Jump to a section

Mathematics - Circle

Practise 56 NDA previous year questions on Circle, 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.

Circle has been asked in 16 of the 21 years of NDA papers analysed (2006–2026), with 56 questions in all. 27% of them were easy, 73% moderate and 0% tough. Most of its questions came from 2024, with 6 questions that year. In the last three years (2024–2026) it had 12 questions across 5 papers, about 2.4 per paper.

The chapter's 7 topics are not weighted equally: Equation of Circle & its intercept (39 questions, 70%), Position of point (5 questions, 9%), and line and circle (4 questions, 7%) have been asked the most. Equation of Circle & its intercept has also led over the last five years, with 14 questions.

  1. 1What is the length of the chord of a unit circle which subtends at the centre of the circle an angle of ?2026 (Phase 1)line and circle
  2. 2Passage: Consider the points , , and . Question: If the points lie on a circle, then what is/are the possible value(s) of ?2026 (Phase 1)Equation of Circle & its intercept
  3. 3Passage: Consider the points , , and . Question: If a circle is drawn through , and , then what is the diameter of the circle ?2026 (Phase 1)Equation of Circle & its intercept
  4. 4What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are and ?2025 (Phase 1)Equation of Circle & its intercept
  5. 5A square is inscribed in a circle and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?2025 (Phase 1)Equation of Circle & its intercept
  6. 6The circle touches the -axis at and -axis at . What is equal to?2025 (Phase 2)Equation of Circle & its intercept
  7. 7If is the centre and is the radius of the circle , then what is the value of ?2024 (Phase 1)Equation of Circle & its intercept
  8. 8What is the maximum number of possible points of intersection of four straight lines and a circle (intersection is between lines as well as 2024 (Phase 2)line and circle
  9. 9The equation of a circle is Which of the following statements are correct? A. The end points of a diameter of the circle are and . B. The en2024 (Phase 2)Equation of Circle & its intercept
  10. 10Consider the points and lying on the parabola . If the vertex is A , then what is equal to?2024 (Phase 2)Position of point
  11. 11Paragraph: A triangle ABC is inscribed in the circle and C have coordinates and respectively. Question: What is equal to?2024 (Phase 2)Equation of Circle & its intercept
  12. 12Paragraph: A triangle ABC is inscribed in the circle and C have coordinates and respectively. Question: What are the coordinates of A ?2024 (Phase 2)Equation of Circle & its intercept
  13. 13Paragraph: The line partitions the circle in two segments. Question: What is the area of minor segment?2023 (Phase 1)Equation of Circle & its intercept
  14. 14Paragraph: The line partitions the circle in two segments. Question: What is the area of major segment?2023 (Phase 1)Equation of Circle & its intercept
  15. 15If is the equation of a chord of the circle , then what are the coordinates of the midpoint of the chord?2023 (Phase 2)Chord with given Middle Point
  16. 16Consider the following in respect of the circle : 1. The circle touches both the axes. 2. The diameter of the circle is 2 a . 3. The centre 2023 (Phase 2)Equation of Circle & its intercept
  17. 17What is the equation of the circle which touches both the axes in the first quadrant and the line ?2022 (Phase 1)Equation of Circle & its intercept
  18. 18The centre of the circle passing through origin and making positive intercepts 4 and 6 on the coordinate axes, lies on the line2022 (Phase 2)Equation of Circle & its intercept
  19. 19A chord subtends an angle at the centre of a unit circle. What is the length of the chord?2021 (Phase 1)line and circle
  20. 20What is the radius of the circle ?2021 (Phase 1)Equation of Circle & its intercept
  21. 21A circle is passing through the points and . What are the coordinates of the centre of the circle?2021 (Phase 2)Equation of Circle & its intercept
  22. 22A circle is passing through the points and . If is the radius of the circle, then which one of the following is correct?2021 (Phase 2)Equation of Circle & its intercept
  23. 23The center of the circle is2020Equation of Circle & its intercept
  24. 24A circle is drawn on the chord of a circle as diameter. The chord lies on the line . What is the equation of the circle?2019 (Phase 1)Equation of Circle & its intercept
  25. 25The circle , cuts an intercept on y -axis equal to2019 (Phase 1)Equation of Circle & its intercept
