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Sunday, 25 October

JEE Main · Maths · Class 12

Three Dimensional Geometry: JEE Main previous year questions

224 questions in 108 of the 108 JEE Main shifts Lumi analysed, asked in 8 of 8 years. Here is what this chapter tests and how.

Study this chapter
Questions
224
in 108 of 108 shifts · 8 of 8 years
Average a shift
1.8
of 25 Maths · 1.9 since 2024 0.1
Typical range
1.7–2.0
questions a shift; fewest 1.2, most 2.5
Weighted estimate
1.9
model, recent years count more · about 7.7 marks
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

What to do

How to spend time on Three Dimensional Geometry

Priority

Must do

One of the 8 Maths chapters that together held the first half of Maths questions in the 108 shifts analysed. How bands are set

Past questions
224in 108 of 108 shifts
Study plan gives it
31 hover 12 months; 24 h over 6
Study this chapter →

Ideas asked most often

  1. Image of a Point in a Line16×
  2. Cartesian Shortest Distance15×
  3. Family of Planes15×
  4. Foot of the Perpendicular12×
  5. Distance Along a Line9×

223 of the 313 ideas in Lumi’s map of this chapter have not been asked or touched in the shifts analysed. Of its idea-tagged questions from 2024 on, 21% tested an idea not asked in an earlier year, so learn the whole chapter, not just the list above.

Within each subject, chapters in NTA's 2026 syllabus are ranked by their average questions a shift over all 8 years analysed (history, not the model). Going down that list, the chapters that together held the first half of the subject's questions are Must do; the next ones, up to 80%, are Should do; the rest are Lower priority.

Key findings

Three Dimensional Geometry at a glance

  1. 01

    79%

    of its 68 questions from 2024 on that Lumi matched to an idea tested one JEE Main had asked in an earlier year; 100% came from a topic asked in an earlier year.

  2. 02

    71%

    of the 313 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    29%

    of its questions asked for a numerical answer, 1.0 times the Maths average.

  4. 04

    20%

    of its questions were rated hard, against 26% across all Maths questions in the same shifts.

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.

0241.7’171.2’201.8’211.8’222.5’231.7’242’251.9’26

Raw count: 2017: 2 in 1 shift · 2020: 14 in 12 shifts · 2021: 52 in 24 shifts · 2022: 50 in 24 shifts · 2023: 36 in 12 shifts · 2024: 37 in 18 shifts · 2025: 16 in 8 shifts · 2026: 17 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step42%
  • Numerical answer29%
  • Calculation23%
  • Application6%
  • Conceptual0%

Most common asks: shortest distance between skew lines (24); distance of point from plane along given direction (7); image of point in plane (6).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Rank, all JEE chapters
#3
of 70 by weighted estimate
Rank in Maths
#2
of 21 chapters
Share of Maths
7.3%
of its questions, all shifts analysed
Busiest year
2023
2.5 questions a shift
Year to year
Steady
varies by about 0.3 questions a shift
Long-run direction
+0.05
questions a shift, per year
Easy questions
9%
20% rated hard
Numerical answer
29%
1.0× the Maths rate
With a figure
0%
graph, diagram or structure
Study time
31 h
24 h on a 6-month plan
Marks per study hour
0.25
#23 of 70 chapters
Foundation for others
66%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 20172
  • 202014
  • 202152
  • 202250
  • 202336
  • 202437
  • 202516
  • 202617
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step61%
  • Calculation32%
  • Application6%
  • Conceptual0%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 313 ideas. In the 108 shifts analysed, JEE Main built a question around 64 of them. Most of the chapter has never been the main idea of a question, so past questions alone leave most of it out.

Asked as the main idea
64
Touched on in a question
26
Never asked
223

Topics

What repeats, topic by topic

This chapter's questions per topic in each year's analysed shifts. The number is the count; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. 6 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
025+questions in that year’s analysed shifts, shaded per shift
  • Lines in 3D

    As a topic: 73 questions in 7 of 8 years, most often single correct, 26% numerical answer. Recent asks: shortest distance between parallel lines; numerical: point on line at given distance; image and foot of point in 3D line.

  • Planes in 3D

    As a topic: 67 questions in 4 of 8 years, most often single correct, 24% numerical answer.

  • Skew Lines

    As a topic: 36 questions in 7 of 8 years, most often single correct, 31% numerical answer.

  • Point-Plane Distance

    As a topic: 28 questions in 6 of 8 years, most often single correct, 36% numerical answer.

