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if sum(r=0)^(25).^(50)C(r)(.^(50-r)C(25-...

if `sum_(r=0)^(25).^(50)C_(r)(.^(50-r)C_(25-r))=k(.^(50)C_25)`, then k equals:

A

`2^(25)`

B

`2^(25) -1`

C

`2^(24)`

D

`(25)^(2)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If sum_(r=0)^(25)(""^(50)C_( r ))(""^(50-r)C_(25-r))=k(""^(50)C_(25)) then k is equal to

    A
    `25)^(2)`
    B
    `2^(25)-1`
    C
    `2^(24)`
    D
    `2^(25)`

  • If sum_(r=0)^(n){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24) , then n is equal to

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    `3`
    B
    `4`
    C
    `5`
    D
    `6`

  • The value of sum_(r=0)^(15)r^(2)((""^(15)C_(r))/(""^(15)C_(r-1))) is equal to

    A
    1085
    B
    560
    C
    680
    D
    1240

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