Match the following:
| List–I | List–II |
|---|---|
| A. Ball and socket joint | I. Inter carpal joint |
| B. Hinge joint | II. Between humerus and Pectoral girdle |
| C. Pivot joint | III. Between carpals and metacarpals |
| D. Gliding joint | IV. Between atlas and axis |
| V. Knee joint |
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 \(P,O,Q\).