Drill down

Topic, idea, question

Open a topic to see every idea JEE Main tested inside it, then open an idea to read the questions. Each row shows its 8 years.

  • Open73 · 33%3108525913

    18 ideas inside

    • OpenRepeated16 · 22%274
    • OpenRepeated12 · 16%432
    • OpenRepeated9 · 12%222
    • OpenRepeated8 · 11%22
    • OpenRepeated7 · 10%22
    • OpenRepeated3 · 4%
    • OpenRepeated3 · 4%2
    • Open3 · 4%3
    • OpenRepeated2 · 3%
    • OpenRepeated2 · 3%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
  • Open67 · 30%8212315
  • Open36 · 16%4761152
  • Open28 · 13%2888
  • Open9 · 4%52
  • Open2 · 1%
  • Open2 · 1%
  • Open1 · 0%

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

The exact ideas JEE Main has asked

Inside the topics, 65 different ideas were tested; 32 came more than once. These are the repeats, then the ideas new since 2024.

Dots are the 8 years with analysed shifts, 2017 to 2026.

Every question

All 224 Three Dimensional Geometry questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 202617 questions

  1. 2 Apr 2026, Shift 1 · Q13If the point of intersection of the lines x+13=y+a5=z+b+17\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7} and x−21=y−b4=z−2a7\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}…MediumSingle correct
  2. 2 Apr 2026, Shift 1 · Q15Let a line L passing through the point (1,1,1)(1, 1, 1) be perpendicular to both the vectors 2i^+2j^+k^2\hat i+2\hat j+\hat k and…MediumSingle correct
  3. 2 Apr 2026, Shift 2 · Q15Let the point AA be the foot of perpendicular drawn from the point P(a,b,0)P(a, b, 0) on the line…MediumSingle correct
  4. 4 Apr 2026, Shift 1 · Q14A line with direction ratios 1,−1,21,-1,2 intersects the lines x2=y3=z+13\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3} and…MediumSingle correct
  5. 4 Apr 2026, Shift 1 · Q15The square of the distance of the point (−2,−8,6)(-2,-8,6) from the line x−11=y−12=z−1\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1} along the line…MediumSingle correct
  6. 4 Apr 2026, Shift 2 · Q13The shortest distance between the lines…EasySingle correct
  7. 4 Apr 2026, Shift 2 · Q14If (2α+1, α2−3α, α−12)\left(2\alpha+1,\,\alpha^2-3\alpha,\,\frac{\alpha-1}{2}\right) is the image of (α,2α,1)(\alpha,2\alpha,1) in the line…MediumSingle correct
  8. 5 Apr 2026, Shift 1 · Q13The square of the distance of the point P(5,6,7)P(5, 6, 7) from the line x−22=y−53=z−24\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4} is equal to:EasySingle correct
  9. 5 Apr 2026, Shift 1 · Q15The square of the distance of the point of intersection of the lines…MediumSingle correct
  10. 5 Apr 2026, Shift 2 · Q14Let a triangle PQR be such that P and Q lie on the line x+38=y−42=z+12\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2} and are at a distance of 6 units from…MediumSingle correct
  11. 5 Apr 2026, Shift 2 · Q15If the distance of the point (a,2,5)(a, 2, 5) from the image of the point (1,2,7)(1, 2, 7) in the line x1=y−11=z−22\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2} is…MediumSingle correct
  12. 6 Apr 2026, Shift 1 · Q15Let the image of the point P(1,6,a)\mathrm{P}(1,6,a) in the line L:x1=y−12=z−a+1b\mathrm{L}:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}, b>0b>0, be…HardSingle correct
  13. 6 Apr 2026, Shift 1 · Q16Let a line L be perpendicular to both the lines L1:x+13=y+35=z+57\mathrm{L}_1:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7} and…MediumSingle correct
  14. 6 Apr 2026, Shift 2 · Q14The shortest distance between the lines x−41=y−32=z−2−3\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3} and x+22=y−64=z−5−5\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5} is :EasySingle correct
  15. 6 Apr 2026, Shift 2 · Q24Let the image of the point P(0,−5,0)(0,-5,0) in the line x−12=y1=z+1−2\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2} be the point R and the image of the point…HardNumerical value
  16. 8 Apr 2026, Shift 2 · Q15Let the foot of perpendicular from the point (λ,2,3)(\lambda, 2, 3) on the line x−41=y−92=z−51\frac{x-4}{1} = \frac{y-9}{2} = \frac{z-5}{1} be the point…MediumSingle correct
  17. 8 Apr 2026, Shift 2 · Q23Let a line L1L_1 pass through the origin and be perpendicular to the lines…MediumNumerical value

