Home
Class 12
MATHS
Prove that (""^(2n)C(0))^(2)-(""^(2n)C...

Prove that
`(""^(2n)C_(0))^(2)-(""^(2n)C_(1))^(2)+(""^(2n)C_(2))-(""^(2n)C_(3))^(2)+......+(""^(2n)C_(2n))^(2)=(-1)^(n)""^(2n)C_(n).`

A

`(-1)^n ""^(2n) C_n`

B

`(-1)^n ((2n+1)) C_n`

C

`(-1) ^(n-1) ""^(2n) C_n`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1C (BINOMIAL THEOREM WITH RATIONAL INDEX)|68 Videos

  • BINOMIAL THEOREM

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) SET - 1|4 Videos

  • BINOMIAL THEOREM

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1A (BINOMIAL THEOREM WITH INTEGRAL INDEX)|149 Videos

  • APPLICATIONS OF DIFFERENTIATION

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET-4 (SPECIAL TYPE QUESTIONS)|15 Videos

  • CIRCLE

    DIPTI PUBLICATION ( AP EAMET)|Exercise Set 4|4 Videos

Similar Questions

Explore conceptually related problems

""^(2n)C_(2)-2""^(n)C_(2)=

""^(2n)C_(n+1)+2. ""^(2n)C_(n) + ""^(2n) C_(n-1) =

Prove that (C_(0) +C_(1)+C_(2)+….+C_(n))^(2)=1 +""^(2n)C_(1) +""^(2n)C_(2) +…..+""^(2n)C_(2n)

""^(2n +1)C_0^2 -""^(2n+1)C_1^2 + ""^(2n+1)C_2^2 -…….- ""^(2n+1)C_(2n+1)^2 =

If ""^(n)C_(8)=""^(n)C_(2) , find ""^(n)C_(2) .

Show that (n !)/(x(x+1)(x+2)...(x+n))=(""^(n)C_(0))/(x)-(""^(n)C_(1))/(x+1) + (""^(n)C_(2))/(x+2)-(""^(n)C_(3))/(x+3) + ...+ ((-1)^(n)""^(n)C_(n))/(x+n) .

Prove that, C_(0) *""^(2n)C_(n)-C_(1)*""^((2n-2))C_(n)+C_(2) *""^((2n-4))C_(n)-…..=2^(n)

Prove that C_(0)^(2)-C_(1)^(2)+C_(2)^(2)-C_(3)^(2)+….+(-1)^(n).C_(n)^(2)={{:((-1)^(n//2)""^(n)C_(n//2)",","if n is even"),(" "0" ,","if n is odd"):}

DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1B (BINOMIAL COEFFICIENTS)
  1. If n is even then C0^2 - C1^2+C2^2-…....+(-1)^n Cn^2=

    Text Solution

    |

  2. ""^((2n + 1))C0 - ""^((2n+ 1))C1 + ""^((2n + 1))C2 - ……+""^((2n + 1))C...

    Text Solution

    |

  3. Prove that (""^(2n)C(0))^(2)-(""^(2n)C(1))^(2)+(""^(2n)C(2))-(""^(2n...

    Text Solution

    |

  4. C1//1-C2//2+C3//3-C4//4+…+(-1)^(n-1) Cn//n=

    Text Solution

    |

  5. C0 - 2^3 . C1 +3^2. C2 - …. + (-1)^n (n+1)^2 . (Cn)=

    Text Solution

    |

  6. Use the identity (1+x)^(m)(1+x)^(n)=(1+x)^(m+n) to prove Vandermonde's...

    Text Solution

    |

  7. C0 - C2 + C4 - C6 +….....

    Text Solution

    |

  8. C1 - C3 + C5 - C7 + …...

    Text Solution

    |

  9. The term independent of x in (1+x)^n (1+(1)/(x))^n is

    Text Solution

    |

  10. If a(n)=sum(r=0)^(n)(1)/(""^(n)C(r)) then sum(r=0)^(n)(r)/(""^(n)C(r))...

    Text Solution

    |

  11. If x+y=1, then sum(r=6)^(n) r ^n Cr x^r . Y^(n-r)=

    Text Solution

    |

  12. If x+y=1 then sum(r=0)^(n) r^2. ^(n) Cr x^r .y^(n-r)=

    Text Solution

    |

  13. the value of (1)/((81)^n)-^(2n) C1. ((10)^2)/((81)^n)+ ^(2n) C1 ((10)^...

    Text Solution

    |

  14. There are two bags each of which contains n balls. A main has to selec...

    Text Solution

    |

  15. The sum of the coefficient of (1+2x-4x^2)^35 is

    Text Solution

    |

  16. The sum of the coefficients of (5x-4y)^n where n is positive integer, ...

    Text Solution

    |

  17. The sum of the coefficients in the expansion of (1+x-3x^2)^(171) is

    Text Solution

    |

  18. The sum of the coefficients of even powers of x in the expansion of (1...

    Text Solution

    |

  19. The sum of the coefficients of even powers of x in the expansion of (...

    Text Solution

    |

  20. The sum of the coefficients of odd powers of x in the expansion of (1+...

    Text Solution

    |