Home
Class 11
MATHS
The sum of series ,^20C0-^20C1+^20C2-^20...

The sum of series `,^20C_0-^20C_1+^20C_2-^20C_3+.....+ ^20C_10` is

A

`(1/2) ^20C_10)`

B

0

C

`,^20C_10`

D

`,-^20C_10`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

The sum of series .^(20)C_0-^(20)C_1+^(20)C_2-^(20)C_3++^(20)C_10 is 1/2 .^(20)C_10 b. 0 c. .^(20)C_10 d. -^(20)C_10

Find the value of .^20 C_0-(.^20C_1)/2+(.^20C_2)/3-(.^20C_3)/4+...

Find the value of .^(20)C_(0) - .^(20)C_(1)+ .^(20)C_(2) - .^(20)C_(3) +"……"-"....." + .^(20)C_(10) . is

The value of .^(20)C_(0)+.^(20)C_(1)+.^(20)C_(2)+.^(20)C_(3)+.^(20)C_(4)+.^(20)C_(12)+.^(20)C_(13)+.^(20)C_(14)+.^(20)C_(15) is

The value of .^(40)C_0+.^40C_1 + .^40C_2 + + .^40C_20

The value of "^30C_0.^30C_10+^30C_1.^30C_11+^30C_2.^30C_(12)+……+^30C_(20) . ^30C_(30

The maximum sum of the series 20+19 1/3+18 2/3+...... is (A) 310 (B) 300 (C) 320 (D) none of these

The value of r for which .^(20)C_(r ). ^(20)C_(0)+ .^(20)C_(r - 1) .^(20)C_(1) + .^(20)C_(r - 2).^(20)C_(2) + …… + .^(20)C_(0) .^(20)C_(r ) is maximum, is

Find the value of .^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10) .

The value of the expression (tan^2 20^0-sin^2 20^0)/(tan^2 20^0+sin^2 20^0) is__________

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. If the 6th term in the expansion of (1/x^(8//3)+x^2log(10)x)^8 is 5600...

    Text Solution

    |

  2. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is

    Text Solution

    |

  3. The sum of series ,^20C0-^20C1+^20C2-^20C3+.....+ ^20C10 is

    Text Solution

    |

  4. ^8C2+^8C3+^8C4+....^8C7 is equal to

    Text Solution

    |

  5. .^18C15+2(.^18C16)+^17C16+1=^nC3, then n is equal to

    Text Solution

    |

  6. The value of 1^2cdotC1+3^2cdotC3+5^2cdotC5+......, is

    Text Solution

    |

  7. Let [x] denotes the greatest integer less then or equal to x. If x=(sq...

    Text Solution

    |

  8. The fractional part of =(2^(4n))/15 is

    Text Solution

    |

  9. If p=(8+3sqrt7)^n and f=p-[p], where [.] denotes the greatest integer ...

    Text Solution

    |

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

    Text Solution

    |

  11. If n in N then value of S=sum(r=0)^n(-1)^r((^nCr)/(^(r+2)Cr)) is

    Text Solution

    |

  12. The value of the expression .^47C4 + sum(j = 1)^5.^(52 - j)C3 is equal...

    Text Solution

    |

  13. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+.....oo

    Text Solution

    |

  14. Determine the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^n.

    Text Solution

    |

  15. If an=sum(r=0)^n1/(^nCr) , then sum(r=0)^nr/(^nCr) equals

    Text Solution

    |

  16. The number of real negative terms in the binomial expansion of (1+ix)^...

    Text Solution

    |

  17. Let f(n)=10^n+3 . 4^(n+2)+5, n in N. The greatest integer which divide...

    Text Solution

    |

  18. The value of the sum of the series 3cdot^nC0+8cdot^nC1+13cdot^nC2-18cd...

    Text Solution

    |

  19. For natural numbers m, n if (1-y)^m(1+y)^n=1+a1y+a2y^2+.... and a1=a2=...

    Text Solution

    |

  20. The coefficient of the term independent of x in the expansion of [((x+...

    Text Solution

    |