JEE Main 202516 questions

  1. 2 Apr 2025, Shift 1 · Q5Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q13Let the vertices Q and R of the triangle PQR lie on the line x+35=y−12=z+43\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, QR=5\mathrm{QR}=5 and the…MediumSingle correct
  3. 2 Apr 2025, Shift 2 · Q14If the image of the point P(1,0,3)P(1, 0, 3) in the line joining the points A(4,7,1)A(4, 7, 1) and B(3,5,3)B(3, 5, 3) is Q(α,β,γ)Q(\alpha, \beta, \gamma), then…MediumSingle correct
  4. 2 Apr 2025, Shift 2 · Q15The line L1L_1 is parallel to the vector a⃗=−3i^+2j^+4k^\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k} and passes through the point (7,6,2)(7, 6, 2) and the line…EasySingle correct
  5. 3 Apr 2025, Shift 1 · Q14Line L1\mathrm{L}_1 passes through the point (1,2,3)(1, 2, 3) and is parallel to zz-axis. Line L2\mathrm{L}_2 passes through the point…MediumSingle correct
  6. 3 Apr 2025, Shift 1 · Q15Let a line passing through the point (4,1,0)(4, 1, 0) intersect the line L1:x−12=y−23=z−34\mathrm{L}_1 : \frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} at the…HardSingle correct
  7. 3 Apr 2025, Shift 2 · Q14Each of the angles β\beta and γ\gamma that a given line makes with the positive yy- and zz-axes, respectively, is half of the angle…MediumSingle correct
  8. 3 Apr 2025, Shift 2 · Q15The distance of the point (7,10,11)(7, 10, 11) from the line x−41=y−40=z−23\frac{x-4}{1} = \frac{y-4}{0} = \frac{z-2}{3} along the line…MediumSingle correct
  9. 4 Apr 2025, Shift 2 · Q14Let the values of p, for which the shortest distance between the lines x+13=y4=z5\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5} and…MediumSingle correct
  10. 4 Apr 2025, Shift 2 · Q15Let A be the point of intersection of the lines L1:x−71=y−50=z−3−1L_1:\frac{x-7}{1}=\frac{y-5}{0}=\frac{z-3}{-1} and…MediumSingle correct
  11. 7 Apr 2025, Shift 1 · Q13Let the line L pass through (1,1,1)(1, 1, 1) and intersect the lines x−12=y+13=z−14\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4} and…MediumSingle correct
  12. 7 Apr 2025, Shift 1 · Q14If the shortest distance between the lines x−12=y−23=z−34\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} and…MediumSingle correct
  13. 7 Apr 2025, Shift 2 · Q16If the equation of the line passing through the point (0,−12,0)\left(0,-\frac{1}{2},0\right) and perpendicular to the lines…MediumSingle correct
  14. 7 Apr 2025, Shift 2 · Q17Consider the lines L1:x−1=y−2=zL_1: x-1=y-2=z and L2:x−2=y=z−1L_2: x-2=y=z-1. Let the feet of the perpendiculars from the point P(5,1,−3)P(5,1,-3) on the lines L1L_1…MediumSingle correct
  15. 8 Apr 2025, Shift 2 · Q15Let the values of λ\lambda for which the shortest distance between the lines x−12=y−23=z−34\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} and…HardSingle correct
  16. 8 Apr 2025, Shift 2 · Q24Let the area of the triangle formed by the lines x+2=y−1=zx + 2 = y - 1 = z, x−35=y−1=z−11\frac{x-3}{5} = \frac{y}{-1} = \frac{z-1}{1} and…HardNumerical value

