When arranging the copper mines of Rajasthan from north to south, the correct order is:
- Khetri (ii), located in the northern part of Rajasthan, is the first.
- Alwar (iv) comes next, located south of Khetri.
- Bhilwara (i) is further south, located in the southern part of the state.
- Udaipur (iii) is located at the southernmost position among the listed cities.
Thus, the correct order is: Khetri (ii), Alwar (iv), Bhilwara (i), and Udaipur (iii).
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 \(P,O,Q\).