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Mathematics - Straight Lines

Practise 193 NDA previous year questions on Straight Lines, compiled from papers spanning 2010 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 NDA tests.

Straight Lines has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 193 questions in all. 28% of them were easy, 72% moderate and 0% tough. Most of its questions came from 2012, with 18 questions that year. In the last three years (2024–2026) it had 27 questions across 5 papers, about 5.4 per paper.

The chapter's 8 topics are not weighted equally: Coordinate System (58 questions, 30%), Basic Forms of Straight Line (38 questions, 20%), and Point and Line (37 questions, 19%) have been asked the most. Over the last five years the most frequent topics have been Basic Forms of Straight Line (13), Coordinate System (10), and Angle between Lines (9).

  1. 1Passage: The equation of a straight line which passes through the origin and makes an angle with the line is . Question: What is the value o2026 (Phase 1)Angle between Lines
  2. 2Passage: The equation of a straight line which passes through the origin and makes an angle with the line is . Question: What is the angle m2026 (Phase 1)Basic Forms of Straight Line
  3. 3Passage: Let , and be the points such that , and are in AP. Question: If , and are in AP, then the points , and are2026 (Phase 1)Point and Line
  4. 4Under what condition will the lines and be perpendicular?2025 (Phase 1)Angle between Lines
  5. 5If and are real numbers between 0 and 1 such that the points , and form an equilateral triangle, then what is equal to?2025 (Phase 1)Coordinate System
  6. 6The vertices of a triangle are , and . The angular bisectors of the triangle meet at . What are the coordinates of ?2025 (Phase 1)Coordinate System
  7. 7Let and be the end points of line segment . Let be the middle point of the line segment . Let be the point situated at a distance units from2025 (Phase 1)Coordinate System
  8. 8is an equilateral triangle and is the altitude on . If the coordinates of are and that of are , then what is the equation of ?2025 (Phase 1)Point and Line
  9. 9For different values of , the equation represents2025 (Phase 2)Concurrency & Family of Lines
  10. 10The equation of the locus of a point equidistant from the points and is . What is the value of ?2025 (Phase 2)Locus
  11. 11What is the sum of the intercepts of the line on the coordinate axes?2025 (Phase 2)Basic Forms of Straight Line
  12. 12Which one of the following is the perpendicular form of the straight line ?2025 (Phase 2)Basic Forms of Straight Line
  13. 13If the vertices and of a square are and respectively, then what is the area of the square?2025 (Phase 2)Coordinate System
  14. 14What is the value of if is the acute angle between the lines whose equations are and ?2025 (Phase 2)Angle between Lines
  15. 15The number of points represented by the equation on the -plane is:2024 (Phase 1)Basic Forms of Straight Line
  16. 16If the variable line passes through the point of intersection of the lines and and meets the coordinate axes in A and B , then what is the l2024 (Phase 1)Concurrency & Family of Lines
  17. 17What is the equation to the straight line passing through the point and perpendicular to the line ?2024 (Phase 1)Derived Forms of Line
  18. 18Two points P and Q lie on line . These two points P and Q are at a distance 2 units from another point . What are the coordinates of the poi2024 (Phase 1)Point and Line
  19. 19If two sides of a square lie on the lines and , then what is the area of the square in square units?2024 (Phase 1)Point and Line
  20. 20ABC is a triangle with . The mid-points of sides are at respectively. What are the coordinates of centroid of the triangle ABC ?2024 (Phase 1)Coordinate System
  21. 21ABC is an acute angled isosceles triangle. Two equal sides AB and AC lie on the lines 0 and . If is one of the equal angles, then what is eq2024 (Phase 1)Angle between Lines
  22. 22Let and are two lines of regression computed from some bivariate datIf is the acute angle between them, then what is the value of ?2024 (Phase 1)Angle between Lines
  23. 23The diagonals of a quadrilateral ABCD are along the lines and . The quadrilateral ABCD may be a2024 (Phase 2)Angle between Lines
  24. 24If and are vertices of a parallelogram, then what is equal to?2024 (Phase 2)Coordinate System
  25. 25Paragraph: ABCD is an isosceles trapezium and AB is parallel to DC . Let be the vertices. Question: What are the coordinates of vertex D ?2024 (Phase 2)Coordinate System
  26. 26Paragraph: ABCD is an isosceles trapezium and AB is parallel to DC . Let be the vertices. Question: What is the point of intersection of the2024 (Phase 2)Coordinate System