JEE Main 202437 questions

  1. 4 Apr 2024, Shift 1 · Q17Let the point, on the line passing through the points P(1,−2,3)(1, -2, 3) and Q(5,−4,7)(5, -4, 7), farther from the origin and at a distance of 9…MediumSingle correct
  2. 4 Apr 2024, Shift 1 · Q29If the shortest distance between the lines x+22=y+33=z−54\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4} and x−31=y−2−3=z+42\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2} is…HardNumerical value
  3. 4 Apr 2024, Shift 2 · Q16Let P be the point of intersection of the lines x−21=y−45=z−21\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1} and…MediumSingle correct
  4. 4 Apr 2024, Shift 2 · Q29Consider a line L passing through the points P(1,2,1)P(1,2,1) and Q(2,1,−1)Q(2,1,-1). If the mirror image of the point A(2,2,2)A(2,2,2) in the line L is…MediumNumerical value
  5. 5 Apr 2024, Shift 1 · Q16If the line 2−x3=3y−24λ+1=4−z\frac{2-x}{3}=\frac{3y-2}{4\lambda+1}=4-z makes a right angle with the line x+33μ=1−2y6=5−z7\frac{x+3}{3\mu}=\frac{1-2y}{6}=\frac{5-z}{7},…MediumSingle correct
  6. 5 Apr 2024, Shift 1 · Q17Let d be the distance of the point of intersection of the lines x+63=y2=z+11\frac{x+6}{3}=\frac{y}{2}=\frac{z+1}{1} and…MediumSingle correct
  7. 5 Apr 2024, Shift 2 · Q17Let (α,β,γ)(\alpha, \beta, \gamma) be the image of the point (8,5,7)(8, 5, 7) in the line x−12=y+13=z−25\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{5}. Then…MediumSingle correct
  8. 5 Apr 2024, Shift 2 · Q28Equation of Line of Shortest Distance · Medium · Numerical value
  9. 6 Apr 2024, Shift 1 · Q17Vector Shortest Distance Formula · Medium · Single correct
  10. 6 Apr 2024, Shift 1 · Q28Foot of the Perpendicular · Medium · Numerical value
  11. 6 Apr 2024, Shift 2 · Q17Image of a Point in a Line · Hard · Single correct
  12. 6 Apr 2024, Shift 2 · Q28Finding an Unknown Parameter from Shortest Distance · Medium · Numerical value
  13. 8 Apr 2024, Shift 1 · Q14Vector Shortest Distance Formula · Medium · Single correct
  14. 8 Apr 2024, Shift 1 · Q17Open the question · Medium · Single correct
  15. 8 Apr 2024, Shift 2 · Q16Cartesian Shortest Distance · Medium · Single correct
  16. 8 Apr 2024, Shift 2 · Q29Image of a Point in a Line · Medium · Numerical value
  17. 9 Apr 2024, Shift 1 · Q15Line Intersecting Two Skew Lines Parallel to a Third · Medium · Single correct
  18. 9 Apr 2024, Shift 1 · Q16Cartesian Shortest Distance · Easy · Single correct
  19. 9 Apr 2024, Shift 2 · Q16Perpendicular Distance from Point to Line · Hard · Single correct
  20. 9 Apr 2024, Shift 2 · Q29Image of a Point in a Line · Medium · Numerical value
  21. 1 Feb 2024, Shift 1 · Q16Cartesian Shortest Distance · Medium · Single correct
  22. 1 Feb 2024, Shift 1 · Q30Equation of Shortest Distance Line · Medium · Numerical value
  23. 1 Feb 2024, Shift 2 · Q15Image of a Point in a Line · Medium · Single correct
  24. 1 Feb 2024, Shift 2 · Q16Parametric Points at Distance r · Medium · Single correct
  25. 27 Jan 2024, Shift 1 · Q17General Point Parameterization · Medium · Single correct
  26. 27 Jan 2024, Shift 1 · Q18Cartesian Shortest Distance · Medium · Single correct
  27. 29 Jan 2024, Shift 1 · Q16Point of Intersection Calculation · Medium · Single correct
  28. 29 Jan 2024, Shift 1 · Q29Line Parallel to Vector Intersecting Two Lines · Hard · Numerical value
  29. 30 Jan 2024, Shift 1 · Q16Foot of the Perpendicular · Medium · Single correct
  30. 30 Jan 2024, Shift 1 · Q28Cartesian Shortest Distance · Medium · Numerical value
  31. 30 Jan 2024, Shift 2 · Q17Line Perpendicular to Two Given Lines · Medium · Single correct
  32. 30 Jan 2024, Shift 2 · Q29Line Through Point Intersecting Two Skew Lines · Medium · Numerical value
  33. 31 Jan 2024, Shift 1 · Q15Line Perpendicular to Two Given Lines · Medium · Single correct
  34. 31 Jan 2024, Shift 1 · Q29Foot of the Perpendicular · Medium · Numerical value
  35. 31 Jan 2024, Shift 2 · Q16Image of a Point in a Line · Medium · Single correct
  36. 31 Jan 2024, Shift 2 · Q17Cartesian Shortest Distance · Medium · Single correct
  37. 31 Jan 2024, Shift 2 · Q29Parametric Points at Distance r · Medium · Numerical value

