\(FeSO_4\) solution mixed with\( (NH_4)_2SO_4 \) solution in\( 1:1\) molar ratio gives the test of \(Fe^{2+}\) ion but \(CuSO_4\) solution mixed with aqueous ammonia in \( 1:4 \) molar ratio does not give the test of \(Cu^{2+}\) ion. Explain why?
\((NH_4)_2SO_4+FeSO_4+6H_2O→FeSO_4.(NH_4)_2SO_4.6H_2O \)
\(Mohr's salt\)
\(CuSO_4+4NH_3+5H_2O→[Cu(NH_3)_4]SO_4.5H_2O\)
\( tetraaminocopper(ii)sulphate\)
Both the compounds i.e.,\(FeSO_4.(NH_4)_2SO_4.6H_2O\) and \( [Cu(NH_3)_4]SO_4.5H_2O \) fall under the category of addition compounds with only one major difference i.e., the former is an example of a double salt, while the latter is a coordination compound. A double salt is an addition compound that is stable in the solid state but that which breaks up into its constituent ions in the dissolved state. These compounds exhibit individual properties of their constituents. For e.g \(FeSO_4.(NH_4)_2SO_4.6H_2O\) breaks into \(Fe^{2+}, NH^{4+}\), and \((SO_4)^{ 2-} \) ions. Hence, it gives a positive test for \(Fe ^{2+}\) ions. A coordination compound is an addition compound which retains its identity in the solid as well as in the dissolved state. However, the individual properties of the constituents are lost. This happens because. \([Cu(NH_3)_4]SO_4.5H_2O\) does not show the test for \(Cu ^{2+}\). The ions present in the solution of \([Cu(NH_3)_4]SO_4.5H_2O\) are \([Cu(NH_3)_4]^{2+}\) and \(SO_4^{2-}\)
(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 \(P,O,Q\).