Step 1: Functions of the lac operon genes.
- 'i' gene: Produces the repressor protein (iii).
- 'z' gene: Produces $\beta$-galactosidase (i), which breaks down lactose.
- 'a' gene: Produces transacetylase (iv).
- 'y' gene: Produces lac permease (ii), which facilitates lactose entry into the cell.
| List I | List II | ||
|---|---|---|---|
| A | Two or more alternative forms of a gene | I | Back cross |
| B | Cross of F1 progeny with homozygous recessive parent | II | Ploidy |
| C | Cross of F progeny with any of the parents | III | Allele |
| D | Number of chromosome sets in plant | IV | Test cross |
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 \(P,O,Q\).