11. $A=\{0,1,2,3,4,5\}$, among the quadratic equations with coefficients from $A$ there are
$\qquad$ equations that have real solutions.
11. 53

First, $a \neq 0$ is obvious, and $b^{2} \geqslant 4 a c, c=0$ is always true. This corresponds to $5 \times 6 \div 30$ groups.
Below, we discuss the case where $c \neq 0$:
(1) $b=0.1$ does not work (since $4 a c > 4$)
(2) $b=2$, there is only one solution $(1,1)$
(3) $b=3, a c \leqslant 2$, there are two solutions $(1,2),(2,1)$
(4) $b=4, a c \leqslant 4$ there are 8 solutions $(1,1),(1,2),(1,3),(1,4),(2,1),(3,1)$, $(4,1),(2,2)$
(5) $b=5, a c \leqslant 6$ there are 12 solutions $(i, 1),(1, i), i=1,2, \cdots, 5,(2,2),(2,3)$, $(3,2)$
Therefore, in total, there are 53 equations with real solutions.