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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Family of Planes

JEE Main asked Family of Planes 15 times in 14 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2023. It belongs to Planes in 3D, in Three Dimensional Geometry (Maths). The longest wait between two years asking it was 1 year. In 2021, 2022 and 2023 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
15
in 14 shifts
Years
4 of 8
First asked
2020
last in 2023
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.08’200.24’210.14’220.21’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 7 in 24 shifts · 2022: 4 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
  • 202223 of 24
  • 20217 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: multi-step.

  • Plane through intersection of two planes
  • Plane through intersection parallel to a line

Difficulty

Easy 1Medium 12Hard 2

3 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. 13 Apr 2023, Shift 1 · Q8Let the equation of plane passing through the line of intersection of the planes x+2y+az=2x+2y+az=2 and x−y+z=3x-y+z=3 be 5x−11y+bz=6a−15x-11y+bz=6a-1. For…MediumSingle correct
  2. 6 Apr 2023, Shift 2 · Q15A plane P contains the line of intersection of the plane r⃗⋅(i^+j^+k^)=6\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=6 and…MediumSingle correct
  3. 6 Apr 2023, Shift 1 · Q13If the equation of the plane passing through the line of intersection of the planes 2x−y+z=32x-y+z=3, 4x−3y+5z+9=04x-3y+5z+9=0 and parallel to the line…MediumSingle correct
  4. 28 Jun 2022, Shift 1 · Q16The acute angle between the planes P1_1 and P2_2, when P1_1 and P2_2 are the planes passing through the intersection of the planes…MediumSingle correct
  5. 28 Jun 2022, Shift 1 · Q17Let the plane P:r⃗⋅a⃗=dP:\vec{r}\cdot\vec{a}=d contain the line of intersection of two planes…HardSingle correct
  6. 27 Jul 2022, Shift 1 · Q17If the plane PP passes through the intersection of two mutually perpendicular planes 2x+ky−5z=12x + ky - 5z = 1 and 3kx−ky+z=53kx - ky + z = 5, k<3k < 3…MediumSingle correct
  7. 26 Jul 2022, Shift 2 · Q27The plane passing through the line L:lx−y+3(1−l)z=1, x+2y−z=2L: lx-y+3(1-l)z=1,\ x+2y-z=2 and perpendicular to the plane 3x+2y+z=63x+2y+z=6 is 3x−8y+7z=43x-8y+7z=4. If θ\theta…HardNumerical value
  8. 17 Mar 2021, Shift 1 · Q87If the equation of the plane passing through the line of intersection of the planes 2x−7y+4z−3=02x-7y+4z-3=0, 3x−5y+4z+11=03x-5y+4z+11=0 and the point…MediumNumerical value
  9. 24 Feb 2021, Shift 2 · Q76The vector equation of the plane passing through the intersection of the planes r⃗⋅(i^+j^+k^)=1\vec{r}\cdot(\hat{i}+\hat{j}+\hat{k})=1 and…EasySingle correct
  10. 31 Aug 2021, Shift 1 · Q76Let the equation of the plane, that passes through the point (1,4,−3)(1, 4, -3) and contains the line of intersection of the planes…MediumSingle correct
  11. 27 Aug 2021, Shift 2 · Q77The equation of the plane passing through the line of intersection of the planes r⃗⋅(i^+j^+k^)=1\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1 and…MediumSingle correct
  12. 27 Aug 2021, Shift 1 · Q72Equation of a plane at a distance 221\sqrt{\frac{2}{21}} from the origin, which contains the line of intersection of the planes x−y−z−1=0x-y-z-1=0…MediumSingle correct
  13. 26 Aug 2021, Shift 2 · Q79Let P be the plane passing through the point (1,2,3)(1,2,3) and the line of intersection of the planes…MediumSingle correct
  14. 26 Aug 2021, Shift 1 · Q75A plane P contains the line x+2y+3z+1=0=x−y−z−6x+2y+3z+1=0=x-y-z-6, and is perpendicular to the plane −2x+y+z+8=0-2x+y+z+8=0. Then which of the following points…MediumSingle correct
  15. 4 Sep 2020, Shift 1 · Q74If the equation of a plane P, passing through the intersection of the planes, x+4y−z+7=0x + 4y - z + 7 = 0 and 3x+y+5z=83x + y + 5z = 8 is…MediumNumerical value

Shifts: 4 Sep 2020, Shift 1, 24 Feb 2021, Shift 2, 17 Mar 2021, Shift 1, 26 Aug 2021, Shift 2, 26 Aug 2021, Shift 1, 27 Aug 2021, Shift 2, 27 Aug 2021, Shift 1, 31 Aug 2021, Shift 1, 28 Jun 2022, Shift 1, 26 Jul 2022, Shift 2, 27 Jul 2022, Shift 1, 6 Apr 2023, Shift 2, 6 Apr 2023, Shift 1, 13 Apr 2023, Shift 1.

Same topic

Other ideas in Planes in 3D

Planes in 3D has 22 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas