1. Let the universal set be the set of real numbers. If $A=\{x \mid \sqrt{x-2} \leqslant 0\}, B=\left\{x \mid 10^{x^{2}-2}=10^{x}\right\}$, then $A \cap \bar{B}$ is
A. $\{2\}$
B. $\{-1\}$
C. $\{x \mid x \leqslant 2\}$
D. $\varnothing$
$$
A=\{2\}, x^{2}-2=x \Rightarrow x^{2}-x-2=(x+1)(x-2)=0 \Rightarrow B=\{-1,2\} \text {. }
$$

Thus, $A \cap \complement_{\mathbf{R}} B=\varnothing$. Therefore, the answer is $D$.