JEE Main · Maths · Straight Lines
Straight Line Distance: JEE Main previous year questions
52 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 21 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 52
- in 50 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.5
- model; history: 0.4 a shift on average, typically 0.3–0.6
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 50 of 108 shifts: 52 questions, #51 of 196 topics.
- 02
50% of its questions since 2020 tested an idea no earlier year had asked; 13 repeated an idea from the year before.
- 03
The most repeated idea is Image of a point in a line, asked 7 times in 6 shifts (2020, 2021, 2022, 2024), most often as “vertex of triangle from angle bisector and side ratio”.
- 04
JEE Main has asked 23 of the 64 ideas in this topic; 31 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (79%); 21% need a numerical answer, 6% are easy and 17% hard. It went up from 0.3 to 0.5 questions a shift since 2024.
- 06
The skill tested most is multi-step (85%), then calculation (12%).
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: 5 in 12 shifts · 2021: 10 in 24 shifts · 2022: 11 in 24 shifts · 2023: 5 in 12 shifts · 2024: 12 in 18 shifts · 2025: 4 in 8 shifts · 2026: 5 in 9 shifts.
- Up to 2023
- 0.3
- a shift, of 25
- Since 2024
- 0.5
- 0.2
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 50/108
- 46% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 52 questions on Straight Line Distance since 2017.
Difficulty
QUESTIONS- Easy3 · 6%
- Medium40 · 77%
- Hard9 · 17%
Format
SHARE- Single correct · 41 Q79%
- Numerical value · 11 Q21%
Skill tested
SHARE- Multi-step · 44 Q85%
- Calculation · 6 Q12%
- Application · 2 Q4%
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 23 of the 64 ideas in this topic. 31 have never been asked yet.
- Asked directly23 · 36%
- Touched inside another question10 · 16%
- Never asked31 · 48%
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.
22 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
23 different ideas were tested; 16 came more than once.
vertex of triangle from angle bisector and side ratio
Single correct · 6 shifts · 2 numericalline cutting two parallel lines length ratio
Single correct · 4 shifts · 1 numericallines through trisection points and intersection
Single correct · 4 shiftspoint at given distances from two lines
Numerical value · 4 shifts · 2 numericalincentre of triangle from midpoints of sides
Single correct · 3 shiftslocus equidistant from two lines
Single correct · 3 shifts · 1 numericalchord length of circle cut by line
Numerical value · 2 shifts · 1 numericalreflected rays equations from mirror line
Numerical value · 2 shifts · 2 numericalside of square from diagonal equations
Single correct · 2 shiftsisosceles right triangle with vertex at origin
Single correct · 2 shiftsdistance measured parallel to a line
Single correct · 2 shiftslocus of point from fixed triangle area
Single correct · 2 shiftsminimum sum of axis intercepts of variable line
Single correct · 2 shiftscentroid of isosceles triangle from line conditions
Numerical value · 2 shifts · 1 numericalperpendicular distance from origin to lines
Single correct · 2 shiftsrange of parameter for point inside triangle
Single correct · 2 shiftsobtuse angle bisector intersecting a line
Single correct · 1 shiftline from normal angle and intercept triangle area
Single correct · 1 shiftfarthest line of a concurrent family from origin
Single correct · 1 shiftlocus of point with distance ratio
Single correct · 1 shiftparallelogram diagonals and distance of vertex
Numerical value · 1 shift · 1 numericaltriangle area then collinear points
Single correct · 1 shiftparameter from triangle area with point on line
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Image of a point in a linevertex of triangle from angle bisector and side ratio | 7 | 6 | Single correctMulti-step | 2 | |
| Distance between parallel linesline cutting two parallel lines length ratio | 4 | 4 | Single correctMulti-step | 1 | |
| Section Ratio by a Linelines through trisection points and intersection | 4 | 4 | Single correctMulti-step | – | |
| Perpendicular distance from pointpoint at given distances from two lines | 4 | 4 | Numerical valueMulti-step | 2 | |
| Incenter via Equidistanceincentre of triangle from midpoints of sides | 3 | 3 | Single correctMulti-step | – | |
| Angle Bisector Locus via Distanceslocus equidistant from two lines | 3 | 3 | Single correctMulti-step | 1 | |
| Chord Length via Perpendicular Distancechord length of circle cut by line | 2 | 2 | Numerical valueMulti-step | 1 | |
| Reflection of a Line in a Linereflected rays equations from mirror line | 2 | 2 | Numerical valueMulti-step | 2 | |
| Square Area from Vertex and Diagonalside of square from diagonal equations | 2 | 2 | Single correctMulti-step | – | |
| Altitude Length of a Triangleisosceles right triangle with vertex at origin | 2 | 2 | Single correctMulti-step | – | |
| Distance Measured Parallel to a Linedistance measured parallel to a line | 2 | 2 | Single correctCalculation | – | |
| Locus of Points at a Fixed Distancelocus of point from fixed triangle area | 2 | 2 | Single correctMulti-step | – | |
| Origin Distance to Intercept Formminimum sum of axis intercepts of variable line | 2 | 2 | Single correctMulti-step | – | |
| Foot of the perpendicularcentroid of isosceles triangle from line conditions | 2 | 2 | Numerical valueMulti-step | 1 | |
| Distance from Origin to a Lineperpendicular distance from origin to lines | 2 | 2 | Single correctMulti-step | – | |
| Position of points relative to linerange of parameter for point inside triangle | 2 | 2 | Single correctApplication | – | |
| Acute and Obtuse Angle Bisectorsobtuse angle bisector intersecting a line | 1 | 1 | Single correctMulti-step | – | |
| Distance from Normal Formline from normal angle and intercept triangle area | 1 | 1 | Single correctMulti-step | – | |
| Extremum Distance to a Family of Linesfarthest line of a concurrent family from origin | 1 | 1 | Single correctMulti-step | – | |
| Locus of Constant Distance Ratiolocus of point with distance ratio | 1 | 1 | Single correctCalculation | – | |
| Area of Parallelogram via Parallel Distancesparallelogram diagonals and distance of vertex | 1 | 1 | Numerical valueMulti-step | 1 | |
| Distance Formula via Determinant Areatriangle area then collinear points | 1 | 1 | Single correctMulti-step | – | |
| Distance via Determinant Areaparameter from triangle area with point on line | 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
Straight Line Distance 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.
