
The total number of shares offered to the public for subscription are:
The total number of shares offered to the public is called the issued share capital.
As per the Notes to Accounts, the issued capital is 75,000 equity shares of \(rupee\) 100 each.
It doesn’t matter how many of those were subscribed or paid-up — the issued figure is what was offered.
Hence, the correct answer is 75,000 shares.
The amount of unissued share capital of the company is:
₹ 25,00,000
₹29,00,000
₹29,60,000
₹20,32,000
Unissued Capital = Authorised Capital – Issued Capital
\[ \text{Unissued Capital} = ₹1,00,00,000 - ₹75,00,000 = ₹25,00,000 \]
The subscribed capital of the company is:
₹71,80,000
₹71,00,000
₹80,00,000
₹1,00,00,000
\[ ₹71,00,000 + ₹1,00,000 = ₹71,80,000 \]
The registered capital of the company is:
₹71,80,000
₹80,00,000
₹1,00,00,000
₹71,00,000
Registered Capital is another name for Authorised Capital.
From the Notes to Accounts:
\[ \text{Authorised Capital} = 1,00,000 \text{ shares} \times ₹100 = ₹1,00,00,000 \]
The amount per share not received on the shares shown under ‘subscribed but not fully paid up capital’ is:
₹100
₹20
₹1,000
₹80
Total unpaid amount = ₹20,000
Number of shares not fully paid = 1,000 shares
\[ \frac{₹20,000}{1,000} = ₹20 \text{ per share unpaid} \]
If the shares shown under ‘subscribed but not fully paid up capital’ are forfeited, ‘Share Forfeiture Account’ will appear at:
₹20,000
₹80,000
₹1,00,000
₹71,00,000
On forfeiture:
Share Capital A/c is debited with the face value: \[ 1,000 \times ₹100 = ₹1,00,000 \]
Calls in Arrears = ₹20,000 (amount not received)
Share Forfeiture A/c = ₹80,000 (amount already received)
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 \(P,O,Q\).