From the 6th century BCE onwards, political power in India saw significant shifts. Though birth in the Kshatriya varna was a traditional claim to kingship, actual power often depended on military ability, support, and resources.
This period witnessed the emergence of powerful states like Magadha and Kosala. Leadership in these states was often acquired through conquest and strategic alliances rather than strictly through lineage.
He is believed to have come from a lower caste background but rose to power through military strength and administrative control, challenging the exclusive claim of Kshatriyas.
With the help of Chanakya, Chandragupta overthrew the Nanda dynasty and founded the Mauryan Empire. His rise signifies the importance of strategy and support over birth-based hierarchy.
Texts like the Arthashastra focus on political pragmatism and administrative efficiency rather than varna-based entitlement. This reflects a shift towards merit and resource mobilization as criteria for rulership.
Thus, although Kshatriya birth was idealized in theory, the actual exercise of political power was often determined by practical considerations like support, strategy, and wealth.
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 \(P,O,Q\).