JEE Main 202336 questions

  1. 6 Apr 2023, Shift 1 · Q13Family of Planes · Medium · Single correct
  2. 6 Apr 2023, Shift 1 · Q14Shortest Distance Between Cube Diagonals · Medium · Single correct
  3. 6 Apr 2023, Shift 1 · Q30Image of a Point in a Plane · Medium · Numerical value
  4. 6 Apr 2023, Shift 2 · Q15Family of Planes · Medium · Single correct
  5. 6 Apr 2023, Shift 2 · Q16Perpendicular Distance from Point to Line · Hard · Single correct
  6. 6 Apr 2023, Shift 2 · Q28Coplanarity Determinant Test · Hard · Numerical value
  7. 8 Apr 2023, Shift 1 · Q15Family of Planes Perpendicular to a Third Plane · Medium · Single correct
  8. 8 Apr 2023, Shift 1 · Q16Shortest Distance Between Skew Lines · Medium · Single correct
  9. 8 Apr 2023, Shift 1 · Q28Distance from Point · Medium · Numerical value
  10. 8 Apr 2023, Shift 2 · Q13Plane Containing a Line and a Point · Medium · Single correct
  11. 8 Apr 2023, Shift 2 · Q14Angle Between a Line and a Plane · Hard · Single correct
  12. 8 Apr 2023, Shift 2 · Q30Plane Through Three Points · Hard · Numerical value
  13. 10 Apr 2023, Shift 1 · Q13Image of a Point · Medium · Single correct
  14. 10 Apr 2023, Shift 1 · Q14Distance from Point · Medium · Single correct
  15. 10 Apr 2023, Shift 1 · Q15Cartesian Shortest Distance · Easy · Single correct
  16. 10 Apr 2023, Shift 2 · Q14Image of a Point in a Plane · Medium · Single correct
  17. 10 Apr 2023, Shift 2 · Q15Point of Intersection Calculation · Hard · Single correct
  18. 10 Apr 2023, Shift 2 · Q29Foot of Perpendicular · Hard · Numerical value
  19. 11 Apr 2023, Shift 1 · Q2Image of a Point in a Plane · Medium · Single correct
  20. 11 Apr 2023, Shift 1 · Q8Plane Perpendicular to Two Planes · Medium · Single correct
  21. 11 Apr 2023, Shift 1 · Q22Line Perpendicular to Two Given Lines · Hard · Numerical value
  22. 11 Apr 2023, Shift 2 · Q15Distance to Plane Through Three Points · Medium · Single correct
  23. 11 Apr 2023, Shift 2 · Q16Distance Along a Line · Hard · Single correct
  24. 11 Apr 2023, Shift 2 · Q28Angle: Line and Plane · Hard · Numerical value
  25. 12 Apr 2023, Shift 1 · Q14Family of Planes Perpendicular to a Third Plane · Hard · Single correct
  26. 12 Apr 2023, Shift 1 · Q15Coplanarity Determinant Test · Hard · Single correct
  27. 12 Apr 2023, Shift 1 · Q29Open the question · Hard · Numerical value
  28. 13 Apr 2023, Shift 1 · Q8Family of Planes · Medium · Single correct
  29. 13 Apr 2023, Shift 1 · Q17Distance Along a Line · Hard · Single correct
  30. 13 Apr 2023, Shift 1 · Q27Image of a Point in a Plane · Medium · Numerical value
  31. 13 Apr 2023, Shift 2 · Q14Plane Through Two Points Parallel to a Vector · Medium · Single correct
  32. 13 Apr 2023, Shift 2 · Q15Coplanarity Determinant Test · Medium · Single correct
  33. 13 Apr 2023, Shift 2 · Q16Foot of the Perpendicular · Medium · Single correct
  34. 15 Apr 2023, Shift 1 · Q14Foot of Perpendicular to a Plane · Medium · Single correct
  35. 15 Apr 2023, Shift 1 · Q15Cartesian Shortest Distance · Medium · Single correct
  36. 15 Apr 2023, Shift 1 · Q29Distance Along a Line · Hard · Numerical value

