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Mathematics - Pair of Lines

Practise 134 MHTCET previous year questions on Pair of Lines, compiled from papers spanning 2007 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty MHTCET tests.

Pair of Lines has been asked in 16 of the 17 years of MHTCET papers analysed (2007–2026), with 134 questions in all. 34% of them were easy, 57% moderate and 8% tough. Most of its questions came from 2020, with 26 questions that year. In the last three years (2024–2026) it had 43 questions across 59 papers, about 0.7 per paper.

The chapter's 7 topics are not weighted equally: Pair of lines through origin (35 questions, 26%), Angle between lines (34 questions, 25%), and general equation of second degree (26 questions, 19%) have been asked the most. Pair of lines through origin has also led over the last five years, with 18 questions. general equation of second degree has produced the most tough questions (4).

  1. 1If the equation represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is..........20 Apr, 2026 (M)general equation of second degree
  2. 2If the angle made by the lines represented by the equation with X-axis are and , then is20 Apr, 2026 (E)homogeneous equation of second degree
  3. 3If the combined equation of angle bisectors of the lines is , then which of the following is true?19 Apr, 2026 (M)combined equation of angle bisector
  4. 4If two lines represented by make angles and with the X-axis, then is...19 Apr, 2026 (E)homogeneous equation of second degree
  5. 5Two lines are given by , then the value of k so that the distance between them is 3 is18 Apr, 2026 (M)general equation of second degree
  6. 6The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by is18 Apr, 2026 (E)general equation of second degree
  7. 7The joint equation of a pair of lines passing through point , one of which is parallel to X-axis and the other makes an angle of with the po17 Apr, 2026 (M)general equation of second degree
  8. 8The measure of the acute angle between the pair of lines is:17 Apr, 2026 (M)Angle between lines
  9. 9If the equation represents a pair of straight lines, then the coordinates of their point of intersection are.........17 Apr, 2026 (E)point of intersection of pair of straight lines
  10. 10If , then the ratio of the slopes of the lines represented by is...16 Apr, 2026 (M)homogeneous equation of second degree
  11. 11The combined equation of the pair of lines passing through the origin and making an angle with the line is...16 Apr, 2026 (E)Pair of lines through origin
  12. 12If is the acute angle between the lines , then the value of16 Apr, 2026 (E)Angle between lines
  13. 13The triangle formed by the lines and is...15 Apr, 2026 (M)Angle between lines
  14. 14If is the acute angle between the lines represented by the equation , then15 Apr, 2026 (M)Angle between lines
  15. 15The line intersects the pair of straight lines at points A and B. Then the co-ordinates of the mid-point of AB are15 Apr, 2026 (E)Pair of lines through origin
  16. 16The joint equation of the pair of lines through the origin and making an angle of with the line is13 Apr, 2026 (M)Pair of lines through origin
  17. 17The pair of straight lines represented by the equation are13 Apr, 2026 (E)homogeneous equation of second degree
  18. 18If the equation represents a pair of straight lines, then the co-ordinates of their point of intersection are13 Apr, 2026 (E)general equation of second degree
  19. 19If the equation represents a pair of straight lines, then their point of intersection is11 Apr, 2026 (M)Condition for 2nd degree equationto represent pair of straight lines
  20. 20If the slope of one of the two lines given by is twice that of the other, then ...11 Apr, 2026 (E)Pair of lines through origin
  21. 21If the distance between the lines represented by is units and then the equations of the lines are11 Apr, 2026 (E)general equation of second degree
  22. 22The equation represents a pair of straight lines. If is the angle between them, then the value of is equal to05 May, 2025 (E)general equation of second degree
  23. 23To convert the equation to homogeneous form the origin is shifted to the point27 Apr, 2025 (E)general equation of second degree
  24. 24If the pair of lines and have one line common, then26 Apr, 2025 (E)homogeneous equation of second degree
  25. 25The joint equation of the bisector of the angle between the lines is25 Apr, 2025 (M)combined equation of angle bisector
  26. 26The slopes of the lines represented by are in the ratio , then25 Apr, 2025 (E)Angle between lines
  27. 27The joint equation of two lines passing through and parallel to the bisectors of the angle between the co-ordinate axes is23 Apr, 2025 (M)Pair of lines through origin