  26. 26For is the ratio of perimeter to area of a circle of radius . Then is equal to2019 (Phase 1)Equation of Circle & its intercept
  27. 27In a circle of diameter 44 cm , the length of a chord is 22 cm . What is the length of minor arc of the chord?2019 (Phase 1)Equation of Circle & its intercept
  28. 28What is the length of the chord of a unit circle which subtends an angle at the centre?2019 (Phase 2)line and circle
  29. 29The equation of a circle whose end points of a diameter are and is2018 (Phase 2)Equation of Circle & its intercept
  30. 30If -axis touches the circle , then the normal at this point intersects the circle at the point2018 (Phase 2)Equation of Circle & its intercept
  31. 31The two circles and intersect at two distinct points. Then which one of the following is correct?2017 (Phase 1)Intersection of Circles
  32. 32What is the equation of the circle which passes through the points and and having its centre on the line ?2017 (Phase 1)Equation of Circle & its intercept
  33. 33The equation of the circle which passes through the points and is2017 (Phase 2)Equation of Circle & its intercept
  34. 34If a circle of radius bunits with centre at touches the line , then what is the value of ?2016 (Phase 1)Tangent to circle
  35. 35Consider the two circles and What is the distance between the centres of the two circles?2016 (Phase 1)Equation of Circle & its intercept
  36. 36Consider the two circles and If the circles intersect at two distinct points, then which one of the following is correct?2016 (Phase 1)Intersection of Circles
  37. 37Consider a circle passing through the origin and the points and . On which line does the centre of the circle lie?2016 (Phase 1)Equation of Circle & its intercept
  38. 38Consider a circle passing through the origin and the points and What is the sum of the squares of the intercepts cut off by the circle on th2016 (Phase 1)Equation of Circle & its intercept
  39. 39What is the radius of the circle passing through the point and having centre at the intersection of the lines and2016 (Phase 2)Equation of Circle & its intercept
  40. 40The point on the parabola nearest to the focus has its abscissa2015 (Phase 1)Position of point
  41. 41Consider the parametric equation What does the equation represent?2015 (Phase 1)Equation of Circle & its intercept
  42. 42A straight line touches the . The value of is2015 (Phase 2)Tangent to circle
  43. 43If the centre of the circle passing through the origin is , then the intercepts cut off by the circle on x -axis and y -axis respectively ar2015 (Phase 2)Equation of Circle & its intercept
  44. 44Consider the circles and . What is the distance between the centres of the two circles?2014 (Phase 2)Equation of Circle & its intercept
  45. 45Consider the circles and . The two circles touch each other if2014 (Phase 2)General Equation of 2nd degree curve
  46. 46What is the product of the perpendiculars drawn from the points upon the line ay ?2014 (Phase 2)Position of point
  47. 47Which one of the following points lies inside a circle of radius 6 and centre at ?2013 (Phase 1)Position of point
  48. 48The radius of the circle passing through the origin is2013 (Phase 2)Equation of Circle & its intercept
  49. 49What is the set of points satisfying the equations and ?2011 (Phase 1)Equation of Circle & its intercept
  50. 50For the equation where , to represent a circle, the condition will be2011 (Phase 1)General Equation of 2nd degree curve

Frequently Asked Questions

1.How many questions are available for Circle?

This chapter includes 56 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 Circle chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Circle an important chapter for NDA Mathematics?

Circle has appeared in 16 of the 17 years of NDA papers covered here, with 56 questions across 28 papers - about 2 per paper it appears in.

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

Of the 56 questions analysed for this chapter, 27% are easy, 73% moderate and 0% tough. 2024 had the most, with 6 questions.

5.Which topics in Circle should I focus on?

These topics have carried the most weightage in Circle:

  • Equation of Circle & its intercept - 39 questions (70%)
  • Position of point - 5 questions (9%)
  • line and circle - 4 questions (7%)
6.Is Circle's weightage in NDA going up or down?

Across all 28 papers analysed, Circle has averaged about 2.0 questions per paper. In the last three years (2024–2026), that average has risen, at about 2.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.