Answer the following questions:
Name two elements of 3d series for which the third ionisation enthalpies are quite high.
Out of KMnO$_4$ and K$_2$MnO$_4$, which one is paramagnetic and why?
Write any one consequence of lanthanoid contraction.
How do you prepare potassium manganate from pyrolusite ore?
Why is the ability of oxygen more than fluorine to stabilise higher oxidation states of transition metals?
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 \(P,O,Q\).