(a)
Bromine has zero oxidation state because it is in free state.
_{0}
${Br}_{2} \longrightarrow {BrO}_{3}^{-}$
Let the oxidation number of Br in ${BrO}_{3}^{-}$ is $x$.
$\ \ \ \ \ x + ( - 2 \times 3) = - 1$
$\ \ \ \ x + ( - 6) = \ - 1$
$\ \ \ \ x = + 6 - 1$
$\ \ \ \ x = + 5$
So, oxidation number changes from 0 to +5.