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Mathematics - Binomial Theorem

Practise 272 JEE Main previous year questions on Binomial Theorem, 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.

Binomial Theorem has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 272 questions in all. 22% of them were easy, 48% moderate and 31% tough. Most of its questions came from 2023, with 48 questions that year. In the last three years (2024–2026) it had 56 questions across 49 papers, about 1.1 per paper.

The chapter's 9 topics are not weighted equally: Terms of Binomial Expansion (143 questions, 53%), Sum of Series (53 questions, 19%), and Remainder and Divisibility Problems (28 questions, 10%) have been asked the most. Terms of Binomial Expansion has also led over the last five years, with 66 questions. Sum of Series has produced the most tough questions (30).

  1. 1If , then is equal to:08 Apr, 2026 (E)Sum of Series
  2. 2If the coefficients of the middle terms in the binomial expansions of and , , are equal, then the value of is:06 Apr, 2026 (M)Terms of Binomial Expansion
  3. 3If , then is equal to __________.06 Apr, 2026 (E)Terms of Binomial Expansion
  4. 4If the sum of the coefficients of and in the expansion of , , is zero, then the value of is __________.05 Apr, 2026 (M)Terms of Binomial Expansion
  5. 5The coefficient of in the expansion of , , is :05 Apr, 2026 (E)Terms of Binomial Expansion
  6. 6Let the smallest value of , for which the coefficient of in , , is for some , be . Then the value of is:04 Apr, 2026 (M)Terms of Binomial Expansion
  7. 7In the expansion of , , if the term independent of is , then is equal to:04 Apr, 2026 (E)Terms of Binomial Expansion
  8. 8The number of elements in the set , is :02 Apr, 2026 (M)Properties of Binomial Coefficients
  9. 9If for , , then equals:02 Apr, 2026 (E)Properties of Binomial Coefficients
  10. 10Given below are two statements : Statement I: is divisible by 7. Statement II: The integral part of is an odd number. In the light of the ab28 Jan, 2026 (E)Integral and Fractional Part of a Number
  11. 11The sum of the coefficients of and in is :28 Jan, 2026 (E)Terms of Binomial Expansion
  12. 12Let up to 13 terms. If , then is equal to24 Jan, 2026 (M)Sum of Series
  13. 13The value of is :23 Jan, 2026 (M)Sum of Series
  14. 14The sum of all possible values of , so that the coefficients of and in the expansion of , are in arithmetic progression is :23 Jan, 2026 (M)Terms of Binomial Expansion
  15. 15The coefficient of in is equal to22 Jan, 2026 (M)Sum of Series
  16. 16Let denote the coefficient of in the binomial expansion of . If , then the value of equals.22 Jan, 2026 (E)Sum of Series
  17. 17If the coefficient of in the expansion of is -56 and the coefficients of and are both zero, then is equal to :21 Jan, 2026 (M)Terms of Binomial Expansion
  18. 18If , then is equal to .21 Jan, 2026 (E)Properties of Binomial Coefficients
  19. 19The product of the last two digits of is08 Apr, 2025 (E)Remainder and Divisibility Problems
  20. 20The number of integral terms in the expansion of is08 Apr, 2025 (E)Integral and Fractional Part of a Number
  21. 21The remainder when is divided by 7 is equal to07 Apr, 2025 (M)Remainder and Divisibility Problems
  22. 22The sum of the series , is equal to07 Apr, 2025 (E)Sum of Series
  23. 23For an integer , if the arithmetic mean of all coefficients in the binomial expansion of is 16 , then the distance of the point from the lin04 Apr, 2025 (M)Terms of Binomial Expansion
  24. 24In the expansion of , if the ratio of term from the beginning to the term from the end is , then the value of is:04 Apr, 2025 (M)Terms of Binomial Expansion
  25. 25If \(1^2 ({ }^{15} C_1 )+2^2 ({ }^{15} C_2 )+3^2 ({ }^{15} C_3 )+ \) \(+15^2 ({ }^{15} C_{15} )=2^m 3^n 5^k\), where \(m, n, k {N}\), then \04 Apr, 2025 (E)Sum of Series
  26. 26The sum of all rational terms in the expansion of is03 Apr, 2025 (M)Terms of Binomial Expansion
