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Sunday, 25 October

JEE Main · Maths · Class 11

Straight Lines: JEE Main previous year questions

99 questions in 81 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
99
in 81 of 108 shifts · 8 of 8 years
Average a shift
0.8
of 25 Maths · 1.0 since 2024 0.3
Typical range
0.7–1.0
questions a shift; fewest 0.6, most 1.2
Weighted estimate
0.9
model, recent years count more · about 3.5 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 Straight Lines

Priority

Lower priority

One of the 7 Maths chapters that shared the last fifth of Maths questions in the 108 shifts analysed. How bands are set

Past questions
99in 81 of 108 shifts
Study plan gives it
15 hover 12 months; 11 h over 6
Study this chapter →

Ideas asked most often

  1. Image of a point in a line7×
  2. Inradius and Circumradius6×
  3. Distance between parallel lines4×
  4. Section Ratio by a Line4×
  5. Perpendicular distance from point4×

31 of the 64 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, 25% 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

Straight Lines at a glance

  1. 01

    75%

    of its 24 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

    48%

    of the 64 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    18%

    of its questions asked for a numerical answer, 0.6 times the Maths average.

  4. 04

    19%

    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.

0240.9’170.8’200.7’210.7’220.6’231.2’241’250.8’26

Raw count: 2017: 1 in 1 shift · 2020: 9 in 12 shifts · 2021: 20 in 24 shifts · 2022: 20 in 24 shifts · 2023: 9 in 12 shifts · 2024: 25 in 18 shifts · 2025: 8 in 8 shifts · 2026: 7 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step65%
  • Numerical answer18%
  • Calculation12%
  • Application5%

Most common asks: locus of midpoint of intercept segment (3); incentre of triangle from midpoints of sides (1); coordinates of intersection from circumcentre condition (1).

Profile

This chapter in numbers

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

Rank, all JEE chapters
#48
of 70 by weighted estimate
Rank in Maths
#16
of 21 chapters
Share of Maths
3.3%
of its questions, all shifts analysed
Busiest year
2024
1.2 questions a shift
Year to year
Steady
varies by about 0.2 questions a shift
Long-run direction
+0.01
questions a shift, per year
Easy questions
8%
19% rated hard
Numerical answer
18%
0.6× the Maths rate
With a figure
0%
graph, diagram or structure
Study time
15 h
11 h on a 6-month plan
Marks per study hour
0.23
#42 of 70 chapters
Foundation for others
21%
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).

  • 20171
  • 20209
  • 202120
  • 202220
  • 20239
  • 202425
  • 20258
  • 20267
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step81%
  • Calculation14%
  • Application5%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 64 ideas. In the 108 shifts analysed, JEE Main built a question around 23 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
23
Touched on in a question
10
Never asked
31

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. 42 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
012+questions in that year’s analysed shifts, shaded per shift
  • Straight Line Distance

    As a topic: 52 questions in 7 of 8 years, most often single correct, 21% numerical answer.

  • Properties of Triangles

    As a topic: 11 questions in 4 of 8 years, most often single correct, 36% numerical answer.

  • Pair of Straight Lines

    As a topic: 6 questions in 4 of 8 years, most often single correct, 17% numerical answer.

  • Circle Tangents

    As a topic: 62 questions in 7 of 8 years, most often single correct, 40% 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.

  • Open45 · 45%481041243

    22 ideas inside

    • OpenRepeated7 · 16%4
    • OpenRepeated4 · 9%
    • OpenRepeated4 · 9%2
    • OpenRepeated3 · 7%
    • OpenRepeated2 · 4%
    • Open2 · 4%2
    • OpenRepeated2 · 4%
    • OpenRepeated2 · 4%
    • OpenRepeated2 · 4%
    • OpenRepeated2 · 4%
    • Open2 · 4%2
    • OpenRepeated2 · 4%
    • OpenRepeated2 · 4%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
  • Open4 · 4%22
  • Open3 · 3%
  • Open2 · 2%
  • Open1 · 1%
  • Open1 · 1%
  • Open1 · 1%

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, 27 different ideas were tested; 15 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 99 Straight Lines 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 20267 questions

