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Mathematics - Sets and Relations

Practise 25 KVPY previous year questions on Sets and Relations, compiled from papers spanning 2011 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. 1Let A be a set consisting of 10 elements. The number of non-empty relations from A to A that are reflexive but not symmetric is2020 (SB/SX)
  2. 2Let N be the set of positive integers. For all n N , let f n = n + 1 1 / 3 - n 1 / 3 and A = n N : f n + 1 1 3 n + 1 2 / 3 f n Then,2019 (SA)
  3. 3The number of ordered pairs a , b of positive integers such that 2 a - 1 b and 2 b - 1 a are both integers is2019 (SB/SX)
  4. 4Let a 0 , a 1 . Then, the set S of all positive real numbers b satisfying 1 + a 2 1 + b 2 = 4 a b is2019 (SB/SX)
  5. 5Let A be the set of vectors a = a 1 , a 2 , a 3 satisfying i = 1 3 a i 2 i 2 = i = 1 3 a i 2 2 i Then,2019 (SB/SX)
  6. 6Let S = x R : cos x + cos 2 x 2 , then2018 (SB/SX)
  7. 7Consider the set A of natural numbers whose units digit is nonzero, such that if this units digit is erased, then the resulting number divid19 Nov, 2017 (SA)
  8. 8The number of positive integers in the set such that has a terminating decimal expansion is19 Nov, 2017 (SA)
  9. 9Let be the set of all ordered pairs of positive integers satisfying the condition . Then05 Nov, 2017 (SA)
  10. 10If are four distinct numbers chosen from the set , then the minimum value of is05 Nov, 2017 (SA)
  11. 11Let be a relation on the set of all natural numbers given by a R b a divides . Which of the following properties does satisfy? I. Reflexivit05 Nov, 2017 (SB/SX)
  12. 12Let be non-empty subsets of satisfying the following conditions: (1) the numbers are distinct; (2) are pairwise disjoint. (Here denotes the 2016 (SA)
  13. 13For any real number , let is a natural number be a set of complex numbers. Then -2016 (SB/SX)
  14. 14For each positive real number , let be the set of all natural numbers such that Let be the complement of in the set of all natural numbers. 2016 (SB/SX)
  15. 15In a cinema hall, the charge per person is Rs. 200 . On the first day, only of the seats were filled. The owner decided to reduce the price 2014 (SA)
  16. 16Let be a set of 5 elements. The number of ordered pairs of subsets of such that satisfies :2014 (SB/SX)
  17. 17For each positive integer n, let . Then the number of elements is for which is :2014 (SB/SX)
  18. 18Let . The number of elements in such that is divisible by 19 is :2014 (SB/SX)
  19. 19For an integer let . Which of the following is true for all2013 (SB/SX)
  20. 20Let and let be a subset of such that no two elements in have their sum divisible by 5 . What is the maximum number of elements possible in ?2012 (SA)
  21. 21The number of ordered pairs , where , such that is a multiple of 5 is2012 (SB/SX)
  22. 22Let and . A subset of is said to be a good subset if for every . Then the number of good subsets of is2012 (SB/SX)
  23. 23The sum of is -2011 (SB/SX)
  24. 24Let be a nonempty set and let denote the collection of all subsets of . Define Then equals -2011 (SB/SX)
  25. 25Let and Then2011 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Sets and Relations?

This chapter includes 25 questions compiled from KVPY papers spanning 2011 to 2020.

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

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

3.Is Sets and Relations an important chapter for KVPY Mathematics?

Sets and Relations has appeared in 9 of the 11 years of KVPY papers covered here, with 25 questions across 15 papers - about 2 per paper it appears in.