  27. 27If then is equal to03 Apr, 2025 (M)Sum of Series
  28. 28Let . If , then k is equal to .03 Apr, 2025 (E)Multinomial Theorem
  29. 29The term independent of in the expansion of is:02 Apr, 2025 (M)Terms of Binomial Expansion
  30. 30If , then is equal to :02 Apr, 2025 (E)Properties of Binomial Coefficients
  31. 31The least value of n for which the number of integral terms in the Binomial expansion of \(( [3]{7}+ [12]{11})^{ {n}}\) is 183, is :29 Jan, 2025 (M)Terms of Binomial Expansion
  32. 32The remainder, when is divided by 23 , is equal to :29 Jan, 2025 (E)Remainder and Divisibility Problems
  33. 33If , then the distance of the point from the line is _________.28 Jan, 2025 (M)Sum of Series
  34. 34Let the coefficients of three consecutive terms and in the binomial expansion of be in a G.P. and let be the number of all possible values o28 Jan, 2025 (E)Terms of Binomial Expansion
  35. 35For some , let the coefficients of the 5 th, 6 th and 7 th terms in the binomial expansion of be in A.P. Then the largest coefficient in the24 Jan, 2025 (M)Terms of Binomial Expansion
  36. 36Suppose A and B are the coefficients of and terms respectively in the binomial expansion of . If , then n is equal to :24 Jan, 2025 (E)Terms of Binomial Expansion
  37. 37The sum of all rational terms in the expansion of is equal to23 Jan, 2025 (M)Terms of Binomial Expansion
  38. 38If in the expansion of , the coefficients of and are 1 and -2 , respectively, then is equal to :23 Jan, 2025 (E)Terms of Binomial Expansion
  39. 39If , then is equal to _______22 Jan, 2025 (M)Sum of Series
  40. 40Let and be the coefficients of and respectively in the expansion of . If u and v satisfy the equations then equals :22 Jan, 2025 (E)Terms of Binomial Expansion
  41. 41If , then is equal to ______22 Jan, 2025 (E)Sum of Series
  42. 42The coefficient of in is . Then a possible value of is :09 Apr, 2024 (M)Terms of Binomial Expansion
  43. 43The remainder when is divided by 21 is__________09 Apr, 2024 (M)Remainder and Divisibility Problems
  44. 44The sum of the coefficient of and in the binomial expansion of is09 Apr, 2024 (E)Terms of Binomial Expansion
  45. 45Let and . If , then the value of is _______08 Apr, 2024 (M)Sum of Series
  46. 46If the term independent of in the expansion of is 105 , then is equal to :08 Apr, 2024 (E)Terms of Binomial Expansion
  47. 47If the second, third and fourth terms in the expansion of are 135,30 and , respectively, then is equal to _______06 Apr, 2024 (M)Terms of Binomial Expansion
  48. 48If the constant term in the expansion of is , then is equal to05 Apr, 2024 (M)Terms of Binomial Expansion
  49. 49If the constant term in the expansion of , is , then is equal to :05 Apr, 2024 (E)Terms of Binomial Expansion
  50. 50The sum of all rational terms in the expansion of is equal to :04 Apr, 2024 (M)Integral and Fractional Part of a Number

Frequently Asked Questions

1.How many questions are available for Binomial Theorem?

This chapter includes 272 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 Binomial Theorem chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Binomial Theorem an important chapter for JEE Main Mathematics?

Binomial Theorem has appeared in 25 of the 25 years of JEE Main papers covered here, with 272 questions across 195 papers - about one per paper it appears in.

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

Of the 272 questions analysed for this chapter, 22% are easy, 48% moderate and 31% tough. 2023 had the most, with 48 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 - 143 questions (53%)
  • Sum of Series - 53 questions (19%)
  • Remainder and Divisibility Problems - 28 questions (10%)
  • Sum of Series has produced the most tough questions (30).
6.Is Binomial Theorem's weightage in JEE Main going up or down?

Across all 195 papers analysed, Binomial Theorem has averaged about 1.4 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.1 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.