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Straight Lines

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 6 times: 2021 Paper 3, 8 Apr 2024, 22 Jan 2025, 24 Jan 2025, 29 Jan 2025, 21 Jan 2026 S2. This one: 21 Jan 2026 S2 See all 6 of this type

    75
    If P is a point on the circle x2+y2=4,Qx^{2} + y^{2} = 4,Q is a point on the straight line 5x+y+2=05x + y + 2 = 0 and x−y+1=0x - y + 1 = 0 is the perpendicular bisector of PQ , then 13 times the sum of abscissa of all such point P is ____\_\_\_\_ .

  2. Question 2

    This type asked 4 times: 2021 Paper 10, 26 Jun 2022, 28 Jan 2026 S1, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 4 of this type

    61
    In 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 orthocenter of the triangle PQRPQR is (α,β)(\alpha,\beta), then 9(α+β)9(\alpha+\beta) is equal to :

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  3. Question 3

    This type asked 4 times: 2021 Paper 24, 28 Jun 2022, 8 Apr 2024, 9 Apr 2024. This one: 9 Apr 2024 See all 4 of this type

    64
    A ray of light coming from the point P(1,2)P(1,2) gets reflected from the point QQ on the xx-axis and then passes through the point R(4,3)R(4,3). If the point SS (h, kk ) is such that PQRSPQRS is a parallelogram, then hk2hk^{2} is equal to:

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  4. Question 4

    This type asked 3 times: 30 Jan 2024, 24 Jan 2026 S1, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 3 of this type

    61
    Let 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 obtuse angle between the lines L2L_{2} and L3L_{3} intersect the line L1L_{1} at the point C . Then BC2:AC2BC^{2}:AC^{2} is equal to :

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  5. Question 5

    This type asked 3 times: 6 Apr 2024, 9 Apr 2024, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 3 of this type

    57
    Among the statements (S1) : If A(5,−1)A(5, - 1) and B(−2,3)B( - 2,3) are two vertices of a triangle, whose orthocentre is (0,0)(0,0), then its third vertex is (−4,−7)( - 4, - 7) and (S2) : If positive numbers 2a,b,c2a,b,c are three consecutive terms of an A.P., then the lines ax+by+c=0ax+by+c=0 are concurrent at (2,−2)(2,-2).

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  6. Question 6

    This type asked 3 times: 8 Apr 2023, 13 Apr 2023, 4 Apr 2025. This one: 4 Apr 2025 See all 3 of this type

    65
    Let the three sides of a triangle are on the lines 4x−7y+10=0,x+y=54x- 7y+ 10 = 0,x+y=5 and 7x+4y=157x+ 4y= 15. Then the distance of its orthocenter from the orthocenter of the triangle formed by the lines x=0,y=0x= 0,y= 0 and x+y=1x+y= 1 is.

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  7. Question 7

    This type asked 3 times: 31 Jan 2024, 6 Apr 2024, 9 Apr 2024. This one: 9 Apr 2024 See all 3 of this type

    68
    A variable line LL passes through the point (3,5)(3,5) and intersects the positive coordinate axes at the points AA and BB. The minimum area of the triangle OABOAB, where OO is the origin, is:

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  8. Question 8

    This type asked 3 times: 26 Jul 2022, 27 Jul 2022, 24 Jan 2023. This one: 24 Jan 2023 See all 3 of this type

    176
    The equations of the sides AB,BCAB,BC and CACA of a triangle ABCABC are: 2x+y=0,x+py=21a,(a≠0)2x + y = 0,x + py = 21a,(a \neq 0) and x−y=3x - y = 3 respectively. Let P(2,a)P(2,a) be the centroid of △ABC\bigtriangleup ABC. Then (BC)2(BC)^{2} is equal to

  9. Question 9

    Asked 2 times: 22 Jan 2025*, 21 Jan 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    54
    Let a point A lie between the parallel lines L1L_{1} and L2L_{2} such that its distances from L1L_{1} and L2L_{2} are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC , where the points B and C lie on the lines L1L_{1} and L2L_{2} respectively, is :

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  10. Question 10

    Asked 2 times: 30 Jan 2023*, 2 Apr 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    144
    Let 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 drawn from the origin to the line LL makes an angle of 45∘45^{\circ} with the positive xx-axis, then the value of b2+c2b^{2}+c^{2} is:

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