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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Family of Planes Perpendicular to a Third Plane

JEE Main asked Family of Planes Perpendicular to a Third Plane 5 times in 5 of the 108 shifts Lumi analysed, in 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 2022 and 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.

00.10.20’170’200.03’210.07’220.14’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 2 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
  • 20232 of 12
  • 20222 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.

  • Plane through line perpendicular to given plane
  • Plane rotated about line of intersection and distance

Difficulty

Easy 0Medium 3Hard 2

Every question was multiple choice.

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. 12 Apr 2023, Shift 1 · Q14Let the plane P: 4x−y+z=104x-y+z=10 be rotated by an angle π2\frac{\pi}{2} about its line of intersection with the plane x+y−z=4x+y-z=4. If α\alpha…HardSingle correct
  2. 8 Apr 2023, Shift 1 · Q15If the equation of the plane containing the line x+2y+3z−4=0=2x+y−z+5x+2y+3z-4=0=2x+y-z+5 and perpendicular to the plane…MediumSingle correct
  3. 26 Jun 2022, Shift 2 · Q14If the plane 2x+y−5z=02x + y - 5z = 0 is rotated about its line of intersection with the plane 3x−y+4z−7=03x - y + 4z - 7 = 0 by an angle of…MediumSingle correct
  4. 26 Jun 2022, Shift 1 · Q15Let the plane 2x+3y+z+20=02x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x−3y+5z=8x - 3y + 5z = 8. If…HardSingle correct
  5. 4 Aug 2021, Shift 2 · Q76The distance of the point (5,6,9)(5,6,9) from the plane, which passes through the line of intersection of the planes x+y−z=1x+y-z=1 and…MediumSingle correct

Shifts: 4 Aug 2021, Shift 2, 26 Jun 2022, Shift 2, 26 Jun 2022, Shift 1, 8 Apr 2023, Shift 1, 12 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