  1. 2 Apr 2026, Shift 1 · Q9Let the mid points of the sides of a triangle ABC be (52,7)\left(\frac{5}{2}, 7\right), (52,3)\left(\frac{5}{2}, 3\right) and (4,5)(4, 5). If its…MediumSingle correct
  2. 4 Apr 2026, Shift 1 · Q11Let the line L1:x+3=0L_1: x+3=0 intersect the lines L2:x−y=0L_2: x-y=0 and L3:3x+y=0L_3: 3x+y=0 at the points A and B, respectively. Let the bisector of the…MediumSingle correct
  3. 4 Apr 2026, Shift 1 · Q12Let the vertex A of a triangle ABC be (1,2)(1,2), and the mid-point of the side AB be (5,−1)(5,-1). If the centroid of this triangle is (3,4)(3,4)…MediumSingle correct
  4. 4 Apr 2026, Shift 2 · Q23Let A,BA,B be points on the two half-lines x−3 ∣y∣=ax-\sqrt3\,|y|=a, a>0a>0 at a distance of aa from their point of intersection PP. The line…HardNumerical value
  5. 5 Apr 2026, Shift 1 · Q11In an equilateral triangle PQR, let the vertex P be at (3,5)(3, 5) and the side QR be along the line x+y=4x + y = 4. If the orthocentre of the…MediumSingle correct
  6. 5 Apr 2026, Shift 2 · Q22From the point (−1,−1)(-1, -1), two rays are sent making angles of 45∘45^\circ with the line x+y=0x+y=0. These rays get reflected from the mirror…HardNumerical value
  7. 8 Apr 2026, Shift 2 · Q10If a straight line drawn through the point of intersection of the lines 4x+3y−1=04x + 3y - 1 = 0 and 3x+4y−1=03x + 4y - 1 = 0, meets the co-ordinate…MediumSingle correct

JEE Main 20258 questions

  1. 2 Apr 2025, Shift 2 · Q10Let the area of the triangle formed by a straight line L:x+by+c=0L : x + by + c = 0 with co-ordinate axes be 48 square units. If the perpendicular…MediumSingle correct
  2. 2 Apr 2025, Shift 2 · Q24Let A(4,−2)A(4, -2), B(1,1)B(1, 1) and C(9,−3)C(9, -3) be the vertices of a triangle ABCABC. Then the maximum area of the parallelogram AFDEAFDE, formed…HardNumerical value
  3. 3 Apr 2025, Shift 1 · Q13A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines…MediumSingle correct
  4. 3 Apr 2025, Shift 2 · Q10Consider the lines x(3λ+1)+y(7λ+2)=17λ+5x(3\lambda + 1) + y(7\lambda + 2) = 17\lambda + 5, λ\lambda being a parameter, all passing through a point P. One of…MediumSingle correct
  5. 7 Apr 2025, Shift 1 · Q11Let ABC be the triangle such that the equations of lines AB and AC be 3y−x=23y - x = 2 and x+y=2x + y = 2, respectively, and the points B and C…MediumSingle correct
  6. 7 Apr 2025, Shift 2 · Q11If the orthocenter of the triangle formed by the lines y=x+1y=x+1, y=4x−8y=4x-8 and y=mx+cy=mx+c is at (3,−1)(3,-1), then m−cm-c is :MediumSingle correct
  7. 8 Apr 2025, Shift 2 · Q10A line passing through the point P(a,0)P(a, 0) makes an acute angle α\alpha with the positive xx-axis. Let this line be rotated about the…HardSingle correct
  8. 8 Apr 2025, Shift 2 · Q11Let aa be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle α\alpha with the positive…MediumSingle correct

