AIDS (Acquired Immuno Deficiency Syndrome) is caused by the Human immunodeficiency virus (HIV) via sexual or blood-blood contact. After entering the human body the HIV virus attacks and enters the macrophages. Inside the macrophages the RNA of the virus replicates with the help of enzyme reverse transcriptase and gives rise to viral DNA. Then this viral DNA incorporates into the host DNA and directs the synthesis of virus particles. At the same time HIV enters helper T-lymphocytes. It replicates and produces viral progeny there. These newly formed progeny viruses get released into the blood attacking other healthy helper T- lymphocytes in the body. As a result the number of T-lymphocytes in the body of an infected person decreases progressively thereby decreasing the immunity of a person.

Study the chemical structure of an addictive drug shown below and answer the questions that follow.
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 \(P,O,Q\).
HIV is a virus that attacks cells that help the body to fight infection and making a person more vulnerable to other infections and diseases. It is spread by contact with certain bodily fluids of a person with HIV. It is most commonly during the unprotected sex or when share injection or drugs equipment.
It is the late stage of HIV infection that occurs when the body’s immune system is badly damaged because of the virus.