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(D) Manganate ion: $MnO_4^{2-}$; Permanganate ion: $MnO_4^-$.$(A)$ Both $MnO_4^{2-}$ and $MnO_4^-$ have tetrahedral geometry due to $d^3s$ hybridizati

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$(A)$ and $(D)$ Only

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(D) Manganate ion: $MnO_4^{2-}$; Permanganate ion: $MnO_4^-$.$(A)$ Both $MnO_4^{2-}$ and $MnO_4^-$ have tetrahedral geometry due to $d^3s$ hybridization of $Mn$. This statement is correct.$(B)$ In $MnO_4^{2-}$, $Mn$ is in $+6$ oxidation state. In $MnO_4^-$, $Mn$ is in $+7$ oxidation state. The statement says $+7$ and $+6$ respectively, which is incorrect.$(C)$ Oxidation of $Mn^{2+}$ by peroxodisulphate $(S_2O_8^{2-})$ yields permanganate $(MnO_4^-)$, not manganate. This statement is incorrect.$(D)$ $MnO_4^{2-}$ ($d^1$ configuration) is paramagnetic. $MnO_4^-$ ($d^0$ configuration) is diamagnetic. This statement is correct.$(E)$ Acidified permanganate acts as an oxidizing agent, not a reducing agent. It oxidizes oxalate, nitrite, and iodide ions. This statement is incorrect.Therefore, only statements $(A)$ and $(D)$ are correct.

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