JEE Main 202425 questions

  1. 4 Apr 2024, Shift 1 · Q16The vertices of a triangle are A(−1,3)(-1, 3), B(−2,2)(-2, 2) and C(3,−1)(3, -1). A new triangle is formed by shifting the sides of the triangle by…MediumSingle correct
  2. 4 Apr 2024, Shift 2 · Q28Consider a triangle ABC having the vertices A(1,2)A(1,2), B(α,β)B(\alpha,\beta) and C(γ,δ)C(\gamma,\delta) and angles ∠ABC=π6\angle ABC=\frac{\pi}{6} and…HardNumerical value
  3. 5 Apr 2024, Shift 1 · Q14Let two straight lines drawn from the origin O intersect the line 3x+4y=123x+4y=12 at the points P and Q such that △OPQ\triangle OPQ is an…MediumSingle correct
  4. 5 Apr 2024, Shift 2 · Q14Let ABCDABCD and AEFGAEFG be squares of side 4 and 2 units, respectively. The point EE is on the line segment ABAB and the point FF is on…MediumSingle correct
  5. 5 Apr 2024, Shift 2 · Q16Let A(−1,1)A(-1, 1) and B(2,3)B(2, 3) be two points and PP be a variable point above the line ABAB such that the area of ΔPAB\Delta PAB is 10. If…MediumSingle correct
  6. 6 Apr 2024, Shift 1 · Q10Let a variable line of slope m>0m>0 passing through the point (4,−9)(4,-9) intersect the coordinate axes at the points AA and BB. The minimum…HardSingle correct
  7. 6 Apr 2024, Shift 2 · Q14If the locus of the point, whose distances from the point (2,1)(2,1) and (1,3)(1,3) are in the ratio 5:45:4, is ax2+by2+cxy+dx+ey+170=0ax^2+by^2+cxy+dx+ey+170=0, then…MediumSingle correct
  8. 6 Apr 2024, Shift 2 · Q15If P(6,1)P(6,1) be the orthocentre of the triangle whose vertices are A(5,−2)A(5,-2), B(8,3)B(8,3) and C(h,k)C(h,k), then the point CC lies on the circle :MediumSingle correct
  9. 8 Apr 2024, Shift 1 · Q5The equations of two sides AB and AC of a triangle ABC are 4x+y=144x+y=14 and 3x−2y=53x-2y=5, respectively. The point (2,−43)\left(2,-\frac{4}{3}\right)…MediumSingle correct
  10. 8 Apr 2024, Shift 1 · Q29If the orthocentre of the triangle formed by the lines 2x+3y−1=02x+3y-1=0, x+2y−1=0x+2y-1=0 and ax+by−1=0ax+by-1=0, is the centroid of another triangle, whose…HardNumerical value
  11. 8 Apr 2024, Shift 2 · Q14If the line segment joining the points (5,2)(5, 2) and (2,a)(2, a) subtends an angle π4\frac{\pi}{4} at the origin, then the absolute value of…MediumSingle correct
  12. 8 Apr 2024, Shift 2 · Q15If the image of the point (−4,5)(-4, 5) in the line x+2y=2x + 2y = 2 lies on the circle (x+4)2+(y−3)2=r2(x+4)^2 + (y-3)^2 = r^2, then r is equal to :EasySingle correct
  13. 8 Apr 2024, Shift 2 · Q22Let a ray of light passing through the point (3,10)(3, 10) reflects on the line 2x+y=62x + y = 6 and the reflected ray passes through the point…MediumNumerical value
  14. 9 Apr 2024, Shift 1 · Q7A variable line L passes through the point (3,5)(3,5) and intersects the positive coordinate axes at the points A and B. The minimum area of…MediumSingle correct
  15. 9 Apr 2024, Shift 1 · Q14A ray of light coming from the point P(1,2)P(1,2) gets reflected from the point Q on the xx-axis and then passes through the point R(4,3)R(4,3).…MediumSingle correct
  16. 9 Apr 2024, Shift 2 · Q14Two vertices of a triangle ABC are A(3,−1)(3,-1) and B(−2,3)(-2,3), and its orthocentre is P(1,1)(1,1). If the coordinates of the point C are…MediumSingle correct
  17. 1 Feb 2024, Shift 2 · Q29Let ABCABC be an isosceles triangle in which AA is at (−1,0)(-1,0), ∠A=2π3\angle A=\frac{2\pi}{3}, AB=ACAB=AC and BB is on the positive xx-axis. If…MediumNumerical value
  18. 27 Jan 2024, Shift 1 · Q15The portion of the line 4x+5y=204x+5y=20 in the first quadrant is trisected by the lines L1L_1 and L2L_2 passing through the origin. The tangent…MediumSingle correct
  19. 29 Jan 2024, Shift 1 · Q14Let (5,a4)\left(5,\frac{a}{4}\right) be the circumcenter of a triangle with vertices A(a,−2)A(a,-2), B(a,6)B(a,6) and C(a4,−2)C\left(\frac{a}{4},-2\right).…MediumSingle correct
  20. 29 Jan 2024, Shift 1 · Q15In a ΔABC\Delta ABC, suppose y=xy=x is the equation of the bisector of the angle BB and the equation of the side ACAC is 2x−y=22x-y=2. If…HardSingle correct
  21. 30 Jan 2024, Shift 1 · Q13A line passing through the point A(9,0)A(9,0) makes an angle of 30∘30^\circ with the positive direction of xx-axis. If this line is rotated…MediumSingle correct
  22. 30 Jan 2024, Shift 2 · Q16If x2−y2+2hxy+2gx+2fy+c=0x^2 - y^2 + 2hxy + 2gx + 2fy + c = 0 is the locus of a point, which moves such that it is always equidistant from the lines…MediumSingle correct
  23. 31 Jan 2024, Shift 1 · Q14Let α,β,γ,δ∈Z\alpha,\beta,\gamma,\delta\in\mathbb{Z} and let A(α,β)A(\alpha,\beta), B(1,0)B(1,0), C(γ,δ)C(\gamma,\delta) and D(1,2)D(1,2) be the vertices of a…MediumSingle correct
  24. 31 Jan 2024, Shift 2 · Q15Let A(a,b)A(a,b), B(3,4)B(3,4) and C(−6,−8)C(-6,-8) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of…MediumSingle correct
  25. 31 Jan 2024, Shift 2 · Q28Let A(−2,−1)A(-2,-1), B(1,0)B(1,0), C(α,β)C(\alpha,\beta) and D(γ,δ)D(\gamma,\delta) be the vertices of a parallelogram ABCDABCD. If the point CC lies on…MediumNumerical value

