Step 1: Understanding Inner and Outer Orbital Complexes. Inner orbital complexes involve the use of \( d \)-orbitals from the inner shell (typically the \( 3d \)-orbitals in transition metals). This type of hybridization leads to low-spin complexes, where ligands coordinate using these inner \( d \)-orbitals.
Outer orbital complexes involve the use of \( d \)-orbitals from the outer shell (typically \( 4d \)-orbitals for transition metals in higher oxidation states). This type of hybridization leads to high-spin complexes, where ligands coordinate using these outer \( d \)-orbitals.
Step 2: Identifying the Hybridization in \( [Co(NH_3)_6]^{3+ \).} Cobalt in the \( +3 \) oxidation state has an electronic configuration of \( 3d^6 \), and the complex \( [Co(NH_3)_6]^{3+} \) uses inner \( 3d \)-orbitals for bonding with the ligands. The \( 3d^2sp^3 \) hybridization results in an inner orbital complex.
Step 3: Identifying the Hybridization in \( [Ni(NH_3)_6]^{2+ \).} Nickel in the \( +2 \) oxidation state has an electronic configuration of \( 3d^8 \), and the complex \( [Ni(NH_3)_6]^{2+} \) uses outer \( 4d \)-orbitals for bonding. The \( sp^3d^2 \) hybridization results in an outer orbital complex. Thus, \( [Co(NH_3)_6]^{3+} \) is an inner orbital complex, while \( [Ni(NH_3)_6]^{2+} \) is an outer orbital complex.
Among SO₃, NF₃, NH₃, XeF₂, CIF$_3$, and SF₆, the hybridization of the molecule with non-zero dipole moment and one or more lone-pairs of electrons on the central atom is:
Given below are two statements: 
Statement (II): Structure III is most stable, as the orbitals having the lone pairs are axial, where the $ \ell p - \beta p $ repulsion is minimum. In light of the above statements, choose the most appropriate answer from the options given below:
Match list-I with list-II and choose the correct option.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).