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JEE Main Straight Lines and Pair of Lines questions

50 Mathematics questions on Straight Lines and Pair of Lines as asked in JEE Main, newest first. 32 come with a worked solution.

  1. A light ray emits from the origin making an angle 30° with the positive x-axis. After getting reflected by the line x + y = 1, if this ray intersects x-axis at Q, then the abscissa of Q is

    2023

  2. Let B and C be the two points on the line y + x = 0 such that B and C are symmetric with respect to the origin. Suppose A is a point on y - 2x = 2 such that triangle ABC is an equilateral triangle. Then, the area of the…

    2023 · with solution

  3. Let z_1 = 2 + 3i and z_2 = 3 + 4i. The set S = \ z ∈ C : |z - z_1|^2 - |z - z_2|^2 = |z_1 - z_2|^2 \ represents a

    2023 · with solution

  4. The equations of the sides AB, BC and CA of a triangle ABC are: 2x + y = 0, x + py = 21a, (a ≠ 0) and x - y = 3 respectively. Let P(2, a) be the centroid of triangle ABC. Then (BC)^2 is equal to

    2023

  5. A triangle is formed by X-axis, Y-axis and the line 3x + 4y = 60. Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is ___.

    2023

  6. A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of 60° with the line x + y = 0. Then, an…

    2019 · with solution

  7. A triangle has a vertex at (1, 2) and the mid-points of the two sides through it are (-1, 1) and (2, 3). Then, the centroid of this triangle is

    2019 · with solution

  8. Two vertices of a triangle are (0, 2) and (4, 3). If its orthocentre is at the origin, then its third vertex lies in which quadrant?

    2019 · with solution

  9. Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true?

    2019 · with solution

  10. Let the equations of two sides of a triangle be 3x - 2y + 6 = 0 and 4x + 5y - 20 = 0. If the orthocentre of this triangle is at (1, 1) then the equation of its third side is

    2019

  11. Lines are drawn parallel to the line 4x - 3y + 2 = 0, at a distance 3/5 from the origin. Then which one of the following points lies on any of these lines?

    2019

  12. The region represented by |x - y| ≤ 2 and |x + y| ≤ 2 is bounded by a

    2019

  13. If the two lines x + (a-1)y = 1 and 2x + a^2y = 1, (a ∈ R - \0, 1\) are perpendicular, then the distance of their point of intersection from the origin is

    2019 · with solution

  14. If lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then

    2019 · with solution

  15. Slope of a line passing through P (2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is

    2019 · with solution

  16. Suppose that the points (h, k), (1, 2) and (-3, 4) lie on the line L_1. If a line L_2 passing through the points (h, k) and (4, 3) is perpendicular to L_1, then k/h equals

    2019

  17. If a straight line passing through the point P(-3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is

    2019 · with solution

  18. If the straight line, 2x - 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals

    2019 · with solution

  19. If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is

    2019

  20. Two sides of a parallelogram are along the lines, x + y = 3 and x - y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is

    2019 · with solution

  21. If the line 3x + 4y - 24 = 0 intersects the X-axis at the point A and the Y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is

    2019 · with solution

  22. A point P moves on the line 2x - 3y + 4 = 0. If Q(1, 4) and R(3, -2) are fixed points, then the locus of the centroid of triangle PQR is a line

    2019 · with solution

  23. A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is

    2018 · with solution

  24. Let k be an integer such that the triangle with vertices (k, -3k), (5, k) and (-k, 2) has area 28 sq units. Then, the orthocentre of this triangle is at the point

    2017 · with solution

  25. Two sides of a rhombus are along the lines, x - y + 1 = 0 and 7x - y - 5 = 0. If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus?

    2016

  26. Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes, then

    2014

  27. If PS is the median of the triangle with vertices P(2,2), Q(6,-1) and R(7,3), then equation of the line passing through (1,-1) and parallel to PS is

    2014

  28. The x-coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as (0, 1), (1, 1) and (1, 0) is

    2013

  29. A straight line L through the point (3, -2) is inclined at an angle 60° to the line √(3)x + y = 1. If L also intersects the X-axis, then the equation of L is

    2011 · with solution

  30. The locus of the orthocentre of the triangle formed by the lines (1+p)x - py + p(1+p) = 0, (1+q)x - qy + q(1+q) = 0 and y = 0, where p ≠ q, is

    2009

  31. Let a and b be non-zero and real numbers. Then, the equation (ax^2 + by^2 + c)(x^2 - 5xy + 6y^2) = 0 represents

    2008

  32. Let O(0, 0), P(3, 4) and Q(6, 0) be the vertices of a triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR and OQR are of equal area. The coordinates of R are

    2007

  33. Area of triangle formed by the lines x + y = 3 and angle bisectors of the pair of straight lines x^2 - y^2 + 2y = 1 is

    2004 · with solution

  34. Orthocentre of triangle with vertices (0, 0), (3, 4) and (4, 0) is

    2003 · with solution

  35. Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals

    2001 · with solution

  36. The number of integer values of m, for which the x-coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is

    2001 · with solution

  37. A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment PQ in the ratio

    2000 · with solution

  38. The incentre of the triangle with vertices (1, √(3)), (0, 0) and (2, 0) is

    2000 · with solution

  39. If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is/are always rational point(s)

    1998

  40. If P(1,2), Q(4,6), R(5,7) and S(a,b) are the vertices of a parallelogram PQRS, then

    1998 · with solution

  41. The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6x - 2y = 7. Then, PQRS must be a

    1998 · with solution

  42. The orthocentre of the triangle formed by the lines xy = 0 and x + y = 1, is

    1995 · with solution

  43. If the sum of the distance of a point from two perpendicular lines in a plane is 1, then its locus is

    1992 · with solution

  44. Line L has intercepts a and b on the coordinate axes. When, the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q, then

    1990 · with solution

  45. If P = (1, 0), Q = (-1, 0) and R = (2, 0) are three given points, then locus of the points satisfying the relation SQ^2 + SR^2 = 2SP^2 is

    1988 · with solution

  46. The points (0, 8/3 ), (1, 3) and (82, 30) are vertices of

    1986 · with solution

  47. The straight lines x + y = 0, 3x + y - 4 = 0, x + 3y - 4 = 0 form a triangle which is

    1983 · with solution

  48. Given the four lines with the equations x + 2y - 3 = 0, 3x + 4y - 7 = 0, 2x + 3y - 4 = 0, 4x + 5y - 6 = 0, then

    1980

  49. The point (4, 1) undergoes the following three transformations successively I. Reflection about the line y = x. II. Transformation through a distance 2 units along the positive direction of X-axis. III. Rotation through…

    1980 · with solution

  50. The points (-a, -b), (0, 0), (a, b) and (a^2, a^3) are

    1979

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