JEE Main · Maths · Three Dimensional Geometry

Planes in 3D: JEE Main previous year questions

Name: Planes in 3D: JEE Main previous year questions
Creator: Lumi

67 questions in the 108 JEE Main shifts Lumi analysed, in 4 of 8 years. Pattern: Gone quiet. 0 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 67; in 49 of 108 shifts
Years asked: 4/8; last asked 2023
Since 2024: Quiet; 0 questions in 2024–26
Weighted estimate: –; history: 0.4 a shift on average, typically 0.0–0.8

Key findings

01
Asked in 4 of 8 years with analysed shifts and in 49 of 108 shifts: 67 questions, #32 of 196 topics. Last asked in 2023.
02
46% of its questions since 2020 tested an idea no earlier year had asked; 28 repeated an idea from the year before.
03
The most repeated idea is Family of Planes, asked 15 times in 14 shifts (2020, 2021, 2022, 2023), most often as “plane through intersection of two planes”.
04
JEE Main has asked 22 of the 59 ideas in this topic; 29 have never been asked, directly or inside another question.
05
Mostly asked as single correct (76%); 24% need a numerical answer, 12% are easy and 21% hard. It went down from 0.7 to 0.0 questions a shift since 2024.
06
The skill tested most is multi-step (73%), then calculation (16%).

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

Raw count: 2017: 0 in 1 shift · 2020: 8 in 12 shifts · 2021: 21 in 24 shifts · 2022: 23 in 24 shifts · 2023: 15 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Up to 2023: 0.7; a shift, of 25
Since 2024: 0.0; -0.7
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 49/108; 45% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 67 questions on Planes in 3D since 2017.

Difficulty

QUESTIONS

84514

Easy8 · 12%
Medium45 · 67%
Hard14 · 21%

Format

Single correct · 51 Q76%
Numerical value · 16 Q24%

Skill tested

Multi-step · 49 Q73%
Calculation · 11 Q16%
Application · 6 Q9%
Conceptual · 1 Q1%

Repeats

New idea, or one asked before?

Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 22 of the 59 ideas in this topic. 29 have never been asked yet.

22829

Asked directly22 · 37%
Touched inside another question8 · 14%
Never asked29 · 49%

Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.

Drill down

Idea, year, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

ideaAskedShareYears’17’20’21’22’23’24’25’26

OpenRepeated15 · 22%22%4/8743
- 6 Apr ’23 S1 · Q13
  If the equation of the plane passing through the line of intersection of the planes $2x-y+z=3$ , $4x-3y+5z+9=0$ and parallel to the line…
  mediumSingle correctAsked the year before
- 6 Apr ’23 S2 · Q15
  A plane P contains the line of intersection of the plane $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=6$ and…
  mediumSingle correctAsked the year before
- 13 Apr ’23 S1 · Q8
  Let the equation of plane passing through the line of intersection of the planes $x+2y+az=2$ and $x-y+z=3$ be $5x-11y+bz=6a-1$ . For…
  mediumSingle correctAsked the year before
- 26 Jul ’22 S2 · Q27
  The plane passing through the line $L: lx-y+3(1-l)z=1,\ x+2y-z=2$ and perpendicular to the plane $3x+2y+z=6$ is $3x-8y+7z=4$ . If $\theta$ …
  hardNumerical valueAsked the year before
- 27 Jul ’22 S1 · Q17
  If the plane $P$ passes through the intersection of two mutually perpendicular planes $2x + ky - 5z = 1$ and $3kx - ky + z = 5$ , $k < 3$ …
  mediumSingle correctAsked the year before
- 28 Jun ’22 S1 · Q16
  Read the question
  mediumSingle correctAsked the year before
- 28 Jun ’22 S1 · Q17
  Read the question
  hardSingle correctAsked the year before
- 26 Aug ’21 S1 · Q75
  Read the question
  mediumSingle correctAsked the year before
- 26 Aug ’21 S2 · Q79
  Read the question
  mediumSingle correctAsked the year before
- 27 Aug ’21 S1 · Q72
  Read the question
  mediumSingle correctAsked the year before
- 27 Aug ’21 S2 · Q77
  Read the question
  mediumSingle correctAsked the year before
- 31 Aug ’21 S1 · Q76
  Read the question
  mediumSingle correctAsked the year before
- 24 Feb ’21 S2 · Q76
  Read the question
  easySingle correctAsked the year before
- 17 Mar ’21 S1 · Q87
  Read the question
  mediumNumerical valueAsked the year before
- 4 Sep ’20 S1 · Q74
  Read the question
  mediumNumerical valueNew idea
OpenRepeated5 · 7%7%3/822
OpenRepeated5 · 7%7%2/84
OpenRepeated5 · 7%7%3/822
Open4 · 6%6%1/84
OpenRepeated4 · 6%6%2/822
OpenRepeated4 · 6%6%3/82
OpenRepeated3 · 4%4%2/82
OpenRepeated3 · 4%4%3/8
OpenRepeated3 · 4%4%2/82
OpenRepeated2 · 3%3%2/8
Open2 · 3%3%1/82
Open2 · 3%3%1/82
OpenRepeated2 · 3%3%2/8
Open1 · 1%1%1/8
Open1 · 1%1%1/8
Open1 · 1%1%1/8
Open1 · 1%1%1/8
Open1 · 1%1%1/8
Open1 · 1%1%1/8
Open1 · 1%1%1/8
Open1 · 1%1%1/8

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

Every idea inside this topic

22 different ideas were tested; 14 came more than once.

