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Mathematics - Pair of Lines

Practise 173 AP EAMCET previous year questions on Pair of Lines, compiled from papers spanning 2001 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty AP EAMCET tests.

Pair of Lines has been asked in 21 of the 24 years of AP EAMCET papers analysed (2001–2024), with 173 questions in all. 29% of them were easy, 51% moderate and 20% tough. Most of its questions came from 2021, with 32 questions that year. In the last three years (2022–2024) it had 25 questions across 28 papers, about 0.9 per paper.

The chapter's 10 topics are not weighted equally: Angle between lines (39 questions, 23%), general equation of second degree (33 questions, 19%), and homogeneous equation of second degree (28 questions, 16%) have been asked the most. Over the last five years the most frequent topics have been general equation of second degree (18), Angle between lines (17), and homogeneous equation of second degree (10). general equation of second degree has produced the most tough questions (9).

  1. 1If one of the lines given by the pair of lines is making an angle with x -axis then27 May, 2025 (M)Pair of Lines
  2. 2If the equation of the pair of straight lines intersecting at and perpendicular to the pair of lines is , then26 May, 2025 (M)Pair of lines through origin
  3. 3PQR is a right angled isosceles triangle with right angle at . If the equation of the line is , then the equation representing the pair of l26 May, 2025 (M)Pair of lines through origin
  4. 4If fy represents a pair of straight lines, then one of the possible values of is26 May, 2025 (E)general equation of second degree
  5. 5If the pair of lines and have exactly one line in common and ' ' is an integer, then the equation of the pair of bisectors of the angles bet24 May, 2025 (M)Pair of Lines through origin
  6. 6If the angle between the pair of lines is and is a positive rational number, then the point of intersection of these two lines is24 May, 2025 (M)general equation of second degree
  7. 7The triangle formed by the lines and is23 May, 2025 (M)Pair of Lines through origin
  8. 8If is the centroid of the triangle formed by the lines and , then23 May, 2025 (M)general equation of second degree
  9. 9If the equation of the pair of lines passing through and perpendicular to the pair of lines is , then23 May, 2025 (E)general equation of second degree
  10. 10If the combined equation of the lines joining the origin to the points of intersection of the curve and the line is , then23 May, 2025 (E)Pair of Lines
  11. 11By rotating the axes about the origin in anti-clockwise direction with certain angle, if the equation is transformed to then22 May, 2025 (M)Pair of lines through origin
  12. 12One line of the pair of lines is perpendicular to one line of the pair of lines . If the combined equation of the two lines other than those22 May, 2025 (M)Pair of Lines through origin
  13. 13If the angle between the lines joining the origin to the points of intersection of and is , then a value of is22 May, 2025 (M)Pair of Lines
  14. 14The transformed equation of when the coordinate axes are rotated about the origin through an angle of in positive direction is22 May, 2025 (E)Pair of Lines
  15. 15If two sides of a triangle are represented by and its orthocentre is , then the equation of the third side is22 May, 2025 (E)general equation of second degree
  16. 16If represents a pair of lines intersecting at , then ah22 May, 2025 (E)general equation of second degree
  17. 17If the transformed equation of the equation after translating the coordinate axes to a new origin is , then21 May, 2025 (M)general equation of second degree
  18. 18If the slopes of both the lines given by are positive and the angle between these lines is , then the product of the perpendiculars21 May, 2025 (M)Pair of Lines
  19. 19If one of the lines represented by bisects the angle between the positive coordinate axes, then21 May, 2025 (M)Angle between lines
  20. 20The equation represents a pair of distinct lines21 May, 2025 (E)general equation of second degree
  21. 21The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve and the23 May, 2024 (M)combined equation of angle bisector
  22. 22The transformed equation of when the origin is shifted to the point is22 May, 2024 (M)general equation of second degree
  23. 23If the slope of one of the pair of lines represented by is 2 , then the angle between the pair of lines is22 May, 2024 (M)Angle between lines
  24. 24The length of -intercept made by pair of lines is22 May, 2024 (M)Angle between lines
  25. 25If the axes are rotated through an angle ' ', then the number of values of such that the transformed equation of contains no linear terms is22 May, 2024 (E)general equation of second degree
  26. 26The equation of a line which makes an angle of with each of the pair of lines is22 May, 2024 (E)homogeneous equation of second degree
