Almost all of us have some role model in our lives. We wish to follow her/him as she/he act as a continuous source of inspiration for us. Write a personality profile of the person who has become a role model for you and has greatly inspired you (200-250 words).
You have been invited to attend the wedding of your friend's sister next week. Respond to the invitation, regretting your inability to accept the invitation. Give a suitable reason (40-50 words).
The roads in your area in a very bad shape. Write a letter to the Editor of English daily highlighting the problem of the dilapidated roads in your area and asking the concerned authorities to improve these roads as soon as possible (120-150 words).
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 \(P,O,Q\).