(a) (i) $\mathrm{Cr}_2\mathrm{O}_7^{2-} + 2\mathrm{OH}^- ightarrow 2\mathrm{CrO}_4^{2-}$ $+ \mathrm{H}_2\mathrm{O}$(ii) $\mathrm{MnO}_4^{-} + 4\mathrm{H}^+ + 3e^- ightarrow \mathrm{MnO}_2$ $+ 2\mathrm{H}_2\mathrm{O}$(b) (i) The transition metals are compounds that form at least 1 stable ion, where the compound has an incomplete $d$ subshell. $\mathrm{Zn}$ is not a transition metal because it forms only ions with all the $3d$ electrons present.(ii) Transition metal shows a variable oxidation state, so they form a large number of complexes.(iii) It is because $\mathrm{Mn}^{2+}$ is more stable than $\mathrm{Mn}^{3+}$ due to stable half filled $3d^5$ configuration, whereas $\mathrm{Cr}^{3+} (t_{2g}) (3d^5)$ are more stable than $\mathrm{Cr}^{2+}$.OR (i) The differences between lanthanoids and actinoids with respect to their structural variability and chemical reactivity are as follows: (a) Actinoids are radioactive, while lanthanoids are not radioactive. (b) The ionisation enthalpies of the early actinoids are lower than those of the early lanthanoids. Actinoids show the oxidation state from +3 (most common) to +7 , while lanthanoids show the oxidation state from +3 up to +7 . (c) Actinoids are more reactive and have more complex magnetic properties than lanthanoids. (ii) Cerium is a lanthanide element that is known to exhibit the oxidation state of 4 (iii) The complete equation is as follows: $\mathrm{MnO}^{4-} + 8\mathrm{H}^+ + 5e^- ightarrow \mathrm{Mn}^{2+}$ $+ 4\mathrm{H}_2\mathrm{O}$(iv) $\mathrm{Mn}^{2+}$ is more paramagnetic because it has more number of unpaired electrons than $\mathrm{Cr}^{3+}$.