Home
Class 12
MATHS
C0 C1+C1 C2 + C2 C3+…+ C(n-1) Cn=...

`C_0 C_1+C_1 C_2 + C_2 C_3+…+ C_(n-1) C_n=`

A

`((2n)!)/((n-1)!(n+1)!)`

B

`((2n)!)/((n-3)!(n+1)!)`

C

`((2n)!)/((n-2)!(n+2)!)`

D

`((2n)!)/((n-1)!(n+2)!)`

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

C_0C_2 + C_1C_3 +C_2C_4+……..+C_(n-2) C_n =

Prove that (C_0 + C_1) (C_1 + C_2) …..(C_(n-1) + C_n) = ((n+1)^n)/(n!) (C_1.C_2.C_3……C_n)

C_1 + 2. C_2 + 3. C_3 + …... + n. C_n=

Prove that C_0.C_3 + C_1.C_4 + C_2.C_5 + …..+C_(n-3).C_n = ""^(2n)C_(n +3)

C_1 + 4.C_2 +7.C_3 +…….+(3n-2).C_n=

Show that C_0 + (C_0 + C_1) + (C_0 +C_1 + C_2)+……. + (C_0 + C_1 + …+C_n)= (n+2).2^(n-1)

If (C_0 + C_1) (C_1+C_2)…(C_(n-1) + C_n)=k C_0 C_1 C_2… C_n then k=

2. C_2 + 6. C_3 + 12. C_4 +….. + n (n-1) . C_n=

DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1B (BINOMIAL COEFFICIENTS)
  1. (C0)/(2)+(C1)/(6)+(C2)/(12)+…..+ (Cn)/((n+1)(n+2))=

    Text Solution

    |

  2. Show that (2^(2) *C(0) )/(1*2)+(2^(3)*C(1))/(2*3)+(2^(4) *C(2))/(3*4)+...

    Text Solution

    |

  3. C0 C1+C1 C2 + C2 C3+…+ C(n-1) Cn=

    Text Solution

    |

  4. If (C0 + C1) (C1+C2)…(C(n-1) + Cn)=k C0 C1 C2… Cn then k=

    Text Solution

    |

  5. If (1)/(1!(n-1)!) + (1)/(3!(n-3)!) + (1)/(5!(n-5)!) +…. =

    Text Solution

    |

  6. sum(r=0)^(n) (""^n Cr)^2 =

    Text Solution

    |

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

    Text Solution

    |

  8. If Cr denotes the binomial coefficient ""^n Cr then (-1) C0^2 + 2C1^2+...

    Text Solution

    |

  9. If n is odd then C0^2 - C1^2+C2^2-…....+(-1)^n Cn^2=

    Text Solution

    |

  10. If n is even then C0^2 - C1^2+C2^2-…....+(-1)^n Cn^2=

    Text Solution

    |

  11. ""^((2n + 1))C0 - ""^((2n+ 1))C1 + ""^((2n + 1))C2 - ……+""^((2n + 1))C...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. C0 - C2 + C4 - C6 +….....

    Text Solution

    |

  17. C1 - C3 + C5 - C7 + …...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |