Match Column-I with Column-II and choose the correct option from the following:
| Column-I (Harappan Sites) | Column-II (Present region) |
|---|---|
| I. Manda | a. Gujarat |
| II. Rakhigarhi | b. Rajasthan |
| III. Nageshwar | c. Haryana |
| IV. Kalibangan | d. Jammu |
I. Manda - d. Jammu: Manda is an Indus Valley Civilization site, located in the state of Jammu and Kashmir. It is known for being the northernmost site of this civilization.
II. Rakhigarhi - c. Haryana: Rakhigarhi is one of the largest Harappan sites located in the state of Haryana. It is known for its complex urban planning and large size.
III. Nageshwar - a. Gujarat: Nageshwar is a Harappan site located near the coast of Gujarat and is known for its shell working industry, which highlights the importance of coastal trade.
IV. Kalibangan - b. Rajasthan: Kalibangan is another significant site, located in the state of Rajasthan, known for its fire altars and a ploughed field that demonstrate the agricultural practices of the Indus Valley Civilization.
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 \(P,O,Q\).