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Mathematics - Circle

Practise 29 JEE Advanced previous year questions on Circle, compiled from papers spanning 2006 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 JEE Advanced tests.

Circle has been asked in 17 of the 27 years of JEE Advanced papers analysed (2000–2026), with 29 questions in all. 31% of them were easy, 48% moderate and 21% tough. Most of its questions came from 2019, with 3 questions that year. In the last three years (2024–2026) it had 2 questions across 6 papers, about 0.3 per paper.

The chapter's 14 topics are not weighted equally: Equation of Circle & its intercept (7 questions, 24%), Tangent to circle (6 questions, 21%), and Chord of Contact (2 questions, 7%) have been asked the most. Over the last five years the most frequent topics have been Tangent to circle (1), Family of Circle (1), and Radical axis and centre (1). Equation of Circle & its intercept has produced the most tough questions (1).

  1. 1Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The circle with centre and touc2026 (Paper 1)Common Tangents
  2. 2Let the straight line touch a circle with center , and radius at a point . Let be the point on the circle such that the line segment is a di2024 (Paper 1)Tangent to circle
  3. 3Let C 1 be the circle of radius 1 with center at the origin. Let C 2 be the circle of radius r with center at the point A = ( 4 , 1 ) , wher2023 (Paper 2)Radical axis and centre
  4. 4Let G be a circle of radius R 0 . Let G 1 , G 2 , , G n be n circles of equal radius r 0 . Suppose each of the n circles G 1 , G 2 , , G n t2022 (Paper 2)Family of Circle
  5. 5A line y = m x + 1 intersects the circle x - 3 2 + y + 2 2 = 25 at the points P and Q . If the midpoint of the line segment P Q has x - coor2019 (Paper 1)line and circle
  6. 6Let the circles C 1 : x 2 + y 2 = 9 and C 2 : x - 3 2 + y - 4 2 = 16 , intersect at the points X and Y . Suppose that another circle C 3 : x2019 (Paper 2)Common Chord
  7. 7Let the circles C 1 : x 2 + y 2 = 9 and C 2 : x - 3 2 + y - 4 2 = 16 , intersect at the points X and Y . Suppose that another circle C 3 : x2019 (Paper 2)Common Chord
  8. 8Paragraph: Let S be the circle in the x y plane defined by the equation x 2 + y 2 = 4 . Question : Let E 1 E 2 and F 1 F 2 be the chords of 2018 (Paper 1)Chord of Contact
  9. 9Paragraph: Let S be the circle in the x y plane defined by the equation x 2 + y 2 = 4 . Question : Let P be a point on the circle S with bot2018 (Paper 1)Locus
  10. 10Let T be the line passing through the points P - 2 , 7 and Q 2 , - 5 . Let F 1 be the set of all pairs of circles S 1 , S 2 such that T is t2018 (Paper 2)Chord with given Middle Point
  11. 11For how many values of p , the circle x 2 + y 2 + 2 x + 4 y - p = 0 and the coordinate axes have exactly three common points?2017 (Paper 1)Equation of Circle & its intercept
  12. 12Let RS be the diameter of the circle x 2 + y 2 = 1 where, S is the point ( 1 , 0 ) . Let P be a variable point (other than R S ) on the circ2016 (Paper 1)Locus
  13. 13The circle C 1 : x 2 + y 2 = 3 , with centre at O, intersects the parabola x 2 = 2 y at the point P in the first quadrant. Let the tangent t2016 (Paper 1)Tangent to circle
  14. 14A circle S passes through the point (0, 1) and is orthogonal to the circles x - 1 2 + y 2 = 16 and x 2 + y 2 = 1 . Then2014 (Paper 1)General Equation of 2nd degree curve
  15. 15Circle(s) touching x -axis at a distance 3 from the origin and having an intercept of length 2 7 on y -axis is (are)2013 (Paper 2)Equation of Circle & its intercept
  16. 16The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line to the circle is2012 (Paper 1)line and circle
  17. 17A tangent is drawn to the circle at the point . A straight line , perpendicular to is a tangent to the circle . Question: A possible equatio2012 (Paper 2)Tangent to circle
  18. 18A tangent is drawn to the circle at the point . A straight line , perpendicular to is a tangent to the circle . Question: A common tangent o2012 (Paper 2)Tangent to circle
  19. 19The circle passing through the point and touching the -axis at , also passes through the point2011 (Paper 2)Equation of Circle & its intercept
  20. 20The straight line divides the circular region into two parts. If , then the number of point(s) in lying inside the smaller part is2011 (Paper 2)Position of point
  21. 21Paragraph: The circle and hyperbola intersect at the points and . Question: Equation of the circle with as its diameter is2010 (Paper 1)Equation of Circle & its intercept
  22. 22Two parallel chords of a circle of radius 2 are at a distance apart. If the chords subtend at the centre, angles of and , where , then the v2010 (Paper 2)Chord of Contact
  23. 23Tangents drawn from the point to the circle touch the circle at the points and . The equation of the circumcircle of is2009 (Paper 1)Equation of Circle & its intercept
  24. 24The centres of two circles and each of unit radius are at a distance of 6 units from each other. Let be the mid-point of the line segment jo2009 (Paper 2)Coaxial systems of circles
  25. 25Paragraph: A circle of radius 1 is inscribed in an equilateral . The points of contact of with the sides are respectively. The line is given2008 (Paper 1)Equation of Circle & its intercept
  26. 26Tangents are drawn from the point to the circle . Statement I The tangents are mutually perpendicular. Statement II The locus of the points 2007 (Paper 1)Director Circle
  27. 27Let be a quadrilateral with area 18 , with side parallel to the side and . Let be perpendicular to and . If a circle is drawn inside the qua2007 (Paper 2)Tangent to circle
  28. 28Match the statements in Column I with the properties Column II.2007 (Paper 2)Tangent to circle
  29. 29Paragraph: Read the following passage and answer the questions. Let be a square of side length 2 units. is the circle through vertices and i2006Equation of Circle & its intercept

Frequently Asked Questions

1.How many questions are available for Circle?

This chapter includes 29 questions compiled from JEE Advanced papers spanning 2006 to 2026.

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

These are JEE Advanced 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 JEE Advanced Mathematics?

Circle has appeared in 17 of the 21 years of JEE Advanced papers covered here, with 29 questions across 23 papers - about one per paper it appears in.

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

Of the 29 questions analysed for this chapter, 31% are easy, 48% moderate and 21% tough. 2019 had the most, with 3 questions.

5.Which topics in Circle should I focus on?

These topics have carried the most weightage in Circle:

  • Equation of Circle & its intercept - 7 questions (24%)
  • Tangent to circle - 6 questions (21%)
  • Chord of Contact - 2 questions (7%)
  • Equation of Circle & its intercept has produced the most tough questions (1).
6.Is Circle's weightage in JEE Advanced going up or down?

Across all 23 papers analysed, Circle has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.