1. Let $[x]$ denote the greatest integer not greater than $x$. Let the set $A=\left\{x \mid x^{2}-[x]=2\right\}, B=\{x|| x \mid<$ $2\}$. Then $A \cap B=(\quad)$.
(A) $(-2,2)$
(B) $[-2,2]$
(C) $\{\sqrt{3},-1\}$
(D) $\{-\sqrt{3}, 1\}$
- 1.C.

Since $x=0 \notin A$, options $(\mathrm{A})$ and $(\mathrm{B})$ are eliminated.
Also, $x=-1, \sqrt{3}$ satisfy the condition, hence the answer is $(\mathrm{C})$.