Home
Class 12
MATHS
C(0)-C(1)+C(2)-C(3)+ . . .+(-1)^(n)C(n) ...

`C_(0)-C_(1)+C_(2)-C_(3)+ . . .+(-1)^(n)C_(n)` is equal to

A

`(2 n) C_(n) `

B

`(-1)^(n)(2 n) C_(n) `

C

`(-1)^(n). 2 n C_(n-1) `

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DIFFERENTIATION

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|221 Videos

  • CIRCLES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|272 Videos

Similar Questions

Explore conceptually related problems

The value of C_(0)+3C_(1)+5C_(2)+7C_(3)+ . . .+(2n+1)C_(n) is:

If C_(0), C_(1), C_(2), C_(3),.., C_(n) are the binomial coefficients in the expansion of (1+x)^(n) , then (C_(0))/(1)+(C_(2))/(3)+(C_(4))/(5)+(C_(6))/(7)+...... =

If '^(n)C_(12) = ""^(n)C_(8) then n is equal to

The mean of the values of 0, 1, 2, …., n, having corresponding weight .^(n)C_(0), .^(n)C_(1), .^(n)C_(2), ....., .^(n)C_(n) respectively is :

If (1+x)^(n)= C_(0)+C_(1).x+C_(2). x^(2)+.. . C_(n). x^(n) in the usual notation then C_(0)^(2)+C_(1)^(2)+C_(2)^(2)+.. .+C_(n)^(2) =

The sum (1)/(2)""^(10)C_(0)-""^(10)C_(1)+2.""^(10)C_(2)-2^(2)*""^(10)C_(3)+ . . .+2^(9)*""^(10)C_(10) equals:

(C_(0))/(1)-(C_(1))/(2)+(C_(2))/(3)+.. . .+((-1)^(n))/(n+1). C_(n) =

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+ . . .+C_(n)x^(n) , then the value of : C_(1)+2C_(2)+3C_(3)+ . . .+nC_(n) is:

The value of C_(1)+4C_(2)+7C_(3)+ . . .+(3n-2)C_(n) is

HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. The total number of terms in the expansion of (x+a)^(51)-(x-a)^(51) af...

    Text Solution

    |

  2. If x, y and r are positive integers , then : ""^xCr+""^rC(r-1)""^yC1+^...

    Text Solution

    |

  3. C(0)-C(1)+C(2)-C(3)+ . . .+(-1)^(n)C(n) is equal to

    Text Solution

    |

  4. If (1 +x + x^(2))^(n) = a(0) + a(1) x + a(2) x^(2) + … + a(2n) x^(2n) ...

    Text Solution

    |

  5. If x^(r) occurs in the expansion of (x+(1)/(x))^(n), then is coefficie...

    Text Solution

    |

  6. If (1+x)^(n)= C(0)+C(1).x+C(2). x^(2)+.. . C(n). x^(n) in the usual n...

    Text Solution

    |

  7. nCr+2. nC(r-1)+nC(r-2)=

    Text Solution

    |

  8. If the coefficients of r^(th) and (r+1)^(th) term in the expansion o...

    Text Solution

    |

  9. Sum of the odd binomial coefficients of (1+x)^(50) is

    Text Solution

    |

  10. If (1+x+x^(2))^(n) = a(0)+a(1) x+a(2) x^(2)+.. .+a(2 n) x^(2 n) then ...

    Text Solution

    |

  11. The coefficient of the term independent of x in the expansion of (sqrt...

    Text Solution

    |

  12. If C(0),C(1),C(2), . . . .,C(n) are binomial coefficients of order n,...

    Text Solution

    |

  13. The sum of the coefficients in the expansion of (1+x-3x^(2))^(3148)

    Text Solution

    |

  14. The middle term in the expansion of((x-(1))/(x))^(18) is...

    Text Solution

    |

  15. If the value of C(0)+2C(1)+3C(2)+ . . .+(n+1)C(n)=576, then n is

    Text Solution

    |

  16. The ninth term of the expansion((3x) (-1)/(2x))^(8) is

    Text Solution

    |

  17. The coefficient of x^(5) in (1+x^(2))^(5)(1+x)^(4) is

    Text Solution

    |

  18. If the coefficient of the r^(th) term and the (r+1)^ (th) term is th...

    Text Solution

    |

  19. The co-efficient of x^(-9) in the expansion of ((x^(2))/(2)-(2)/(x)...

    Text Solution

    |

  20. Let (1+x^(2))^(2)(1+x)^(n) = sum(k=0)^(n+4) a(k) x^(k) . If a(1) , a...

    Text Solution

    |