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Mathematics - Binomial Theorem

Practise 108 NTA Abhyas (JEE Main) questions on Binomial Theorem. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Binomial Theorem has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 108 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1If k = 0 100 k k + 1 C k 100 = a 2 100 + b c , where a , b , c N , then the least value of a + b + c 100 is equal to
  2. 2The coefficient of the term independent of x in x 3 + 3 x 2 10 i s
  3. 3If the coefficient of x 7 in ax 2 + 1 bx 1 1 is equal to the coefficient of x - 7 in ax - 1 bx 2 1 1 , then a and b satisfy the relation
  4. 4The number obtained after dividing the number formed by the last three digits of 17 256 by 100 is
  5. 5The value of x for which the fourth term in the expansion of 5 2 5 log 5 4 x + 44 + 1 5 log 5 2 x - 1 + 7 3 8 is 336 can be equal to
  6. 6The coefficient of x 4 in the expansion of 1 + 5 x + 9 x 2 + 13 x 3 + 17 x 4 + . … … 1 + x 2 11 is equal to
  7. 7The coefficient of x 20 in the expansion of 1 + x 2 40 x 2 + 2 + 1 x 2 - 5 is
  8. 8The value of ∑ i = 1 n C n + 1 i - C n i is equal to
  9. 9The coefficient of x 6 in the expansion of 1 + x + x 2 6 is
  10. 10The term independent of x in the expansion of the expression 1 + x + 2 x 3 3 2 x 2 - 1 3 x 9 is equal to
  11. 11The coefficient of x 13 in the expansion of 1 - x 5 1 + x + x 2 + x 3 4 is
  12. 12The coefficient of x n in the polynomial ( x + 2 n + 1 C 0 ) ( x + 2 n + 1 C 1 ) ( x + 2 n + 1 C 2 ) ..... ( x + 2 n + 1 C n ) is
  13. 13The ratio of the fifth term from the beginning to the fifth term from the end in the expansion of 2 4 + 1 3 4 n is 6 : 1 . If n = 20 λ , the
  14. 14The coefficient of x 6 in the expansion of 1 - x 8 1 + x 12 is equal to
  15. 15The coefficient of x 7 in a x 2 + 1 b x 11 and the coefficient of x - 7 in a x - 1 b x 2 11 are equal, then the value of a b is equal to
  16. 16If r = 0 25 C r 50 . C 25 - r 50 - r = K C 25 50 , then K is equal to
  17. 17The remainder obtained when 7 100 is divided by 13 is
  18. 18The value of r = 0 n r + 2 r + 1 C r n is equal to
  19. 19If 5 97 is divided by 52 , then the remainder obtained is
  20. 20If the coefficient of x 6 in the expansion of 2 + x 3 3 + x 2 5 + x 3 is K , then the value of K 100 is
  21. 21The last term in the expansion of 2 1 3 + 2 - 1 2 n is 3 - 5 3 l o g 3 8 . Then, the value of the fifth term is
  22. 22The coefficient of x 8 in the expansion of 1 + x 2 2 ! + x 4 4 ! + x 6 6 ! + x 8 8 ! 2 is
  23. 23Let denote the number of terms in the expansion of 1 + 5 x + 10 x 2 + 10 x 3 + 5 x 4 + x 5 20 . If unit s place and ten s place digits in 3
  24. 24The value of n + 2 · C 0 n ⋅ 2 n + 1 - n + 1 · C 1 n ⋅ 2 n + n · C 2 n ⋅ 2 n - 1 - . . . . to n + 1 terms is equal to
  25. 25If 1 ! 2 + 2 ! 2 + 3 ! 2 + ⋯ + 99 ! 2 + 100 ! 2 is divided by 100 , then the remainder obtained is
  26. 26The coefficient of x 24 in 1 + x 2 12 1 + x 12 1 + x 24 is
  27. 27If 1 3 99 - 1 9 93 is divided by 162 , then the remainder is
  28. 28In the expansion of a x + b 2020 , if the coefficients of x 2 and x 3 are equal, then the value of 9 100 b a is equal to
  29. 29If C 0 , C 1 , C 2 , . . . . . , C 20 are the binomial coefficients in the expansion of 1 + x 20 , then the value of C 1 C 0 + 2 C 2 C 1 + 3
  30. 30If 1 + x + 2 x 2 20 = a 0 + a 1 x + a 2 x 2 + . . . . + a 40 x 40 , then the value of a 0 + a 2 + a 4 + . . . . . + a 38 is
  31. 31The coefficient of x 4 in the expansion of 1 - x - 2 x 2 8 is
  32. 32If the sum of the coefficients in the expansion of 1 + 3 x n lies between 4000 and 10000 , then the value of the greatest coefficient must b
  33. 33The number of terms in the expansion of 5 1 6 + 7 1 9 1824 which are integers is
  34. 34The value of the expression k = 0 27 k C k 27 1 3 k 2 3 27 - k is equal to
  35. 35The last two digits of the number 23 14 are
  36. 36If the sixth term in the expansion of 1 x 8 3 + x 2 log 10 ⁡ x 8 is 5600 , then the value of x is
  37. 37If n 2 and , , R , then the value of S = C 0 - + C 1 + + 2 + 2 2 C 2 - + 3 + 3 2 C 3 + . . . . upto n + 1 terms is equal to (where, C r deno
  38. 38If 1 + x n = C 0 + C 1 x + C 2 x 2 + . . . . + C n x n and r = 0 50 C r 2 r + 1 = m ! n ! 2 , then the value of m + n is equal to (where C r
  39. 39The number of integral terms in the expansion of 5 1 6 + 7 1 9 1824 is
  40. 40The coefficient of x 10 in the expansion of 1 + x 15 + 1 + x 16 + 1 + x 17 + . . . + 1 + x 30 is
  41. 41If 5 3 53 - 3 3 3 is divided by 10 , then the remainder obtained is
  42. 42The coefficient of x 8 in the expansion of 1 + x + x 2 + x 3 4 is
  43. 43The greatest term in the expansion of 3 + 2 x 51 , where x = 1 5 , is
  44. 44The coefficient of x 9 in the expansion of 1 + x + x 2 + x 3 3 1 - x 6 is
  45. 45The term independent of x in the expansion of x - 1 x 4 x + 1 x 3 is
  46. 46If 1 + x - 2 x 2 6 = 1 + a 1 x + a 2 x 2 + . . . + a 12 x 12 , then the value of a 2 + a 4 + . . . + a 12 is
  47. 47If C 0 , C 1 , C 2 , … . . , C n are binomial coefficients, ( where C r = n C r ) , then the value of C 0 - C 1 + C 2 - C 3 + . . . + - 1 n
  48. 48The value of the numerically greatest term in the expansion of 4 - 3 x 7 when x = 2 3 is equal to
  49. 49The coefficient of the 2 m + 1 t h and 4 m + 5 t h terms in the expansion of 1 + x 100 are equal, then the value of m 2 is equal to
  50. 50The number of different terms in the expansion of 1 - x 201 1 + x + x 2 200 is

Frequently Asked Questions

1.How many questions are available for Binomial Theorem?

This chapter includes 108 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

These are NTA Abhyas (JEE Main) questions specifically for the Binomial Theorem chapter. Questions from other exams like JEE Main or JEE Advanced are organised separately under their respective exam sections.

3.What is the difficulty level of Binomial Theorem questions in NTA Abhyas (JEE Main)?

Of the 108 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

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

All of this chapter's questions come from a single topic: Uncategorized.