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Find k if sum ( i = 0) ^( 100) ""^(150...

Find k if
`sum _( i = 0) ^( 100) ""^(150) C _(i) . ""^(350) C _(100 - i) . ( 150 - i ) = k.""^(500) C _(100)`

A

50

B

100

C

120

D

150

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • Find the sum of the series sum_(r=0)^(50)(""^(100-r)C_(25))/(100-r)

    A
    `(1)/(25)[""^(100)C_(25)+""^(50)C_(25)]`
    B
    `(1)/(25)[""^(100)C_(25)-""^(51)C_(25)]`
    C
    `(1)/(25)[""^(100)C_(25)-""^(49)C_(25)]`
    D
    `(1)/(25)[""^(100)C_(25)-""^(50)C_(26)]`

  • ( i + sqrt(3) )^(100) + (i - sqrt(3))^(100) + 2 ^(100) =

    A
    1
    B
    `-1`
    C
    0
    D
    none

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