(a) (i) ${\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}+2{\mathrm{OH}}^{-}\mathit{─}\mathit{─}\mathit{─}\mathit{─}▸2{\mathrm{CrO}}_4^{2-}$ $+{\mathrm{H}}_2\mathrm{O}$
(ii) ${\mathrm{MnO}}_4^{-}+4{\mathrm{H}}^{+}+3{\mathrm{e}}^{-}\mathit{─}\mathit{─}\mathit{─}\mathit{─}▸{\mathrm{MnO}}_2$ $+2{\mathrm{H}}_2\mathrm{O}$
(b) (i) The transition metals are compounds that form at least 1 stable ion, where the compound has an incomplete $\mathit{d}$ subshell. $\mathrm{Zn}$ is not a transition metal because it forms only ions with all the $3\mathit{d}$ 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 $3{\mathit{d}}^5$ configuration, whereas ${\mathrm{Cr}}^{3+}\left({\mathit{t}}_{2\mathit{g}}\right)\left(3{\mathit{d}}^5\right)$ 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:
${\mathrm{MnO}}^{4-}+8{\mathrm{H}}^{+}+5{\mathrm{e}}^{-}\mathit{─}\mathit{─}\mathit{─}\mathit{─}▸{\mathrm{Mn}}^{2+}$ $+4{\mathrm{H}}_2\mathrm{O}$
(iv) ${\mathrm{Mn}}^{2+}$ is more paramagnetic because it has more number of unpaired electrons than ${\mathrm{Cr}}^{3+}$.