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Mathematics - Pair of Lines

Practise 117 TS 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 TS EAMCET tests.

Pair of Lines has been asked in 21 of the 24 years of TS EAMCET papers analysed (2001–2024), with 117 questions in all. 32% of them were easy, 50% moderate and 18% tough. Most of its questions came from 2022, with 18 questions that year. In the last three years (2022–2024) it had 29 questions across 17 papers, about 1.7 per paper.

The chapter's 9 topics are not weighted equally: Angle between lines (28 questions, 24%), general equation of second degree (22 questions, 19%), and homogeneous equation of second degree (20 questions, 17%) have been asked the most. Over the last five years the most frequent topics have been general equation of second degree (12), Angle between lines (11), and homogeneous equation of second degree (6). Angle between lines has produced the most tough questions (5).

  1. 1If is the point of intersection of the pair of lines then04 May, 2025 (M)general equation of second degree
  2. 2If the equations and represent the four sides of a square, then04 May, 2025 (E)general equation of second degree
  3. 3If is the transformed equation of when the origin is shifted to the point by translation of axes, then03 May, 2025 (M)general equation of second degree
  4. 4If is the angle between the lines and , then the product of the slopes of given lines is03 May, 2025 (M)Pair of Lines
  5. 5If the slopes of the lines represented by the equation are in the ratio , then the value of h such that both the lines make acute angles wit03 May, 2025 (E)Pair of Lines
  6. 6If is the new origin to be chosen to eliminate first degree terms from the equation by translation and if is the angle with which the axes a02 May, 2025 (M)general equation of second degree
  7. 7If represent a pair of parallel lines then02 May, 2025 (M)general equation of second degree
  8. 8The value of ' ' for which the equation represents a pair of perpendicular lines is02 May, 2025 (E)general equation of second degree
  9. 9If is the point of intersection of the pair of lines then10 May, 2024 (M)point of intersection of pair of straight lines
  10. 10The combined equation of a possible pair of adjacent sides of a square with area 16 square units whose centre is the point of intersection o10 May, 2024 (E)Angle between lines
  11. 11If the line forms an equilateral triangle with , then10 May, 2024 (E)point of intersection of pair of straight lines
  12. 12Let be the distance between the parallel lines and . Let and be two lines that are at the distance of and from the line . Then the combined 14 May, 2023 (M)Condition for 2nd degree equationto represent pair of straight lines
  13. 13For , the equation represents a pair of distinct lines14 May, 2023 (M)Condition for 2nd degree equationto represent pair of straight lines
  14. 14The point of concurrence of all the chords of the curve which subtend a right angle at the origin is14 May, 2023 (E)Angle between lines
  15. 15Let the line passing through the point of intersection of the lines and divide the line segment joining the points and in the ratio . If the13 May, 2023 (M)point of intersection of pair of straight lines
  16. 16When the origin is shifted to the point by translati:g the coordinate axes, the equation is changed to . Again by rotating the coordinate ax13 May, 2023 (E)general equation of second degree
  17. 17The range of ' ' so that represents two distinct lines is12 May, 2023 (M)Condition for 2nd degree equationto represent pair of straight lines
  18. 18Two tangents are drawn from the point to the parabola . If is the angle between these tangents, then12 May, 2023 (M)Angle between lines
  19. 19If is the acute angle between the lines joining the origin to the points of intersection of the curve and the straight line then12 May, 2023 (E)homogeneous equation of second degree
  20. 204 different pairs of lines are given in List I and the cosine of the angle between every pair of lines is given in List II. Match the follow20 Jul, 2022 (M)Angle between lines
  21. 21If represents a pair of perpendicular lines and represents a pair of coincident lines then20 Jul, 2022 (M)Angle between lines
  22. 22The line meets the curve at two points and . Let be the origin. If the line segments and are perpendicular to each other, then20 Jul, 2022 (M)general equation of second degree
  23. 23By rotating the axes through an angle of in the anti-clockwise direction about the origin, the equation becomes then20 Jul, 2022 (E)general equation of second degree
  24. 24If is the acute angle between the pair of lines and , then20 Jul, 2022 (E)Angle between lines
  25. 25The number of real values of for which the pair of lines represented by are at right angles to each other, is20 Jul, 2022 (E)Angle between lines
  26. 26If is the equation of pair of lines passing through the origin and perpendicular to the pair of lines , then19 Jul, 2022 (M)Pair of lines through origin
  27. 27represents two coincident if19 Jul, 2022 (M)homogeneous equation of second degree
