Jump to a section

Mathematics - Binomial Theorem

Practise 85 NDA previous year questions on Binomial Theorem, 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.

Binomial Theorem has been asked in 16 of the 21 years of NDA papers analysed (2006–2026), with 85 questions in all. 15% of them were easy, 80% moderate and 5% tough. Most of its questions came from 2022, with 9 questions that year. In the last three years (2024–2026) it had 19 questions across 5 papers, about 3.8 per paper.

The chapter's 6 topics are not weighted equally: Terms of Binomial Expansion (48 questions, 56%), Properties of Binomial Coefficients (25 questions, 29%), and Integral and Fractional Part of a Number (7 questions, 8%) have been asked the most. Terms of Binomial Expansion has also led over the last five years, with 15 questions. Terms of Binomial Expansion has produced the most tough questions (2).

  1. 1A set contains elements. If the number of subsets of which contain at most elements is , then what is the value of ?2026 (Phase 1)Sum of Series
  2. 2What is the greatest value of satisfying the inequality ?2026 (Phase 1)Properties of Binomial Coefficients
  3. 3Passage: Let be a positive integer and be a real number lying between and . Further, and . Question: Consider the following statements : I. 2026 (Phase 1)Integral and Fractional Part of a Number
  4. 4Passage: Let be a positive integer and be a real number lying between and . Further, and . Question: What is the multiplicative inverse of ?2026 (Phase 1)Integral and Fractional Part of a Number
  5. 5Passage: Let be a positive integer and be a real number lying between and . Further, and . Question: What is the value of ?2026 (Phase 1)Integral and Fractional Part of a Number
  6. 6Passage: Let be a positive integer and be a real number lying between and . Further, and . Question: What is the value of ?2026 (Phase 1)Integral and Fractional Part of a Number
  7. 7Passage: Let be a positive integer and be a real number lying between and . Further, and . Question: What is the value of ?2026 (Phase 1)Integral and Fractional Part of a Number
  8. 8What is the number of rational terms in the expansion of ?2025 (Phase 1)Terms of Binomial Expansion
  9. 9If the sum of binomial coefficients in the expansion of is 256, then the greatest binomial coefficient occurs in which one of the following 2025 (Phase 1)Properties of Binomial Coefficients
  10. 10If , where is a natural number, then what is the value of ?2025 (Phase 1)Terms of Binomial Expansion
  11. 11What is the remainder when is divided by ?2025 (Phase 2)Remainder and Divisibility Problems
  12. 12Which one of the following is the greatest coefficient in the expansion of ?2025 (Phase 2)Terms of Binomial Expansion
  13. 13What is the coefficient of in the expansion of ?2024 (Phase 1)Terms of Binomial Expansion
  14. 14If the 4th term in the expansion of is , then that is the value of ?2024 (Phase 1)Terms of Binomial Expansion
  15. 15In a binomial expansion of , the sum of middle terms is zero. What is the value of ?2024 (Phase 1)Terms of Binomial Expansion
  16. 16In the expansion of , if the coefficient of is 35 , then what is the value of ?2024 (Phase 2)Terms of Binomial Expansion
  17. 17What is the remainder when is divided by 36 for ?2024 (Phase 2)Remainder and Divisibility Problems
  18. 18Paragraph: Let and , where U is an integer and {V}+ {W}$ equal to?2024 (Phase 2)Integral and Fractional Part of a Number
  19. 19Paragraph: Let and , where U is an integer and ( {U}+ {V}) {W}$ ?2024 (Phase 2)Integral and Fractional Part of a Number
  20. 20If the sixth term in the binomial expansion of is 5600 , then what is the value of ?2023 (Phase 1)Terms of Binomial Expansion
  21. 21How many terms are there in the expansion of ?2023 (Phase 1)Terms of Binomial Expansion
  22. 22Consider the following statements for a fixed natural number : 1. is greatest if 2. is greatest if and Which of the statements given above i2023 (Phase 1)Properties of Binomial Coefficients
  23. 23A set S contains (2n +1) elements. There are 4096 subset of S which contain at most n elements. what is n equal to2023 (Phase 2)Properties of Binomial Coefficients
  24. 24Let What is equal to?2023 (Phase 2)Sum of Series
  25. 25Let What is equal to?2023 (Phase 2)Properties of Binomial Coefficients