JEE Main 20239 questions

  1. 6 Apr 2023, Shift 1 · Q12Section Ratio by a Line · Medium · Single correct
  2. 8 Apr 2023, Shift 1 · Q13Open the question · Medium · Single correct
  3. 10 Apr 2023, Shift 2 · Q28Area of Parallelogram via Parallel Distances · Hard · Numerical value
  4. 11 Apr 2023, Shift 1 · Q19Open the question · Medium · Single correct
  5. 11 Apr 2023, Shift 2 · Q26Angle Bisector Locus via Distances · Hard · Numerical value
  6. 12 Apr 2023, Shift 1 · Q13Origin Distance to Intercept Form · Medium · Single correct
  7. 13 Apr 2023, Shift 2 · Q12Open the question · Medium · Single correct
  8. 15 Apr 2023, Shift 1 · Q12Open the question · Medium · Single correct
  9. 15 Apr 2023, Shift 1 · Q25Open the question · Hard · Numerical value

JEE Main 202220 questions

  1. 25 Jul 2022, Shift 1 · Q12Distance Measured Parallel to a Line · Medium · Single correct
  2. 25 Jul 2022, Shift 2 · Q10Perpendicular distance from point · Medium · Single correct
  3. 26 Jul 2022, Shift 1 · Q28Open the question · Medium · Numerical value
  4. 27 Jul 2022, Shift 1 · Q18Section Ratio by a Line · Medium · Single correct
  5. 27 Jul 2022, Shift 2 · Q11Open the question · Hard · Single correct
  6. 28 Jul 2022, Shift 1 · Q7Open the question · Hard · Single correct
  7. 29 Jul 2022, Shift 1 · Q8Condition of tangency · Hard · Single correct
  8. 29 Jul 2022, Shift 1 · Q13Inradius and Circumradius · Hard · Single correct
  9. 29 Jul 2022, Shift 2 · Q11Square Area from Vertex and Diagonal · Hard · Single correct
  10. 29 Jul 2022, Shift 2 · Q13Inradius and Circumradius · Medium · Single correct
  11. 24 Jun 2022, Shift 1 · Q23Open the question · Hard · Numerical value
  12. 24 Jun 2022, Shift 2 · Q10Distance Formula via Determinant Area · Medium · Single correct
  13. 26 Jun 2022, Shift 1 · Q11Altitude Length of a Triangle · Medium · Single correct
  14. 27 Jun 2022, Shift 1 · Q12Foot of the perpendicular · Medium · Single correct
  15. 27 Jun 2022, Shift 2 · Q29Perpendicular distance from point · Medium · Numerical value
  16. 28 Jun 2022, Shift 1 · Q25Image of a point in a line · Medium · Numerical value
  17. 28 Jun 2022, Shift 2 · Q12Section Ratio by a Line · Medium · Single correct
  18. 29 Jun 2022, Shift 1 · Q13Open the question · Medium · Single correct
  19. 29 Jun 2022, Shift 2 · Q13Orthocenter of Triangle with Pair of Lines · Hard · Single correct
  20. 30 Jun 2022, Shift 1 · Q13Open the question · Easy · Single correct

