On the given political outline map of India, locate and label the following with appropriate signs:
(i) Amravati – Buddhist site
(ii) Varanasi – Ancient city
(iii) (a) Vijayanagara – An Empire of 14th century
OR
(iii) (b) Orissa – Territory of 14th century
(i) Amravati - Buddhist Site: Amravati, a major Buddhist site in Andhra Pradesh, is located in the Guntur district. You should mark it in the map in the central Andhra Pradesh.
(ii) Varanasi - Ancient City: Varanasi, also known as Benaras, is one of the oldest living cities of the world. It is located in Uttar Pradesh, along the banks of the Ganges. You should mark it on the map in the Eastern part of Uttar Pradesh.
(iii)(a) Vijayanagara - An Empire of 14th Century: Vijayanagara was a major empire in South India during the 14th to 16th centuries, with its capital in Hampi (present day Karnataka), and it is located in south-central Karnataka.
OR
(b) Orissa - Territory of 14th century: Orissa, is located in Eastern India along the coast of Bay of Bengal. You can mark this area along the coast of modern day Odisha.
On the same political outline map of India, two places related with the centres of revolt of 1857 one marked as A and B. Identify them and write their names on the lines marked near them.
(A) Delhi
(B) Calcutta
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 \(P,O,Q\).