Mathematics - Circle
Practise 36 KCET previous year questions on Circle, compiled from papers spanning 2007 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KCET tests.
Circle has been asked in 10 of the 20 years of KCET papers analysed (2007–2026), with 36 questions in all. 33% of them were easy, 39% moderate and 28% tough. Most of its questions came from 2009, with 7 questions that year. In the last three years (2024–2026) it had 1 question across 3 papers, about 0.3 per paper.
The chapter's 11 topics are not weighted equally: Chord of Contact (8 questions, 22%), Equation of Circle & its intercept (7 questions, 19%), and Tangent to circle (4 questions, 11%) have been asked the most. Over the last five years the most frequent topics have been Intersection of Circles (1). Chord of Contact has produced the most tough questions (3).
- 1If in two circles, arcs of the same length subtend angles and at the centre, then the ratio of their radii is2024Intersection of Circles
- 2If \( x=2+3 \) and \( y=1-3 \) represent a circle then the centre and radius is2016Locus
- 3If the function \( f(x) \) defined by \[ f(x)= {x^{100}}{100}+ {x^{99}}{99}+ + {x^{2}}{2}+x+1, { then } f^{ }(0)= \]2014Equation of Circle & its intercept
- 4A tangent is drawn to the circle at point and it meets the line at , then is equal to2013Tangent to circle
- 5The area of the circle having its centre at and touching the line is2013Equation of Circle & its intercept
- 6The number of real circles cutting orthogonally the circle is2013Family of Circle
- 7The length of the chord of the circle intercepted by the -axis is2013Chord of Contact
- 8The least and the greatest distances of the point from the circle2012Position of point
- 9If the straight line touches the circle , then the value of is2012Tangent to circle
- 10The number of circles that touch the coordinate axes and the line whose slope is and -initercept is 1 , is2012Equation of Circle & its intercept
- 11The perimeter of a sector is a constant. If its area is to be maximum, then the sectorial angle is2012Chord of Contact
- 12The equations of the two tangents from to the circle are2012Tangent to circle
- 13The total number of common tangents of and is2011Common Tangents
- 14The centre of a circle which cuts and orthogonally is2011Intersection of Circles
- 15The chord of the circle which is bisected at is perpendicular to the line2010Chord of Contact
- 16The straight line cuts the and -axes at and . The area of , where is the origin, is 12 sq unit. The equation of the circle having as diamete2010Equation of Circle & its intercept
- 17A wire of length is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is2010Chord of Contact
- 18Two circles centred at and intersect each other. If the radii are equal, the equation of the common chord is2010Common Chord
- 19Equation of the circle centred at touching the circle externally, is2010Family of Circle
- 20The points and are concyclic, if is2010Position of point
- 21A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes , when it has traced2009Chord of Contact
- 22The locus of the mid points of the chords of the circle which subtend a right angle at the origin is2009Chord of Contact
- 23The length of the chord joining the points and , of the circle is2009Chord of Contact
- 24The number of common tangents to the circles and is2009Common Tangents
- 25The coordinates of the centre of the smallest circle passing through the origin and having as a diameter are2009Equation of Circle & its intercept
- 26The length of the diameter of the circle which cuts three circles orthogonally, is2009Intersection of Circles
- 27If the circle intersects the hyperbola in four points and , then2009Locus
- 28The equation of the smallest circle passing through the points and is2008Equation of Circle & its intercept
- 29The perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle. Then, the angle at the centre of the sect2008Chord of Contact
- 30The point lies outside the circle2008Position of point
- 31If the circles and touch each other internally, then is equal to2008Coaxial systems of circles
- 32The number of common tangents to the circles and is2007Common Tangents
- 33If is a tangent to the circle , the values of are2007Tangent to circle
- 34The equation of two circles which touch the -axis at and make an intercept of 8 units on -axis are2007Equation of Circle & its intercept
- 35. If the radical centre of the above three circles exists, then which of the following cannot be the value of ?2007Radical axis and centre
- 36If the circles and cut orthogonally, then the length of the common chord of the circles is2007Intersection of Circles
Frequently Asked Questions
1.How many questions are available for Circle?
This chapter includes 36 questions compiled from KCET papers spanning 2007 to 2024.
2.Are these questions only from KCET, or from other exams too?
These are KCET 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 KCET Mathematics?
Circle has appeared in 10 of the 20 years of KCET papers covered here, with 36 questions across 10 papers - about 4 per paper it appears in.
4.What is the difficulty level of Circle questions in KCET?
Of the 36 questions analysed for this chapter, 33% are easy, 39% moderate and 28% tough. 2009 had the most, with 7 questions.
5.Which topics in Circle should I focus on?
These topics have carried the most weightage in Circle:
- Chord of Contact - 8 questions (22%)
- Equation of Circle & its intercept - 7 questions (19%)
- Tangent to circle - 4 questions (11%)
- Chord of Contact has produced the most tough questions (3).
6.Is Circle's weightage in KCET going up or down?
Across all 10 papers analysed, Circle has averaged about 3.6 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.