JEE Main 202120 questions

  1. 3 Aug 2021, Shift 1 · Q72Distance between parallel lines · Medium · Single correct
  2. 3 Aug 2021, Shift 1 · Q88Open the question · Easy · Numerical value
  3. 4 Aug 2021, Shift 1 · Q72Position of points relative to line · Medium · Single correct
  4. 4 Aug 2021, Shift 2 · Q89Foot of the perpendicular · Medium · Numerical value
  5. 26 Aug 2021, Shift 1 · Q72Angle Bisector Locus via Distances · Hard · Single correct
  6. 27 Aug 2021, Shift 1 · Q67Open the question · Medium · Single correct
  7. 27 Aug 2021, Shift 2 · Q74Open the question · Medium · Single correct
  8. 31 Aug 2021, Shift 1 · Q73Distance from Origin to a Line · Medium · Single correct
  9. 31 Aug 2021, Shift 2 · Q72Locus of Points at a Fixed Distance · Medium · Single correct
  10. 24 Feb 2021, Shift 1 · Q73Open the question · Medium · Single correct
  11. 24 Feb 2021, Shift 2 · Q62Symmetric Functions · Medium · Single correct
  12. 25 Feb 2021, Shift 1 · Q70Image of a point in a line · Easy · Single correct
  13. 26 Feb 2021, Shift 1 · Q63Open the question · Easy · Single correct
  14. 25 Jul 2021, Shift 2 · Q77Equation of angle bisectors · Easy · Single correct
  15. 16 Mar 2021, Shift 2 · Q75Open the question · Medium · Single correct
  16. 17 Mar 2021, Shift 1 · Q73Open the question · Medium · Single correct
  17. 18 Mar 2021, Shift 1 · Q69Open the question · Medium · Single correct
  18. 18 Mar 2021, Shift 1 · Q77Conditions for Integer Solutions · Medium · Single correct
  19. 18 Mar 2021, Shift 1 · Q78Open the question · Medium · Single correct
  20. 18 Mar 2021, Shift 2 · Q67Distance from Origin to a Line · Medium · Single correct

JEE Main 20209 questions

  1. 8 Jan 2020, Shift 1 · Q54Distance via Determinant Area · Medium · Single correct
  2. 9 Jan 2020, Shift 1 · Q64Open the question · Easy · Single correct
  3. 2 Sep 2020, Shift 2 · Q64Position of points relative to line · Medium · Single correct
  4. 3 Sep 2020, Shift 2 · Q63Open the question · Medium · Single correct
  5. 4 Sep 2020, Shift 1 · Q64Open the question · Medium · Single correct
  6. 4 Sep 2020, Shift 1 · Q69Open the question · Medium · Single correct
  7. 4 Sep 2020, Shift 2 · Q64Open the question · Medium · Single correct
  8. 5 Sep 2020, Shift 1 · Q74Distance between parallel lines · Medium · Numerical value
  9. 6 Sep 2020, Shift 2 · Q64Image of a point in a line · Easy · Single correct

JEE Main 20171 question

  1. 2 Apr 2017 (offline) · Q78Open the question · 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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