Give explanation for each of the following observations:
(a) Mn3+ is an oxidizing agent, whereas Cr2+ is a reducing agent (both d4 configuration).
(b) Actinoid contraction is greater than lanthanoid contraction.
(c) Transition metals form interstitial compounds with H, B, C, N.
(a) Mn3+ is an oxidizing agent, whereas Cr2+ is a reducing agent (both d4 configuration).
Mn3+ readily gains an electron to become the more stable Mn2+, hence acts as an oxidizing agent. Cr2+ loses an electron to form Cr3+, which is more stable due to half-filled t2g orbitals (d3), thus acts as a reducing agent.
(b) Actinoid contraction is greater than lanthanoid contraction.
Actinoids have 5f orbitals that are more diffused and poorly shielded compared to 4f orbitals in lanthanoids. This leads to a greater effective nuclear charge and stronger contraction across the series.
(c) Transition metals form interstitial compounds with H, B, C, N.
Transition metals have vacant d-orbitals and lattice voids where small atoms like H, B, C, N can fit without disturbing the structure, forming interstitial compounds which are hard and have high melting points.
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 \(P,O,Q\).