Home
Class 12
MATHS
If f(x)=1-x+x^2-x^3+...+x^(15)+x^(16)-x^...

If `f(x)=1-x+x^2-x^3+...+x^(15)+x^(16)-x^(17)` , then the coefficient of `x^2inf(x-1)` is `826` b. `816` c. `822` d. none of these

A

826

B

816

C

822

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x) = 1-x+x^(2)-x^(3)+"……"-x^(15)+x^(16)-x^(17)= (1-x^(18))/(1+x)`
`rArr f(x-1)= (1-(x-1)^(18))/(x)`
Therefore, required coefficient of `x^(2)` is equal to coefficient of `x^(3)` in `1-(x-1)^(18)`, which is given by `.^(18)C_(3)=816`.
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.8|10 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The coefficient of x^5in(1+2x+3x^2+....)^(-3//2)i s(|x|<1) 21 b. 25 c. 26 d. none of these

If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is

The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s -99^2 b. 1 c. -2500 d. none of these

The coefficient of x^4 in (x//2-3//x^2)^10 is (405)/(256) b. (504)/(259) c. (450)/(263) d. none of these

Coefficient of x^(18)in(1+x+2x^2+3x^3++18 x^(18))^2 equal to 995 b. 1005 c. 1235 d. none of these

The number of distinct terms in the expansion of (x+1/x+x^2+1/(x^2))^(15) is/are (with respect to different power of x ) 255 b. 61 c. 127 d. none of these

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

The coefficient of x^n in (1+x)^(101)(1-x+x^2)^(100) is nonzero, then n cannot be of the form 3r+1 b. 3r c. 3r+2 d. none of these

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If f(x)= |1x x+1 2x x(x-1)(x+1) x3 x(x-1) x(x-1)(x-2) (x+1)x(x-1)| then f(500) is equal to 0 b. 1 c. 500 d. -500

CENGAGE-BINOMIAL THEOREM-Exercise (Single)
  1. The coefficient of x^r[0lt=rlt=(n-1)] in lthe expansion of (x+3)^(n-1)...

    Text Solution

    |

  2. If (1+2x+3x^2)^(10)=a0+a1x+a2x^2++a(20)x^(20),t h e na1 equals 10 b. 2...

    Text Solution

    |

  3. If f(x)=1-x+x^2-x^3+...+x^(15)+x^(16)-x^(17) , then the coefficient of...

    Text Solution

    |

  4. Let f(x0=a0+a1x+a2x^2++an x^n+ and (f(x))/(1-x)=b0+b1x+b2x^2++bn x^n+ ...

    Text Solution

    |

  5. Statement 1: The coefficient of x^n is (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^...

    Text Solution

    |

  6. In the expansion of (3^(-x//4)+3^(5x//4))^(n) the sum of binomial coef...

    Text Solution

    |

  7. The sum of the coefficients of even power of x in the expansion of (1+...

    Text Solution

    |

  8. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is ...

    Text Solution

    |

  9. If the sum of the coefficients in the expansion of (a + b)^(n) is 4096...

    Text Solution

    |

  10. The value of ^20 C0+^(20)C1+^(20)C2+^(20)C3+^(20)C4+^(20)C 12+^(20)C 1...

    Text Solution

    |

  11. The sum of series ^(20)C0-^(20)C1+^(20)C2-^(20)C3++^(20)C 10 is

    Text Solution

    |

  12. If (3+x^(2008)+x^(2009))^(2010)=a0+a1x+a2x^2++an x^n , then the value ...

    Text Solution

    |

  13. Value of sum(k=1)^oosum(r=0)^k1/(3^k)(^k Cr) is 2/3 b. 4/3 c. 2 d. 1

    Text Solution

    |

  14. The value of sum(r=0)^(10)(r)^(20)Cr is equal to 20(2^(18)+^(19)C(10))...

    Text Solution

    |

  15. [(^n C0+^n C3+)1//2(^n C1+^n C2+^n C4+^n C5]^2+3//4(^n C1-^n C2+^n C4-...

    Text Solution

    |

  16. The value of sum(r=1)^(n+1)(sum(k=1)^n^k C(r-1))(w h e r er ,k ,n in ...

    Text Solution

    |

  17. The sum sumsum(0leilejle10) (""^(10)C(j))(""^(j)C(r-1)) is equal to

    Text Solution

    |

  18. The value of "^(1000)C(50)+^(999)C(49)+^(998)C(48)+......+^(950)C(0) i...

    Text Solution

    |

  19. If sum(r=0)^n{ar(x-alpha+2)^r-br(alpha-x-1)^r}=0, then prove that bn-(...

    Text Solution

    |

  20. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

    Text Solution

    |