To solve the problem, we need to explain how community sports events like ‘Run for a Specific Cause’ and ‘Run for Unity’ reflect the social and developmental progress of a country.
1. Run for a Specific Cause:
Definition:
A ‘Run for a Specific Cause’ is a community-driven event where individuals come together to participate in a run aimed at raising awareness or support for a particular social, environmental, or health-related issue.
Key Features:
Importance and Reflection of Progress:
2. Run for Unity:
Definition:
A ‘Run for Unity’ is a mass participation event organized to promote the message of national integration, peace, and communal harmony.
Key Features:
Importance and Reflection of Progress:
Final Answer:
Events like ‘Run for a Specific Cause’ and ‘Run for Unity’ highlight how community sports can unite people for social awareness and national integration. These runs reflect a country’s progress through civic engagement, inclusivity, and the promotion of health and harmony in society.
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 \(P,O,Q\).