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Mathematics - Sequences and Series

Practise 36 KVPY previous year questions on Sequences and Series, 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. 1Let x and y be two positive real numbers such that x + y = 1 . Then the minimum value of 1 x + 1 y is-2020 (SA)
  2. 2Let a = n = 101 200 2 n k = 101 n 1 k ! and b = n = 101 200 2 201 - 2 n n ! Then a b is2020 (SB/SX)
  3. 3Let a n , n 1 , be an arithmetic progression with first term 2 and common difference 4 . Let M n be the average of the first n terms. Then t2019 (SA)
  4. 4The number of three digit numbers a b c such that the arithmetic mean of b and c and the square of their geometric mean are equal is2019 (SA)
  5. 5Suppose the sum of the first m terms of an arithmetic progression is n and the sum of its first n terms is m where m n . Then, the sum of th2018 (SA)
  6. 6The number of different possible values for the sum x + y + z , where x , y , z are real number such that x 4 + 4 y 4 + 16 z 4 + 64 = 32 x y2018 (SB/SX)
  7. 7Let be a positive integer and let be the lengths of the sides of arbitrary - sided non-degenerate polygon P. Suppose Consider the following 19 Nov, 2017 (SA)
  8. 8Let be the infinite sum given by where is a sequence defined by and for . If is expressed in the form , where are coprime positive integers,19 Nov, 2017 (SB/SX)
  9. 9The number of 5-tuples of positive integers such that I. are the measures of angles of a convex pentagon in degrees ; II. ; III , e are in a19 Nov, 2017 (SB/SX)
  10. 10Let be the roots of the polynomial equation Then19 Nov, 2017 (SB/SX)
  11. 11Let and be the arithmetic mean, geometric mean and harmonic mean, respetively of two distinct positive real numbers. If is the smallest of t05 Nov, 2017 (SA)
  12. 12Let for Put and Then05 Nov, 2017 (SB/SX)
  13. 13Let be non-zero real numbers such that , Then2016 (SA)
  14. 14Let be the sum of areas of the squares whose sides are parallel to coordinate axes. Let be the sum of areas of the slanted squares as shown 2016 (SA)
  15. 15The number of triples of real numbers satisfying the equation is2016 (SB/SX)
  16. 16The largest perfect square that divides is2015 (SB/SX)
  17. 17The population of cattle in a farm increases so that the difference between the population in year . If the populations in year 2010,2011 we2014 (SA)
  18. 18Suppose are are integers such that where for . The sum is2014 (SA)
  19. 19The value of is equal to2014 (SA)
  20. 20The sum of all positive integers for which is also an integer is.2014 (SA)
  21. 21For a real number let denote the largest integer less than or equal to The smallest positive integer for which the integral exceeds 60 is2014 (SB/SX)
  22. 22Let be an integer. For a permutation of we let Let be the sum of the roots of and let denote the sum over all permutation of of the number .2014 (SB/SX)
  23. 23Let be three non-negative integers such that . The maximum possible value of is2013 (SA)
  24. 24Let be natural numbers in an arithmetic progression such that is the cube of an integer and is square of an integer. The least possible valu2013 (SA)
  25. 25Let be real numbers such that for every natural number . Then is equal to2013 (SB/SX)
  26. 26For a real number let denote the largest integer less than or equal to and . The smallest possible integer value of for which exceeds 2013 i2013 (SB/SX)
  27. 27The sides of a triangle are distinct positive integers in an arithmetic progression. If the smallest side is 10 , the number of such triangl2012 (SA)
  28. 28For to exceed , the maximum value of is2012 (SA)
  29. 29Consider and Then -2012 (SB/SX)
  30. 30Define a sequence by for . Then2012 (SB/SX)
  31. 31Consider an incomplete pyramid of balls on a square base having 18 layers; and having 13 balls on each side of the top layer. Then the total2011 (SA)
  32. 32The expression lies in the interval2011 (SA)
  33. 33Suppose is a natural number such that , where is the square root of . Then is -2011 (SB/SX)
  34. 34The arithmetic mean and the geometric mean of two distinct 2 -digit numbers and are two integers one of which can be obtained by reversing t2011 (SB/SX)
  35. 35The minimum value of for which2011 (SB/SX)
  36. 36Suppose the sides of a triangle form a geometric progression with common ratio r. Then lies in the interval-2010 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Sequences and Series?

This chapter includes 36 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 Sequences and Series chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Sequences and Series an important chapter for KVPY Mathematics?

Sequences and Series has appeared in 11 of the 11 years of KVPY papers covered here, with 36 questions across 21 papers - about 2 per paper it appears in.