JEE Main 202250 questions

  1. 25 Jul 2022, Shift 1 · Q14Plane Containing a Line and a Point · Hard · Single correct
  2. 25 Jul 2022, Shift 2 · Q15Plane Perpendicular to Two Planes · Medium · Single correct
  3. 25 Jul 2022, Shift 2 · Q16Cartesian Shortest Distance · Medium · Single correct
  4. 26 Jul 2022, Shift 1 · Q14Perpendicular Distance from Point to Line · Medium · Single correct
  5. 26 Jul 2022, Shift 1 · Q30General Point Parameterization · Hard · Numerical value
  6. 26 Jul 2022, Shift 2 · Q15Direction of Line of Intersection · Medium · Single correct
  7. 26 Jul 2022, Shift 2 · Q22Plane Containing Two Lines · Hard · Numerical value
  8. 26 Jul 2022, Shift 2 · Q27Family of Planes · Hard · Numerical value
  9. 27 Jul 2022, Shift 1 · Q17Family of Planes · Medium · Single correct
  10. 27 Jul 2022, Shift 1 · Q23Intersection Point of Line and Plane · Hard · Numerical value
  11. 27 Jul 2022, Shift 2 · Q14Image of a Point in a Line · Medium · Single correct
  12. 27 Jul 2022, Shift 2 · Q15Direction of Line of Intersection · Medium · Single correct
  13. 28 Jul 2022, Shift 1 · Q16Foot of Perpendicular · Hard · Single correct
  14. 28 Jul 2022, Shift 1 · Q22Perpendicular Diagonals of a Rhombus · Medium · Numerical value
  15. 28 Jul 2022, Shift 2 · Q75Coplanarity Determinant Test · Medium · Single correct
  16. 28 Jul 2022, Shift 2 · Q76Plane Through Point Parallel to Two Vectors · Medium · Single correct
  17. 29 Jul 2022, Shift 1 · Q9Distance Along a Line · Medium · Single correct
  18. 29 Jul 2022, Shift 1 · Q23Point of Intersection Calculation · Hard · Numerical value
  19. 29 Jul 2022, Shift 2 · Q14Foot of Perpendicular · Medium · Single correct
  20. 29 Jul 2022, Shift 2 · Q15Coplanarity of Four Points · Medium · Single correct
  21. 30 Jul 2022, Shift 2 · Q77Angle Bisector Planes · Medium · Single correct
  22. 30 Jul 2022, Shift 2 · Q87Cartesian Shortest Distance · Hard · Numerical value
  23. 24 Jun 2022, Shift 1 · Q24General Point Parameterization · Medium · Numerical value
  24. 24 Jun 2022, Shift 1 · Q30Vector Shortest Distance Formula · Medium · Numerical value
  25. 24 Jun 2022, Shift 2 · Q14Cartesian Shortest Distance · Medium · Single correct
  26. 24 Jun 2022, Shift 2 · Q15Perpendicular Bisector Plane · Medium · Single correct
  27. 25 Jun 2022, Shift 1 · Q17Image of a Point · Medium · Single correct
  28. 25 Jun 2022, Shift 1 · Q28Plane Through Point Parallel to Two Vectors · Medium · Numerical value
  29. 25 Jun 2022, Shift 2 · Q9Relative Position of Two Points · Medium · Single correct
  30. 25 Jun 2022, Shift 2 · Q30Vector Shortest Distance Formula · Hard · Numerical value
  31. 26 Jun 2022, Shift 1 · Q14Angle from Symmetric Equations · Medium · Single correct
  32. 26 Jun 2022, Shift 1 · Q15Family of Planes Perpendicular to a Third Plane · Hard · Single correct
  33. 26 Jun 2022, Shift 2 · Q14Family of Planes Perpendicular to a Third Plane · Medium · Single correct
  34. 26 Jun 2022, Shift 2 · Q15Plane Containing Two Lines · Medium · Single correct
  35. 27 Jun 2022, Shift 1 · Q14Parallelism Condition · Medium · Single correct
  36. 27 Jun 2022, Shift 1 · Q30Image of a Point · Medium · Numerical value
  37. 27 Jun 2022, Shift 2 · Q13Foot of the Perpendicular · Medium · Single correct
  38. 27 Jun 2022, Shift 2 · Q14Cartesian Shortest Distance · Medium · Single correct
  39. 28 Jun 2022, Shift 1 · Q15Direction of Line of Intersection · Hard · Single correct
  40. 28 Jun 2022, Shift 1 · Q16Family of Planes · Medium · Single correct
  41. 28 Jun 2022, Shift 1 · Q17Family of Planes · Hard · Single correct
  42. 28 Jun 2022, Shift 2 · Q16Plane Perpendicular to Two Planes · Medium · Single correct
  43. 28 Jun 2022, Shift 2 · Q21Image of a Point in a Line · Medium · Numerical value
  44. 29 Jun 2022, Shift 1 · Q3Image of a Point · Easy · Single correct
  45. 29 Jun 2022, Shift 1 · Q23Foot of Perpendicular · Medium · Numerical value
  46. 29 Jun 2022, Shift 1 · Q29Direction of Line of Intersection · Medium · Numerical value
  47. 29 Jun 2022, Shift 2 · Q12Condition for Line to Lie in Plane · Medium · Single correct
  48. 29 Jun 2022, Shift 2 · Q14Plane Containing a Line and a Point · Hard · Single correct
  49. 30 Jun 2022, Shift 1 · Q16Distance Along a Line · Medium · Single correct
  50. 30 Jun 2022, Shift 1 · Q28Perpendicular Distance from Point to Line · Hard · Numerical value

