Give Reasons:
(I) \( \text{Ce}^{4+} \) in aqueous solution is a good oxidising agent.
(II) The actinoid contraction is greater from element to element than lanthanoid contraction.
(III) \( E^\circ_{\text{M}^{2+}/\text{M}} \) value is more negative than expected, whereas \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \) is positive.
(I) \( \text{Ce}^{4+} \) in aqueous solution is a good oxidising agent.
Reason: \( \text{Ce}^{4+} \) is a strong oxidising agent because it has a high tendency to accept an electron and reduce to \( \text{Ce}^{3+} \). The high charge on \( \text{Ce}^{4+} \) (a +4 oxidation state) and the relatively small ionic radius of \( \text{Ce}^{4+} \) compared to its reduced form \( \text{Ce}^{3+} \) give it a high electron affinity, making it an effective oxidant in aqueous solutions.
(II) The actinoid contraction is greater from element to element than lanthanoid contraction.
Reason: The actinoid contraction is greater than the lanthanoid contraction because the 5f-electrons in actinides experience poor shielding by other f-electrons, resulting in a greater increase in effective nuclear charge as the atomic number increases. In contrast, lanthanides with 4f-electrons experience better shielding; therefore, the contraction is less significant. This explains why the atomic sizes in the actinide series decrease more significantly across the series than in the lanthanide series.
(III) \( E^\circ_{\text{M}^{2+}/\text{M}} \) value is more negative than expected, whereas \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \) is positive.
Reason: The \( E^\circ_{\text{M}^{2+}/\text{M}} \) value is more negative than expected due to the large increase in ionization energy as we remove electrons from the second ionization state, leading to a stronger pull by the nucleus. On the other hand, \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \) is positive because copper has a stable electronic configuration with a filled 3d10 subshell, making it more resistant to oxidation and thus having a positive electrode potential. Copper, being a transition metal, has a more favorable reduction potential than other elements like iron, leading to a positive standard electrode potential for the Cu2+/Cu system.
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 \(P,O,Q\).