30 Jan 2024, Shift 1, 31 Jan 2024, Shift 2, 1 Feb 2024, Shift 1, 8 Apr 2024, Shift 2, 9 Apr 2024, Shift 1, 7 Apr 2025, Shift 1, 6 Apr 2026, Shift 2.

Same topic

Other ideas in Skew Lines

Skew Lines has 8 ideas JEE Main has asked; 4 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas