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Binomial Theorem

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  1. 201.The ratio of the coefficient of the middle term in the expansion of (1+x)^20 and the sum o…
  2. 202.If 3^64^4k is the term independent of x in the binomial expansion of (x4-12x^2)^12, then k…
  3. 203.37^22+210^22-44 when divided by 18 leaves the remainder Answer: 15
  4. 204.If the coefficient of a^7b^8 in the expansion of (a+2b+4ab)^10 is k2^16, then k is equal t…
  5. 205.If the sum of the coefficients of all even powers of x in the product (1+x+x^2++x^2n)(1-x+…
  6. 206.The coefficient of x^4 in the expansion of (1+x+x^2)^10 is ________.
  7. 207.If and be the coefficients of x^4 and x^2 respectively in the expansion of (x+x^2-1)^6+(x-…
  8. 208.In the expansion of (x+1x)^16, if l_1 is the least value of the term independent of x when…
  9. 209.If p denotes the fractional part of the number p, then 3^2008 is equal to:
  10. 210.The natural number m, for which the coefficient of x in the binomial expansion of (x^m+1x^…
  11. 211.The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^6 in powers of x, is __________.
  12. 212.Let (2x^2+3x+4)^10=_r=0^20a_rx^r.
  13. 213.If the constant term in the binomial expansion of ( x-kx^2)^10 is 405, then |k| equals:
  14. 214.If for some positive integer n, the coefficients of three consecutive terms in the binomia…
  15. 215.If the number of integral terms in the expansion of (3^1/2+5^1/8)^n is exactly 33, then th…
  16. 216.If the term independent of x in the expansion of (32x^2-13x)^9 is k, then 18k is equal to:
  17. 217.Let >0,>0 be such that ^3+^2=4.
  18. 218.For a positive integer n, (1+1x)^n is expanded in increasing powers of x.
  19. 219.The value of _r=0^20^50-rC_6 is equal to:
  20. 220.Let (x+10)^50+(x-10)^50=a_0+a_1x+a_2x^2++a_50x^50 for all x R; then a_2a_0 is equal to:
  21. 221.If the third term in the binomial expansion of (1+x^_2x)^5 equals 2560, then a possible va…
  22. 222.The positive value of for which the co-efficient of x^2 in the expression x^2( x+x^2)^10 i…
  23. 223.If the fractional part of the number 2^40315 is k15, then k is equal to:
  24. 224.The total number of irrational terms in the binomial expansion of (7^1/5-3^1/10)^60 is:
  25. 225.A ratio of the 5th term from the beginning to the 5th term from the end in the binomial ex…
  26. 226.The sum of the real values of x for which the middle term in the binomial expansion of (x^…
  27. 227.The value of r for which ^20C_r,^20C_0+^20C_r-1,^20C_1+^20C_r-2,^20C_2++^20C_0,^20C_r is m…
  28. 228.If _r=0^25^50C_r^50-rC_25-r=K(^50C_25), then K is equal to:
  29. 229.The coefficient of t^4 in the expansion of (1-t^61-t)^3 is:
  30. 230.The smallest natural number n, such that the coefficient of x in the expansion of (x^2+1x)…
  31. 231.If the fourth term in the Binomial expansion of (2x+x^_8x)^6 (x>0) is 208^7, then a value …
  32. 232.If some three consecutive coefficients in the binomial expansion of (x+1)^n in powers of x…
  33. 233.The sum of the co-efficients of all even degree terms in x in the expansion of (x+x^3-1)^6…
  34. 234.If the fourth term in the binomial expansion of (1x^1+_10x+x^1/12)^6 is equal to 200, and …
  35. 235.The term independent of x in the expansion of 160(2x^2-3x^2)^6-x^881(2x^2-3x^2)^6 is equal…
  36. 236.If ^20C_1+(2^2)^20C_2+(3^2)^20C_3++(20^2)^20C_20=A(2^), then the ordered pair (A,) is equa…
  37. 237.The coefficient of x^18 in the product (1+x)(1-x)^10(1+x+x^2)^9 is:
  38. 238.If the coefficients of x^2 and x^3 are both zero, in the expansion of the expression (1+ax…
  39. 239.The sum of the series 2^20C_0+5^20C_1+8^20C_2+11^20C_3++62^20C_20 is equal to:
  40. 240.The coefficient of x^10 in the expansion of (1+x)^2(1+x^2)^3(1+x^3)^4 is equal to:
  41. 241.If n is the degree of the polynomial, [√5x^3+1-√5x^3-1]^-8+[√5x^3+1+√5x^3-1]^-8 and m is t…
  42. 242.The coefficient of x^2 in the expansion of the product (2-x^2)[(1+2x+3x^2)^6+(1-4x^2)^6] i…
  43. 243.The sum of the co-efficients of all odd degree terms in the expansion of (x+x^3-1)^5+(x-x^…
  44. 244.If (27)^999 is divided by 7, then the remainder is:
  45. 245.The coefficient of x^-5 in the binomial expansion of (x+1x^2/3-x^1/3+1-x-1x-x^1/2)^10 wher…
  46. 246.The value of (^21C_1-^10C_1)+(^21C_2-^10C_2)+(^21C_3-^10C_3)++(^21C_10-^10C_10) is:
  47. 247.If the coefficients of x^-2 and x^-4 in the expansion of (x^1/3+12x^1/3)^18, (x>0), are m …
  48. 248.If the number of terms in the expansion of (1-2x+4x^2)^n, x0, is 28, then the sum of the c…
  49. 249.If the coefficients of the three successive terms in the binomial expansion of (1+x)^n are…
  50. 250.The term independent of x in the binomial expansion of (1-1x+3x^5)(2x^2-1x)^8 is: