IMO, the answer is D

Logical way:
Mod (1-X) refers to the magnitude of the difference between 1 and X on the number line. If distance between 1 and X should be less than 1; then X should lie at a point less than a unit distance from 1. That would boil down to [spoiler](0,2)[/spoiler]

Arithmetic way:
Mod (1-x) < 1

is equivalent to -1 < 1-X < 1

Subtract 1 across the board (to get rid of the 1 just before X)

-2 < -X < 0

Multiply by -1 across the board (to get rid of the -ve sign of X)

[spoiler]2 > X > 0; which is equivalent to 0 < X < 2[/spoiler].

Hope this helps.