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(B) $(1)$ Manganese $(Mn)$ has the electronic configuration $[Ar] 3d^5 4s^2$ and can exhibit oxidation states up to $+7$ (e.g.,in $KMnO_4$). This stat

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$(1)$ and $(5)$

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(B) $(1)$ Manganese $(Mn)$ has the electronic configuration $[Ar] 3d^5 4s^2$ and can exhibit oxidation states up to $+7$ (e.g.,in $KMnO_4$). This statement is correct.$(2)$ Zinc $(Zn)$ has a completely filled $3d^{10}$ configuration,so it cannot form colored ions. This statement is incorrect.$(3)$ In $[CoF_6]^{3-}$,$Co$ is in the $+3$ oxidation state $(3d^6)$. $F^-$ is a weak field ligand,so it does not cause pairing of electrons. Thus,it has $4$ unpaired electrons and is paramagnetic. This statement is incorrect.$(4)$ Scandium $(Sc)$ has the configuration $[Ar] 3d^1 4s^2$ and exhibits only a $+3$ oxidation state. It cannot exhibit a $+4$ state. This statement is incorrect.$(5)$ Zinc $(Zn)$ has the configuration $[Ar] 3d^{10} 4s^2$ and exhibits only a $+2$ oxidation state due to the loss of $4s$ electrons. This statement is correct.Therefore,statements $(1)$ and $(5)$ are correct.

Which of the following statements are correct? $(1)$ Manganese can exhibit a $+7$ oxidation state. $(2)$ Zinc forms colored ions. $(3)$ $[CoF_6]^{3-}$ is diamagnetic. $(4)$ $Sc$ can exhibit a $+4$ oxidation state. $(5)$ $Zn$ exhibits only a $+2$ oxidation state.

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