If the $A.M.$ of two numbers is greater than $G.M.$ of the numbers by $2$ and the ratio of the numbers is $4:1$, then the numbers are

If $a, b, c$ are in $GP$ and $4a, 5b, 4c$ are in $AP$ such that $a + b + c = 70$,  then value of $a^3 + b^3 + c^3$ is

If $A.M.$ and $G.M.$ of roots of a quadratic equation are $8$ and $5,$ respectively, then obtain the quadratic equation.

The geometric and harmonic means of two numbers $x_1$ and $x_2$ are $18$ and $16\frac {8}{13}$ respectively. The value of $|x_1 -x_2|$ is

If the minimum value of $f(x)=\frac{5 x^{2}}{2}+\frac{\alpha}{x^{5}}, x>0$, is 14 , then the value of $\alpha$ is equal to.

Let $a , b , c$ and $d$ be positive real numbers such that $a+b+c+d=11$. If the maximum value of $a^5 b^3 c^2 d$ is $3750 \beta$, then the value of $\beta$ is