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) Delhi: Delhi was an important site of the 1857 revolt, and was the capital of the Mughal Empire. It is located on the banks of the river Yamuna. You should label the location marked as A in the map as Delhi.
(B) Calcutta: Calcutta, also known as Kolkata, was a major center of British power, and an important place in 1857 revolt. You should label the location marked as B as Calcutta in the map.
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
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 \(P,O,Q\).