At room temperature, the energy band gap of different materials have been listed in the table below. Correctly match the energy band gap (List-I) with the corresponding material (List-II).
| LIST-I (Energy band gap) | LIST-II (Material) |
|---|---|
| A. \( E_g = 0.67 \) eV | I. Polymer |
| B. \( E_g = 1.1 \) eV | II. Germanium |
| C. \( E_g = 1.43 \) eV | III. Silicon |
| D. \( E_g > 5 \) eV | IV. Gallium Arsenide |
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 \(P,O,Q\).