1. Given sets
$$
A=\{1,2,3,4,5\}, B=\{2,3,4,5,6\} \text {. }
$$

Then the set
$C=\{(a, b) \mid a \in A, b \in B$, and the equation $x^{2}+2 a x+b^{2}=0$ has real roots $\}$ has how many elements? $(\quad$.
(A) 7
(B) 8
(C) 9
(D) 10
-,1.D.
When $a>0, b>0$, the equation $x^{2}+2 a x+b^{2}=0$ has real roots if and only if $a \geqslant b$.
Thus, $C=\{(a, b) \mid a, b \in A, a \geqslant b\}$.
Therefore, the number of elements in set $C$ is equal to 10.