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Mathematics - Binomial Theorem

Practise 10 JEE Advanced previous year questions on Binomial Theorem, compiled from papers spanning 2010 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Advanced tests.

Binomial Theorem has been asked in 10 of the 27 years of JEE Advanced papers analysed (2000–2026), with 10 questions in all. 40% of them were easy, 30% moderate and 30% tough. Most of its questions came from 2025, with 1 question that year. In the last three years (2024–2026) it had 1 question across 6 papers, about 0.2 per paper.

The chapter's 3 topics are not weighted equally: Terms of Binomial Expansion (6 questions, 60%), Sum of Series (2 questions, 20%), and Series involving Product of Coefficients (2 questions, 20%) have been asked the most. Terms of Binomial Expansion has also led over the last five years, with 2 questions. Terms of Binomial Expansion has produced the most tough questions (1).

  1. 1Let be real numbers such that for every real number . let be the largest among the numbers for . The the value of is ______2025 (Paper 2)Terms of Binomial Expansion
  2. 2Let a and b be two nonzero real numbers. If the coefficient of x 5 in the expansion of a x 2 + 70 27 b x 4 is equal to the coefficient of x 2023 (Paper 1)Terms of Binomial Expansion
  3. 3For nonnegative integers s and r , let s r = s ! r ! s - r ! if r s 0 if r s . For positive integers m and n , let g m , n = p = 0 m + n f m2020 (Paper 2)Series involving Product of Coefficients
  4. 4Suppose det k = 0 n k k = 0 n C k n k 2 k = 0 n C k n k k = 0 n C k n 3 k = 0 , holds for some positive integer n . Then k = 0 n C k n k + 12019 (Paper 2)Sum of Series
  5. 5Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + + 10 10 C 10 2 , where 10 C r , r 1,2 , . , 10 denote binomial coefficients. Then, the value of2018 (Paper 2)Series involving Product of Coefficients
  6. 6Let m be the smallest positive integer such that the coefficient of x 2 in the expansion of 1 + x 2 + 1 + x 3 + + 1 + x 49 + 1 + m x 50 is 32016 (Paper 1)Sum of Series
  7. 7The coefficient of x 9 in the expansion of 1 + x 1 + x 2 1 + x 3 1 + x 100 is2015 (Paper 2)Terms of Binomial Expansion
  8. 8Coefficient of x 11 in the expansion of 1 + x 2 4 1 + x 3 7 1 + x 4 12 is2014 (Paper 2)Terms of Binomial Expansion
  9. 9The coefficients of three consecutive terms of 1 + x n + 5 are in the ratio 5 : 10 : 14 . Then n =2013 (Paper 1)Terms of Binomial Expansion
  10. 10For , let and denote, respectively, the coefficient of in the expansions of , and . Then is equal to2010 (Paper 2)Terms of Binomial Expansion

Frequently Asked Questions

1.How many questions are available for Binomial Theorem?

This chapter includes 10 questions compiled from JEE Advanced papers spanning 2010 to 2025.

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

These are JEE Advanced 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 JEE Advanced Mathematics?

Binomial Theorem has appeared in 10 of the 21 years of JEE Advanced papers covered here, with 10 questions across 10 papers - about one per paper it appears in.

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

Of the 10 questions analysed for this chapter, 40% are easy, 30% moderate and 30% tough. 2025 had the most, with 1 question.

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

These topics have carried the most weightage in Binomial Theorem:

  • Terms of Binomial Expansion - 6 questions (60%)
  • Sum of Series - 2 questions (20%)
  • Series involving Product of Coefficients - 2 questions (20%)
  • Terms of Binomial Expansion has produced the most tough questions (1).
6.Is Binomial Theorem's weightage in JEE Advanced going up or down?

Across all 10 papers analysed, Binomial Theorem has averaged about 1.0 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.2 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.