Given below are two statements:
Statement I: Each electron in $$e_g$$ orbitals destabilizes the orbitals by $$+0.6 \Delta_o$$ and each electron in the $$t_{2g}$$ orbitals stabilizes the orbitals by $$-0.4 \Delta_o$$ in an octahedral field on the basis of crystal field theory.
Statement II: All the d-orbitals of the transition metals have the same energy in their free atomic state but when a complex is formed the ligands destroy the degeneracy of these orbitals on the basis of crystal field theory.
In the light of the above statements, choose the correct answer from the options given below

Statement I: Each electron in $$e_g$$ orbitals destabilizes the orbitals by $$+0.6 \Delta_o$$ and each electron in the $$t_{2g}$$ orbitals stabilizes the orbitals by $$-0.4 \Delta_o$$ in an octahedral field on the basis of crystal field theory.

Correct, 

According to Crystal Field Theory (CFT), in an octahedral compound, the $$d$$ orbitals split into two halves: the lower energy $$t_2g$$ and higher energy $$e_g$$. To maintain the average energy each electron of $$t_2g$$ lowers the energy by $$-0.4 \Delta_o$$ ($$i.e$$ stabilization), while each electron in $$e_g$$ orbitals raises the energy by $$+0.6 \Delta_o$$ ($$i.e$$ destabilization).

This is the basis of Crystal Field Theory (CFT).

Representation 

$$t_{2g}=-0.4\Delta_o$$ 

$$e_g=+0.6\Delta_o$$

Statement II: All the d-orbitals of the transition metals have the same energy in their free atomic state but when a complex is formed the ligands destroy the degeneracy of these orbitals on the basis of crystal field theory.

Correct, 

In a free, isolated transition metal atom or ion, the five $$d$$ orbitals possesses same energy level $$i.e$$ they are "degenarate" . When the complex is formed the negative field of the ligands interact differently with various $$d$$ orbitals which destroys the degeneracy, which leads to splitting in the energy.