The product of $n$ positive numbers is unity. Their sum is

If $a,\;b,\;c$ are in $A.P.$ as well as in $G.P.$, then

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

Let $a, b, c, d\, \in \, R^+$ and $256\, abcd \geq  (a+b+c+d)^4$ and $3a + b + 2c + 5d = 11$ then $a^3 + b + c^2 + 5d$ is equal to :-

If the arithmetic mean of two numbers be $A$ and geometric mean be $G$, then the numbers will be

Let $a_{1}, a_{2}, \ldots, a_{10}$ be an $AP$ with common difference $-3$ and $\mathrm{b}_{1}, \mathrm{~b}_{2}, \ldots, \mathrm{b}_{10}$ be a $GP$ with common ratio $2.$ Let $c_{k}=a_{k}+b_{k}, k=1,2, \ldots, 10 .$ If $c_{2}=12$ and $\mathrm{c}_{3}=13$, then $\sum_{\mathrm{k}=1}^{10} \mathrm{c}_{\mathrm{k}}$ is equal to ..... .