Let `a_(1),a_(2)…,a_(n)` be a non-negative real numbers such that `a_(1)+a_(2)+…+a_(n)=m` and let `S=sum_(iltj) a_(i)a_(j)`, thenA. `Sle(m^(2))/(2)`B. `Sgt(m^(2))/(2)`C. `Slt(m)/(2)`D. `Sgt(m^(2))/(2)`

Let `a_(1),a_(2)…,a_(n)` be a non-negative real numbers such that `a

1.	Let `a_(1),a_(2)…,a_(n)` be a non-negative real numbers such that `a_(1)+a_(2)+…+a_(n)=m` and let `S=sum_(iltj) a_(i)a_(j)`, thenA. `Sle(m^(2))/(2)`B. `Sgt(m^(2))/(2)`C. `Slt(m)/(2)`D. `Sgt(m^(2))/(2)`
Answer» Correct Answer - A We have, `m^(2)=(a_(1)+a_(2)+...+a_(n))^(2)` `implies" "m^(2)=underset(i=1)overset(n)suma_(i)""^(2)+2underset(iltj)overset(n)suma_(i)a_(j)` `implies" "m^(2)=underset(i=1)overset(n)suma_(i)""^(2)+2" S"` `implies" "m^(2)-2S=underset(i=1)overset(n)suma_(i)""^(2)impliesm^(2)-2Sge0impliesSle(m^(2))/(2)`

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