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Binomial Theorem

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  1. 301.If the third term in the binomial expansion of [( 1 + x^ _2x )^5] equals 2560, then a poss…
  2. 302.Let (x + 10)50 + (x - 10)50 = a0 + a1x + a2x2 + .
  3. 303.Let Sn = 1 + q + q2 + .
  4. 304.The value of r for which 20Cr 20C0 + 20Cr-1 20C1 + 20Cr-2 20C2 + .
  5. 305.The sum of the real values of x for which the middle term in the binomial expansion of [( …
  6. 306.The term independent of x in the expansion of [( 1 60 - x^8 81 ).( 2x^2 - 3 x^2 )^6] is eq…
  7. 307.If 20C1 + (22) 20C2 + (32) 20C3 + .....
  8. 308.The coefficient of x18 in the product (1 + x) (1 -- x)10 (1 + x + x2)9 is :
  9. 309.If some three consecutive in the binomial expansion of (x + 1)n is powers of x are in the …
  10. 310.If the fourth term in the binomial expansion of [( 2 x + x^ _8x )^6] (x > 0) is 20 87, the…
  11. 311.The coefficient of t4 in the expansion of [( 1 - t^6 1 - t )^3] is :
  12. 312.If the term independent of x in the expansion of [( 3 2x^2 - 1 3x )^9] is k, then 18 k is …
  13. 313.If the number of integral terms in the expansion of (31/2 + 51/8)n is exactly 33, then the…
  14. 314.The coefficient of x7 in the expression (1 + x)10 + x(1 + x)9 + x2(1 + x)8 + ......+ x10 i…
  15. 315.The greatest positive integer k, for which 49k + 1 is a factor of the sum 49125 + 49124 + …
  16. 316.If [ ] and [ ] be the coefficients of x4 and x2 respectively in the expansion of [( x + x^…
  17. 317.Let [ x ] denote greatest integer less than or equal to x.
  18. 318.The value of [_r = 0^6 ( ^6C_r,.,^6C_6 - r ) ] is equal to :
  19. 319.If the fourth term in the expansion of [(x + x^ _2x)^7] is 4480, then the value of x where…
  20. 320.Let (1 + x + 2x2)20 = a0 + a1x + a2x2 + ....
  21. 321.For the natural numbers m, n, if [(1 - y)^m(1 + y)^n = 1 + a_1y + a_2y^2 + ....
  22. 322.The coefficient of x256 in the expansion of (1 - x)101 (x2 + x + 1)100 is :
  23. 323.If [n 2] is a positive integer, then the sum of the series [^n + 1C_2 + 2( ^2C_2 + ^3C_2 +…
  24. 324.If b is very small as compared to the value of a, so that the cube and other higher powers…
  25. 325.If ^20C_r is the co-efficient of xr in the expansion of (1 + x)20, then the value of [_r =…
  26. 326.A possible value of 'x', for which the ninth term in the expansion of [ 3^ _3 25^x - 1 + 7…
  27. 327.The remainder when 32022 is divided by 5 is :
  28. 328.The coefficient of x101 in the expression [(5 + x)^500 + x(5 + x)^499 + x^2(5 + x)^498 + ,…
  29. 329.If [1 2,.,3^10 + 1 2^2,.,3^9 + ,,.....,, + ,,1 2^10,.,3 = K 2^10,.,3^10], then the remaind…
  30. 330.[_pmatrix i,j = 0 i j pmatrix ^n ^nC_i,^nC_j ] is equal to
  31. 331.The term independent of x in the expansion of [(1 - x^2 + 3x^3)( 5 2x^3 - 1 5x^2 )^11,,x 0…
  32. 332.If [_k = 1^31 ( ^31C_k )( ^31C_k - 1 ) - _k = 1^30 ( ^30C_k )( ^30C_k - 1 ) = (60!) (30!)(…
  33. 333.Let n [] 5 be an integer.
  34. 334.If the constant term in the expansion of [( 3x^3 - 2x^2 + 5 x^5 )^10] is 2k.l, where l is …
  35. 335.For two positive real numbers a and b such that [1 a^2 + 1 b^3 = 4], then minimum value of…
  36. 336.If the coefficients of x and x^2 in [(1+x)^p(1-x)^q] are 4 and -5 respectively, then 2 p+3…
  37. 337.If the [1011^ th ] term from the end in the binominal expansion of [((4 x)/(5)-(5)/(2 x))^…
  38. 338.The value of [_r = 0^22 ^22C_r^23C_r ] is
  39. 339.If the coefficient of x^15 in the expansion of [(a x^3+1~b x^1 / 3)^15] is equal to the co…
  40. 340.If ^2 n C_3: ^n C_3=10: 1, then the ratio [(n^2+3 n):(n^2-3 n+4)] is :
  41. 341.If A denotes the sum of all the coefficients in the expansion of (1-3 x+10 x^2)^n and B de…
  42. 342.Let a be the sum of all coefficients in the expansion of [(1-2 x+2 x^2)^2023(3-4 x^2+2 x^3…
  43. 343.If the constant term in the expansion of [([5]3x+2 x[3]5)^12, x 0], is [ 2^8 [5]3], then […
  44. 344.Let , , and be the coefficients of x^7, x^5, x^3 and x respectively in the expansion of [a…
  45. 345.Suppose A and B are the coefficients of 30^ th and 12^ th terms respectively in the binomi…
  46. 346.For an integer n 2, if the arithmetic mean of all coefficients in the binomial expansion o…
  47. 347.In the expansion of ([3]2+1[3]3)^n, n ~N, if the ratio of 15^ th term from the beginning t…