To determine the correct answer, let's analyze both the assertion and the reason provided.
Assertion (A): "We cannot form a p-n junction diode by taking a slab of a p-type semiconductor and physically joining it to another slab of an n-type semiconductor."
This assertion is true. When a p-type and an n-type semiconductor are physically joined without a continuous lattice structure, it does not result in a functional p-n junction diode. This is because there will be a high concentration of defects and inconsistencies at the interface, preventing proper charge carrier movement and the establishment of a depletion region necessary for diode function.
Reason (R): "In a p-type semiconductor \( \eta_e \gg \eta_h \) while in an n-type semiconductor \( \eta_h \gg \eta_e \)."
This reason is false. In a p-type semiconductor, the concentration of holes (\( \eta_h \)) is much greater than the concentration of electrons (\( \eta_e \)), i.e., \( \eta_h \gg \eta_e \). Conversely, in an n-type semiconductor, the concentration of electrons (\( \eta_e \)) is much greater than the concentration of holes (\( \eta_h \)), i.e., \( \eta_e \gg \eta_h \).
Given that the assertion is true while the reason provided is incorrectly stated, we conclude:
Correct Answer: Assertion (A) is true, but Reason (R) is false.
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 \(P,O,Q\).