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
Correct Answer: C
Solution :
\[a=\frac{x+y}{2},g=\sqrt{xy}\] 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.
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