JEE Main · Maths · Three Dimensional Geometry

Point-Plane Distance: JEE Main previous year questions

Name: Point-Plane Distance: JEE Main previous year questions
Creator: Lumi

28 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Gone quiet. 1 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 28; in 24 of 108 shifts
Years asked: 6/8; last asked 2026
Since 2024: Quiet; 1 question in 2024–26
Weighted estimate: –; history: 0.4 a shift on average, typically 0.0–0.6

Key findings

01
Asked in 6 of 8 years with analysed shifts and in 24 of 108 shifts: 28 questions, #118 of 196 topics. The years that asked it were 1.8 apart on average.
02
19% of its questions since 2020 tested an idea no earlier year had asked; 15 repeated an idea from the year before.
03
The most repeated idea is Distance Along a Line, asked 9 times in 9 shifts (2020, 2021, 2022, 2023, 2026), most often as “distance of point from plane along given direction”.
04
JEE Main has asked 7 of the 62 ideas in this topic; 51 have never been asked, directly or inside another question.
05
Mostly asked as single correct (64%); 36% need a numerical answer, 7% are easy and 21% hard. It went down from 0.6 to 0.0 questions a shift since 2024.
06
The skill tested most is multi-step (61%), then calculation (39%).

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

Up to 2023: 0.6; a shift, of 25
Since 2024: 0.0; -0.5
Usual gap: 1.8 yrs; between years asking it
Shifts with it: 24/108; 22% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 28 questions on Point-Plane Distance since 2017.

Difficulty

QUESTIONS

206

Easy2 · 7%
Medium20 · 71%
Hard6 · 21%

Format

Single correct · 18 Q64%
Numerical value · 10 Q36%

Skill tested

Multi-step · 17 Q61%
Calculation · 11 Q39%

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 7 of the 62 ideas in this topic. 51 have never been asked yet.

751

Asked directly7 · 11%
Touched inside another question4 · 6%
Never asked51 · 82%

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

OpenRepeated9 · 32%32%5/8223
- 4 Apr ’26 S1 · Q15
  The square of the distance of the point $(-2,-8,6)$ from the line $\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1}$ along the line…
  mediumSingle correct
- 11 Apr ’23 S2 · Q16
  Let the line passing through the points $P(2, -1, 2)$ and $Q(5, 3, 4)$ meet the plane $x - y + z = 4$ at the point $R$ . Then the distance…
  hardSingle correctAsked the year before
- 13 Apr ’23 S1 · Q17
  The distance of the point $(-1,2,3)$ from the plane $\vec{r}\cdot\left(\hat{i}-2\hat{j}+3\hat{k}\right)=10$ parallel to the line of the…
  hardSingle correctAsked the year before
- 15 Apr ’23 S1 · Q29
  Let the plane P contain the line $2x+y-z-3=0=5x-3y+4z+9$ and be parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$ . Then…
  hardNumerical valueAsked the year before
- 29 Jul ’22 S1 · Q9
  If the foot of the perpendicular from the point $A(-1, 4, 3)$ on the plane $P : 2x + my + nz = 4$ , is…
  mediumSingle correctAsked the year before
- 30 Jun ’22 S1 · Q16
  The distance of the point $(3, 2, -1)$ from the plane $3x - y + 4z + 1 = 0$ along the line $\frac{2-x}{2} = \frac{y-3}{2} = \frac{z+1}{1}$ …
  mediumSingle correctAsked the year before
- 27 Aug ’21 S1 · Q73
  The distance of the point $(1, -2, 3)$ from the plane $x-y+z=5$ measured parallel to a line, whose direction ratios are $2, 3, -6$ is :
  mediumSingle correctAsked the year before
- 16 Mar ’21 S2 · Q83
  If the distance of the point (1, $-2$ , 3) from the plane $x+2y-3z+10=0$ measured parallel to the line,…
  mediumNumerical valueAsked the year before
- 4 Sep ’20 S2 · Q67
  The distance of the point $(1, -2, 3)$ from the plane $x-y+z=5$ measured parallel to the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}$ is :
  mediumSingle correctNew idea
OpenRepeated8 · 29%29%4/833
OpenRepeated5 · 18%18%3/83
OpenRepeated3 · 11%11%2/82
Open1 · 4%4%1/8
Open1 · 4%4%1/8
Open1 · 4%4%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

7 different ideas were tested; 4 came more than once.

Distance Along a Line9×
distance of point from plane along given direction
Single correct · 9 shifts · 2 numerical
Image of a Point8×
image of point in plane
Single correct · 8 shifts · 3 numerical
Foot of Perpendicular5×
distance between feet of perpendiculars
Numerical value · 5 shifts · 3 numerical
Distance from Point3×
distance of point from plane from traces
Single correct · 3 shifts · 1 numerical
Distance to Plane Through Three Points1×
distance of points from plane through three points
Single correct · 1 shift
Generating Parallel Planes at a Given Distance1×
parallel planes at given distance
Numerical value · 1 shift · 1 numerical
Unknown Parameter from Distance1×
distance from plane with normal from two lines
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Distance Along a Linedistance of point from plane along given direction	9	9	Single correctCalculation	2
Image of a Pointimage of point in plane	8	8	Single correctCalculation	3
Foot of Perpendiculardistance between feet of perpendiculars	5	5	Numerical valueMulti-step	3
Distance from Pointdistance of point from plane from traces	3	3	Single correctMulti-step	1
Distance to Plane Through Three Pointsdistance of points from plane through three points	1	1	Single correctMulti-step	–
Generating Parallel Planes at a Given Distanceparallel planes at given distance	1	1	Numerical valueCalculation	1
Unknown Parameter from Distancedistance from plane with normal from two lines	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

Point-Plane Distance questions, year by year

The opening words of each question as it appeared in the official paper, with the idea it 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

Point-Plane Distance questions, year by year

JEE Main 20261 question in 1 shift

JEE Main 20238 questions in 6 shifts

JEE Main 20228 questions in 7 shifts

JEE Main 20218 questions in 8 shifts

JEE Main 20201 question in 1 shift

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