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Find the number of all three elements su...

Find the number of all three elements subsets of the set`{a_1, a_2, a_3, ........... a_n}` which contain `a_3dot`

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The number of all three element subsets of the set {a_(1),a_(2),a_(3)......a_(n)} which contain a_(3) , is

FOr an integer nlt2, we have real numbers a_1,a_2,a_3,a_4,..........,a_n such that a_2+a_3+a_4+.......+a_n=a1 and a_1+a_3+a_4+...........+a_n=a_2...............a_1+a_2+a_3+..............+a_(n-1)=a_n what is the value of a_1+a_2+a_3+........+a_n?

Knowledge Check

  • The number of all three elements subsets of the set {a_1, a_2, a_3 ….a_n} which contain a_3 is

    A
    `""^nC_3`
    B
    `""^(n-1) C_3`
    C
    `""^(n-1)C_2`
    D
    none of these

  • 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)`

  • Let a_1=0 and a_1,a_2,a_3 …. , a_n be real numbers such that |a_i|=|a_(i-1) + 1| for all I then the A.M. Of the number a_1,a_2 ,a_3 …., a_n has the value A where :

    A
    `A lt -1/2`
    B
    `A lt -1`
    C
    `A ge -1/2`
    D
    A=-2

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