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Mathematics - Functions

Practise 53 KCET previous year questions on Functions, compiled from papers spanning 2007 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KCET tests.

Functions has been asked in 18 of the 20 years of KCET papers analysed (2007–2026), with 53 questions in all. 72% of them were easy, 25% moderate and 4% tough. Most of its questions came from 2023, with 7 questions that year. In the last three years (2024–2026) it had 9 questions across 3 papers, about 3 per paper.

The chapter's 11 topics are not weighted equally: Domain (11 questions, 21%), Composite Function (11 questions, 21%), and Types of Function (Mapping) (10 questions, 19%) have been asked the most. Over the last five years the most frequent topics have been Composite Function (6), Domain (5), and Inverse of a Function (2). Domain has produced the most tough questions (1).

  1. 1The domain of the function is2026Domain
  2. 2for , is a function whose graph is the reflection of the graph of in the line , then is2026Inverse of a Function
  3. 3Domain of the function , given by is2025Domain
  4. 4If , where greatest integer , then which of the following is not true?2025Domain
  5. 5Let the functions " f " and " g " be given by and given by , where is the set of real numbers Consider the following statements: Statement (2025Types of Function (Mapping)
  6. 6If , where denotes the greatest integer function, then2024Periodicity
  7. 7Let be given . Then, is2024Inverse of a Function
  8. 8Let be defined by . Then, the pre images of 17 and -3 . respectively are2024Number of Solutions
  9. 9Let and Then,2024Composite Function
  10. 10If , where and are integers, and , then and are respectively2023Basics of Functions
  11. 11and defined by and . Which one of the following is not true?2023Composite Function
  12. 12Let be defined by and by , then is2023Composite Function
  13. 13Let the relation be defined in by , if , then is2023Range
  14. 14Let and then is invertible in the domain2023Composite Function
  15. 15If the function is , then the point of discontinuity of the composite function is2023Composite Function
  16. 16If and are two functions with and , then is equals to2023Composite Function
  17. 17The domain of the function is2022Domain
  18. 18If the set contains 7 elements and set contains 8 elements, then the number of bijections from to is2022Defintion of Function
  19. 19If be defined by then is2022Functional Equation
  20. 20Domain is, where [] denotes a greatest integer function2022Domain
  21. 21Domain of is2021Domain
  22. 22defined by is equal to2021Defintion of Function
  23. 23Let is not a positive integer Define as , then is2021Types of Function (Mapping)
  24. 24The function is one-one in the interval2021Types of Function (Mapping)
  25. 25Domain of the function where is greatest integer is2021Domain
  26. 26The standard deviation of the data , 10 is2020Range
  27. 27If a relation on the set be defined by , then is2020Domain
  28. 28The domain of the function defined by is2020Number of Solutions
  29. 29The domain of the function \( f: R R \) defined by \( f(x)= {x^{2}-7 x+12} \) is2019Domain
  30. 30\( f: R R \) and \( g:[0, ) R \) is defined by \( f(x)=x^{2} \) and \( g(x)= {x} \). Which one of the following is not true?2019Composite Function
  31. 31If \( A=\{x x N, x 5\}, B= \{x x Z, x^{2}-5 x+6=0 \} \), then the number of onto functions from \( A \) to \( B \) is2019Types of Function (Mapping)
  32. 32Let be two functions defined as and . Then for is2018Composite Function
  33. 33\( {A} \) is a set having \( 6 \) distinct elements. The number of distinct functions from \( {A} \) to \( {A} \) which are notbijections is2018Types of Function (Mapping)
  34. 34Let \( f: R R \) be defined by \( f(x)= \{ {array}{cc}2 x ; & x>3 \\ x^{2} ; & 1 Then \( f(-1)+f(2)+f(4) \) is2018Composite Function
  35. 35The derivative of \( ^{-1} (2 x^{2}-1 ) \) w.r.t \( ^{-1} x \) is2017Types of Function (Mapping)
  36. 36\( { 2 x- 2 }{ x- } d x \) is equal to2017Composite Function
  37. 37\( _{-5}^{5}|x+2| d x \) is equal to2017Range
  38. 38If \( {a}, {b}, {c} \) are unit vectors such that \( {a}+ {b}+ {c}= {0} \) then the value of \( {a} {b}+ {b} {c}+ {c} {a} \) is equal to2017Range
  39. 39The Set A has \( 4 \) elements and the Set B has \( 5 \) elements then the number of injective mappings that can be defined from A to B is2016Types of Function (Mapping)
  40. 40Let \( f: R R \) be defined by \( f(x)=2 x+6 \) which is a bijective mapping then \( f^{-1}(x) \) is given by2016Inverse of a Function
  41. 41The middle term of expansion of \( ( {10}{x}+ {x}{10} )^{10} \)2015Types of Function (Mapping)
  42. 42The shaded region shown in fig. is given by the inequation2015Domain
  43. 43If the function \( g(x) \) is defined by \[ g(x)= { ^{200}}{200}+ { ^{199}}{199}+ { ^{198}}{198}+ + { ^{2}}{2}+ +5, { then } g^{ }(0)= \]2015Composite Function
  44. 44Let \( S \) be the set of all real numbers. A relation \( R \) has been defined on \( S \) by \( a R b |a-b| 1 \), then \( R \) is2014Range
  45. 45The local minimum value of the function \(f^{ }\) given by \(f(x)=3+|x|\), \(x R\) is.2014Types of Function (Mapping)
  46. 46A stone is dropped into a quiet lake and waves move in circles at the speed of \( 5 {cms}^{-1} \). At that instant, when the radius of circu2014Inverse of a Function
  47. 47A gardener is digging a plot of land. As he gets tired, he works more slowly. After 't' minutes he is digging at a rate of \( {2}{ {t}} \) s2014Domain
  48. 48The range of the function , where denotes the greatest integer , is2013Range
  49. 49If is defined by , then2012Inverse of a Function
  50. 50If is an even function, then is2012Odd and Even Functions

Frequently Asked Questions

1.How many questions are available for Functions?

This chapter includes 53 questions compiled from KCET papers spanning 2007 to 2026.

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

These are KCET 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 KCET Mathematics?

Functions has appeared in 18 of the 20 years of KCET papers covered here, with 53 questions across 18 papers - about 3 per paper it appears in.

4.What is the difficulty level of Functions questions in KCET?

Of the 53 questions analysed for this chapter, 72% are easy, 25% moderate and 4% tough. 2023 had the most, with 7 questions.

5.Which topics in Functions should I focus on?

These topics have carried the most weightage in Functions:

  • Domain - 11 questions (21%)
  • Composite Function - 11 questions (21%)
  • Types of Function (Mapping) - 10 questions (19%)
  • Domain has produced the most tough questions (1).
6.Is Functions's weightage in KCET going up or down?

Across all 18 papers analysed, Functions has averaged about 2.9 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 3.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.