  28. 28If the lines joining the origin to the points of intersection of the line and the curve are at right angles then the sum of all the possible19 Jul, 2022 (M)Condition for 2nd degree equationto represent pair of straight lines
  29. 29For , if and , then all the lines given by are19 Jul, 2022 (E)Pair of lines through origin
  30. 30If is the acute angle between the pair of lines and is a point on then19 Jul, 2022 (E)Pair of lines through origin
  31. 31The equation of the pair of straight lines passing through the point and perpendicular to the pair of lines is then19 Jul, 2022 (E)Pair of lines through origin
  32. 32a x 2 - 4 x y - 2 y 2 = 0 represents a pair of lines. If is the angle between these lines, cos = 1 5 and the possible values of a are a 1 an18 Jul, 2022 (M)Angle between lines
  33. 33Let L 1 , L 2 be the lines represented by the equation 4 x 2 - 5 x y + 3 y 2 = 0 . Let L 3 , L 4 be two lines passing through the point 4 , 18 Jul, 2022 (M)general equation of second degree
  34. 34The equation x 2 - y 2 + a x + b = 0 represents a pair of lines for the ordered pair a , b =18 Jul, 2022 (M)Condition for 2nd degree equationto represent pair of straight lines
  35. 35If the slope of one of the lines represented by 5 x 2 + 40 3 x y + k y 2 = 0 is 3 , then the angle between the pair of lines is18 Jul, 2022 (E)Angle between lines
  36. 36If a line L is common to the pairs of lines 6 x 2 - x y - 12 y 2 = 0 and 15 x 2 + 14 x y - 8 y 2 = 0 , then the combined equation the other 18 Jul, 2022 (E)point of intersection of pair of straight lines
  37. 37If L is a line passing through the point - 1 , 1 and parallel to the common line of the pairs of lines 6 x 2 - x y - 12 y 2 = 0 and 15 x 2 +18 Jul, 2022 (E)Homogenization of curve
  38. 38If the pair of lines joining the origin to the points of intersection of the line with the curve are at right angles, then the point lies on06 Aug, 2021 (M)homogeneous equation of second degree
  39. 39The numbers and are such that one of the lines of . Coincides with one of the lines of . If the two lines other than that line are perpendic06 Aug, 2021 (E)Pair of lines through origin
  40. 40If an angular bisector of the coordinate axes is one of the lines of , then sum of all possible values of is06 Aug, 2021 (E)combined equation of angle bisector
  41. 41From the point ( 3 , - 4 ) perpendicular lines L 1 and L 2 are drawn on each of the lines S 2 x 2 + 3 x y - 2 y 2 - 7 x + y + 3 = 0 . The ar05 Aug, 2021 (M)Angle between lines
  42. 42The line x 3 + y 2 = 1 and a pair of lines both passing through origin forms an isosceles triangle. If this pair of lines are perpendicular,05 Aug, 2021 (M)Angle between lines
  43. 43Consider the lines L 1 4 x + 5 y - 6 = 0 , L 2 2 x + 3 y - 4 = 0 , L 3 3 x - y + 2 = 0 . If the line L 1 = 0 intersects the lines L 2 = 0 an05 Aug, 2021 (E)homogeneous equation of second degree
  44. 44The product of the length of perpendiculars from origin to the pair of lines x 2 + 3 y 2 + 4 x y - 4 x - 10 y + 3 = 0 is05 Aug, 2021 (E)general equation of second degree
  45. 45If a x 2 + 2 h x y + b y 2 + 2 g x + 2 f y + c = 0 represents a pair of lines, which of the following statements is true?05 Aug, 2021 (E)Condition for 2nd degree equationto represent pair of straight lines
  46. 46The transformed equation of the curve 2 x 2 + y 2 - 3 x + 5 y - 8 = 0 when the origin is translated to the point ( - 1 , 2 ) is04 Aug, 2021 (M)homogeneous equation of second degree
  47. 47The equation 3 a x 2 - 16 x y - a 2 - 10 y 2 = 0 represents04 Aug, 2021 (E)homogeneous equation of second degree
  48. 48The angle between the pair of straight lines 3 y 2 - 8 x y - 3 x 2 - 29 x + 3 y - 18 = 0 is04 Aug, 2021 (E)general equation of second degree
  49. 49Let be a parallelogram. The equation of one diagonal is and the combined equation of the sides is . If is centroid of the triangle , then14 Sep, 2020 (M)Pair of lines through origin
  50. 50The acute angle between the pair of straight lines joining the origin to the points of intersection of the line with the pair of straight li14 Sep, 2020 (M)Angle between lines

Frequently Asked Questions

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

This chapter includes 117 questions compiled from TS EAMCET papers spanning 2001 to 2025.

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

These are TS 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 TS EAMCET Mathematics?

Pair of Lines has appeared in 22 of the 25 years of TS EAMCET papers covered here, with 117 questions across 58 papers - about 2 per paper it appears in.

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

Of the 117 questions analysed for this chapter, 32% are easy, 50% moderate and 18% tough. 2022 had the most, with 18 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 - 28 questions (24%)
  • general equation of second degree - 22 questions (19%)
  • homogeneous equation of second degree - 20 questions (17%)
  • Angle between lines has produced the most tough questions (5).
6.Is Pair of Lines's weightage in TS EAMCET going up or down?

Across all 58 papers analysed, Pair of Lines has averaged about 2.0 questions per paper. In the last three years (2022–2024), that average has fallen, at about 1.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.