JEE Main 20265 questions in 5 shifts
- 2 Apr, Shift 1Q9Let the mid points of the sides of a triangle ABC be , and . If its…
Idea: Incenter via Equidistance
MediumSingle correct - 2 Apr, Shift 2Q10Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines…
Idea: Chord Length via Perpendicular Distance
New ideaMediumSingle correct - 4 Apr, Shift 1Q11Let the line intersect the lines and at the points A and B, respectively. Let the bisector of the…
Idea: Acute and Obtuse Angle Bisectors
New ideaMediumSingle correct - 5 Apr, Shift 2Q22From the point , two rays are sent making angles of with the line . These rays get reflected from the mirror…
Idea: Reflection of a Line in a Line
HardNumerical value - 6 Apr, Shift 1Q22Let the centre of the circle be in the first quadrant and lie on the line . Let the area of an equilateral…
Idea: Chord Length via Perpendicular Distance
New ideaMediumNumerical value
JEE Main 20254 questions in 4 shifts
- 2 Apr, Shift 2Q10Let the area of the triangle formed by a straight line with co-ordinate axes be 48 square units. If the perpendicular…
Idea: Distance from Normal Form
New ideaMediumSingle correct - 3 Apr, Shift 1Q13A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines…
Idea: Distance between parallel lines
Asked the year beforeMediumSingle correct - 3 Apr, Shift 2Q10Consider the lines , being a parameter, all passing through a point P. One of…
Idea: Extremum Distance to a Family of Lines
New ideaMediumSingle correct - 8 Apr, Shift 2Q11Let be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle with the positive…
Idea: Square Area from Vertex and Diagonal
MediumSingle correct
JEE Main 202412 questions in 11 shifts
- 4 Apr, Shift 1Q16The vertices of a triangle are A, B and C. A new triangle is formed by shifting the sides of the triangle by…
Idea: Distance between parallel lines
MediumSingle correct - 5 Apr, Shift 1Q14Let two straight lines drawn from the origin O intersect the line at the points P and Q such that is an…
Idea: Altitude Length of a Triangle
MediumSingle correct - 5 Apr, Shift 2Q16Let and be two points and be a variable point above the line such that the area of is 10. If…
Idea: Locus of Points at a Fixed Distance
MediumSingle correct - 6 Apr, Shift 1Q10Let a variable line of slope passing through the point intersect the coordinate axes at the points and . The minimum…
Idea: Origin Distance to Intercept Form
Asked the year beforeHardSingle correct - 6 Apr, Shift 2Q14If the locus of the point, whose distances from the point and are in the ratio , is , then…
Idea: Locus of Constant Distance Ratio
New ideaMediumSingle correct - 8 Apr, Shift 2Q15If the image of the point in the line lies on the circle , then r is equal to :
Idea: Image of a point in a line
EasySingle correct - 8 Apr, Shift 2Q22Let a ray of light passing through the point reflects on the line and the reflected ray passes through the point…
Idea: Image of a point in a line
MediumNumerical value - 9 Apr, Shift 1Q14A ray of light coming from the point gets reflected from the point Q on the -axis and then passes through the point .…
Idea: Image of a point in a line
MediumSingle correct - 27 Jan, Shift 1Q15The portion of the line in the first quadrant is trisected by the lines and passing through the origin. The tangent…
Idea: Section Ratio by a Line
Asked the year beforeMediumSingle correct - 29 Jan, Shift 1Q15In a , suppose is the equation of the bisector of the angle and the equation of the side is . If…
Idea: Image of a point in a line
HardSingle correct - 30 Jan, Shift 2Q16If is the locus of a point, which moves such that it is always equidistant from the lines…
Idea: Angle Bisector Locus via Distances
Asked the year beforeMediumSingle correct - 31 Jan, Shift 2Q15Let , and respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of…
Idea: Distance Measured Parallel to a Line
MediumSingle correct
JEE Main 20235 questions in 5 shifts
- 6 Apr, Shift 1Q12The straight lines and pass through the origin and trisect the line segment of the line between the axes. If…
Idea: Section Ratio by a Line
Asked the year beforeMediumSingle correct - 8 Apr, Shift 2Q12Let , and be the mid-points of the sides of a triangle with incentre at the point . If the focus of the…
Idea: Incenter via Equidistance
