During the Mughal era, the village Panchayat served as an important local institution responsible for administering justice, managing community affairs, and representing the concerns of the rural population.
The Panchayat was typically composed of respected elders from the village community, including the muqaddam (village headman) and the patwari (village record keeper). It settled disputes related to land, caste issues, thefts, and domestic conflicts.
The Panchayat acted as a collective voice for the villagers, especially in dealings with local officials such as revenue collectors (zamindars) or Mughal amils. It often resisted unjust taxes or exploitation.
Panchayats upheld village customs, regulated water usage, land sharing, and forest access. This role ensured that the customary rights of peasants were protected against encroachment.
During famines, invasions, or revenue failure, Panchayats negotiated relief, organized community resources, and appealed to authorities for help. They acted as mediators between the state and rural society.
Thus, Panchayats during the Mughal era were more than just judicial bodies—they were vital grassroots institutions that advocated for and protected the rights and interests of common people in rural India.
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 \(P,O,Q\).