  28. 28The equation , where is real number, represents pair of lines. If is acute angle between the lines, then23 Apr, 2025 (E)general equation of second degree
  29. 29If the pair of straight lines and the line are concurrent, then the value of k is equal to22 Apr, 2025 (M)general equation of second degree
  30. 30The distance between the lines represented by is ...... units21 Apr, 2025 (E)general equation of second degree
  31. 31The acute angle between the diagonals of a parallelogram whose vertices are and is20 Apr, 2025 (M)Angle between lines
  32. 32The distance between the lines represented by the equation is20 Apr, 2025 (M)general equation of second degree
  33. 33If the equation represents a pair of lines, then20 Apr, 2025 (E)general equation of second degree
  34. 34If and are the slopes of the lines represented by satisfying the condition , then .19 Apr, 2025 (M)homogeneous equation of second degree
  35. 35If and are perpendicular distances (in units) from point to the pair of lines , then the value of is16 May, 2024 (E)homogeneous equation of second degree
  36. 36The joint equation of two lines through the origin, each making an angle with measure of with the positive Y -axis, is11 May, 2024 (M)Pair of lines through origin
  37. 37The joint equation of pair of lines through the origin, each of which makes an angle of with Y -axis, is11 May, 2024 (E)Pair of lines through origin
  38. 38The number of integer values of , for which -coordinate of the point of intersection of the lines and is also an integer, is10 May, 2024 (E)point of intersection of pair of straight lines
  39. 39If an equation represents a pair of lines, then09 May, 2024 (M)Condition for 2nd degree equationto represent pair of straight lines
  40. 40The joint equation of pair of lines through the origin and making an angle of with the line is09 May, 2024 (E)Pair of lines through origin
  41. 41The combined equation of two lines through the origin and making an angle of with the line , is04 May, 2024 (E)Pair of lines through origin
  42. 42The equation of pair of lines and can be written as . Then the equation of the pair of the angle bisectors of the lines is03 May, 2024 (E)combined equation of angle bisector
  43. 43If the equation represents a pair of parallel lines then the value of is02 May, 2024 (E)Condition for 2nd degree equationto represent pair of straight lines
  44. 44The perpendiculars are drawn to lines and from the origin making an angle and respectively with positive direction of -axis. If both the lin14 May, 2023 (M)homogeneous equation of second degree
  45. 45The centroid of the triangle formed by the lines and is14 May, 2023 (E)Pair of lines through origin
  46. 46If the angle between the lines given by is , then the value of is13 May, 2023 (M)Angle between lines
  47. 47Let be a right angled isosceles triangle, right angled at . If the equation of the line PR is , then the combined equation representing the 13 May, 2023 (E)Angle between lines
  48. 48Let be a right angled isosceles triangle, right angled at . If the equation of the line is , then the equation representing the pair of line12 May, 2023 (M)general equation of second degree
  49. 49If the pair of lines given by are perpendicular to each other, then is12 May, 2023 (E)Angle between lines
  50. 50If the angle between the lines represented by the equation is , then the value of is11 May, 2023 (M)Angle between lines

Frequently Asked Questions

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

This chapter includes 134 questions compiled from MHTCET papers spanning 2007 to 2026.

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

These are MHTCET 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 MHTCET Mathematics?

Pair of Lines has appeared in 16 of the 17 years of MHTCET papers covered here, with 134 questions across 89 papers - about 2 per paper it appears in.

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

Of the 134 questions analysed for this chapter, 34% are easy, 57% moderate and 8% tough. 2020 had the most, with 26 questions.

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

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

  • Pair of lines through origin - 35 questions (26%)
  • Angle between lines - 34 questions (25%)
  • general equation of second degree - 26 questions (19%)
  • general equation of second degree has produced the most tough questions (4).
6.Is Pair of Lines's weightage in MHTCET going up or down?

Across all 89 papers analysed, Pair of Lines has averaged about 1.5 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.