  27. 27Let and be two lines of regression computed from some bivariate data. If and are regression coefficients of lines of regression of on and on2024 (Phase 2)Angle between Lines
  28. 28Paragraph: A quadrilateral is formed by the lines . and . Question: What is the equation of diagonal through origin?2023 (Phase 1)Basic Forms of Straight Line
  29. 29Paragraph: A quadrilateral is formed by the lines . and . Question: What is the equation of other diagonal?2023 (Phase 1)Basic Forms of Straight Line
  30. 30If two lines of regression are and , then what is the value of when ?2023 (Phase 1)Basic Forms of Straight Line
  31. 31The points and are:2023 (Phase 2)Point and Line
  32. 32For what value of is the line parallel to the line ?2023 (Phase 2)Angle between Lines
  33. 33The line cuts the line joining and at R . What is PR : RQ equal to ?2023 (Phase 2)Coordinate System
  34. 34What is the sum of the intercepts of the line whose perpendicular distance from origin is 4 units and the angle which the normal makes with 2023 (Phase 2)Basic Forms of Straight Line
  35. 35Consider the inequations and . Which one of the following points lies in the common region?2022 (Phase 1)Position of a point
  36. 36If the points with coordinates and are collinear, then what is the value of where ?2022 (Phase 1)Point and Line
  37. 37What is the equation of the straight line which passes through the point and cuts off equal intercepts from the axes?2022 (Phase 1)Basic Forms of Straight Line
  38. 38A straight line passes through the point of intersection of and . It cuts equal intercepts in the fourth quadrant. What is the sum of the ab2022 (Phase 1)Basic Forms of Straight Line
  39. 39Under which one of the following conditions are the lines and parallel ?2022 (Phase 1)Angle between Lines
  40. 40What is the equation of the locus of the mid-point of the line segment obtained by cutting the line , (where is a real number) by the coordi2022 (Phase 1)Locus
  41. 41If the point is equidistant from the points and where , then which one of the following is correct?2022 (Phase 1)Coordinate System
  42. 42Consider the following statements in respect of the line passing through origin and inclining at an angle of with the positive direction of 2022 (Phase 2)Basic Forms of Straight Line
  43. 43If is the mid-point of a line segment between the axes, then what is the equation of the line?2022 (Phase 2)Basic Forms of Straight Line
  44. 44The base of an equilateral triangle with side 8 cm lies along the -axis such that the mid-point of is at the origin and lies above the origi2022 (Phase 2)Basic Forms of Straight Line
  45. 45What is the interior angle of a regular octagon of side length 2 cm ?2021 (Phase 1)Coordinate System
  46. 46A parallelogram has three consecutive vertices , and . The fourth vertex is2021 (Phase 1)Coordinate System
  47. 47If the lines and are perpendicular, then which one of the following is correct?2021 (Phase 1)Angle between Lines
  48. 48If and are in AP , then the straight line will always pass through a fixed point. The fixed point is2021 (Phase 1)Basic Forms of Straight Line
  49. 49If the image of the point by a line mirror is 2), then what is the equation of the line mirror?2021 (Phase 1)Point and Line
  50. 50Consider the following statements in respect of the points and : 1. The points lie on a straight line. 2. The points always lie in the first2021 (Phase 1)Point and Line

Frequently Asked Questions

1.How many questions are available for Straight Lines?

This chapter includes 193 questions compiled from NDA papers spanning 2010 to 2026.

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

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

3.Is Straight Lines an important chapter for NDA Mathematics?

Straight Lines has appeared in 17 of the 17 years of NDA papers covered here, with 193 questions across 32 papers - about 6 per paper it appears in.

4.What is the difficulty level of Straight Lines questions in NDA?

Of the 193 questions analysed for this chapter, 28% are easy, 72% moderate and 0% tough. 2012 had the most, with 18 questions.

5.Which topics in Straight Lines should I focus on?

These topics have carried the most weightage in Straight Lines:

  • Coordinate System - 58 questions (30%)
  • Basic Forms of Straight Line - 38 questions (20%)
  • Point and Line - 37 questions (19%)
6.Is Straight Lines's weightage in NDA going up or down?

Across all 32 papers analysed, Straight Lines has averaged about 6.0 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 5.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.