The History of Pataliputra
Each city had a history of its own. Pataliputra, for instance, began as a village known as Pataligrama. Then, in the fifth century BCE, the Magadhan rulers decided to shift their capital from Rajagaha to this settlement and renamed it. By the fourth century BCE, it was the capital of the Mauryan Empire and one of the largest cities in Asia. Subsequently, its importance apparently declined. When the Chinese pilgrim Xuan Zang visited the city in the seventh century CE, he found it in ruins, and with a very small population.
What message did Xuan Zang wish to convey about Pataliputra?
Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
|---|---|---|---|
| (A) | Ziggurat | I. | Sumerians |
| (B) | Assyrian Lamassu | II. | Assyrians |
| (C) | Stele of Hammurabi | III. | Babylonian |
| (D) | Cylinder Seals | IV. | Akkadian |
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 \(P,O,Q\).