Harmonic Mean

Let the harmonic mean and geometric mean of two positive number be in the ratio $4: 5$. then the ratio of two number is $\lambda (\lambda <1),$ find $11\lambda$. 

If $2\left(y-a\right)$ is the harmonic mean between $y-x$ and $y-z$, then $x-a, y-a$ and $z-a$ are in

If $2\left(y – a\right)$ is the $\mathrm{H}.\mathrm{M}.$ between $y – x$ and $y – z$, then $x-a,\mathrm{ }\mathrm{ }y-a,\mathrm{ }\mathrm{ }z-a$ are in

The harmonic mean between two numbers is $14\frac{2}{5}$ and the geometric mean is $24$. The greater number between them is

If $\mathrm{G}.\mathrm{M}.$ and $\mathrm{H}.\mathrm{M}.$ of two numbers are $10$ and $8$ respectively. The numbers are

If $H$ is the harmonic mean between $p$ and $q$, then the value of $\frac{H}{p}+\frac{H}{q}$ is

$\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the $\mathrm{A}.\mathrm{M}.$ of $a$ and $b,$ if $n=$

If $a_i>0, i=1, 2, 3,...,50$ and $a_1+a_2+a_3+...+a_{50}=50$, then the minimum value of $\frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}+...+\frac{1}{a_{50}}$  is equal to.

The harmonic mean of the roots of the equation.
$\left(5+\sqrt{2}\right)x^2-\left(4+\sqrt{5}\right)x+8+2\sqrt{5}=\mathrm{0\; is}$