Uma and Umesh were partners in a firm sharing profits and losses in the ratio of 2:3. On 31st March, 2024, their Balance Sheet was given. Daya was admitted with 2:3:5 profit sharing ratio, bringing in capital and goodwill. Various revaluations and adjustments were also made. Journalise the transactions related to Daya’s admission.
Journal Entries in the Books of Uma, Umesh and Daya
1. Bank A/c Dr. ₹12,00,000 To Daya's Capital A/c ₹10,00,000 To Premium for Goodwill A/c ₹2,00,000 (Being capital and goodwill brought in by Daya)
2. Premium for Goodwill A/c Dr. ₹2,00,000 To Uma’s Capital A/c ₹80,000 To Umesh’s Capital A/c ₹1,20,000 (Being goodwill distributed in sacrificing ratio of 2:3)
3. Land and Building A/c Dr. ₹2,00,000 To Revaluation A/c ₹2,00,000 (Being increase in value of Land and Building)
4. Revaluation A/c Dr. ₹10,000 To Furniture A/c ₹10,000 (Being depreciation of furniture @ 10% on ₹1,00,000)
5. Provision for Doubtful Debts A/c Dr. ₹5,000 Bad Debts A/c Dr. ₹3,000 To Debtors A/c ₹8,000 (Being ₹3,000 bad debts written off and old provision removed)
6. Revaluation A/c Dr. ₹4,000 To Provision for Doubtful Debts A/c ₹4,000 (Being new provision created @ 5% of ₹80,000)
7. Revaluation A/c Dr. ₹1,86,000 To Uma’s Capital A/c ₹74,400 To Umesh’s Capital A/c ₹1,11,600 (Being profit on revaluation distributed in old ratio 2:3)
8. General Reserve A/c Dr. ₹75,000 To Uma’s Capital A/c ₹30,000 To Umesh’s Capital A/c ₹45,000 (Being distribution of general reserve in 2:3)
9. Workmen Compensation Fund A/c Dr. ₹25,000 To Uma’s Capital A/c ₹10,000 To Umesh’s Capital A/c ₹15,000 (Being distribution of Workmen Compensation Fund)
10. Outstanding Electricity Bill A/c Dr. ₹10,000 To Bank A/c ₹10,000 (Being payment of outstanding electricity bill)

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 \(P,O,Q\).