Read the following statements: Assertion (A) and Reason (R). Choose the correct alternative from those given below:
Assertion (A): The equilibrium level of income is determined when ex-ante spending and ex-ante output are equal.
Reason (R): The equilibrium level of income may or may not be the same as the full employment level of output.
Assertion (A): This is true because the equilibrium level of income is achieved when planned (ex-ante) spending equals planned (ex-ante) output, ensuring no unintended inventory changes.
Reason (R): This is also true because the equilibrium level of income is not necessarily the same as the full employment output. It can occur below or above the full employment level depending on the level of aggregate demand.
Conclusion: Although both statements are correct, the reason does not fully explain the assertion in terms of equilibrium determination.
In the light of the given statements, choose the correct alternative from the following:
Option (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Option (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is {not} the correct explanation of Assertion (A).
Option (C) Assertion (A) is true, but Reason (R) is false.
Option (D) Assertion (A) is false, but Reason (R) is true.
Correct Answer: (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is {not} the correct explanation of Assertion (A).
If the marginal cost of a firm is given as the function of output, \( C'(Q) = 2e^{0.2Q} \), and if the fixed cost is 75, find the total cost function.
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 \(P,O,Q\).