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Mathematics - Definite Integration

Practise 110 NDA previous year questions on Definite Integration, 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.

Definite Integration has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 110 questions in all. 10% of them were easy, 87% moderate and 3% tough. Most of its questions came from 2024, with 13 questions that year. In the last three years (2024–2026) it had 20 questions across 5 papers, about 4 per paper.

The chapter's 5 topics are not weighted equally: Properties of Definite Integration (85 questions, 77%), Definite Integration by Substitution (15 questions, 14%), and Definite Integration by Parts (7 questions, 6%) have been asked the most. Properties of Definite Integration has also led over the last five years, with 26 questions. Properties of Definite Integration has produced the most tough questions (3).

  1. 1Passage: Let . Question: What is the value of ?2026 (Phase 1)Properties of Definite Integration
  2. 2Passage: Let . Question: What is equal to ?2026 (Phase 1)Properties of Definite Integration
  3. 3Passage: Let and . Question: What is equal to ?2026 (Phase 1)Properties of Definite Integration
  4. 4Passage: Let and . Question: What is equal to ?2026 (Phase 1)Properties of Definite Integration
  5. 5Consider the following for the two (02) items that follow: Let , where is the greatest integer function. What is equal to?2025 (Phase 1)Properties of Definite Integration
  6. 6What is , where is the greatest integer function and is a natural number?2025 (Phase 2)Properties of Definite Integration
  7. 7If and , then which one of the following is correct?2025 (Phase 2)Definite Integration by Substitution
  8. 8What is equal to?2024 (Phase 1)Properties of Definite Integration
  9. 9Let and . If , then which one of the following is correct?2024 (Phase 1)Properties of Definite Integration
  10. 10What is equal to?2024 (Phase 1)Properties of Definite Integration
  11. 11Let What is equal to?2024 (Phase 1)Properties of Definite Integration
  12. 12Let What is equal to?2024 (Phase 1)Leibnitz Rule of Differentiation
  13. 13Let and where [.] is greatest integer function. What is equal to?2024 (Phase 1)Properties of Definite Integration
  14. 14Let and where [.] is greatest integer function. What is equal to?2024 (Phase 1)Properties of Definite Integration
  15. 15Let What is equal to?2024 (Phase 1)Definite Integration by Substitution
  16. 16Paragraph: Let Question: What is equal to?2024 (Phase 2)Definite Integration by Substitution
  17. 17Paragraph: Let Question: What is equal to?2024 (Phase 2)Properties of Definite Integration
  18. 18Paragraph: Let and . Question: What is equal to?2024 (Phase 2)Properties of Definite Integration
  19. 19Paragraph: Let , where and . Question: What is equal to?2024 (Phase 2)Properties of Definite Integration
  20. 20Paragraph: Let , where and . Question: What is I equal to?2024 (Phase 2)Properties of Definite Integration
  21. 21Paragraph: Let and Question: What is the value of ?2023 (Phase 1)Properties of Definite Integration
  22. 22Paragraph: Let and Question: What is the value of ?2023 (Phase 1)Properties of Definite Integration
  23. 23Paragraph: Let and Question: What is the value of ?2023 (Phase 1)Properties of Definite Integration
  24. 24Paragraph: Let Question: What is equal to when ?2023 (Phase 1)Properties of Definite Integration
  25. 25Paragraph: Let Question: What is equal to when ?2023 (Phase 1)Properties of Definite Integration
  26. 26Let What is equal to?2023 (Phase 2)Properties of Definite Integration
  27. 27Let What is I equal to?2023 (Phase 2)Properties of Definite Integration
  28. 28What is equal to?2023 (Phase 2)Properties of Periodic Functions
  29. 29What is equal to?2022 (Phase 1)Definite Integration by Substitution
  30. 30What is equal to?2022 (Phase 1)Properties of Definite Integration
  31. 31What is equal to?2022 (Phase 2)Properties of Definite Integration
  32. 32If , then what is the value of2022 (Phase 2)Properties of Periodic Functions
  33. 33What is equal to?2022 (Phase 2)Properties of Definite Integration
  34. 34What is equal to?2021 (Phase 1)Properties of Definite Integration
  35. 35If then what is equal to?2021 (Phase 1)Properties of Definite Integration
  36. 36If , then what is equal to?2021 (Phase 2)Definite Integration by Substitution
  37. 37If , then is2021 (Phase 2)Properties of Definite Integration
  38. 38If satisfies , then what is equal to?2021 (Phase 2)Properties of Definite Integration
  39. 39What is equal to?2021 (Phase 2)Properties of Definite Integration
  40. 40What is equal to?2021 (Phase 2)Properties of Definite Integration
  41. 41What is the value of ?2020Definite Integration by Substitution
  42. 42is equal to2019 (Phase 1)Properties of Definite Integration
  43. 43is equal to2019 (Phase 1)Definite Integration by Substitution
  44. 44Paragraph: Consider the integrals Question: What is the value of ?2019 (Phase 2)Properties of Definite Integration
  45. 45Paragraph: Consider the integrals Question: What is the value of ?2019 (Phase 2)Properties of Definite Integration
  46. 46What is equal to?2018 (Phase 1)Definite Integration by Parts
  47. 47What is equal to?2018 (Phase 1)Definite Integration by Parts
  48. 48What is equal to (where [.] is the greatest integer function)?2018 (Phase 1)Properties of Definite Integration
  49. 49What is the value of ?2018 (Phase 1)Properties of Definite Integration
  50. 50If and , then what are the values of a and b respectively?2018 (Phase 1)Properties of Definite Integration

Frequently Asked Questions

1.How many questions are available for Definite Integration?

This chapter includes 110 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 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 NDA Mathematics?

Definite Integration has appeared in 17 of the 17 years of NDA papers covered here, with 110 questions across 32 papers - about 3 per paper it appears in.

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

Of the 110 questions analysed for this chapter, 10% are easy, 87% moderate and 3% tough. 2024 had the most, with 13 questions.

5.Which topics in Definite Integration should I focus on?

These topics have carried the most weightage in Definite Integration:

  • Properties of Definite Integration - 85 questions (77%)
  • Definite Integration by Substitution - 15 questions (14%)
  • Definite Integration by Parts - 7 questions (6%)
  • Properties of Definite Integration has produced the most tough questions (3).
6.Is Definite Integration's weightage in NDA going up or down?

Across all 32 papers analysed, Definite Integration has averaged about 3.4 questions per paper. In the last three years (2024–2026), that average has risen, at about 4.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.