The number of terms common to the two $A$.$P$.'s $3, 7, 11, \ldots, 407$ and $2, 9, 16, \ldots, 709$ is

If $A_1, A_2$ are the two $A.M.'s$ between two numbers $a$ and $b$ and $G_1, G_2$ are two $G.M.'s$ between the same two numbers,then $\frac{A_1 + A_2}{G_1 G_2} = $

The sum of numbers from $250$ to $1000$ which are divisible by $3$ is

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an arithmetic sequence are $a$,$b$,and $c$ respectively,then the value of $[a(q - r) + b(r - p) + c(p - q)]$ is:

The number of $5$-tuples $(a, b, c, d, e)$ of positive integers such that:
$I.$ $a, b, c, d, e$ are the measures of angles of a convex pentagon in degrees.
$II.$ $a \leq b \leq c \leq d \leq e$.
$III.$ $a, b, c, d, e$ are in an arithmetic progression.

Let $x, y, z$ be positive real numbers such that $x + y + z = 12$ and $x^3y^4z^5 = (0.1)(600)^3$. Then $x^3 + y^3 + z^3$ is equal to