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.
Reason (R): In a p-type semiconductor, \( n_e \gg n_h \) while in an n-type semiconductor \( n_h \gg n_e \).
To determine the truth of the assertion and the reason provided, we need to evaluate them based on semiconductor physics.
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.
Explanation: A p-n junction diode is formed by doping a single crystal of semiconductor material such that one side becomes p-type and the other becomes n-type. This ensures a continuous lattice structure and a seamless junction. Simply joining two slabs physically would introduce interface defects and create a lack of a continuous crystal lattice, leading to high recombination of charge carriers at the interface and ineffective diode operation. Thus, the assertion is true under practical conditions required for effective diode function, but a simple physical joining does not form a functional diode due to discontinuities.
Reason (R): In a p-type semiconductor, \( n_e \gg n_h \) while in an n-type semiconductor \( n_h \gg n_e \).
Explanation: This reason is technically incorrect. In a p-type semiconductor, the majority carriers are holes (\( n_h \)), and in an n-type semiconductor, the majority carriers are electrons (\( n_e \)). Therefore, \( n_h \gg n_e \) is true for p-type, and \( n_e \gg n_h \) is true for n-type, which is the opposite of the given reason.
The correct answer: Assertion (A) is false and Reason (R) is also false.
Assuming in forward bias condition there is a voltage drop of \(0.7\) V across a silicon diode, the current through diode \(D_1\) in the circuit shown is ________ mA. (Assume all diodes in the given circuit are identical) 
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 \(P,O,Q\).