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Arithmetic mean a, geometric mean G and ...

Arithmetic mean a, geometric mean G and Harmonic mean H to n positive numbers `a_1,a_2,a_3,…..,a_n` are given by `A=(a_1+a_2+……………+a_n)/n, G=(a_1 a_2 a_n)^(1/2) and G= n/(1/H_1+1/H_2+………+1/H_n)` There is a relation in A, G and H given by `AgeGgeH` equality holds if and only if `a_1=a_2=..............=a_n` On the basis of above information answer the following question If `a_rgt0 or r=1,2,.......6 and a_1+a_2+.....+a_6=3, M=(a_1+a_2)(a_3+a_4)(a_5+a_6)`. Then the set of all possible values of M is (A) `(0,3]` (B) `(0,2]` (C) `(0,1]` (D) none of these

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