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((30)/(0)) ((30)/(10)) - ((30)/(1)) ((30...

`((30)/(0)) ((30)/(10)) - ((30)/(1)) ((30)/(11)) + ((30)/(2)) ((30)/(12)) + …. + ((30)/(2)) ((30)/(30))` is equal to

A

`((30),(10))`

B

`((30),(15))`

C

`((60),(30))`

D

`((31),(10))`

Text Solution

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The correct Answer is:
A
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If ((n),(r)) denotes nC_r , then Evaluate 2^15((30),(0))((30),(15))-2^14((30),(1))((29),(14))+2^13 ((30),(2))((28),(13))...............-((30),(15))((15),(0))

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
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    C
    `""^(60)C_(30)`
    D
    `""^(40)C_(30)`
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    A
    7
    B
    14
    C
    `(5)/(2)`
    D
    `(7)/(2)`
  • (2 tan 30^(@))/(1 + tan^(2)30^(@)) =

    A
    `sin30^(@)`
    B
    `sin60^(@)`
    C
    `cos60^(@)`
    D
    `tan60^(@)`
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