Home
Class 11
MATHS
If n is even and ""^(n)C(0)lt""^(n)C(1...

If n is even and
`""^(n)C_(0)lt""^(n)C_(1) lt ""^(n)C_(2) lt ....lt ""^(n)C_(r) gt ""^(n)C_(r+1) gt""^(n)C_(r+2) gt......gt""^(n)C_(n)`, then, r=

A

`(n)/(2)`

B

`(n-1)/(2)`

C

`(n-2)/(2)`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • BINOMIAL THEOREM AND ITS APPLCIATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Assertion Reason Type|13 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

Similar Questions

Explore conceptually related problems

For ""^(n) C_(r) + 2 ""^(n) C_(r-1) + ""^(n) C_(r-2) =

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

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

If ""^(n)C_(3) + ""^(n)C_4 gt ""^(n+1) C_3 , then.

""^(n)C_(r)+2""^(n)C_(r-1)+^(n)C_(r-2) is equal to

""^(n)C_(n-r)+3.""^(n)C_(n-r+1)+3.""^(n)C_(n-r+2)+""^(n)C_(n-r+3)=""^(x)C_(r)

The expression ""^(n)C_(r)+4.""^(n)C_(r-1)+6.""^(n)C_(r-2)+4.""^(n)C_(r-3)+""^(n)C_(r-4)

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

""^(n-2)C_(r)+2""^(n-2)C_(r-1)+""^(n-2)C_(r-2) equals :

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

OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Exercise
  1. Find the remainder when 32^(32^32) is divided by 7

    Text Solution

    |

  2. If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient ...

    Text Solution

    |

  3. If n gt 1, then (1+x)^(n)-nx-1 is divisible by :

    Text Solution

    |

  4. The number of terms with integral coefficients in the expansion of (...

    Text Solution

    |

  5. The term independent of x in the expansion of (1 - x)^(2) (x + (1)/(...

    Text Solution

    |

  6. The range of the values of term independent of x in the expansion of (...

    Text Solution

    |

  7. If the sum of the coefficients in the expansion of (alpha x^(2 ) -2...

    Text Solution

    |

  8. If the coefficients of r^(th) and (r+1)^(th)terms in expansion of (3+7...

    Text Solution

    |

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

    Text Solution

    |

  10. about to only mathematics

    Text Solution

    |

  11. If n > 3, then x y C0-(x-1)(y-1)C1+(x-2)(y-2)C2-(x-3)(y-3)C3+...........

    Text Solution

    |

  12. The coefficient of x^(5) in the expansion of (1+x^(2))/(1 +x) ,|x| ...

    Text Solution

    |

  13. Find the digit at the unit's place in the number 17^1995 + 11^1995-7^1...

    Text Solution

    |

  14. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

    Text Solution

    |

  15. Let (1+x)^(n)=sum(r=0)^(n)a(r)x^(r)* Then (1+(a(1))/(a(0)))(1+(a(2))/(...

    Text Solution

    |

  16. If n is even and ""^(n)C(0)lt""^(n)C(1) lt ""^(n)C(2) lt ....lt ""^(...

    Text Solution

    |

  17. The coefficient x^5 in the expansion of (2 - x + 3x^2)^6 is

    Text Solution

    |

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

    Text Solution

    |

  19. The coefficient of x^(8) y^(6) z^(4) in the expansion of (x + y + z)...

    Text Solution

    |

  20. The value of 1xx2xx3xx4+2xx3xx4xx5+3xx4xx5xx6+…+n(n +1) (n +2) (n +...

    Text Solution

    |