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Mathematics - Functions

Practise 227 JEE Main previous year questions on Functions, compiled from papers spanning 2002 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 JEE Main tests.

Functions has been asked in 22 of the 25 years of JEE Main papers analysed (2002–2026), with 227 questions in all. 22% of them were easy, 52% moderate and 26% tough. Most of its questions came from 2023, with 34 questions that year. In the last three years (2024–2026) it had 66 questions across 49 papers, about 1.3 per paper.

The chapter's 10 topics are not weighted equally: Types of Function (Mapping) (57 questions, 25%), Domain (44 questions, 19%), and Functional Equation (42 questions, 19%) have been asked the most. Types of Function (Mapping) has also led over the last five years, with 33 questions. Types of Function (Mapping) has produced the most tough questions (22).

  1. 1Let be a function defined as . Let , , where . If , , then the area of the region bounded by the curves , , and is:08 Apr, 2026 (E)Composite Function
  2. 2Let be a polynomial function such that , and . Then is equal to ________.08 Apr, 2026 (E)Functional Equation
  3. 3Let be the base of natural logarithm and let and be two bijective functions such that is strictly decreasing and is strictly increasing. If 06 Apr, 2026 (M)Inverse of a Function
  4. 4Let be defined as . Then is :06 Apr, 2026 (E)Types of Function (Mapping)
  5. 5The sum of all the integral values of such that the equation , , has at least one solution, is:05 Apr, 2026 (M)Range
  6. 6Let . The number of one-one functions such that , and , is __________.05 Apr, 2026 (M)Types of Function (Mapping)
  7. 7Let be a function such that , . Let the maximum value of on be . If the area of the region bounded by the curves and , , is , then is equal 05 Apr, 2026 (E)Functional Equation
  8. 8Let denote the greatest integer function. If the domain of the function is , then is equal to:04 Apr, 2026 (M)Domain
  9. 9The number of functions , which are not onto, is:04 Apr, 2026 (M)Types of Function (Mapping)
  10. 10For the function defined by , among the two statements: (I) The set contains exactly two elements, and (II) The set is an empty set,04 Apr, 2026 (E)Inverse of a Function
  11. 11Let for some , be a function satisfying for all . If and , then the value of is:04 Apr, 2026 (E)Functional Equation
  12. 12If the domain of the function is , then the value of is _______.02 Apr, 2026 (M)Domain
  13. 13If and , then is equal to:28 Jan, 2026 (M)Composite Function
  14. 14Given below are two statements: Statement I: The function defined by is one-one. Statement II: The function defined by is many-one. In the l28 Jan, 2026 (E)Types of Function (Mapping)
  15. 15The sum of all the elements in the range of , , where , is :28 Jan, 2026 (E)Range
  16. 16If the domain of the function is , then equals:24 Jan, 2026 (M)Domain
  17. 17Let be a function such that , where . Then is equal to24 Jan, 2026 (E)Functional Equation
  18. 18Consider two sets and . Then the number of onto functions is equal to23 Jan, 2026 (E)Types of Function (Mapping)
  19. 19If the domain of the function is , then is equal to22 Jan, 2026 (M)Domain
  20. 20The number of distinct real solutions of the equation is22 Jan, 2026 (M)Number of Solutions
  21. 21Let the domain of the function be . Then is equal to :22 Jan, 2026 (E)Domain
  22. 22Let and be functions satisfying and , for all . If , then n is equal to:22 Jan, 2026 (E)Functional Equation
  23. 23Let the domain of the function be and the domain of be . Then is equal to ________08 Apr, 2025 (E)Domain
  24. 24If the range of the function , , is , then is equal to :07 Apr, 2025 (E)Range
  25. 25Let be defined as and . If the range of the function is , then is equal to04 Apr, 2025 (M)Range
  26. 26Consider the sets , , and . The total number of one-one functions from the set D to the set C is:04 Apr, 2025 (M)Types of Function (Mapping)
  27. 27Let be a continuous function satisfying and for all . If , then is equal to04 Apr, 2025 (M)Functional Equation
  28. 28Let and . If , and , then the value of is:04 Apr, 2025 (E)Functional Equation
  29. 29Let the domains of the functions and be and , respectively. Then is equal to :-04 Apr, 2025 (E)Domain
  30. 30If the domain of the function then is equal to03 Apr, 2025 (M)Domain
  31. 31Let be a function such that . Then is equal to03 Apr, 2025 (E)Functional Equation
  32. 32If the domain of the function is , then is equal to03 Apr, 2025 (E)Domain
  33. 33If the domain of the function is , then is equal to :02 Apr, 2025 (E)Domain
  34. 34If the domain of the function is and the domain of the function is , then is equal to :29 Jan, 2025 (E)Domain
  35. 35Let be a function defined by , then the value of is28 Jan, 2025 (M)Defintion of Function
  36. 36If , then is equal to28 Jan, 2025 (M)Defintion of Function
  37. 37Let denote the greatest integer less than or equal to . Then the domain of is :28 Jan, 2025 (E)Domain
  38. 38Let A be defined by and be defined by . If both the functions are onto and or , then is equal to :28 Jan, 2025 (E)Types of Function (Mapping)
  39. 39Let be a polynomial of degree 2, satisfying . If , then the sum of squares of all possible values of is :28 Jan, 2025 (E)Functional Equation
  40. 40Let be a function such that . If the , then is equal to24 Jan, 2025 (M)Defintion of Function
  41. 41Let . Then the value of is equal to24 Jan, 2025 (M)Functional Equation
  42. 42Preview not available - open to view this question.24 Jan, 2025 (E)Number of Solutions
  43. 43Preview not available - open to view this question.24 Jan, 2025 (E)Types of Function (Mapping)
  44. 44Number of functions , that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ________.24 Jan, 2025 (E)Defintion of Function
  45. 45Let and . Then the domain of is23 Jan, 2025 (M)Composite Function
  46. 46Let the range of the function be . Then the distance of the point from the line is :23 Jan, 2025 (E)Range
  47. 47Let and . Then the number of many-one functions such that is equal to :22 Jan, 2025 (E)Types of Function (Mapping)
  48. 48If the domain of the function is , then is equal to :09 Apr, 2024 (M)Domain
  49. 49If a function satisfies for all and , then the largest natural number such that is equal to _________09 Apr, 2024 (M)Functional Equation
  50. 50Let the range of the function be . If and are respectively the A.M. and the G.M. of and , then is equal to09 Apr, 2024 (E)Range

Frequently Asked Questions

1.How many questions are available for Functions?

This chapter includes 227 questions compiled from JEE Main papers spanning 2002 to 2026.

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

These are JEE Main questions specifically for the Functions chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Functions an important chapter for JEE Main Mathematics?

Functions has appeared in 22 of the 25 years of JEE Main papers covered here, with 227 questions across 152 papers - about one per paper it appears in.

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

Of the 227 questions analysed for this chapter, 22% are easy, 52% moderate and 26% tough. 2023 had the most, with 34 questions.

5.Which topics in Functions should I focus on?

These topics have carried the most weightage in Functions:

  • Types of Function (Mapping) - 57 questions (25%)
  • Domain - 44 questions (19%)
  • Functional Equation - 42 questions (19%)
  • Types of Function (Mapping) has produced the most tough questions (22).
6.Is Functions's weightage in JEE Main going up or down?

Across all 152 papers analysed, Functions has averaged about 1.5 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.