HardSingle correct - 10 Apr, Shift 2Q28Let the equations of two adjacent sides of a parallelogram ABCD be and . If the equation of its one diagonal…
Idea: Area of Parallelogram via Parallel Distances
New ideaHardNumerical value - 11 Apr, Shift 2Q26If the line is the angular bisector of the lines and , then…
Idea: Angle Bisector Locus via Distances
HardNumerical value - 12 Apr, Shift 1Q13If the point lies on the curve traced by the mid-points of the line segments of the lines…
Idea: Origin Distance to Intercept Form
New ideaMediumSingle correct
JEE Main 202211 questions in 10 shifts
- 25 Jul, Shift 1Q12A line, with the slope greater than one, passes through the point and intersects the line at the point…
Idea: Distance Measured Parallel to a Line
New ideaMediumSingle correct - 25 Jul, Shift 2Q10Let the point be at a unit distance from each of the two lines , and . If lies below…
Idea: Perpendicular distance from point
Asked the year beforeMediumSingle correct - 27 Jul, Shift 1Q18Let , , be vertices of a triangle , be a point on side , and and be the…
Idea: Section Ratio by a Line
New ideaMediumSingle correct - 29 Jul, Shift 2Q11Let , be the slopes of two adjacent sides of a square of side a such that . If one…
Idea: Square Area from Vertex and Diagonal
New ideaHardSingle correct - 24 Jun, Shift 2Q10Let the area of the triangle with vertices , and be 4 sq. units. If the points…
Idea: Distance Formula via Determinant Area
New ideaMediumSingle correct - 24 Jun, Shift 2Q30Let be a parabola with vertex and focus and be its mirror image with respect to the line . Then…
Idea: Reflection of a Line in a Line
New ideaMediumNumerical value - 26 Jun, Shift 1Q11Let R be the point and let P and Q be two points on the line such that PQR is an equilateral triangle. Then the area…
Idea: Altitude Length of a Triangle
New ideaMediumSingle correct - 27 Jun, Shift 1Q12In an isosceles triangle ABC, the vertex A is and the equation of the base BC is . Let the point B lie on the line…
Idea: Foot of the perpendicular
Asked the year beforeMediumSingle correct - 27 Jun, Shift 2Q29Let a circle of radius lie below the -axis. The line passes through the centre of the circle and…
Idea: Perpendicular distance from point
Asked the year beforeMediumNumerical value - 28 Jun, Shift 1Q25A ray of light passing through the point P(2, 3) reflects on the -axis at point A and the reflected ray passes through the point Q(5,…
Idea: Image of a point in a line
Asked the year beforeMediumNumerical value - 28 Jun, Shift 2Q12Let a triangle be bounded by the lines ; and the line , which passes through the point P(2, 3),…
Idea: Section Ratio by a Line
New ideaMediumSingle correct
JEE Main 202110 questions in 10 shifts
- 3 Aug, Shift 1Q72The sum of the values of 'a' for which circles of radius , touch the straight lines, and…
Idea: Distance between parallel lines
Asked the year beforeMediumSingle correct - 4 Aug, Shift 1Q72If is an interior point of the triangle formed by the lines, , and , then the set of all values of k is…
Idea: Position of points relative to line
Asked the year beforeMediumSingle correct - 4 Aug, Shift 2Q89One side of a square lies along the line and its one vertex is . If and are its two vertices on the line…
Idea: Foot of the perpendicular
New ideaMediumNumerical value - 26 Aug, Shift 1 · Q72Angle Bisector Locus via DistancesNew ideaHard
- 26 Aug, Shift 2 · Q69Perpendicular distance from pointAsked the year beforeMedium
- 31 Aug, Shift 1 · Q73Distance from Origin to a LineNew ideaMedium
- 31 Aug, Shift 2 · Q72Locus of Points at a Fixed DistanceNew ideaMedium
- 25 Feb, Shift 1 · Q70Image of a point in a lineAsked the year beforeEasy
- 17 Mar, Shift 2 · Q73Incenter via EquidistanceNew ideaMedium
- 18 Mar, Shift 2 · Q67Distance from Origin to a LineNew ideaMedium
JEE Main 20205 questions in 5 shifts
- 8 Jan, Shift 1 · Q54Distance via Determinant AreaNew ideaMedium
- 2 Sep, Shift 2 · Q64Position of points relative to lineNew ideaMedium
- 4 Sep, Shift 2 · Q74Perpendicular distance from pointNew ideaHard
- 5 Sep, Shift 1 · Q74Distance between parallel linesNew ideaMedium
- 6 Sep, Shift 2 · Q64Image of a point in a lineNew ideaEasy
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.
More topics in Straight Lines
This is the only topic tagged in this chapter.