Name the members of the lanthanoid series which exhibit +4 oxidation state and those which exhibit +2 oxidation state. Try to correlate this type of behavior with the electronic configurations of these elements.
The lanthanides that exhibit +2 and +4 states are shown in the given table. The atomic numbers of the elements are given in the parenthesis.
| +2 | +4 |
| Nd(60) | Ce(58) |
| Sm(62) | Pr(59) |
| Eu(63) | Nd(60) |
| Tm(69) | Tb(65) |
| Yb(70) | Dy(66) |
Ce after forming Ce4+ attains a stable electronic configuration of [Xe].
Tb after forming Tb4+ attains a stable electronic configuration of [Xe] 4f7.
Eu after forming Eu2+ attains a stable electronic configuration of [Xe] 4f7.
Yb after forming Yb2+ attains a stable electronic configuration of [Xe] 4f14.
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 \(P,O,Q\).

Lanthanoids are at the top of these two-row, while actinoids are at the bottom row.
Lanthanoids are inclusive of 14 elements, with atomic numbers 58-71:
These elements are also called rare earth elements. They are found naturally on the earth, and they're all radioactively stable except promethium, which is radioactive. A trend is one of the interesting properties of the lanthanoid elements, called lanthanide contraction.