On the basis of the given data, estimate the value of National Income (NNPFC):
| S.No. | Items | Amount (in ₹ Crore) |
| (i) | Household Consumption Expenditure | 1,800 |
| (ii) | Gross Business Fixed Capital Formation | 1,150 |
| (iii) | Gross Residential Construction Expenditure | 1,020 |
| (iv) | Government Final Consumption Expenditure | 2,170 |
| (v) | Excess of Imports over Exports | 720 |
| (vi) | Inventory Investments | 540 |
| (vii) | Gross Public Investments | 1,300 |
| (viii) | Net Indirect Taxes | 240 |
| (ix) | Net Factor Income from Abroad | (-) 250 |
| (x) | Consumption of Fixed Capital | 440 |
National Income (NNPFC) is calculated by subtracting the depreciation (Consumption of Fixed Capital) from the Gross National Product (GNP).
First, let's calculate the Gross National Product (GNP) at factor cost: \[ \text{GNP} = C + I + G + (X - M) + \text{Net Factor Income from Abroad} \] Where: - \(C\) is the Household Consumption Expenditure = ₹1,800 crore
- \(I\) is the Gross Business Fixed Capital Formation + Gross Residential Construction Expenditure + Inventory Investments + Gross Public Investments = ₹1,150 + ₹1,020 + ₹540 + ₹1,300 = ₹4,010 crore
- \(G\) is the Government Final Consumption Expenditure = ₹2,170 crore
- \((X - M)\) is the Excess of Imports over Exports = ₹720 crore
- Net Factor Income from Abroad = ₹-250 crore
Substituting these values into the GNP equation: \[ \text{GNP} = 1,800 + 4,010 + 2,170 + 720 + (-250) = 8,450 \text{ crore} \] Now, to calculate National Income (NNPFC), we subtract the consumption of fixed capital (depreciation): NNPFC = GNP - Consumption of Fixed Capital
NNPFC = 8,450 - 440 = 8,010 crore
Thus, the value of National Income (NNPFC) is ₹8,010 crore.
| S. No. | Particulars | Amount (in ₹ crore) |
|---|---|---|
| (i) | Operating Surplus | 3,740 |
| (ii) | Increase in unsold stock | 600 |
| (iii) | Sales | 10,625 |
| (iv) | Purchase of raw materials | 2,625 |
| (v) | Consumption of fixed capital | 500 |
| (vi) | Subsidies | 400 |
| (vii) | Indirect taxes | 1,200 |
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 \(P,O,Q\).