For the complex \([Ni(CO)_4]\), nickel is in the +0 oxidation state. The electronic configuration of Ni is \( 3d^8 4s^2 \). - Hybridization: In \([Ni(CO)_4]\), the CO ligands are strong field ligands that cause the pairing of the 3d electrons, resulting in the hybridization \( sp^3 \). The geometry of the complex is tetrahedral.
- Magnetic character: Since all electrons are paired in the complex, it is diamagnetic.
Explanation:
- In the presence of CO, which is a strong field ligand, the 3d electrons are paired, leading to a tetrahedral geometry with \( sp^3 \) hybridization and no unpaired electrons, thus the complex is diamagnetic.
(i) Draw the diagram which indicates the splitting of d-orbitals in tetrahedral field.
(ii) Write any one limitation of valence bond theory.
(i)[Ni(CN)₄]²⁻ and [Ni(CO)(_4)] have different structures, but do not differ in their magnetic behaviour. Explain.
(ii) Write the formula of Tetraamineaquachloridocobalt(III)chloride.
(i) Write two postulates of Werner's coordination theory.
(ii) Draw the geometrical isomers of [(NH_3)_3(NO_2)_3] and give their structures.
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 \(P,O,Q\).