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Mathematics - Circle

Practise 20 KVPY previous year questions on Circle, compiled from papers spanning 2010 to 2018. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KVPY tests.

  1. 1Let x 0 , y 0 be fixed real numbers such that x 0 2 + y 0 2 1 . If x , y are arbitrary real numbers such that x 2 + y 2 1 , then the minimum2018 (SA)
  2. 2Let T be a circle with diameter A B and centre O . Let l be the tangent to T at B . For each point M on T different from A , consider the ta2018 (SB/SX)
  3. 3A spherical ball is kept at the corner of a rectangular room such that the ball touches two (Perpendicular) walls and lies on the floor. If 19 Nov, 2017 (SB/SX)
  4. 4Let be the circle in -plane which touches the -axis at point , the -axis at point and the unit circle at point externally. If denotes the or05 Nov, 2017 (SA)
  5. 5Let a and be two positive real numbers such that . Let and be, respectively, the areas of circles with radii and . Then the maximum possible2016 (SA)
  6. 6Let be a square of side length 1 , and a circle passing through and , and touching . The radius of is2015 (SA)
  7. 7The sides of a right -angled triangle are integers. The length of one of the sides is 12. The largest possible radius of the in circle of su2015 (SB/SX)
  8. 8Circles and , of radii and respectively, touch each other as shown in figure. The line , which is parallel to the line joining the centres o2015 (SB/SX)
  9. 9Suppose and are two unequal circles; and are the direct common tangents to these circles. A transverse common tangent cuts in and in . If , 2014 (SA)
  10. 10On the circle with center , points are such that . A point is located on the tangent at to the circle such that and are on the opposite side2014 (SA)
  11. 11Let be the circle in the plane. For each , let be the line passing through and . Note that intersects in two points, one of which is Let be 2014 (SB/SX)
  12. 12Let be a circle of radius 1 .for , let be a circle whose area equals the area of a square inscribed in Then Area equals:2014 (SB/SX)
  13. 13Let and let , be circles with radii , respectively. Assume that and touch externally for . It is also given that the -axis and the line are 2014 (SB/SX)
  14. 14Tangents to a circle at points and on the circle intersect at a point . If and then the radius of the circle is2013 (SA)
  15. 15Two line segments and are constrained to move along the and axes, respectively, in such a way that the points A, B, C, D are concyclic. If a2013 (SB/SX)
  16. 16A circle is drawn in a sector of a larger circle of radius , as shown in the adjacent figure. The smaller circle is tangent to the two bound2012 (SA)
  17. 17Suppose is a point on the circle with centre and radius 1 , as shown in the figure ; is a point outside the circle such that and . Let be th2012 (SA)
  18. 18Suppose two perpendicular tangents can be drawn from the origin to the circle , for some real . then2012 (SB/SX)
  19. 19Three circles each of radius 1 , touch one another externally and they lie between two parallel lines. The minimum possible distance between2011 (SA)
  20. 20Among all cyclic quadrilaterals inscribed in a circle of radius with one of its angles equal to . Consider the one with maximum possible are2010 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Circle?

This chapter includes 20 questions compiled from KVPY papers spanning 2010 to 2018.

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

These are KVPY 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 KVPY Mathematics?

Circle has appeared in 9 of the 11 years of KVPY papers covered here, with 20 questions across 15 papers - about one per paper it appears in.