The geometric mean of two numbers is $6$ and their arithmetic mean is $6.5 $. The numbers are
$(3,12)$
$(4, 9)$
$(2, 18)$
$(7, 6)$
If the $A.M.$ is twice the $G.M.$ of the numbers $a$ and $b$, then $a:b$ will be
If $a, b$ are positive real numbers such that the lines $a x+9 y=5$ and $4 x+b y=3$ are parallel, then the least possible value of $a +b$ is
Let $x, y>0$. If $x^{3} y^{2}=2^{15}$, then the least value of $3 x +2 y$ is
The $A.M., H.M.$ and $G.M.$ between two numbers are $\frac{{144}}{{15}}$, $15$ and $12$, but not necessarily in this order. Then $H.M., G.M.$ and $A.M.$ respectively are
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 ..... .