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The value of (30 0)(30 10)-(30 1)(30 11)...

The value of `(30 0)(30 10)-(30 1)(30 11)+(30 2)(30 12)++(30 20)(30 30)=` `^60 C 20` b. `^30 C 10` c. `^60 C 30` d. `^40 C 30`

A

`""^(60)C_(20)`

B

`""^(30)C_(10)`

C

`""^(60)C_(30)`

D

`""^(40)C_(30)`

Text Solution

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The correct Answer is:
B
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The value of (30,0)(30,10)-(30,1)(30,11)+(30,2)(30,11)-.........+(30,20)(30,30), where (n,r)=nC_(r) is a.(30,10) b.(30,15) c.(60,30)d.(31,10)

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Knowledge Check

  • The value of ((30),(10)) ((30),(10))-((30),(1)) ((30),(11))+((30),(2))((30),(12))+...+((30),(20)) ((30),(30)) is

    A
    `""^(40)C_(20)`
    B
    `""^(30)C_(10)`
    C
    `""^(60)C_(30)`
    D
    `""^(40)C_(30)`

  • The value of (tan 30^@+ tan 60^@)/(cos 30^@) is:

    A
    `sqrt3 +3`
    B
    `8//3`
    C
    `8//sqrt3`
    D
    `1+sqrt3`

  • The value of sum_(r=0)^(10) (-1)^(r).4^(10-r)""^(30)C_(r)""^(30-r)C_(10-r) is equal to

    A
    `.^(30)C_(10) xx 2^(10)`
    B
    `.^(30)C_(9) xx 4^(10)`
    C
    `.^(30)C_(10) xx 3^(10)`
    D
    `.^(30)C_(9) xx 4^(10)`

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