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Mathematics - Permutation Combination

Practise 31 KVPY previous year questions on Permutation Combination, 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. 1If the integers from 1 to 2021 are written as a single integer like 123 91011 20202021 , then the 2021 st digit (counted from the left) in t2020 (SA)
  2. 2The number of permutations of the letters a 1 , a 2 , a 3 , a 4 , a 5 in which the first letter a 1 does not occupy the first position (from2020 (SA)
  3. 3There are m books in black cover and n books in blue cover, and all books are different. The number of ways these m + n books can be arrange2020 (SA)
  4. 4The number of four-letter words that can be formed with letters a , b , c such that all three letters occur is2019 (SB/SX)
  5. 5Let E denote the set of letters of the English alphabet, V = a , e , i , o , u and C be the complement of V in E . Then, the number of four-2019 (SB/SX)
  6. 6Let m (respectively, n ) be the number of 5 -digit integers obtained by using the digits 1 , 2 , 3 , 4 , 5 with repetitions (respectively, w2018 (SA)
  7. 7The number of four-letter words that can be formed with letters a , b , c such that all three letters occur is2018 (SB/SX)
  8. 8Let R be a rectangle, C be a circle, and T be a triangle in the plane. The maximum possible number of points common to the perimeters of R ,2018 (SB/SX)
  9. 9Suppose is a given line segment in the plane and is a scalene triangle. The number of points A in the plane such that the triangle with vert19 Nov, 2017 (SA)
  10. 10Let be the set of all permutations of such that is not a permutation of for any . Then the number of elements in is19 Nov, 2017 (SB/SX)
  11. 11Thirty two persons are randomly seated around a circular table at equal intervals. Two persons and are said to be within earshot of each oth19 Nov, 2017 (SB/SX)
  12. 12Let be nonzero real numbers, of which are positive and remaining are negative. The number of ordered pairs , for which is positive, is Simil05 Nov, 2017 (SA)
  13. 13The largest power of 2 that divides is05 Nov, 2017 (SA)
  14. 14Consider the set . The number of ways in which one can choose three distinct numbers from Aso that the product of the chosennumbers is divis05 Nov, 2017 (SA)
  15. 15The number of noncongruent integer-sided triangles whose sides belong to the set is-2016 (SB/SX)
  16. 16Three schools send 2,4 and 6 students, respectively, to a summer camp. The 12 students must be accommodated in 6 rooms numbered in such a wa2016 (SB/SX)
  17. 17The largest non-negative integer such that divides is.2015 (SA)
  18. 18How many ways are there to arrange the letters of the word EDUCATION so that all the following three conditions hold? the vowels occur in th2015 (SA)
  19. 19The number of distinct primes dividing is2015 (SA)
  20. 20Let and let a subset of be chosen so that every pair of elements of A differ by at least 3. (For example, if can be or among others). When ,2015 (SB/SX)
  21. 21The number of 6 -digit numbers of the form ababab (in base 10 each of which is a product of exactly 6 distinct primes is2014 (SA)
  22. 22The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is 170 . 2014 (SA)
  23. 23The number of all 3 -digit numbers abc (in base10) for which is2014 (SA)
  24. 24Ten points lie in a plane so that no three of them are collinear. The number of lines passing through exactly two of these points and dividi2013 (SA)
  25. 25How many natural numbers are there such that is a perfect square?2013 (SA)
  26. 26In a tournament with five teams, each team plays against every other team exctly once. Each game is won by one of the playing teams and the 2013 (SB/SX)
  27. 27The number of integers with and containing at most two distinct digits is2013 (SB/SX)
  28. 28How many ordered pairs of integers satisfy ?2012 (SA)
  29. 29Three children, each accompanied by a guardian, seek admission in a school. The principal want to interview all the 6 persons one after the 2012 (SB/SX)
  30. 30How many six-digit numbers are there in which no digit is repeated, even digits appear at even places, odd digits appear at odd places and t2010 (SB/SX)
  31. 31The number of rectangles that can be obtained by joining four of the twelve vertices of a 12 -sided regular polygon is-2010 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Permutation Combination?

This chapter includes 31 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 Permutation Combination chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Permutation Combination an important chapter for KVPY Mathematics?

Permutation Combination has appeared in 10 of the 11 years of KVPY papers covered here, with 31 questions across 16 papers - about 2 per paper it appears in.