2. In the range of real numbers, let
$$
x=\left(\frac{\sqrt{(a-2)(|a|-1)}+\sqrt{(a-2)(1-|a|)}}{1+\frac{1}{1-a}}+\frac{5 a+1}{1-a}\right)^{1988} .
$$

Then the unit digit of $x$ is
(A) 1 ;
(B) 2 ;
(C) 4 ;
(D) 6 .
2. (D)

To make both radicals meaningful, we must have $(a-2)(|a|-1) \geqslant 0$ and $(a-2)(1-|a|) \geqslant 0$.
However, $(a-2)(1-|a|)=-(a-2)(|a|-1)$,
so it can only be that $(a-2)(|a|-1)=0$,
Solving this gives $a_{1}=2, a_{2}=1, a_{3}=-1$.
If $a_{1}=2$, then $1+\frac{1}{1-a}=0$; if $a_{2}=1$, then $1-a=0$, both of which make the denominator zero. Therefore, only $a_{3}=-1$ is valid.
In this case, $x=\left[\frac{5 \times(-1)+1}{1-(-1)}\right]^{1988}=(-2)^{1988}$
$$
=2^{4 \times 497}=16^{497},
$$

Thus, the units digit of $x$ is 6.