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Mathematics - Binomial Theorem

Practise 45 Manipal (MET) previous year questions on Binomial Theorem, compiled from papers spanning 2010 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty Manipal (MET) tests.

Binomial Theorem has been asked in 15 of the 15 years of Manipal (MET) papers analysed (2010–2024), with 45 questions in all. 49% of them were easy, 47% moderate and 4% tough. Most of its questions came from 2021, with 7 questions that year. In the last three years (2022–2024) it had 5 questions across 3 papers, about 1.7 per paper.

The chapter's 6 topics are not weighted equally: Terms of Binomial Expansion (22 questions, 49%), Properties of Binomial Coefficients (8 questions, 18%), and Remainder and Divisibility Problems (8 questions, 18%) have been asked the most. Terms of Binomial Expansion has also led over the last five years, with 6 questions. Binomial Theorem for Negative Index has produced the most tough questions (1).

  1. 1If the number of terms in the expansion of having integral coefficients is , then the vaule of is (where [.] denotes greater integer functio2024Terms of Binomial Expansion
  2. 2If the coefficient of in the expansion of is equal to , the is equal to2024Properties of Binomial Coefficients
  3. 3If the coefficients of and in the expansion of in powers of are both zero, then is equal to2023Properties of Binomial Coefficients
  4. 4Last two digits in be____2023Remainder and Divisibility Problems
  5. 5The coefficient of the middle term in the binomial expansion in powers of of and is the same, if is equal to2022Properties of Binomial Coefficients
  6. 6If , then is equal to2021Properties of Binomial Coefficients
  7. 7The middle term in the expansion of is2021Terms of Binomial Expansion
  8. 8The term independent of in the expansion of is2021Terms of Binomial Expansion
  9. 9In the usual notation, is equal to2021Sum of Series
  10. 10The middle term of is2021Terms of Binomial Expansion
  11. 11The coefficient of in the expansion of is2021Terms of Binomial Expansion
  12. 12The value of is2021Properties of Binomial Coefficients
  13. 13The coefficient of in is2020Terms of Binomial Expansion
  14. 14The remainder obtained when is divided by 14 is2019Remainder and Divisibility Problems
  15. 15The remainder obtained when is divided by 124 is2019Remainder and Divisibility Problems
  16. 16The coefficient of in the expansion of is2018Terms of Binomial Expansion
  17. 17The statement , when divided 8 , always leaves the remainder2018Remainder and Divisibility Problems
  18. 18If , then one of the values of is2018Remainder and Divisibility Problems
  19. 19The least positive remainder when is divided by 124 is2018Remainder and Divisibility Problems
  20. 20If the coefficients of the th term and the th term in the expansion of are in the ratio , then is equal to2018Terms of Binomial Expansion
  21. 21The first three terms in the expansion of are 1, and . Then, the values of and are respectively2018Terms of Binomial Expansion
  22. 22The coefficient of in the expansion of is2017Binomial Theorem for Negative Index
  23. 23The middle term of is2017Properties of Binomial Coefficients
  24. 24If , then is equal to2017Terms of Binomial Expansion
  25. 25If and , where , then is2016Properties of Binomial Coefficients
  26. 26Sum of the last 30 coefficients in the expansion of , when expanded in ascending power of is2016Sum of Series
  27. 27The coefficient of the term independent of in the expansion of is2016Terms of Binomial Expansion
  28. 28The number of positive integers satisfying the inequality is2016Properties of Binomial Coefficients
  29. 29If there is a term containing in , then2015Terms of Binomial Expansion
  30. 30The term independent of in the expansion of , is2015Terms of Binomial Expansion
  31. 31Middle term in the expansion of is2014Terms of Binomial Expansion
  32. 32If the term free from in the expansion of is 405 , then the value of is2014Terms of Binomial Expansion
  33. 33A person is permitted to select at least one and at most coins from a collection of distinct coins. It the total number of ways in which he 2013Sum of Series
  34. 34The value of in the expression , if the third term in the expansion is , is2013Terms of Binomial Expansion
  35. 35is equal to2013Sum of Series
  36. 36The middle term in the expansion of is2012Terms of Binomial Expansion
  37. 37The least positive remainder when is divided by 124 is2012Remainder and Divisibility Problems
  38. 38Given positive integers and the coefficient of (3r) th and th terms in the binomial expansion of are equal, then2012Terms of Binomial Expansion
  39. 39If , then is equal to2011Sum of Series
  40. 40The coefficient of in the expansion of is2011Multinomial Theorem
  41. 41The least remainder when is divided by 5 , is2011Remainder and Divisibility Problems
  42. 42The term independent of in is2010Terms of Binomial Expansion
  43. 43The greatest coefficient in the expansion of is2010Terms of Binomial Expansion
  44. 44The number of terms in the expansion of which are integers, is equal to2010Terms of Binomial Expansion
  45. 45The constant term in the expansion of is2010Terms of Binomial Expansion

Frequently Asked Questions

1.How many questions are available for Binomial Theorem?

This chapter includes 45 questions compiled from Manipal (MET) papers spanning 2010 to 2024.

2.Are these questions only from Manipal (MET), or from other exams too?

These are Manipal (MET) 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 Manipal (MET) Mathematics?

Binomial Theorem has appeared in 15 of the 15 years of Manipal (MET) papers covered here, with 45 questions across 15 papers - about 3 per paper it appears in.

4.What is the difficulty level of Binomial Theorem questions in Manipal (MET)?

Of the 45 questions analysed for this chapter, 49% are easy, 47% moderate and 4% tough. 2021 had the most, with 7 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 - 22 questions (49%)
  • Properties of Binomial Coefficients - 8 questions (18%)
  • Remainder and Divisibility Problems - 8 questions (18%)
  • Binomial Theorem for Negative Index has produced the most tough questions (1).
6.Is Binomial Theorem's weightage in Manipal (MET) going up or down?

Across all 15 papers analysed, Binomial Theorem has averaged about 3.0 questions per paper. In the last three years (2022–2024), that average has fallen, at about 1.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.