1. Face value of each share = rupee 10 2. Premium on issue = rupee 2 3. Total amount due per share (Face Value + Premium) \[ = rupee 10 + rupee 2 = rupee 12 \] 4. Total unpaid amount per share \[ = rupee 3 { (First Call)} + rupee 1 { (Final Call)} = rupee 4 \] 5. Forfeited amount per share \[ = {Total Due} - {Unpaid Amount} = rupee 12 - rupee 4 = rupee 8 \] 6. Minimum reissue price per share
- The minimum price at which forfeited shares can be reissued must be at least equal to the forfeited amount per share.
- The maximum discount allowed on reissue is the forfeited amount of rupee8.
- The minimum price per share: \[ = {Face Value} - {Maximum Discount} = rupee 10 - rupee 6 = rupee 4 \] Thus, the minimum price per share at which these shares can be reissued is rupee4 (Option A).
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 \(P,O,Q\).