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Binomial Theorem

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  1. 251.The sum of coefficients of integral power of x in the binomial expansion (1-2 x)^50 is:
  2. 252.If the coefficients of x^3 and x^4 in the expansion of (1+ax+bx^2)(1-2x)^18 in powers of x…
  3. 253.If X=4^n-3n-1:n N and Y=9(n-1):n N, where N is the set of natural numbers, then X Y is equ…
  4. 254.The number of terms in the expansion of (1+x)^101(1+x^2-x)^100 in powers of x is:
  5. 255.If 1+x^4+x^5=_i=0^5a_i(1+x)^i, for all x in R, then a_2 is:
  6. 256.If (2+ x3)^55 is expanded in the ascending powers of x and the coefficients of powers of x…
  7. 257.The coefficient of x^1012 in the expansion of (1+x^n+x^253)^10, (where n22 is any positive…
  8. 258.If the 7th term in the binomial expansion of ([3]84+√3^ x)^9, x>0, is equal to 729, then x…
  9. 259.If for positive integers r>1,n>2, the coefficients of the (3r)th and (r+2)th powers of x i…
  10. 260.The sum of the rational terms in the binomial expansion of (2^1/2+3^1/5)^10 is:
  11. 261.The term independent of x in expansion of (x+1x^2/3-x^1/3+1-x-1x-x^1/2)^10 is:
  12. 262.The ratio of the coefficient of x^15 to the term independent of x in the expansion of (x^2…
  13. 263.If n is a positive integer, then (√3+1)^2n-(√3-1)^2n is:
  14. 264.If f(y)=1-(y-1)+(y-1)^2-(y-1)^3+-(y-1)^17, then the coefficient of y^2 in it is:
  15. 265.The number of terms in the expansion of (y^1/5+x^1/10)^55, in which powers of x and y are …
  16. 266.The middle term in the expansion of (1-1x)^n(1-x)^n in powers of x is:
  17. 267.Statement -1: For each natural number n, (n+1)^7-1 is divisible by 7.
  18. 268.The coefficient of x^7 in the expansion of (1-x-x^2+x^3)^6 is:
  19. 269.Let S_1=_j=1^10j(j-1),^10C_j, S_2=_j=1^10j,^10C_j, and S_3=_j=1^10j^2,^10C_j.
  20. 270.The remainder left out when 8^2n-(62)^2n+1 is divided by 9 is:
  21. 271.Statement -1: _r=0^n(r+1),^nC_r=(n+2)2^n-1 Statement-2: _r=0^n(r+1),^nC_rx^r=(1+x)^n+nx(1+…
  22. 272.In a shop there are five types of ice-creams available.
  23. 273.In the binomial expansion of (a-b)^n, n5, the sum of 5th and 6th terms is zero, then a/b e…
  24. 274.The sum of the series ^20C_0-^20C_1+^20C_2-^20C_3+-+^20C_10 is:
  25. 275.For natural numbers m,n, if (1-y)^m(1+y)^n=1+a_1y+a_2y^2+ and a_1=a_2=10, then (m,n) is:
  26. 276.If the coefficient of x^7 in (ax^2+1bx)^11 equals the coefficient of x^-7 in (ax-1bx^2)^11…
  27. 277.If x is so small that x^3 and higher powers of x may be neglected, then (1+x)^3/2-(1+12x)^…
  28. 278.The coefficient of x^n in expansion of (1+x)(1-x)^n is:
  29. 279.The coefficient of the middle term in the binomial expansion in powers of x of (1+ x)^4 an…
  30. 280.The number of integral terms in the expansion of (√3+[8]5)^256 is:
  31. 281.If x is positive, the first negative term in the expansion of (1+x)^27/5 is:
  32. 282.r and n are positive integers, r>1, n>2, and coefficient of (r+2)th term and 3rth term in …
  33. 283.The coefficients of x^p and x^q in the expansion of (1+x)^p+q are:
  34. 284.The positive integer just greater than (1+0.0001)^10000 is:
  35. 285.If the sum of the coefficients in the expansion of (a+b)^n is 4096, then the greatest coef…
  36. 286.If [S_n = _r = 0^n 1 ^nC_r ,,and,,t_n = _r = 0^n r ^nC_r,, ]then [t_ n S_n] is equal to
  37. 287.If x is so small that x^3 and higher powers of x may be neglected, then [( 1 + x )^3 2 - (…
  38. 288.If the expansion in powers of x of the function [1 ( 1 - ax )( 1 - bx )] is [a_0 + a_1x + …
  39. 289.For natural numbers m , n, if [( 1 - y )^m( 1 + y )^n,, = 1 + a_1y + a_2y^2 + ..........] …
  40. 290.In the binomial expansion of [( a - b )^n,,,,n 5,] the sum of 5^th and 6^th terms is zero,…
  41. 291.Statement - 1 : [_r = 0^n ( r + 1 ),^nC_r = ( n + 2 )2^n - 1. ] Statement - 2 : [_r = 0^n …
  42. 292.If the number of terms in the expansion of [( 1 - 2 x + 4 x^2 )^n,,x 0,] is 28, then the s…
  43. 293.If the coefficients of x-2 and x-4 in the expansion of [( x^1 3 + 1 2x^1 3 )^18,( x > 0 ),…
  44. 294.For x [ ] R, x [ ] -1, if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + .
  45. 295.The coefficien of x10 in the expansion of (1 + x)2(1 + x2)3(1 + x3)4 is equal to :
  46. 296.If n is the degree of the polynomial, [[ 2 5x^3 + 1 - 5x^3 - 1 ]^8 + ] [[ 2 5x^3 + 1 + 5x^…
  47. 297.The coefficient of x2 in the expansion of the product (2-x2) .((1 + 2x + 3x2)6 + (1 - 4x2)…
  48. 298.The smallest natural number n, such that the coefficient of x in the expansion of [( x^2 +…
  49. 299.If the coefficients of x2 and x3 are both zero, in the expansion of the expression (1 + ax…
  50. 300.If [_i = 1^20 ( ^20C_i - 1 ^20C_i + ^20C_i - 1 ) ^3 = k 21] then k is equal to