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For $$CrO_2Cl_2$$ (Chromyl chloride):
Let the oxidation state of $$Cr$$ be $$x$$.
$$x + 2(\text{O.S. of } O) + 2(\text{O.S. of } Cl) = 0$$
$$x + 2(-2) + 2(-1) = 0$$
$$x - 4 - 2 = 0 \implies x = +6$$
For $$[Cr(CN)_6]^{3-}$$:
Let the oxidation state of $$Cr$$ be $$x$$.
$$x + 6(\text{O.S. of } CN) = -3$$
$$x + 6(-1) = -3$$
$$x - 6 = -3 \implies x = +3$$
For $$Cr_2O_3$$:
Let the oxidation state of $$Cr$$ be $$x$$.
$$2x + 3(\text{O.S. of } O) = 0$$
$$2x + 3(-2) = 0$$
$$2x = 6 \implies x = +3$$
For $$[MnO_4]^-$$ (Permanganate ion):
Let the oxidation state of $$Mn$$ be $$y$$.
$$y + 4(\text{O.S. of } O) = -1$$
$$y + 4(-2) = -1$$
$$y - 8 = -1 \implies y = +7$$
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