(i) Providing Managers with Useful Insights into Reality
- Principles of management provide valuable insights by helping managers learn from past mistakes and solve recurring problems quickly.
- Adherence to these principles enhances managerial knowledge, ability, and understanding of complex business situations.
- This leads to better decision-making and efficient problem-solving in organizations.
(ii) Scientific Decisions
- Management principles ensure that decisions are made scientifically rather than arbitrarily.
- Decisions based on these principles are free from bias and rely on objective assessment of business situations.
- This enhances accuracy, consistency, and effectiveness in managerial decision-making.
(iii) Fulfilling Social Responsibility
- Modern businesses operate in an environment where public awareness and expectations regarding corporate social responsibility are high.
- Principles of management emphasize ethical practices and social responsibility, ensuring businesses contribute to societal well-being.
- Management theories continue to evolve in response to social and environmental demands.
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 \(P,O,Q\).