  27. 27If the slope of one of the lines in the pair of lines is thrice the slope of the second line, then22 May, 2024 (E)homogeneous equation of second degree
  28. 28Suppose the axes are to be rotated through an angle so as to remove the form from the equation . Then in the new coordinate system the equat21 May, 2024 (E)Pair of lines through origin
  29. 29If the pair of lines represented by and have one line in common, then the sum of all possible values of is21 May, 2024 (E)point of intersection of pair of straight lines
  30. 30If the slope of one line of the pair of lines is thrice the slone of the other line, then20 May, 2024 (M)homogeneous equation of second degree
  31. 31If the equation of the pair of straight lines passing through the point and perpendicular to the pair of lines is , then20 May, 2024 (M)Condition for 2nd degree equationto represent pair of straight lines
  32. 32If A are four points and the point of intersection of the lines AB and CD is , then20 May, 2024 (M)point of intersection of pair of straight lines
  33. 33If and two of the lines represented by are perpendicular, then17 May, 2023 (M)homogeneous equation of second degree
  34. 34The absolute value of the tangent of the difference of the angles made by the lines with the -axis is17 May, 2023 (M)homogeneous equation of second degree
  35. 35If the lines given by are perpendicular to each other, then15 May, 2023 (M)Pair of lines through origin
  36. 36If the area of the triangle formed by the lines and is sq. units, then15 May, 2023 (M)Angle between lines
  37. 37If represents two sides of a triangle and is its third side, then the distance between the orthocenter and the circumcentre of that triangle15 May, 2023 (E)homogeneous equation of second degree
  38. 38For , if the slope of one of the lines represented by is twice that of the other, then the value of is08 Jul, 2022 (E)Angle between lines
  39. 39Suppose and are the points at which the line meets the pair of straight lines . If , then a value of is08 Jul, 2022 (E)point of intersection of pair of straight lines
  40. 40If represents a pair of straight lines, then the value of is07 Jul, 2022 (E)Condition for 2nd degree equationto represent pair of straight lines
  41. 41The equations of the lines perpendicular to and passing through is07 Jul, 2022 (E)Pair of lines through origin
  42. 42The two pairs of straight lines and constitute a06 Jul, 2022 (E)general equation of second degree
  43. 43The distance between the lines represented by is equal to06 Jul, 2022 (E)general equation of second degree
  44. 44Suppose the slopes and of the lines represented by satisfy and . Then, which of the following is true?05 Jul, 2022 (M)Angle between lines
  45. 45Suppose that the sides passing through the vertex of a triangle are bisected at right angles by the lines . Then, the centoid of the triangl05 Jul, 2022 (M)general equation of second degree
  46. 46Find the value(s) of such that the distance between the two parallel lines represented by is 3 units25 Aug, 2021 (M)general equation of second degree
  47. 47If represents a pair of lines with slopes and , then the value of equals25 Aug, 2021 (M)homogeneous equation of second degree
  48. 48The three lines given by the combined equation represents25 Aug, 2021 (M)homogeneous equation of second degree
  49. 49The angle between the lines is25 Aug, 2021 (M)Angle between lines
  50. 50Which among the following represents the combined equation of a pair of lines through point and parallel to the lines represented by .25 Aug, 2021 (E)Pair of lines through origin

Frequently Asked Questions

1.How many questions are available for Pair of Lines?

This chapter includes 173 questions compiled from AP EAMCET papers spanning 2001 to 2025.

2.Are these questions only from AP EAMCET, or from other exams too?

These are AP EAMCET questions specifically for the Pair of Lines chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Pair of Lines an important chapter for AP EAMCET Mathematics?

Pair of Lines has appeared in 22 of the 25 years of AP EAMCET papers covered here, with 173 questions across 71 papers - about 2 per paper it appears in.

4.What is the difficulty level of Pair of Lines questions in AP EAMCET?

Of the 173 questions analysed for this chapter, 29% are easy, 51% moderate and 20% tough. 2021 had the most, with 32 questions.

5.Which topics in Pair of Lines should I focus on?

These topics have carried the most weightage in Pair of Lines:

  • Angle between lines - 39 questions (23%)
  • general equation of second degree - 33 questions (19%)
  • homogeneous equation of second degree - 28 questions (16%)
  • general equation of second degree has produced the most tough questions (9).
6.Is Pair of Lines's weightage in AP EAMCET going up or down?

Across all 71 papers analysed, Pair of Lines has averaged about 2.4 questions per paper. In the last three years (2022–2024), that average has fallen, at about 0.9 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.