JEE Main 202152 questions

  1. 3 Aug 2021, Shift 1 · Q68Plane Through Three Points · Hard · Single correct
  2. 3 Aug 2021, Shift 1 · Q75Intersection Point of Line and Plane · Medium · Single correct
  3. 3 Aug 2021, Shift 1 · Q76Equation of a Parallel Plane · Easy · Single correct
  4. 3 Aug 2021, Shift 2 · Q76Perpendicularity Condition · Hard · Single correct
  5. 3 Aug 2021, Shift 2 · Q77Distance from Point · Medium · Single correct
  6. 4 Aug 2021, Shift 1 · Q87Angle with Coordinate Axes · Easy · Numerical value
  7. 4 Aug 2021, Shift 1 · Q88Plane Through Three Points · Medium · Numerical value
  8. 4 Aug 2021, Shift 2 · Q75Point of Intersection Calculation · Medium · Single correct
  9. 4 Aug 2021, Shift 2 · Q76Family of Planes Perpendicular to a Third Plane · Medium · Single correct
  10. 26 Aug 2021, Shift 1 · Q75Family of Planes · Medium · Single correct
  11. 26 Aug 2021, Shift 1 · Q88Open the question · Hard · Numerical value
  12. 26 Aug 2021, Shift 2 · Q70Angle via Direction Ratios · Medium · Single correct · has a figure
  13. 26 Aug 2021, Shift 2 · Q79Family of Planes · Medium · Single correct
  14. 26 Aug 2021, Shift 2 · Q89Foot of Perpendicular · Hard · Numerical value
  15. 27 Aug 2021, Shift 1 · Q72Family of Planes · Medium · Single correct
  16. 27 Aug 2021, Shift 1 · Q73Distance Along a Line · Medium · Single correct
  17. 27 Aug 2021, Shift 2 · Q76Angle via Direction Cosines · Medium · Single correct
  18. 27 Aug 2021, Shift 2 · Q77Family of Planes · Medium · Single correct
  19. 27 Aug 2021, Shift 2 · Q87Image of a Point · Medium · Numerical value
  20. 31 Aug 2021, Shift 1 · Q76Family of Planes · Medium · Single correct
  21. 31 Aug 2021, Shift 1 · Q87Point of Intersection Calculation · Medium · Numerical value
  22. 31 Aug 2021, Shift 2 · Q74Perpendicular Distance from Point to Line · Medium · Single correct
  23. 31 Aug 2021, Shift 2 · Q90Condition for Line to Lie in Plane · Medium · Numerical value
  24. 24 Feb 2021, Shift 1 · Q76Plane Perpendicular to Two Planes · Easy · Single correct
  25. 24 Feb 2021, Shift 1 · Q77Intersection Point of Line and Plane · Easy · Single correct
  26. 24 Feb 2021, Shift 2 · Q61Image of a Point in a Line · Medium · Single correct
  27. 24 Feb 2021, Shift 2 · Q76Family of Planes · Easy · Single correct
  28. 24 Feb 2021, Shift 2 · Q88Vector Shortest Distance Formula · Medium · Numerical value
  29. 25 Feb 2021, Shift 1 · Q73Angle from Linear and Quadratic DC Equations · Medium · Single correct
  30. 25 Feb 2021, Shift 1 · Q74Cartesian Symmetric Form · Medium · Single correct
  31. 25 Feb 2021, Shift 2 · Q73Projection of Line Segment on Plane · Medium · Single correct
  32. 25 Feb 2021, Shift 2 · Q88Line Perpendicular to Two Given Lines · Hard · Numerical value
  33. 26 Feb 2021, Shift 1 · Q62Coplanarity of Four Points · Medium · Single correct
  34. 26 Feb 2021, Shift 1 · Q79Equation of a Parallel Plane · Easy · Single correct
  35. 26 Feb 2021, Shift 1 · Q87Normal and Point Form · Medium · Numerical value
  36. 26 Feb 2021, Shift 2 · Q61Image of a Point · Easy · Single correct
  37. 26 Feb 2021, Shift 2 · Q76Foot of the Perpendicular · Medium · Single correct
  38. 22 Jul 2021, Shift 2 · Q63Finding an Unknown Parameter from Shortest Distance · Medium · Single correct
  39. 22 Jul 2021, Shift 2 · Q69Foot of the Perpendicular · Medium · Single correct
  40. 25 Jul 2021, Shift 1 · Q69Foot of the Perpendicular · Medium · Single correct
  41. 25 Jul 2021, Shift 2 · Q82Coplanarity Determinant Test · Easy · Numerical value
  42. 16 Mar 2021, Shift 2 · Q61Foot of the Perpendicular · Medium · Single correct
  43. 16 Mar 2021, Shift 2 · Q70Open the question · Medium · Single correct
  44. 16 Mar 2021, Shift 2 · Q83Distance Along a Line · Medium · Numerical value
  45. 17 Mar 2021, Shift 1 · Q76Plane Containing a Line and a Point · Easy · Single correct
  46. 17 Mar 2021, Shift 1 · Q87Family of Planes · Medium · Numerical value
  47. 17 Mar 2021, Shift 2 · Q77Plane Containing a Line and a Point · Hard · Single correct
  48. 17 Mar 2021, Shift 2 · Q88Open the question · Hard · Numerical value
  49. 18 Mar 2021, Shift 1 · Q85Perpendicular Bisector Plane · Easy · Numerical value
  50. 18 Mar 2021, Shift 1 · Q86Generating Parallel Planes at a Given Distance · Medium · Numerical value
  51. 18 Mar 2021, Shift 2 · Q87Plane Containing One Line and Parallel to Other · Medium · Numerical value
  52. 18 Mar 2021, Shift 2 · Q88Image of a Point · Medium · Numerical value

