On $31^{\text {st }}$ March, 2024, following is the Balance Sheet of Bhavik Limited :
Bhavik Ltd.
Balance Sheet as at $31^{\text {st }}$ March 2024
I. Equity and Liabilities :
| Particulars | Note No. | $31-3-2024$ (₹) | $31-3-2023$ (₹) |
| 1. Shareholders funds | |||
| (a) Share Capital | 12,00,000 | 10,00,000 | |
| (b) Reserves and Surplus | 1 | 4,00,000 | 3,00,000 |
| 2. Non-current liabilities | |||
| Long-term borrowings | 2 | 6,00,000 | 10,00,000 |
| 3. Current Liabilities | 5,00,000 | 1,00,000 | |
| (a) Trade Payables | 3 | 3,00,000 | 4,00,000 |
| (b) Short-term provisions | |||
| Total | 30,00,000 | 28,00,000 |
II. Assets :
| 1. Non-current Assets | |||
| (a) Property, Plant and Equipment and Intangible Assets | |||
| Property plant and equipment | 4 | 19,00,000 | 15,00,000 |
| (b) Non-current Investments | 3,00,000 | 4,00,000 | |
| 2. Current Assets | |||
| (a) Inventories | 4,50,000 | 3,50,000 | |
| (b) Trade Receivables | 2,50,000 | 4,50,000 | |
| (c) Cash and Cash Equivalents | 1,00,000 | 1,00,000 | |
| Total | 30,00,000 | 28,00,000 |
Notes to Accounts :
| Note | Particulars | $31-3-2024$ (₹) | $31-3-2023$ (₹) |
| No. | |||
| 1. | Reserves and Surplus i.e. Balance in Statement of Profit and Loss | 4,00,000 | 3,00,000 |
| 2. | Long-term borrowings | ||
| 10% Debentures | 6,00,000 | 10,00,000 | |
| 3. | Short-term provisions | ||
| Provision for tax | 3,00,000 | 4,00,000 | |
| 4. | Property plant and equipment | ||
| Plant and Machinery | 21,50,000 | 16,00,000 | |
| Less : Accumulated Depreciation | 2,50,000 | 1,00,000 | |
| 19,00,000 | 15,00,000 |
Additional Information :
Calculate :
Let's calculate the cash flows from investing and financing activities.
Write the main head and subhead of following items : (i) Creditors
(ii) Patent
(iii) Stock
Match List-I with List-II:
\[\begin{array}{|c|c|} \hline \text{List-I} & \text{List-II} \\ \hline \text{(A) Reserves and Surplus} & \text{(I) Share Options Outstanding Account} \\ \hline \text{(B) Non-current Liabilities} & \text{(II) Long-term provisions} \\ \hline \text{(C) Current Liabilities} & \text{(III) Short-term borrowing} \\ \hline \text{(D) Shareholder's Fund} & \text{(IV) Calls in arrear} \\ \hline \end{array}\]
Choose the correct answer from the options given below:
Star and Moon were partners in a firm sharing profits in the ratio of 3 : 2. On 31st March, 2024 the Balance Sheet of the firm was as follows: 
They admitted Sun into partnership on 1st April, 2024 for 1/10 share. It was agreed as follows:
Sun brings ₹6,00,000 as capital but could not bring goodwill in cash.
Goodwill is valued at ₹4,00,000.
Provision on debtors is required @10%.
Interest on Bank Loan for 6 months is due @12% p.a.
Liability to workers is ₹15,000 against Workmen Compensation Reserve.
Unrecorded stock of ₹40,000 is taken by Star at ₹38,000.
Prepare Revaluation Account and Partners’ Capital Accounts.
Debtors appearing in the Balance Sheet of a firm were as follows: 
On dissolution of firm, bad debts were ₹40,000 and the remaining debtors were realised at 5% discount. How much amount was realised from Debtors?
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 \(P,O,Q\).