| Date | Particulars | Dr. (₹) | Cr. (₹) |
|---|---|---|---|
| 1st April, 2023 | Bank A/c Dr. To 9% Debentures A/c To Securities Premium A/c (Being 20,000 9% debentures issued at 5% premium) | ₹21,00,000 | ₹20,00,000 ₹1,00,000 |
| 30th Sept, 2023 | Interest on Debentures A/c Dr. To Debentureholders A/c (Being half-yearly interest due on 20,000 debentures @ 9%) | ₹90,000 | ₹90,000 |
| 30th Sept, 2023 | Debentureholders A/c Dr. To Bank A/c (Being payment of half-yearly interest) | ₹90,000 | ₹90,000 |
| 31st March, 2024 | Interest on Debentures A/c Dr. To Debentureholders A/c (Being interest due for second half-year) | ₹90,000 | ₹90,000 |
| 31st March, 2024 | Debentureholders A/c Dr. To Bank A/c (Being interest paid for second half-year) | ₹90,000 | ₹90,000 |
| 31st March, 2024 | Profit and Loss A/c Dr. To Interest on Debentures A/c (Being total interest expense transferred to P&L) | ₹1,80,000 | ₹1,80,000 |
Note: Interest is paid half-yearly, hence twice ₹90,000 is due and paid.
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 \(P,O,Q\).