The problem requires us to analyze an assertion and a reason to choose the correct explanation. Let's break down the statements:
Assertion (A): The maximum number of partners in a partnership firm is 50.
Reason (R): By virtue of the Companies Act 2013, the Central Government is empowered to prescribe the maximum number of partners in a firm. The Central Government has prescribed the maximum number of partners in a firm to be 50.
Now, let's evaluate the truth of these statements:
The Companies Act 2013 gives the Central Government authority to set the maximum number of partners in a partnership firm. Consequently, a notification from the Central Government has indeed prescribed this number to be 50. Thus, both the assertion and the reason are correct statements.
Moreover, the reason directly explains why the assertion is true, since the determination of partner limits is derived from the authority granted by the Companies Act 2013 and the Central Government's subsequent specification of the number 50.
Therefore, the correct option is:
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (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 \(P,O,Q\).