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The number of all subsets of a set conta...

The number of all subsets of a set containing `2n+1` elements which contains more than `n` elements is

A

`2^(n)`

B

`2^(2n)`

C

`2^(n+1)`

D

`2^(2n-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
`.^(2n+1)C_(n+1)+ .^(2n+1)C_(n+2)+…+ .^(2n+1)C_(2n+1)`
`=1/2((.^2n+1)C_(0)+ .^(2n+1)C_(1)+ .^(2n+1)C_(3)+…+ .^(2n+1)C_(2n+1))=2 .^(2n)`
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Knowledge Check

  • The number of subsets of set containing n distinct object is

    A
    `""^(n)C_(1)+""^(n)C_(2)+""^(n)C_(3)+…+""^(n)C_(n-1)`
    B
    `2^(n)-1`
    C
    `""^(n)C_(0)+""^(n)C_(1)+…+""^(n)C_(n)`
    D
    `2^(n)+1`

  • The number of elements of the power set of a set containing n elements is

    A
    `2^(n-1)`
    B
    `2^(n)`
    C
    `2^(n)-1`
    D
    `2^(n+1)`

  • A set contains n elements. The power set contains

    A
    n elemets
    B
    `2^(n)` elements
    C
    `n^(2)` elemets
    D
    none of these

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