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Mathematics - Functions

Practise 129 NDA previous year questions on Functions, compiled from papers spanning 2010 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 NDA tests.

Functions has been asked in 16 of the 21 years of NDA papers analysed (2006–2026), with 129 questions in all. 33% of them were easy, 64% moderate and 2% tough. Most of its questions came from 2024, with 16 questions that year. In the last three years (2024–2026) it had 32 questions across 5 papers, about 6.4 per paper.

The chapter's 11 topics are not weighted equally: Composite Function (38 questions, 29%), Range (19 questions, 15%), and Domain (17 questions, 13%) have been asked the most. Composite Function has also led over the last five years, with 14 questions. Composite Function has produced the most tough questions (1).

  1. 1Consider the following statements in respect of the function in the interval : I. The function attains maximum value. II. The function attai2026 (Phase 1)Range
  2. 2If , then what is equal to ?2026 (Phase 1)Functional Equation
  3. 3Passage: Consider the curves and . Question: What is the number of points of intersection of the curves ?2026 (Phase 1)Number of Solutions
  4. 4Consider the following for the two (02) items that follow: Let the function , where and is an integer. What is the range of the function?2025 (Phase 1)Range
  5. 5Consider the following for the two (02) items that follow: Let the curve . What is the domain of the function ?2025 (Phase 1)Domain
  6. 6Consider the following for the two (02) items that follow: Let . If , then what is the value of ?2025 (Phase 1)Defintion of Function
  7. 7Consider the following for the two (02) items that follow: Let . Consider the following statements: I. is one-one function. II. is onto func2025 (Phase 1)Types of Function (Mapping)
  8. 8Consider the following for the two (02) items that follow: The function satisfies for all positive real values of and , and . What is equal 2025 (Phase 1)Functional Equation
  9. 9Consider the following for the two (02) items that follow: The function satisfies for all positive real values of and , and . What is equal 2025 (Phase 1)Functional Equation
  10. 10Consider the following for the two (02) items that follow: A function is such that for all real values of and , and . What is equal to?2025 (Phase 1)Functional Equation
  11. 11Consider the following for the two (02) items that follow: A function is such that for all real values of and , and . What is equal to?2025 (Phase 1)Functional Equation
  12. 12For the following two (02) items: Consider the function ( , ). What is equal to?2025 (Phase 2)Composite Function
  13. 13For the following two (02) items: Consider the function ( , ). What is equal to?2025 (Phase 2)Composite Function
  14. 14For the following two (02) items: Consider the function . What is the domain of the function?2025 (Phase 2)Domain
  15. 15For the following two (02) items: Consider the function . What is equal to?2025 (Phase 2)Composite Function
  16. 16For the following two (02) items: Consider the function . What is the inverse of the function?2025 (Phase 2)Inverse of a Function
  17. 17Let . Which of the following is/are bijective functions from A to itself? 1. 2. Select the correct answer using the code given below:2024 (Phase 1)Types of Function (Mapping)
  18. 18Let and . What is the number of onto functions from A to B ?2024 (Phase 1)Types of Function (Mapping)
  19. 19If and are such that , then which one of the following holds?2024 (Phase 1)Composite Function
  20. 20Which one of the following is correct in respect of and ?2024 (Phase 1)Domain
  21. 21Let and be two functions such that and o . What is equal to?2024 (Phase 1)Composite Function
  22. 22Let What is equal to?2024 (Phase 1)Functional Equation
  23. 23Let and , where [.] is the greatest integer function. If is not an integer but positive, then what is the value of ?2024 (Phase 2)Domain
  24. 24If and such that , then what is the value of2024 (Phase 2)Composite Function
  25. 25What is the minimum value of the function2024 (Phase 2)Range
  26. 26If , then for how many real values of will be the GM of and ?2024 (Phase 2)Composite Function
  27. 27If , where is the greatest integer function, then what is the sum of all integer solutions?2024 (Phase 2)Defintion of Function
  28. 28Let for all real . If , then what is the value of ?2024 (Phase 2)Functional Equation
  29. 29Paragraph: Let and . Question: Which one of the following is ?2024 (Phase 2)Composite Function
  30. 30Paragraph: Let and . Question: Which one of the following is ?2024 (Phase 2)Composite Function
  31. 31Paragraph: Let . Question: What is equal to?2024 (Phase 2)Defintion of Function
  32. 32Paragraph: Let and . Question: Consider the following statements : A. is an odd function. B. is an odd function. Which of the statements giv2024 (Phase 2)Odd and Even Functions
  33. 33A mapping defined as . If is to be onto, then what are and equal to?2023 (Phase 1)Types of Function (Mapping)
  34. 34Paragraph: Consider the function , where Question: At what value of does the function attain minimum value?2023 (Phase 1)Range
  35. 35Paragraph: Consider the function , where Question: What is the minimum value of the function?2023 (Phase 1)Range
  36. 36If and , then what is equal to?2023 (Phase 1)Composite Function
  37. 37What is the range of the function if the domain is the set of real numbers?2023 (Phase 1)Range
  38. 38Consider the following statements: 1. The relation defined by is a function 2. The relation defined by is a function. Which of the statement2023 (Phase 2)Defintion of Function
  39. 39A function satisfies , where . If , then what is equal to?2023 (Phase 2)Functional Equation
  40. 40Let and Which one of the following is a possible expression for g(x)?2023 (Phase 2)Composite Function
  41. 41Let and What is g(15) equal to?2023 (Phase 2)Composite Function
  42. 42Let a function f be defined on and What is equal to?2023 (Phase 2)Functional Equation
  43. 43A function is defined by What is the range of the function?2023 (Phase 2)Range
  44. 44Let . What is the domain of the function?2023 (Phase 2)Domain
  45. 45Consider the following statements in respect of the function where [.] is the greatest integer function: 1. Its derivative is 0 at 2. It is 2022 (Phase 1)Domain
  46. 46What is the domain of the function ?2022 (Phase 1)Domain
  47. 47If , then what is equal to?2022 (Phase 1)Functional Equation
  48. 48If , then what is equal to?2022 (Phase 1)Composite Function
  49. 49Consider the following in respect of the function : 1. Its domain is 2. It is a continuous function 3. It is differentiable at Which of the 2022 (Phase 1)Domain
  50. 50Paragraph: Let be a function satisfying for all such that : Question: What is equal to ?2022 (Phase 2)Functional Equation

Frequently Asked Questions

1.How many questions are available for Functions?

This chapter includes 129 questions compiled from NDA papers spanning 2010 to 2026.

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

These are NDA 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 NDA Mathematics?

Functions has appeared in 16 of the 17 years of NDA papers covered here, with 129 questions across 30 papers - about 4 per paper it appears in.

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

Of the 129 questions analysed for this chapter, 33% are easy, 64% moderate and 2% tough. 2024 had the most, with 16 questions.

5.Which topics in Functions should I focus on?

These topics have carried the most weightage in Functions:

  • Composite Function - 38 questions (29%)
  • Range - 19 questions (15%)
  • Domain - 17 questions (13%)
  • Composite Function has produced the most tough questions (1).
6.Is Functions's weightage in NDA going up or down?

Across all 30 papers analysed, Functions has averaged about 4.3 questions per paper. In the last three years (2024–2026), that average has risen, at about 6.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.