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Mathematics - Basic of Mathematics

Practise 61 KVPY previous year questions on Basic of Mathematics, compiled from papers spanning 2010 to 2020. 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. 1The number of ordered pairs x , y of positive integers satisfying 2 x + 3 y = 5 x y is2020 (SA)
  2. 2Let x , y be real numbers such that x 2 y 0 and 2 log x - 2 y = log x + log y . Then the possible value s of x y2020 (SB/SX)
  3. 3Let N be the least positive integer such that whenever a non-zero digit c is written after the last digit of N, the resulting number is divi2019 (SA)
  4. 4The number of pairs ( a , b ) of positive real numbers satisfying a 4 + b 4 1 and a 2 + b 2 1 is2018 (SA)
  5. 5Let x k be real numbers such that x k k 4 + k 2 + 1 for 1 k 2018 . Denote N = k = 1 2018 k . Consider the following inequalities. I. k = 1 22018 (SB/SX)
  6. 6In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is . If further 44 girls leave the class,19 Nov, 2017 (SA)
  7. 7In a Mathematics test, the average marks of boys is and the average marks of girls is with . If the average marks of all students is , the r19 Nov, 2017 (SA)
  8. 8If , where and are nonzero rational numbers, then equals05 Nov, 2017 (SA)
  9. 9Let be positive integers such that and . Which of the following statements are true? I. 4 divides or 4 divides . II. 3 divides or 3 divides 05 Nov, 2017 (SB/SX)
  10. 10The number of solution pairs of the simultaneous equations and is05 Nov, 2017 (SB/SX)
  11. 11Let , be real numbers such that . Then05 Nov, 2017 (SB/SX)
  12. 12Consider a cuboid all of whose edges are integers and whose base is square. Suppose the sum of all its edges is numerically equal to the sum2016 (SA)
  13. 13Let be positive reals. Which of the following implies ?2015 (SA)
  14. 14A triangular corner is cut from a rectangular piece of paper and the resulting pentagon has sides in some order. The ratio of the area of th2015 (SA)
  15. 15Given are three cylindrical buckets whose circular bases are of radii units, respectively, Initially water is filled in these buckets upto t2015 (SA)
  16. 16The least positive integer for which is2015 (SA)
  17. 17A man standing on a railway platform noticed that a train took 21 seconds to cross the platform (this means the time elapsed from the moment2015 (SA)
  18. 18If is the smallest natural number such that is a perfect square, then the number of digits in is2015 (SA)
  19. 19Let be an integer. Which of the following sets of numbers nec essarily contains a multiple of2015 (SA)
  20. 20In the figure given below, If the areas of the two regions are equal then which of the following is true?2015 (SA)
  21. 21Let be a trapezium with AD parallel to BC. Assume there is a point is interior of the segment such that and . Then the ratio of the area of 2015 (SA)
  22. 22If , then equals.2015 (SB/SX)
  23. 23The shortest distance from the origin to a variable point on the sphere is2015 (SB/SX)
  24. 24Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the center of this sector (i.e., the angle betwe2015 (SB/SX)
  25. 25Suppose are positive integers such that Then is equal to2015 (SB/SX)
  26. 26In a quadrilateral , which is not a trapezium, it is known that . Moreover, . Then.2014 (SA)
  27. 27Let and be two 2 -digit numbers such that is obtained by reversing the digits of Suppose they also satisfy for some positive integer . The v2014 (SA)
  28. 28A semi-circle of diameter 1 unit sits at the top of a semi-circle of diameter 2 units. The shaded region inside the smaller semi-circle but 2014 (SA)
  29. 29For a real number we denote by [r] the largest integer less than or equal to r. If are real numbers with then which of the following stateme2014 (SB/SX)
  30. 30For a real number let denote the largest integer less than or equal to r. Let be a real number which is not an integer, and let be the small2014 (SB/SX)
  31. 31If are natural numbers such that , then the minimum possible value of is2013 (SA)
  32. 32In the figure given below, is a regular hexagon of side length , and are squares. Then the ratio Area Area equals2013 (SA)
  33. 33A person is running around a circular track completing one round every seconds. Another person running in the opposite direction meets every2013 (SA)
  34. 34Let be non-zero real numbers such that and , then is equal to2013 (SA)
  35. 35Let be a square and let be point on segment such that . Let be a point on segment such that . Then the ratio of the area of quadrilateral to2013 (SA)
  36. 36On each face of a cuboid, the sum of its perimeter and its area is written. Among the six numbers so written, there are three distinct numbe2013 (SA)
  37. 37The least positive integer for which is2013 (SA)
  38. 38In a rectangle , points and are the midpoints of and , respectively. Lines and when extended intersect at , lines and when extended intersec2013 (SA)
  39. 39Suppose the height of a pyramid with a square base is decreased by and the lengths of the sides of its square base are increased by (where .2013 (SA)
  40. 40Let be a closed polygon with 10 sides and 10 vertices (assume that the sides do not intersect except at the vertices). Let be the number of 2013 (SB/SX)
  41. 41Let be a positive integer such that Let be the number of digits in the binary expansion of . Then the minimum and the maximum possible value2013 (SB/SX)
  42. 42Suppose that the earth is a sphere of radius 6400 kilometers. The height from the earth's surface from where exactly a fourth of the earth's2013 (SB/SX)
  43. 43In the adjacent figures, which has the shortest path -2012 (SA)
  44. 44A regular octagon is formed by cutting congruent isosceles right- angled triangles from the corners of a square. If the square has side- len2012 (SA)
  45. 45In the figure AHKF, FKDE and HBCK are unit squares ; AD and BF intersect in . Then the ratio of the areas of triangles AXF and ABF is -2012 (SA)
  46. 46If are positive real numbers such that , then is -2012 (SA)
  47. 47A train leaves Pune at and reaches Mumbai at . Another train leaves Mumbai at and reaches Pune at . Assuming that the two trains travels at 2012 (SA)
  48. 48The square root of is -2012 (SA)
  49. 49Let be positive integers such that is a rational number, then which of the following is always an integer?2012 (SA)
  50. 50When a bucket is half full, the weight of the bucket and the water is . When the bucket is two - thirds full, the total weight is . What is 2012 (SA)

Frequently Asked Questions

1.How many questions are available for Basic of Mathematics?

This chapter includes 61 questions compiled from KVPY papers spanning 2010 to 2020.

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

These are KVPY questions specifically for the Basic of Mathematics chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Basic of Mathematics an important chapter for KVPY Mathematics?

Basic of Mathematics has appeared in 11 of the 11 years of KVPY papers covered here, with 61 questions across 19 papers - about 3 per paper it appears in.