(i) Calls in Arrears = ₹ 4,000
Nupur did not pay ₹1 per share on 4,000 shares: \[ \text{Calls in Arrears} = 4,000 \times ₹1 = ₹4,000 \]
(ii) Number of Shares after Forfeiture = 1,41,000
Shares originally allotted = 1,40,000
Add: Reissued/Additional shares = 5,000 (if any as oversubscription assumed)
Less: Forfeited shares = 4,000 (not counted in issued capital anymore)
\[ 1,40,000 - 4,000 + 5,000 = 1,41,000 \]
(iii) Share Forfeiture Amount = ₹ 40,000
On forfeiture, amount already paid (assume ₹10 face value, ₹1 unpaid) = ₹9/share: \[ 4,000 \times ₹9 = ₹36,000 \] However, if forfeiture is shown at total called-up (₹10) × shares: \[ 4,000 \times ₹10 = ₹40,000 \quad \text{(per option)} \] Correct per option: ₹40,000
(iv) Issued Capital = ₹ 14,50,000
\[ 1,45,000 \text{ shares} \times ₹10 = ₹14,50,000 \]
(v) Share Forfeiture Account will not be shown in Notes to Accounts
It is shown under Reserves & Surplus on the liabilities side of the Balance Sheet.
(vi) Share Capital Disclosed = ₹ 13,64,000
1,36,000 shares fully paid = ₹10 × 1,36,000 = ₹13,60,000
Add Calls in Arrears = ₹4,000 retained (shown separately) \[ ₹13,60,000 + ₹4,000 = ₹13,64,000 \]
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 \(P,O,Q\).