If the ratio of $H.M.$ and $G.M.$ between two numbers $a$ and $b$ is $4:5$,then the ratio of the two numbers will be

If $a$ and $b$ are the roots of $x^{2}-3x+p=0$ and $c$ and $d$ are roots of $x^{2}-12x+q=0$,where $a, b, c, d$ form a $G.P.$,prove that $(q+p):(q-p)=17:15$.

Suppose $a, b, c$ are in $A.P.$ and $a^2, b^2, c^2$ are in $G.P.$ If $a < b < c$ and $a + b + c = \frac{3}{2}$,then the value of $a$ is

If $a, b, c$ are in $AP$,and $b-a, c-b, a$ are in $GP$,then $a: b: c$ is

Let $x_{1}, x_{2}$ be the roots of $x^{2}-3x+a=0$ and $x_{3}, x_{4}$ be the roots of $x^{2}-12x+b=0$. If $x_{1} < x_{2} < x_{3} < x_{4}$ and $x_{1}, x_{2}, x_{3}, x_{4}$ are in $GP$, then $ab$ equals:

If $a, b, c$ are in $A.P.$ and $a^2, b^2, c^2$ are in $H.P.$,then