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Mathematics - Binomial Theorem

Practise 45 WBJEE previous year questions on Binomial Theorem, compiled from papers spanning 2009 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 WBJEE tests.

Binomial Theorem has been asked in 17 of the 18 years of WBJEE papers analysed (2009–2026), with 45 questions in all. 13% of them were easy, 58% moderate and 29% tough. Most of its questions came from 2011, with 5 questions that year. In the last three years (2024–2026) it had 7 questions across 3 papers, about 2.3 per paper.

The chapter's 9 topics are not weighted equally: Terms of Binomial Expansion (11 questions, 24%), Properties of Binomial Coefficients (11 questions, 24%), and Sum of Series (10 questions, 22%) have been asked the most. Over the last five years the most frequent topics have been Sum of Series (2), Terms of Binomial Expansion (2), and Properties of Binomial Coefficients (2). Sum of Series has produced the most tough questions (5).

  1. 1The term independent of in the expansion of is equal to2026Terms of Binomial Expansion
  2. 2If and , then the value of is2026Properties of Binomial Coefficients
  3. 3If , then the value of is2025Properties of Binomial Coefficients
  4. 4Let denote the term independent of in the expansion of , then equals2025Terms of Binomial Expansion
  5. 5The coefficient of in the expansion of is2024Multinomial Theorem
  6. 6If then is equal to2024Sum of Series
  7. 7If n is a positive integer, the value of is2024Sum of Series
  8. 8Let for all . Then2022Comparison between two numbers
  9. 9For , if , then is equal to2021Terms of Binomial Expansion
  10. 10The co-efficient of in the expansion of is2021Multinomial Theorem
  11. 11The remainder when times 7 is divided by 48 is2021Remainder and Divisibility Problems
  12. 12If are the Binomial co-efficients in the expansion of , then the value of is2020Properties of Binomial Coefficients
  13. 13The number of irrational terms in the expansion of is2019Properties of Binomial Coefficients
  14. 14equal to2018Properties of Binomial Coefficients
  15. 15The number is divisible by2018Remainder and Divisibility Problems
  16. 16If is even posirive integer, then the condition that the greatest term in the expansion of may also have the greatest coefficient, is2018Terms of Binomial Expansion
  17. 17Let Then2017Binomial Theorem for Rational Index
  18. 18If then the value of is2016Properties of Binomial Coefficients
  19. 19In the expansion of the coefficient of is2016Series involving Product of Coefficients
  20. 20If and then the value of is2016Properties of Binomial Coefficients
  21. 21The number of irrational terms in the binomial expansion of is2015Properties of Binomial Coefficients
  22. 22If the coefficient of in is equal to the coefficient of in then and will satisfy the relation2014Terms of Binomial Expansion
  23. 23The value of the sum is2014Series involving Product of Coefficients
  24. 24Let Then, equals2014Sum of Series
  25. 25The coefficient of in the infinite series expansion of for is2014Terms of Binomial Expansion
  26. 26Let be a positive even integer. If the ratio of the largest coefficient and the 2nd largest coefficient in the expansion of is Then, the num2013Terms of Binomial Expansion
  27. 27is equal to2012Sum of Series
  28. 28The value of2012Sum of Series
  29. 29Let and If and then is equal to2012Sum of Series
  30. 30The coefficient of in the expansion of2012Properties of Binomial Coefficients
  31. 31The number \((101)^{100}-1\) is divisible by2011Remainder and Divisibility Problems
  32. 32If \(A\) and \(B\) are coefficients of \(x^{ {n}}\) in the expansions of \((1+x)^{2 {n}}\) and \((1+x)^{2 {n}-1}\) respectively, then \( {A}2011Terms of Binomial Expansion
  33. 33If \( {n} > 1\) is an integer and \( {x} 0\), then \((1+ {x})^{ {n}}- {nx}-1\) is divisible by2011Remainder and Divisibility Problems
  34. 34If \({ }^n C_4,{ }^n C_5\) and \({ }^n C_6\) are in A.P., then \(n\) is2011Properties of Binomial Coefficients
  35. 35\({ }^{15} {C}_3+{ }^{15} {C}_5+ +{ }^{15} {C}_{15}=\)2011Sum of Series
  36. 36If , then is just greater than integer2010Properties of Binomial Coefficients
  37. 37If in the expansion of , the sum of the 5 th and 6 th term is zero, then the value of is2010Terms of Binomial Expansion
  38. 38will be divisible by2010Remainder and Divisibility Problems
  39. 39Sum of the last 30 coeffivients in the expansion of , when expanded in ascending powers of is2010Sum of Series
  40. 40If , then the value of is2010Sum of Series
  41. 41If denote the co-efficients in the expansion of then the value of is2009Sum of Series
  42. 42For each is divisible by where is a set of natural numbers2009Remainder and Divisibility Problems
  43. 43If the co-efficients of and in the expansion of be same, then the value of ' ' is2009Terms of Binomial Expansion
  44. 44Using binomial theorem, the value of correct to 3 decimal places is2009Terms of Binomial Expansion
  45. 45The coefficient of , where is any positive integer, in the expansion of is2009Binomial Theorem for Negative Index

Frequently Asked Questions

1.How many questions are available for Binomial Theorem?

This chapter includes 45 questions compiled from WBJEE papers spanning 2009 to 2026.

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

These are WBJEE 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 WBJEE Mathematics?

Binomial Theorem has appeared in 17 of the 18 years of WBJEE papers covered here, with 45 questions across 17 papers - about 3 per paper it appears in.

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

Of the 45 questions analysed for this chapter, 13% are easy, 58% moderate and 29% tough. 2011 had the most, with 5 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 - 11 questions (24%)
  • Properties of Binomial Coefficients - 11 questions (24%)
  • Sum of Series - 10 questions (22%)
  • Sum of Series has produced the most tough questions (5).
6.Is Binomial Theorem's weightage in WBJEE going up or down?

Across all 17 papers analysed, Binomial Theorem has averaged about 2.6 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 2.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.