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Mathematics - Definite Integration

Practise 32 KVPY previous year questions on Definite Integration, 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 value of the integral - / 2 / 2 sin 2 x 1 + e x d x is2020 (SB/SX)
  2. 2Let f ( x ) = x sin x , x ( 0 , 1 ) 1 , x = 0 , Consider the integral I n = n 0 1 / n f ( x ) e - n x d x Then lim n I n2020 (SB/SX)
  3. 3The value of the integral 1 3 ( x - 2 ) 4 sin 3 ( x - 2 ) + ( x - 2 ) 2019 + 1 d x is2020 (SB/SX)
  4. 4Let be the set of natural numbers. For n , define I n = 0 x sin 2 n ( x ) sin 2 n ( x ) + cos 2 n ( x ) d x . Then for m , n2020 (SB/SX)
  5. 5The value of the integral 1 2 + 1 x 2 - 1 x 2 + 1 1 1 + x 4 d x is2020 (SB/SX)
  6. 6Suppose a continuous function f : 0 , R satisfies f x = 2 0 x t f t d t + 1 , x 0 . Then, f 1 equals2019 (SB/SX)
  7. 7Let f : 0 , 1 0 , 1 be a continuous function such that x 2 + f x 2 1 for all x 0 , 1 and 0 1 f x d x = 4 Then, 1 2 1 2 f x 1 - x 2 d x equal2019 (SB/SX)
  8. 8For x R , let f x = | sin x | and g x = 0 x f t d t . Let p x = g x - 2 x . Then2019 (SB/SX)
  9. 9Let J = 0 1 x 1 + x 8 d x Consider the following assertions: I . J 1 4 II . J 8 Then,2019 (SB/SX)
  10. 10The value of the integral 0 1 - | sin 8 x | d x is2018 (SB/SX)
  11. 11Let for all natural numbers . Then the sequence satisfies19 Nov, 2017 (SB/SX)
  12. 12Let , where is a non-negative integer. Then is19 Nov, 2017 (SB/SX)
  13. 13The number of continuous functions that satisfy05 Nov, 2017 (SB/SX)
  14. 14Let for Then the value of the integral is05 Nov, 2017 (SB/SX)
  15. 15Let be a continuous function defined on such that . Then the range of2016 (SB/SX)
  16. 16Define a function by Where is a fixed natural number, Then is2015 (SB/SX)
  17. 17Let be a fixed real number. Then the integral is equal to.2015 (SB/SX)
  18. 18Let be a continuous function such that . Which of the following statements is NOT necessarily true?2014 (SB/SX)
  19. 19A continuous function satisfies the equation . Which of the following options is true ?2014 (SB/SX)
  20. 20For a real number let denote the largest integer less than or equal to and . Let be positive integer. Then is equal to :2014 (SB/SX)
  21. 21Let , where is a non negative integer Then equal2014 (SB/SX)
  22. 22Let be a positive integer. For a real number , let denote the largest integer not exceeding and Then is equal to2013 (SB/SX)
  23. 23For let be a family of quadratic polynomials in with variable coefficients. Let . Which of the following statements are true? (I) for all . 2013 (SB/SX)
  24. 24The value of is2012 (SB/SX)
  25. 25Let and be the integer part and fractional part of a real number respectively. The value of the integral is2012 (SB/SX)
  26. 26The value of the integral , where , is -2012 (SB/SX)
  27. 27The value2012 (SB/SX)
  28. 28For each positive integer , define minimum , for . Let . Then is equal to-2011 (SB/SX)
  29. 29Let denote the largest integer not exceeding and . Then is equal to -2011 (SB/SX)
  30. 30Let be defined by the largest prime factor of . Then is equal to -2011 (SB/SX)
  31. 31The value of is-2010 (SB/SX)
  32. 32Let , where is a non-negative integer. Then is equal to-2010 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Definite Integration?

This chapter includes 32 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 Definite Integration chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Definite Integration an important chapter for KVPY Mathematics?

Definite Integration has appeared in 11 of the 11 years of KVPY papers covered here, with 32 questions across 12 papers - about 3 per paper it appears in.