2. (10 points) The clock struck the year 2013, and Brother Xiaoming sighed: This is the first year in my life that I will spend without any repeated digits. It is known that Brother Xiaoming was born in a year that is a multiple of 19. Therefore, in 2013, Brother Xiaoming's age is ( ) years old.
A. 16
B. 18
C. 20
D. 22
【Analysis】From 1990 to 2012, each year contains repeated digits, among which the number that is a multiple of 19 is only $1900+95=1995$, then subtract 1995 from 2013 to get the answer.

【Solution】Solution: From 1990 to 2012, each year contains repeated digits, among which the number that is a multiple of 19 is only $1900+95=1995$,
$$
2013-1995=18 \text { (years); }
$$

Therefore, the answer is: B.