If the arithmetic mean of two positive numbers is $A$,their geometric mean is $G$,and their harmonic mean is $H$,then $H$ is equal to:

The sum of three decreasing numbers in $A.P.$ is $27$. If $-1, -1, 3$ are added to them respectively,the resulting series is in $G.P.$ The numbers are

The product of $n$ positive numbers is $1$. The sum of these numbers cannot be less than what value?

If $a, b, c$ are in geometric progression,then in which progression are $\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ such that the equations $ax^2 + 2bx + c = 0$ and $dx^2 + 2ex + f = 0$ have common roots?

The geometric mean of two numbers is $6$ and their arithmetic mean is $6.5$. The numbers are

If $a_1, a_2, \dots, a_n$ are positive real numbers such that $a_1 \cdot a_2 \cdot \dots \cdot a_n = 1$,then their sum is: