Correct option is (1) Both Statement I and Statement II are true
In \( [Co(NH_3)6]3+, Co^3\)
Electronic configuration of \(Co^{3+} :\)

In presence of \(NH_3\) ligand, pairing of electrons takes place and it becomes diamagnetic complex ion. In presence of \(NH_3\) ligand :

\(\therefore \) \([Co (NH_3)_6]^{3+} \) is octahedral with \(d^2sp^3\) hybridisation and it is diamagnetic in nature.
In case of \([CoF_6]^{3-}\), Co is in +3 oxidation state and it is having \(3d^6\) configuration. In presence of weak field \(F ^-\) ligand, pairing does not take place.
In presence of \(F^-\) ligands :

\(\therefore\) In \([CoF_6]^{3-},\) \(Co ^{3+}\) is \(sp^3 d^2\) hybridised with four unpaired electrons, so it is paramagnetic in nature.