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Mathematics - Functions

Practise 29 KVPY previous year questions on Functions, 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 x be the greatest integer less than or equal to x , for a real number x . Then the equation x 2 = x + 1 has2020 (SA)
  2. 2Let x be the greatest integer less than or equal to x , for a real number x . Then the following sum 2 2020 + 1 2 2018 + 1 + 3 2020 + 1 3 202020 (SA)
  3. 3Let R be the set of all real numbers and f : R R be a continuous function. Suppose | f ( x ) - f ( y ) | | x - y | for all real numbers x an2020 (SB/SX)
  4. 4Let A denote the set of all real numbers x such that x 3 - [ x ] 3 = ( x - [ x ] ) 3 , where [ x ] is the greatest integer less than or equa2020 (SB/SX)
  5. 5Let f x = x sin 1 x when x 0 1 when x = 0 and A = x R : f x = 1 Then, A has2019 (SB/SX)
  6. 6Let f : R R be a continuous function such that f x 2 = f x 3 for all x R . Consider the following statements. I. f is an odd function. II. f2019 (SB/SX)
  7. 7What is the probability that a human individual would receive the entire haploid set of chromosomes from his/her grandfather?2018 (SB/SX)
  8. 8Let f : 0 , 1 - 1 , 1 and g : - 1 , 1 0 , 2 be two functions such that g is injective and g o f : 0 , 1 0 , 2 is surjective. Then,2018 (SB/SX)
  9. 9Number of functions f : 0 , 1 0 , 1 satisfying f x - f y = x - y for all x , y in 0 , 1 is2018 (SB/SX)
  10. 10Let f : 0 , 1 R be an injective continuous function that satisifes the condition - 1 f 0 f 1 1 Then, the number of functions g : - 1 , 1 0 ,2018 (SB/SX)
  11. 11Let and be a constant such that for all , y real and . Then the least possible value of is19 Nov, 2017 (SB/SX)
  12. 12Define a function for all real . The least positive value of is19 Nov, 2017 (SB/SX)
  13. 13The fractional part of a real number is , where is the greatest integer less than or equal to . Let and be the fractional parts of and respe05 Nov, 2017 (SB/SX)
  14. 14Let be the set of real numbers and be defined by , where is the greatest integer less than or equal to , and Which of the following statemen05 Nov, 2017 (SB/SX)
  15. 15Let be the set of real numbers and be given by . We now make the following assertions: I. There exists a real number such that for all II. T05 Nov, 2017 (SB/SX)
  16. 16Let be a function defined on the set of all positive integers such that for all positive integers . If and , the value of is2016 (SA)
  17. 17The graph of the function is shown below. Define , for Which of the following statements are true? I. There are infinitely many for which II2016 (SB/SX)
  18. 18If be a polynomial with real coefficients such that , for all . Consider the following statements : I. is an even function. II. can be expre2016 (SB/SX)
  19. 19The number of continuous function such that for all and is :2016 (SB/SX)
  20. 20For a real number , let denote the largest integer less than or equal to , and let The number of solutions to be equation with is2015 (SA)
  21. 21Let be the set of all real numbers and let be a fucntion to such that , for all Then is equal to.2014 (SA)
  22. 22Let and . Which of the following statements are true? (I) Domain of Domain of (II) Domain of Domain of (III) Domain of Domain of (V) Domain 2013 (SB/SX)
  23. 23Let be the function with Then if and only if -2012 (SB/SX)
  24. 24Let for all . Let and generally for Let Which of the following is a multiple of P -2012 (SB/SX)
  25. 25The mid- point of the domain of the function for real is2012 (SB/SX)
  26. 26Which of the following intervals is a possible domain of the function , where is the greatest integer not exceeding and ?2011 (SB/SX)
  27. 27Let , and Then2011 (SB/SX)
  28. 28The minimum distance between a point on the curve and a point on the curve is -2011 (SB/SX)
  29. 29Suppose . The smallest possible integer value of for all is -2011 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Functions?

This chapter includes 29 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 Functions chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Functions an important chapter for KVPY Mathematics?

Functions has appeared in 10 of the 11 years of KVPY papers covered here, with 29 questions across 13 papers - about 2 per paper it appears in.