JEE Main · Maths · Three Dimensional Geometry
Angle Between Lines: JEE Main previous year questions
9 questions in the 108 JEE Main shifts Lumi analysed, in 4 of 8 years. Pattern: Frequent. 1 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 9
- in 9 of 108 shifts
- Years asked
- 4/8
- last asked 2026
- Weighted estimate
- 0.1
- model; history: 0.1 a shift on average, typically 0.0–0.1
Key findings
- 01
Asked in 4 of 8 years with analysed shifts and in 9 of 108 shifts: 9 questions, #180 of 196 topics. The years that asked it were 1.7 apart on average.
- 02
100% of its questions since 2020 tested an idea no earlier year had asked; none repeated an idea from the year before.
- 03
No idea in this topic has been asked twice: every question tested something new.
- 04
JEE Main has asked 9 of the 64 ideas in this topic; 51 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (78%); 22% need a numerical answer, 11% are easy and 22% hard.
- 06
The skill tested most is multi-step (78%), then application (22%).
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: 0 in 12 shifts · 2021: 5 in 24 shifts · 2022: 2 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.
- Up to 2023
- 0.1
- a shift, of 25
- Since 2024
- 0.0
- 0.0
- Usual gap
- 1.7 yrs
- between years asking it
- Shifts with it
- 9/108
- 8% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 9 questions on Angle Between Lines since 2017.
Difficulty
QUESTIONS- Easy1 · 11%
- Medium6 · 67%
- Hard2 · 22%
Format
SHARE- Single correct · 7 Q78%
- Numerical value · 2 Q22%
Skill tested
SHARE- Multi-step · 7 Q78%
- Application · 2 Q22%
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.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 9 of the 64 ideas in this topic. 51 have never been asked yet.
- Asked directly9 · 14%
- Touched inside another question4 · 6%
- Never asked51 · 80%
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.
- 25 Feb ’21 S1 · Q73Let be the angle between the lines whose direction cosines satisfy the equations and . Then…
mediumSingle correctNew idea
- 25 Feb ’21 S1 · Q73
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
9 different ideas were tested; none came more than once.
angle with line perpendicular to two lines
Single correct · 1 shiftline meeting plane with given angle
Numerical value · 1 shift · 1 numericalangle between lines in non-standard symmetric form
Single correct · 1 shiftparameter from parallel lines given direction cosine relations
Single correct · 1 shiftangle from direction cosine equations
Single correct · 1 shiftangle between lines from direction cosine equations
Single correct · 1 shiftheight of cuboid from angle between diagonals
Single correct · 1 shiftcount lines making equal angles with axes
Numerical value · 1 shift · 1 numericalangle between lines with ap-dependent direction ratios
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Line Perpendicular to Two Given Linesangle with line perpendicular to two lines | 1 | 1 | Single correctMulti-step | – | |
| Angle: Line and Planeline meeting plane with given angle | 1 | 1 | Numerical valueMulti-step | 1 | |
| Angle from Symmetric Equationsangle between lines in non-standard symmetric form | 1 | 1 | Single correctMulti-step | – | |
| Parallelism Conditionparameter from parallel lines given direction cosine relations | 1 | 1 | Single correctMulti-step | – | |
| Angle from Linear and Quadratic DC Equationsangle from direction cosine equations | 1 | 1 | Single correctMulti-step | – | |
| Angle via Direction Cosinesangle between lines from direction cosine equations | 1 | 1 | Single correctMulti-step | – | |
| Angle via Direction Ratiosheight of cuboid from angle between diagonals | 1 | 1 | Single correctApplication | – | |
| Angle with Coordinate Axescount lines making equal angles with axes | 1 | 1 | Numerical valueApplication | 1 | |
| Perpendicularity Conditionangle between lines with ap-dependent direction ratios | 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
Angle Between Lines 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.
JEE Main 20261 question in 1 shift
- 6 Apr, Shift 1Q16Let a line L be perpendicular to both the lines and…
Idea: Line Perpendicular to Two Given Lines
New ideaMediumSingle correct
JEE Main 20231 question in 1 shift
- 11 Apr, Shift 2Q28Let the line , meet the plane at the point…
Idea: Angle: Line and Plane
New ideaHardNumerical value
JEE Main 20222 questions in 2 shifts
- 26 Jun, Shift 1Q14If the two lines and are…
Idea: Angle from Symmetric Equations
New ideaMediumSingle correct - 27 Jun, Shift 1Q14If two straight lines whose direction cosines are given by the relations , are parallel, then the positive value…
Idea: Parallelism Condition
New ideaMediumSingle correct
JEE Main 20215 questions in 5 shifts
- 3 Aug, Shift 2Q76Let and be two lines passing through the points and …
Idea: Perpendicularity Condition
New ideaHardSingle correct - 4 Aug, Shift 1Q87Maximum number of lines, through the origin which make equal angles with the three coordinate axes in XYZ-space, is ________.
Idea: Angle with Coordinate Axes
New ideaEasyNumerical value - 26 Aug, Shift 2Q70A hall has a square floor of dimension (see the figure) and vertical walls. If the angle GPH between…
Idea: Angle via Direction Ratios
New ideaMediumSingle correct · figure - 27 Aug, Shift 2Q76The angle between the straight lines, whose direction cosines are given by the equations and , is :
Idea: Angle via Direction Cosines
New ideaMediumSingle correct - 25 Feb, Shift 1Q73Let be the angle between the lines whose direction cosines satisfy the equations and . Then…
Idea: Angle from Linear and Quadratic DC Equations
New ideaMediumSingle correct
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.