(C) The battle of Talikota proved disastrous for Vijayanagara empire: This statement is correct. The Battle of Talikota in 1565 CE was a major turning point that led to the decline of the Vijayanagara Empire. The defeat at this battle severely weakened the kingdom.
(A) This empire was founded by the rulers of Saluva dynasty: This is incorrect as the Vijayanagara Empire was founded by Harihara I and Bukka I, who were from the Sangama dynasty.
(B) This empire became powerful after the death of Krishnadeva Raya: This is incorrect as the empire reached its peak of power and prosperity during the rule of Krishnadeva Raya. His death marked the start of its decline.
(D) Their land revenue system was taken from Mansabdari system: The Vijayanagara empire had a unique revenue system different from the Mansabdari system used by the Mughals.
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 \(P,O,Q\).