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Binomial Theorem

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  1. 151.If the coefficient of x^10 in the binomial expansion of ( x5^1/4+√5x^1/3)^60 is 5^k l, whe…
  2. 152.If the sum of the coefficients of all the positive powers of x, in the Binomial expansion …
  3. 153.If _k=1^3131k31k-1-_k=1^3030k30k-1=(60!)(30!)(31!) where R, then the value of 16 is equal …
  4. 154.The number of positive integers k such that the constant term in the binomial expansion of…
  5. 155.The term independent of x in the expansion of (1-x^2+3x^3)(52x^3-15x^2)^11, x0, is:
  6. 156.If the constant term in the expansion of (3x^3-2x^2+5x)^10 is 2^k l, where l is an odd int…
  7. 157.Let n5 be an integer.
  8. 158.Let the coefficients of x^-1 and x^-3 in the expansion of (2x^1/5-1x^1/5)^15, x>0, be m an…
  9. 159.If the maximum value of the term independent of t in the expansion of (t^2x^1/5+(1-x)^1/10…
  10. 160.The remainder when (11)^1011+(1011)^11 is divided by 9 is
  11. 161.If the coefficients of x and x^2 in the expansion of (1+x)^p(1-x)^q, p,q15, are -3 and -5 …
  12. 162._i,j=0 j^n^nC_i,^nC_j is equal to
  13. 163.The remainder when (2021)^2022+(2022)^2021 is divided by 7 is
  14. 164.Let for the 9th term in the binomial expansion of (3+6x)^n, in the increasing powers of 6x…
  15. 165.The remainder when 7^2022+3^2022 is divided by 5 is:
  16. 166.Let the coefficients of the middle terms in the expansion of (1√6+ x)^4, (1-3 x)^2 and (1-…
  17. 167.If 1+(2+^49C_1+^49C_2++^49C_49)(^50C_2+^50C_4++^50C_50) is equal to 2^n m, where m is odd,…
  18. 168.Let the ratio of the fifth term from the beginning to the fifth term from the end in the b…
  19. 169.If _k=1^10k^2(^10C_k)^2=2200L, then L is equal to _______.
  20. 170.If n2 is a positive integer, then the sum of the series ^n+1C_2+2(^2C_2+^3C_2+^4C_2++^nC_2…
  21. 171.For integers n and r, let n,r=^nC_r if n r0, and 0 otherwise.
  22. 172.The value of -^15C_1+2^15C_2-3^15C_3+-15^15C_15+^14C_1+^14C_3+^14C_5++^14C_11 is
  23. 173.If the remainder when x is divided by 4 is 3, then the remainder when (2020+x)^2022 is div…
  24. 174.Let m,n N and (2,n)=1.
  25. 175.The maximum value of the term independent of t in the expansion of (tx^1/5+(1-x)^1/10t)^10…
  26. 176.The term independent of x in the expansion of (x+1x^2/3-x^1/3+1-x-1x-x^1/2)^10, x1, is equ…
  27. 177.Let ^nC_r denote the binomial coefficient of x^r in the expansion of (1+x)^n.
  28. 178.If the fourth term in the expansion of (x+x^_2x)^7 is 4480, then the value of x, where x N…
  29. 179.If (2021)^3762 is divided by 17, then the remainder is Answer: 4
  30. 180.Let the coefficients of third, fourth and fifth terms in the expansion of (x+ax^2)^n, x0, …
  31. 181.If n is the number of irrational terms in the expansion of (3^1/4+5^1/8)^60, then (n-1) is…
  32. 182.Let [x] denote the greatest integer x.
  33. 183.The value of _r=0^6(^6C_r^6C_6-r) is equal to
  34. 184.Let n be a positive integer.
  35. 185.The term independent of x in the expansion of (x+1x^2/3-x^1/3+1-x-1x-x^1/2)^10, where x0,1…
  36. 186.If b is very small compared to a, so that the cube and higher powers of b/a can be neglect…
  37. 187.The sum of all those terms which are rational numbers in the expansion of (2^1/3+3^1/4)^12…
  38. 188.If the greatest value of the term independent of x in the expansion of (x+ax)^10 is 10!(5!…
  39. 189.For natural numbers m,n, if (1-y)^m(1+y)^n=1+a_1y+a_2y^2++a_m+ny^m+n and a_1=a_2=10, then …
  40. 190.The coefficient of x^256 in the expansion of (1-x)^101(x^2+x+1)^100 is
  41. 191.The number of rational terms in the binomial expansion of (4^1/4+5^1/6)^120 is .......
  42. 192.If the constant term in Binomial expansion of (2x^r+1x^2)^10 is 180, then r is equal to An…
  43. 193.The number of elements in the set n1,2,,100:(11)^n>(10)^n+(9)^n is Answer: 96
  44. 194.The lowest integer which is greater than (1+110^100)^10^100 is
  45. 195.If the co-efficient of x^7 and x^8 in the expansion of (2+ x3)^n are equal, then the value…
  46. 196._k=0^20(^20C_k)^2 is equal to
  47. 197.If ^20C_r is the coefficient of x^r in the expansion of (1+x)^20, then the value of _r=0^2…
  48. 198.Let n,k=^nC_k for 0 k n, else 0.
  49. 199.If the coefficients of x^7 in (x^2+1bx)^11 and x^-7 in (x-1bx^2)^11, b0, are equal, then t…
  50. 200.A possible value of x, for which the ninth term in the expansion of (3^_3√5^x-1+7+3^-18_3(…