$[{Fe}({NH}_3)_6]^{3+}$
Step 1: Inner orbital complexes use low-spin configurations with $d^2sp^3$ hybridization, whereas outer orbital complexes use high-spin configurations with $sp^3d^2$ hybridization.
Step 2: Fluoride ($F^-$) is a weak field ligand and does not cause strong crystal field splitting. As a result, cobalt in $[{CoF}_6]^{3-}$ adopts an outer orbital configuration with $sp^3d^2$ hybridization.
Step 3: The other complexes:
$[{Co}({NH}_3)_6]^{3+}$ and $[{Fe}({CN})_6]^{3-}$ involve strong field ligands, leading to inner orbital configurations.
$[{Co}({C}_2{O}_4)_3]^{3-}$ also forms an inner orbital complex.
Step 4: Since $[{CoF}_6]^{3-}$ is an outer orbital complex, the correct answer is (C).
In the complex ion Fe(C2O4)3 the Co-ordination number of Fe is
Let \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\tan^2 x}{1+5^x} \, dx \). Then: