The Government of India, in the initial years of economic development, emphasized on a greater role of the public sector in the industrial development.
Justify the statement, giving reasons in support of your answer.
In the early years after independence, India adopted a socialist pattern of economy to address socio-economic inequalities and promote rapid industrialization.
The Industrial Policy Resolutions of 1948 and 1956 emphasized the dominant role of the public sector to: Ensure equitable resource distribution: Public sector investment ensured equitable growth across sectors and regions.
Build basic and strategic industries: Industries such as defense, atomic energy, and heavy machinery required large-scale investments, which the private sector could not provide.
Regulate private monopolies: A dominant public sector minimized the risk of exploitative practices by private enterprises.
Self-reliance: Public sector development helped reduce dependence on foreign imports, laying the foundation for economic self-sufficiency.
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 \(P,O,Q\).