| Column I (Pillars of Human Development) | Column II (Characteristics) |
|---|---|
| a. Equity | iv. Equal access of opportunities for everyone |
| b. Sustainability | iii. Each generation must ensure the availability of choices and opportunities to its future generations |
| c. Productivity | i. Providing better health facilities to everyone |
| d. Empowerment | ii. Good governance and people-oriented policies |
The pillars of human development and their correct characteristics are as follows:
Hence, option (B) correctly matches all pairs.
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 \(P,O,Q\).