• # question_answer $a,\,g,\,h$ are arithmetic mean, geometric mean and harmonic mean between two positive numbers x and y respectively. Then identify the correct statement among the following [Karnataka CET 2001] A) h is the harmonic mean between a  and g B) No such relation exists between a, g and h C) g  is the geometric mean between a and h D) A  is the arithmetic mean between g  and h

$a=\frac{x+y}{2},g=\sqrt{xy}$ and $h=\frac{2xy}{x+y}$ ${{g}^{2}}={{\left( \sqrt{xy} \right)}^{2}}=xy$...(i), ah$=\frac{x+y}{2}.\frac{2xy}{x+y}=xy$     ...(ii) From (i) and (ii), we get ${{g}^{2}}=ah$ or $g=\sqrt{ah}$, therefore g is the G.M. between a and h.