JEE Main · Maths · Conic Sections
Pair of Straight Lines: JEE Main previous year questions
6 questions in the 108 JEE Main shifts Lumi analysed, in 4 of 8 years. Pattern: Frequent. 2 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 6
- in 6 of 108 shifts
- Years asked
- 4/8
- last asked 2026
- Weighted estimate
- 0.1
- model; history: 0.0 a shift on average, typically 0.0–0.1
Key findings
- 01
Asked in 4 of 8 years with analysed shifts and in 6 of 108 shifts: 6 questions, #190 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 6 of the 62 ideas in this topic; 56 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (83%); 17% need a numerical answer, 17% are easy and 67% hard.
- 06
The skill tested most is multi-step (83%), then calculation (17%).
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: 2 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.
- Up to 2023
- 0.0
- a shift, of 25
- Since 2024
- 0.1
- 0.0
- Usual gap
- 1.7 yrs
- between years asking it
- Shifts with it
- 6/108
- 6% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 6 questions on Pair of Straight Lines since 2017.
Difficulty
QUESTIONS- Easy1 · 17%
- Medium1 · 17%
- Hard4 · 67%
Format
SHARE- Single correct · 5 Q83%
- Numerical value · 1 Q17%
Skill tested
SHARE- Multi-step · 5 Q83%
- Calculation · 1 Q17%
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 6 of the 62 ideas in this topic. 56 have never been asked yet.
- Asked directly6 · 10%
- Touched inside another question0 · 0%
- Never asked56 · 90%
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
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
3 ideas inside
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
6 different ideas were tested; none came more than once.
locus of foot of perpendicular
Numerical value · 1 shift · 1 numericalangle subtended at origin by segment
Single correct · 1 shiftangle between pair of tangents to conic
Single correct · 1 shiftcentroid of triangle from two sides and orthocenter
Single correct · 1 shiftangle bisectors of a pair of lines
Single correct · 1 shiftangle subtended by chord at origin
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Chord Subtending Right Angle via Homogenizationlocus of foot of perpendicular | 1 | 1 | Numerical valueMulti-step | 1 | |
| Angle between pair of linesangle subtended at origin by segment | 1 | 1 | Single correctMulti-step | – | |
| Combined Equation of Tangents (SS1=T^2)angle between pair of tangents to conic | 1 | 1 | Single correctMulti-step | – | |
| Orthocenter of Triangle with Pair of Linescentroid of triangle from two sides and orthocenter | 1 | 1 | Single correctMulti-step | – | |
| Equation of angle bisectorsangle bisectors of a pair of lines | 1 | 1 | Single correctCalculation | – | |
| Homogenization of curvesangle subtended by chord at origin | 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
Pair of Straight 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
- 8 Apr, Shift 2Q24Consider the circle . Let a variable chord AB of the circle C subtend a right angle at the origin. If…
Idea: Chord Subtending Right Angle via Homogenization
New ideaHardNumerical value
JEE Main 20241 question in 1 shift
- 8 Apr, Shift 2Q14If the line segment joining the points and subtends an angle at the origin, then the absolute value of…
Idea: Angle between pair of lines
New ideaMediumSingle correct
JEE Main 20222 questions in 2 shifts
- 26 Jul, Shift 2Q11The acute angle between the pair of tangents drawn to the ellipse from the point is
Idea: Combined Equation of Tangents (SS1=T^2)
New ideaHardSingle correct - 29 Jun, Shift 2Q13The distance of the origin from the centroid of the triangle whose two sides have the equations and and…
Idea: Orthocenter of Triangle with Pair of Lines
New ideaHardSingle correct
JEE Main 20212 questions in 2 shifts
- 25 Feb, Shift 2Q70If the curve intersects the line at two points P and Q, then the angle subtended by the line segment PQ at…
Idea: Homogenization of curves
New ideaHardSingle correct - 25 Jul, Shift 2Q77Let the equation of the pair of lines, and , can be written as . Then the equation of the pair of the angle…
Idea: Equation of angle bisectors
New ideaEasySingle 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.