JEE Main 202014 questions

  1. 8 Jan 2020, Shift 1 · Q65Cartesian Shortest Distance · Medium · Single correct
  2. 8 Jan 2020, Shift 2 · Q66Image of a Point in a Plane · Medium · Single correct
  3. 9 Jan 2020, Shift 1 · Q75Scalar and Vector Projection · Easy · Numerical value
  4. 9 Jan 2020, Shift 2 · Q74Distance Between Parallel Planes · Hard · Numerical value
  5. 2 Sep 2020, Shift 1 · Q66Plane Through Two Points Parallel to a Vector · Medium · Single correct
  6. 2 Sep 2020, Shift 2 · Q67Plane Containing Two Lines · Medium · Single correct
  7. 3 Sep 2020, Shift 1 · Q65Foot of the Perpendicular · Medium · Single correct
  8. 3 Sep 2020, Shift 1 · Q66Condition for Intersection of Two Lines · Easy · Single correct
  9. 3 Sep 2020, Shift 2 · Q66Perpendicular Bisector Plane · Easy · Single correct
  10. 3 Sep 2020, Shift 2 · Q75Plane Containing Two Lines · Medium · Numerical value
  11. 4 Sep 2020, Shift 1 · Q74Family of Planes · Medium · Numerical value
  12. 4 Sep 2020, Shift 2 · Q67Distance Along a Line · Medium · Single correct
  13. 5 Sep 2020, Shift 1 · Q66Image of a Point in a Line · Medium · Single correct
  14. 6 Sep 2020, Shift 2 · Q67Intercept Form of Plane · Medium · Single correct

JEE Main 20172 questions

  1. 2 Apr 2017 (offline) · Q82Unknown Parameter from Distance · Medium · Single correct
  2. 2 Apr 2017 (offline) · Q83Image of a Point · Medium · Single correct

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

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