Explanation of the Companies Act, 2013 limit According to Section 464 of the Companies Act, 2013, a partnership firm can have a maximum of 50 partners unless it is registered as a company.
Calculating the remaining number of partners that can be added Currently, the partnership firm has 45 partners. The maximum allowable limit is 50 partners. \[ {Remaining partners that can be admitted} = 50 - 45 = 5 \]
Conclusion of the Solution Therefore, only 5 more partners can be admitted into the partnership firm.
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 \(P,O,Q\).