Download JNU 2020 Physical Science (Phyh) Question Paper

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Exam Date: 05-Oct-2020

Exam Time: 09:00-12:00

Examination: 1. Course Code - Ph.D.

2. Field of Study - Physical Science (PHYH)

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SECTION 1 - SECTION 1

Case Study - 1 to 3 (Question Id - 53)

A sphere of radius R carries a polarization $\stackrel{?}{P}\left(r\right)=kr\stackrel{?}{r}$ where k is a constant and $\stackrel{?}{r}$ is the vector from the center of the sphere. Answer the following three questions for this problem.

Question No.1 (Question Id - 54)

The surface bound charge s_b is :

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(A) $\frac{kr}{4R^2}$

(B) $\frac{kmi>r}{4p{e}_{0}4R^2}$

(C) kR

(D) kR (Correct Answer)

Question No.2 (Question Id - 55)

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The volume bound charge (?_b) is :

(A) $\frac{1}{4p{e}_{0}4R^3}3k$

(B) -3kr

(C) -3k (Correct Answer)

(D) $\frac{9k{r}^3}{4p{e}_0{r}^3}$

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Question No.3 (Question Id - 56)

The electric field outside the sphere is :

(A) 4pkR²

(B) $\frac{1}{3}4pk{R}^3+4pk{R}^2$

(C) 0 (Correct Answer)

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(D) $\frac{k}{3e_0}$

Question No.4 (Question Id - 7)

Consider the differential equation $\frac{d^{2}y}{d{x}^2}+{?}^{2}y=0$ . The solution of this equation can be expressed in the series form as: $y\left(x\right)=\underset{n=0}{\overset{8}{?}}{C}_n{x}^n$ . Which of the following is the correct recursion relation for the coefficients of this series ?

(A) $C_{n+2}=-\frac{{?}^2}{(n+2)(n+1)}{C}_n$ (Correct Answer)

(B) $C_n=\frac{{?}^2}{n(n+1)}{C}_{n+1}$

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(C) $C_n=\frac{{?}^2}{n(n-1)}{C}_{n-1}$

(D) $C_{n+2}=\frac{{?}^2}{(n+2)(n+1)}{C}_n$

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Question No.5 (Question Id - 14)

For an atom with an electronic configuration np² (where n is the principal quantum number of a shell), the possible values of total angular momentum L and total spin S in the ground state are :

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(A) L = 2 and S = 0

(B) L = 2 and S = 1

(C) L = 1 and S = 1 (Correct Answer)

(D) L = 1 and S = 0

Question No.6 (Question Id - 2)

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Which one of the following two-particle state $|k_1,k_2?$ correctly describes two identical bosons in the plane wave states given by the wave-vectors $\stackrel{?}{k_1}$ and $\stackrel{?}{k_2}$ ?

(A) $|k_1,k_2?=e^{i{k}_1{r}_1}+e^{i{k}_2{r}_2}$

(B) $|k_1,k_2?=e^{i{k}_1{r}_1}+e^{i{k}_2{r}_2}$

(C) $|k_1,k_2?=\frac{1}{\sqrt{2}}(e^{i{k}_1{r}_1}+e^{i{k}_2{r}_2})$ (Correct Answer)

(D) $|k_1,k_2?=\frac{1}{\sqrt{2}}(e^{i{k}_1{r}_1}+e^{i{k}_2{r}_2})$

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Question No.7 (Question Id - 11)

Electrons are ejected from calcium surface when monochromatic light of wavelength 488 nm falls on it. The work function of calcium is 2.28 eV. What is the maximum kinetic energy of the emitted electron ? (Planck's constant, h = 4.14 x 10^-15 eV·sec; speed of light, c = 3 x 10⁸ m/sec)

(A) 0.026 eV

(B) 26 eV

(C) 2.6 eV

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(D) 0.26 eV (Correct Answer)

Question No.8 (Question Id - 4)

Which one of the following is not true about the superconductors ?

(A) Type-II superconductors realize a mixed state between the critical magnetic fields H_c1 and H_c2.

(B) In Type-I superconductors, the penetration depth (?) is smaller than the coherence length (?).

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(C) According to BCS theory, the copper pairs are formed due to electron-phonon interaction.

(D) Superconductivity is characterized by strongly paramagnetic behavior. (Correct Answer)

Question No.9 (Question Id - 15)

Consider a vector $\stackrel{?}{v}=x_1\stackrel{?}{a_1}+x_2\stackrel{?}{a_2}+x_3\stackrel{?}{a_3}$ in a real three dimensional vector space spanned by three basis vectors $\stackrel{?}{a_1}$ , $\stackrel{?}{a_2}$ and $\stackrel{?}{a_3}$ . Consider a new basis of three vectors : $\stackrel{?}{b_1}=\stackrel{?}{a_1}$ , $\stackrel{?}{b_2}=\stackrel{?}{a_1}+\stackrel{?}{a_2}$ , and $\stackrel{?}{b_3}=\stackrel{?}{a_1}+\stackrel{?}{a_2}+\stackrel{?}{a_3}$ . Let the vector $\stackrel{?}{v}$ given above be denoted in this new basis as: $\stackrel{?}{v}=y_1\stackrel{?}{b_1}+y_2\stackrel{?}{b_2}+y_3\stackrel{?}{b_3}$ . If the transformation matrix V between the components of the vector $\stackrel{?}{v}$ in the two bases is defined as: $x_i=\underset{j=1}{\overset{3}{?}}{V}_{ij}{y}_j$ for i = 1, 2, 3, then

(A) $V=\left[\begin{array}{ccc}1& 1& 1\\ 1& 1& 0\\ 1& 0& 0\end{array}\right]$

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(B)

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(C) $V=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& -1& 1\end{array}\right]$ (Correct Answer)

(D) $V=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 0& 1& 1\end{array}\right]$

Question No.10 (Question Id - 5)

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Which one of the following expressions is correct for the Helmholtz free energy F(T, V, N) of a thermodynamic system in canonical ensemble ? Here, P is pressure, V is volume, N is the number of particles, µ is chemical potential, and T is temperature.

(A) F = -PV + µN (Correct Answer)

(B) F = PV + µN

(C) F = - PV - µN

(D) F = µN

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Question No.11 (Question Id - 1)

Let the angular momentum eigenstates with quantum number j be denoted as |j, m?, where m = - j, - j + 1, ..., j - 1, j. For a system of two angular momenta j₁ and j₂, any state can be described as a linear superposition of their product states |j₁, m₁?|j₂, m₂?. For j₁ = 1 and j₂ = 1/2, which of the following is the correct expression for the total angular momentum eigenstate with quantum numbers j_total = 3/2 and m_total = 1/2 ?

(A)

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