Balance the following equations by the oxidation number method:
$(a) Fe^{+2} + H^{+} + Cr_2O_7^{-2} \to Cr^{+3} + Fe^{+3} + H_2O$
$(b) I_2 + NO_3^- \to NO_2 + IO_3^-$
$(c) I_2 + S_2O_3^{-2} \to I^{-} + S_4O_6^{-2}$
$(d) MnO_4^- + C_2O_4^{-2} \to Mn^{+2} + CO_2$
$(a) Fe^{+2} + H^{+} + Cr_2O_7^{-2} \to Cr^{+3} + Fe^{+3} + H_2O$
$(b) I_2 + NO_3^- \to NO_2 + IO_3^-$
$(c) I_2 + S_2O_3^{-2} \to I^{-} + S_4O_6^{-2}$
$(d) MnO_4^- + C_2O_4^{-2} \to Mn^{+2} + CO_2$
(A) $(a) 6 Fe^{+2} + 14 H^{+} + Cr_2O_7^{-2} \to 2 Cr^{+3} + 6 Fe^{+3} + 7 H_2O$
$(b) I_2 + 10 NO_3^- + 8 H^{+} \to 10 NO_2 + 2 IO_3^- + 4 H_2O$
$(c) I_2 + 2 S_2O_3^{-2} \to 2 I^{-} + S_4O_6^{-2}$
$(d) 2 MnO_4^- + 16 H^{+} + 5 C_2O_4^{-2} \to 2 Mn^{+2} + 10 CO_2 + 8 H_2O$
$(b) I_2 + 10 NO_3^- + 8 H^{+} \to 10 NO_2 + 2 IO_3^- + 4 H_2O$
$(c) I_2 + 2 S_2O_3^{-2} \to 2 I^{-} + S_4O_6^{-2}$
$(d) 2 MnO_4^- + 16 H^{+} + 5 C_2O_4^{-2} \to 2 Mn^{+2} + 10 CO_2 + 8 H_2O$
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