Step 1: Assertion (A) is correct as it reflects the widely recognized view that consuming a diet rich in diverse vegetables, fruits, and plant-based foods can lower cancer risk due to beneficial phytochemicals.
Step 2: Reason (R) is also accurate, acknowledging that non-nutritive components like fiber and phytochemicals are part of a healthy diet. However, Reason (R) does not directly explain how these components reduce cancer risk, thus it does not provide a sufficient explanation for Assertion (A).
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 \(P,O,Q\).