The probabilities of three mutually exclusive outcomes of an
experiment $$0.25(1 — x), 0.5(1 — 2x)$$ and $$0.25(1 + 4x)$$ respectively.
Which of the following holds for the value of x ?

As all 3 are mutually exclusive, we can assume (in one extreme case) that these 3 form the entire range of probability and hence,
0.25(1-x) + 0.5(1-2x) + 0.25 (1+4x) = 1 which gives us x = 0 
Hence, x is bound by 0 on one end. 

Also, none of the probabilities can be negative as any event probability is atleast 0. Hence, for the second event, we can see that x cnnot be greater than 0.5
hence, x is bounded from 0 to 0.5