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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Coplanarity Determinant Test

JEE Main asked Coplanarity Determinant Test 5 times in 5 of the 108 shifts Lumi analysed, in 2021, 2022 and 2023. It belongs to Skew Lines, in Three Dimensional Geometry (Maths). The longest wait between two years asking it was 1 year. In 2023 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
3 of 8
First asked
2021
last in 2023
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.03’210.04’220.21’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 3 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

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

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20233 of 12
  • 20221 of 24
  • 20211 of 24
  • 20200 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: multi-step.

  • Identify line coplanar with given line
  • Parameter extremum when lines intersect

Difficulty

Easy 1Medium 2Hard 2

2 of the 5 questions had a numerical answer.

Every question

All 5 questions

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

  1. 13 Apr 2023, Shift 2 · Q15The line, that is coplanar to the line x+3−3=y−11=z−55\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}, isMediumSingle correct
  2. 12 Apr 2023, Shift 1 · Q15Let the lines l1:x+53=y+41=z−α−2l_1: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2} and l2:3x+2y+z−2=0=x−3y+2z−13l_2: 3x+2y+z-2=0=x-3y+2z-13 be coplanar. If the point…HardSingle correct
  3. 6 Apr 2023, Shift 2 · Q28If the lines x−12=2−y−3=z−3α\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z-3}{\alpha} and x−45=y−12=zβ\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta} intersect, then the…HardNumerical value
  4. 28 Jul 2022, Shift 2 · Q75Let the lines x−1λ=y−21=z−32\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2} and x+26−2=y+183=z+28λ\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda} be coplanar and…MediumSingle correct
  5. 25 Jul 2021, Shift 2 · Q82If the lines x−k1=y−22=z−33\frac{x-k}{1}=\frac{y-2}{2}=\frac{z-3}{3} and x+13=y+22=z+31\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+3}{1} are co-planar, then the value of…EasyNumerical value

Shifts: 25 Jul 2021, Shift 2, 28 Jul 2022, Shift 2, 6 Apr 2023, Shift 2, 12 Apr 2023, Shift 1, 13 Apr 2023, 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