  26. 26Let What is equal to ?2023 (Phase 2)Properties of Binomial Coefficients
  27. 27How many terms are there in the expansion of ?2022 (Phase 1)Terms of Binomial Expansion
  28. 28Consider the following statements in respect of the expansion of : 1. Among all the coefficients of the terms, the coefficient of the 6th te2022 (Phase 1)Terms of Binomial Expansion
  29. 29What is the value of ?2022 (Phase 1)Properties of Binomial Coefficients
  30. 30In the expansion of , what is the th term from the end (when arranged in descending powers of )?2022 (Phase 1)Terms of Binomial Expansion
  31. 31What is equal to?2022 (Phase 2)Properties of Binomial Coefficients
  32. 32Paragraph: Consider the binomial expansion of : Question: What is the value of if the coefficients of and are equal ?2022 (Phase 2)Terms of Binomial Expansion
  33. 33Paragraph: Consider the binomial expansion of : Question: What is the ratio of the coefficients of middle terms in the expansion (when expan2022 (Phase 2)Terms of Binomial Expansion
  34. 34Paragraph: Consider the binomial expansion of : Question: Under what condition the coefficients of and are equal?2022 (Phase 2)Terms of Binomial Expansion
  35. 35If , then what is the probability that is a multiple of 7?2022 (Phase 2)Properties of Binomial Coefficients
  36. 36If are the coefficients in the expansion of , then what is the value of ?2021 (Phase 1)Properties of Binomial Coefficients
  37. 37What is the coefficient of the middle term in the expansion of ?2021 (Phase 1)Terms of Binomial Expansion
  38. 38What is equal to?2021 (Phase 1)Properties of Binomial Coefficients
  39. 39What is the sum of the coefficients of first and last terms in the expansion of , where is a natural number?2021 (Phase 1)Terms of Binomial Expansion
  40. 40How many terms are there in the expansion of where ?2021 (Phase 2)Terms of Binomial Expansion
  41. 41Consider the expansion of . Let and be the coefficients of first, second, and terms respectively. What is ( ) equal to?2021 (Phase 2)Terms of Binomial Expansion
  42. 42What is the sum of the last five coefficients in the expansion of when it is expanded in ascending powers of ?2020Properties of Binomial Coefficients
  43. 43The term independent of in the binomial expansion of is equal to2020Terms of Binomial Expansion
  44. 44If , then what is equal to?2020Terms of Binomial Expansion
  45. 45What is the number of terms in the expansion of2019 (Phase 1)Terms of Binomial Expansion
  46. 46In the expansion of , the first three terms are respectively and . What is n equal to?2019 (Phase 1)Terms of Binomial Expansion
  47. 47How many terms are there in the expansion of ?2019 (Phase 2)Terms of Binomial Expansion
  48. 48If the middle term in the expansion of , then what is the value of ?2019 (Phase 2)Terms of Binomial Expansion
  49. 49If the constant term in the expansion of is 405 , then what can be the values of ?2019 (Phase 2)Terms of Binomial Expansion
  50. 50In the expansion of , if the coefficients of and terms are equal, then what is the value of ?2018 (Phase 1)Terms of Binomial Expansion

Frequently Asked Questions

1.How many questions are available for Binomial Theorem?

This chapter includes 85 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 Binomial Theorem chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Binomial Theorem an important chapter for NDA Mathematics?

Binomial Theorem has appeared in 16 of the 17 years of NDA papers covered here, with 85 questions across 29 papers - about 3 per paper it appears in.

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

Of the 85 questions analysed for this chapter, 15% are easy, 80% moderate and 5% tough. 2022 had the most, with 9 questions.

5.Which topics in Binomial Theorem should I focus on?

These topics have carried the most weightage in Binomial Theorem:

  • Terms of Binomial Expansion - 48 questions (56%)
  • Properties of Binomial Coefficients - 25 questions (29%)
  • Integral and Fractional Part of a Number - 7 questions (8%)
  • Terms of Binomial Expansion has produced the most tough questions (2).
6.Is Binomial Theorem's weightage in NDA going up or down?

Across all 29 papers analysed, Binomial Theorem has averaged about 2.9 questions per paper. In the last three years (2024–2026), that average has risen, at about 3.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.