To solve this problem, we need to identify the ion that exhibits both d-d transition and paramagnetism.$\newline$Let's analyze each option:$\newline$• Option 1: $MnO_4^- \newline$ - In $MnO_4^-,$ manganese is in the +7 oxidation state.$\newline$ - The electronic configuration of Mn in this state is $[Ar] 3d^0. \newline$ - Since there are no d-electrons, d-d transitions are not possible, and it is diamagnetic.$\newline$• Option 2: $Cr_2O_7^{2-} \newline$ - In $Cr_2O_7^{2-},$ chromium is in the +6 oxidation state.$\newline$ - The electronic configuration of Cr in this state is $[Ar] 3d^0. \newline$ - Similar to MnO_4^-, there are no d-electrons, so no d-d transitions, and it is diamagnetic.$\newline$• Option 3: $CrO_4^{2-} \newline$ - In $CrO_4^{2-},$ chromium is also in the +6 oxidation state.$\newline$ - The electronic configuration is $[Ar] 3d^0,$ so no d-d transitions, and it is diamagnetic.$\newline$• Option 4: $MnO_4^{2+} \newline$ - In $MnO_4^{2+},$ manganese is in the +6 oxidation state.$\newline$ - The electronic configuration of Mn in this state is $[Ar] 3d^1. \newline$ - With one d-electron, d-d transitions are possible, and it is paramagnetic due to the unpaired electron.$\newline$Therefore, the correct option is Option 4, as $MnO_4^{2+}$ exhibits both d-d transition and paramagnetism.