To solve the problem, we need to state the fitness index score formula used in the Harvard Step Test and list the standard norms used to interpret the score.
1. Fitness Index Score Formula (Harvard Step Test):
The Harvard Step Test evaluates cardiovascular fitness based on recovery time after exercise. The formula to calculate the Fitness Index (FI) is:
Fitness Index (FI) = \( \frac{\text{Duration of exercise in seconds} \times 100}{2 \times \text{Sum of 3 pulse counts}} \)
Explanation:
2. Norms for Fitness Index Score:
The following standards are used to assess the fitness level:
| Fitness Index Score | Rating |
|---|---|
| Above 96 | Excellent |
| 83 – 96 | Good |
| 68 – 82 | Average |
| Below 68 | Poor |
Final Answer:
The Fitness Index Score for the Harvard Step Test is calculated using the formula:
FI = \( \frac{\text{Exercise Duration (sec)} \times 100}{2 \times \text{Sum of 3 Pulse Counts}} \).
The norms are: Above 96 – Excellent, 83–96 – Good, 68–82 – Average, and Below 68 – Poor.
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 \(P,O,Q\).