(b)
Oxidation state of Mn in ${Mn}^{2 +} = + 2$
Let oxidation state of Mn in ${MnO}_{2} = x$
$\ \therefore$ $x + (2 \times - 2) = 0$
$\ \therefore$ $x =$+4
$(iii)\ \ \ Let\ the\ oxidation\ state\ of\ Mn\ in\ K{MnO}_{4} = x$
$\therefore$ $+ 1 + x + ( - 2 \times 4) = 0$
$\ \ \therefore\ \ \ x = + 7$
(iv) Let oxidation state of Mn in $K_{2}{MnO}_{4} = x$
$\therefore\ \ \ \ ( + 1 \times 2) + x + ( - 2 \times 4) = 0$
$\therefore\ \ \ x = + 6$
$\therefore\ \ \$Increasing order of oxidation states is
$(i) < (ii) < (iv) < (iii)$