Learn

Friday, 9 October

JEE Main Maths · Class 11

Straight Lines: JEE Main previous year questions

Straight Lines had 42 questions in the 42 JEE Main shifts Lumi analysed, about 0.8 a shift, asked in 32 of 42 shifts. It ranks 15 of 22 Maths chapters by questions; 19% of its questions were hard.

Questions
42
in 32 of 42 shifts
A shift, on average
0.8
of 25 Maths questions
Since 2024
+0.3
0.7 a shift in 2017–23, 1.1 in 2024–26
Numerical answer
6
14% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
07141’172’204’214’223’2313’248’257’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20202
  • 20214
  • 20224
  • 20233
  • 202413
  • 20258
  • 20267
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

4 topics and 16 distinct ideas; 4 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

22 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
4 repeat

Study it on Lumi

Straight Lines: the interactive lesson

Every question

All 42 Straight Lines questions

Newest first. Each opens with its options and the official answer.

2026 7 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

2025 8 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

2024 13 questions

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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

2023 3 questions

  1. 6 Apr 2023, Shift 1 · Q12The straight lines l1l_1 and l2l_2 pass through the origin and trisect the line segment of the line L:9x+5y=45L: 9x+5y=45 between the axes. If…MediumSingle correct
  2. 11 Apr 2023, Shift 1 · Q19Let R be a rectangle given by the lines x=0x = 0, x=2x = 2, y=0y = 0 and y=5y = 5. Let A(α,0)A(\alpha, 0) and B(0,β)B(0, \beta), α∈[0,2]\alpha \in [0, 2]…MediumSingle correct
  3. 13 Apr 2023, Shift 2 · Q12Let (α,β)(\alpha,\beta) be the centroid of the triangle formed by the lines 15x−y=8215x-y=82, 6x−5y=−46x-5y=-4 and 9x+4y=179x+4y=17. Then α+2β\alpha+2\beta and…MediumSingle correct

2022 4 questions

  1. 25 Jul 2022, Shift 1 · Q12A line, with the slope greater than one, passes through the point A(4,3)\mathrm{A}(4,3) and intersects the line x−y−2=0x-y-2=0 at the point…MediumSingle correct
  2. 28 Jul 2022, Shift 1 · Q7For t∈(0,2π)t\in(0,2\pi), if ABC is an equilateral triangle with vertices A(sin⁡t,−cos⁡t)A(\sin t,-\cos t), B(cos⁡t,sin⁡t)B(\cos t,\sin t) and C(a,b)C(a,b) such that its…HardSingle correct
  3. 24 Jun 2022, Shift 1 · Q23Let A(3a,a)A\left(\frac{3}{\sqrt{a}}, \sqrt{a}\right), a>0a>0, be a fixed point in the xyxy-plane. The image of A in yy-axis be B and the image…HardNumerical value
  4. 29 Jun 2022, Shift 1 · Q13The distance between the two points A and A' which lie on y=2y = 2 such that both the line segments AB and A'B (where B is the point…MediumSingle correct

2021 4 questions

  1. 16 Mar 2021, Shift 2 · Q75Let A(-1, 1), B(3, 4) and C(2, 0) be given three points. A line y=mxy=mx, m>0m>0, intersects lines AC and BC at point P and Q respectively.…MediumSingle correct
  2. 18 Mar 2021, Shift 1 · Q69If α,β\alpha,\beta are natural numbers such that 100α−199β=(100)(100)+(99)(101)+(98)(102)+…+(1)(199)100^{\alpha}-199\beta=(100)(100)+(99)(101)+(98)(102)+\ldots+(1)(199), then the slope of…MediumSingle correct
  3. 18 Mar 2021, Shift 1 · Q77The number of integral values of m so that the abscissa of point of intersection of lines 3x+4y=93x+4y=9 and y=mx+1y=mx+1 is also an integer, is :MediumSingle correct
  4. 18 Mar 2021, Shift 1 · Q78The equation of one of the straight lines which passes through the point (1, 3) and makes an angle tan⁡−1(2)\tan^{-1}(\sqrt{2}) with the straight…MediumSingle correct

2020 2 questions

  1. 8 Jan 2020, Shift 1 · Q54Let two points be A(1,−1)A(1,-1) and B(0,2)B(0,2). If a point P(x′,y′)P(x',y') be such that the area of ΔPAB=5\Delta PAB=5 sq. units and it lies on the line,…MediumSingle correct
  2. 6 Sep 2020, Shift 2 · Q64Let L denote the line in the xyxy-plane with xx and yy intercepts as 3 and 1 respectively. Then the image of the point (−1,−4)(-1,-4) in this…EasySingle correct

2017 1 questions

  1. 2 Apr 2017 (offline) · Q78Let k be an integer such that the triangle with vertices (k,−3k)(k,-3k), (5,k)(5,k) and (−k,2)(-k,2) has area 28 sq. units. Then the orthocentre of…MediumSingle correct

Pattern: Asked most years.