Family of Planes15×
plane through intersection of two planes
Single correct · 14 shifts · 3 numerical
Family of Planes Perpendicular to a Third Plane5×
plane through line perpendicular to given plane
Single correct · 5 shifts
Image of a Point in a Plane5×
image of point in plane
Single correct · 5 shifts · 2 numerical
Plane Containing a Line and a Point5×
image of point in plane through line and point
Single correct · 5 shifts
Plane Perpendicular to Two Planes4×
plane perpendicular to two planes
Single correct · 4 shifts
Direction of Line of Intersection4×
direction ratios of line of intersection of planes
Single correct · 4 shifts · 1 numerical
Plane Containing Two Lines4×
parameter from distance to plane through two lines
Numerical value · 4 shifts · 2 numerical
Plane Through Three Points3×
foot of perpendicular on line of intersection of planes
Numerical value · 3 shifts · 2 numerical
Intersection Point of Line and Plane3×
line-plane intersection point
Single correct · 3 shifts · 1 numerical
Perpendicular Bisector Plane3×
perpendicular bisector plane coefficients
Single correct · 3 shifts · 1 numerical
Plane Through Two Points Parallel to a Vector2×
plane through points parallel to line
Single correct · 2 shifts
Condition for Line to Lie in Plane2×
distance of plane from origin with line lying in it
Numerical value · 2 shifts · 1 numerical
Plane Through Point Parallel to Two Vectors2×
intercepts and volume of plane through point
Numerical value · 2 shifts · 1 numerical
Equation of a Parallel Plane2×
point on plane parallel to given plane
Single correct · 2 shifts
Angle Between a Line and a Plane1×
plane parameters from angle and distance
Single correct · 1 shift
Foot of Perpendicular to a Plane1×
foot of perpendicular on plane through three points
Single correct · 1 shift
Angle Bisector Planes1×
acute angle bisector plane of two planes
Single correct · 1 shift
Relative Position of Two Points1×
position of points relative to plane
Single correct · 1 shift
Normal and Point Form1×
plane through point perpendicular to line
Numerical value · 1 shift · 1 numerical
Projection of Line Segment on Plane1×
length of projection of vector on plane
Single correct · 1 shift
Distance Between Parallel Planes1×
distance between plane and plane through two lines
Numerical value · 1 shift · 1 numerical
Intercept Form of Plane1×
line normal to plane from centroid of intercepts
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Family of Planesplane through intersection of two planes	15	14	Single correctMulti-step	3
Family of Planes Perpendicular to a Third Planeplane through line perpendicular to given plane	5	5	Single correctMulti-step	–
Image of a Point in a Planeimage of point in plane	5	5	Single correctMulti-step	2
Plane Containing a Line and a Pointimage of point in plane through line and point	5	5	Single correctMulti-step	–
Plane Perpendicular to Two Planesplane perpendicular to two planes	4	4	Single correctCalculation	–
Direction of Line of Intersectiondirection ratios of line of intersection of planes	4	4	Single correctMulti-step	1
Plane Containing Two Linesparameter from distance to plane through two lines	4	4	Numerical valueMulti-step	2
Plane Through Three Pointsfoot of perpendicular on line of intersection of planes	3	3	Numerical valueMulti-step	2
Intersection Point of Line and Planeline-plane intersection point	3	3	Single correctCalculation	1
Perpendicular Bisector Planeperpendicular bisector plane coefficients	3	3	Single correctApplication	1
Plane Through Two Points Parallel to a Vectorplane through points parallel to line	2	2	Single correctMulti-step	–
Condition for Line to Lie in Planedistance of plane from origin with line lying in it	2	2	Numerical valueCalculation	1
Plane Through Point Parallel to Two Vectorsintercepts and volume of plane through point	2	2	Numerical valueMulti-step	1
Equation of a Parallel Planepoint on plane parallel to given plane	2	2	Single correctApplication	–
Angle Between a Line and a Planeplane parameters from angle and distance	1	1	Single correctMulti-step	–
Foot of Perpendicular to a Planefoot of perpendicular on plane through three points	1	1	Single correctMulti-step	–
Angle Bisector Planesacute angle bisector plane of two planes	1	1	Single correctMulti-step	–
Relative Position of Two Pointsposition of points relative to plane	1	1	Single correctMulti-step	–
Normal and Point Formplane through point perpendicular to line	1	1	Numerical valueMulti-step	1
Projection of Line Segment on Planelength of projection of vector on plane	1	1	Single correctMulti-step	–
Distance Between Parallel Planesdistance between plane and plane through two lines	1	1	Numerical valueMulti-step	1
Intercept Form of Planeline normal to plane from centroid of intercepts	1	1	Single correctMulti-step	–

Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas

Every question

Planes in 3D questions, year by year

The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.

Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.

Key findings

Questions a shift, year by year

Difficulty, format and skill

Difficulty

Format

Skill tested

New idea, or one asked before?

Coverage of the topic

Idea, year, question

Every idea inside this topic

Planes in 3D questions, year by year

JEE Main 202315 questions in 10 shifts

JEE Main 202223 questions in 16 shifts

JEE Main 202121 questions in 16 shifts

JEE Main 20208 questions in 7 shifts

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