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GATE Physics 2022

  • Paper code: PH
  • Language: English
  • 44 pages
GATE Physics 2022 question paper, GATE 2022, Physics, page 1 of 44
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GATE 2022 Physics (PH)
GATE 2022 General Aptitude
Q.1 – Q.5 Carry ONE mark each.


Q.1       You should _________ when to say _________.


      (A) no / no


      (B) no / know


      (C) know / know


      (D) know / no




Q.2       Two straight lines pass through the origin (x , y ) = (0,0). One of them passes
          through the point (x , y ) = (1,3) and the other passes through the point
          (x , y ) = (1,2).

          What is the area enclosed between the straight lines in the interval [0, 1] on
          the x-axis?


      (A) 0.5


      (B) 1.0


      (C) 1.5


      (D) 2.0




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Q.3       If

          p∶q=1∶2

          q∶r=4∶3

          r∶s=4∶5

          and u is 50% more than s, what is the ratio p ∶ u?


      (A) 2 ∶ 15


      (B) 16 ∶ 15


      (C) 1: 5


      (D) 16: 45




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Q.4        Given the statements:

                 P is the sister of Q.
                 Q is the husband of R.
                 R is the mother of S.
                 T is the husband of P.

           Based on the above information, T is ______ of S.


      (A) the grandfather


      (B) an uncle


      (C) the father


      (D) a brother




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Q.5       In the following diagram, the point R is the center of the circle. The lines PQ
          and ZV are tangential to the circle. The relation among the areas of the squares,
          PXWR, RUVZ and SPQT is




      (A) Area of SPQT = Area of RUVZ = Area of PXWR


      (B) Area of SPQT = Area of PXWR  Area of RUVZ


      (C) Area of PXWR = Area of SPQT  Area of RUVZ


      (D) Area of PXWR = Area of RUVZ  Area of SPQT




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GATE 2022 Physics (PH)


Q. 6 – Q. 10 Carry TWO marks each.




Q.6        Healthy eating is a critical component of healthy aging. When should one start
           eating healthy? It turns out that it is never too early. For example, babies who
           start eating healthy in the first year are more likely to have better overall health
           as they get older.

           Which one of the following is the CORRECT logical inference based on the
           information in the above passage?


      (A) Healthy eating is important for those with good health conditions, but not for
           others


      (B) Eating healthy can be started at any age, earlier the better


      (C) Eating healthy and better overall health are more correlated at a young age, but
           not older age


      (D) Healthy eating is more important for adults than kids




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Q.7       P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ x per
          month for 8 months of the year in a partnership business. The profit is shared in
          proportion to the total investment made in that year.


          If at the end of that investment year, Q receives   of the total profit, what is the

          value of x (in ₹)?


      (A) 2500


      (B) 3000


      (C) 4687


      (D) 8437




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Q.8                                    16
                                                                    14
                                       14
                                       12                11
                                       10          9



                           Frequency
                                       8                        7
                                       6
                                                                             4
                                       4    3
                                                                         2
                                       2
                                       0
                                            3      4     5      6    7   8   9
                                                               Marks


          The above frequency chart shows the frequency distribution of marks obtained
          by a set of students in an exam.

          From the data presented above, which one of the following is CORRECT?


      (A) mean > mode > median


      (B) mode > median > mean


      (C) mode > mean > median


      (D) median > mode > mean




Q.9       In the square grid shown on the left, a person standing at P2 position is required
          to move to P5 position.


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         The only movement allowed for a step involves, “two moves along one
           direction followed by one move in a perpendicular direction”. The permissible
           directions for movement are shown as dotted arrows in the right.

           For example, a person at a given position Y can move only to the positions
           marked X on the right.

           Without occupying any of the shaded squares at the end of each step, the
           minimum number of steps required to go from P2 to P5 is


                   1     2    3     4     5

              P

              Q

              R

              S

              T

                                                Example: Allowed steps for a person at Y



     (A) 4


      (B) 5


      (C) 6


     (D) 7




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Q.10




             Consider a cube made by folding a single sheet of paper of appropriate shape.
             The interior faces of the cube are all blank. However, the exterior faces that are
             not visible in the above view may not be blank.

             Which one of the following represents a possible unfolding of the cube?


       (A)




       (B)




       (C)




       (D)




                             END OF THE QUESTION PAPER


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Q.11 – Q.35 Carry ONE mark Each



Q.11    For the Op-Amp circuit shown below, choose the correct output waveform
        corresponding to the input V = 1.5 sin 20πt (in Volts). The saturation voltage
        for this circuit is V = ±10 V.




(A)




(B)




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(C)




(D)




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Q.12    Match the order of β – decays given in the left column to appropriate clause in the
        right column. Here X(I ) and Y(I ) are nuclei with intrinsic spin I and parity π.


              1. X           →Y                          i)     First forbidden β-decay


              2. X           →Y                          ii)    Second forbidden β-decay


              3. X(3 ) → Y(0 )                           iii)   Third forbidden β-decay

              4. X(4 ) → Y(0 )                           iv)    Allowed β-decay




(A)     1 – i, 2 – ii, 3 – iii, 4 – iv


(B)     1 – iv, 2 – i, 3 – ii, 4 – iii


(C)     1 – i, 2 – iii, 3 – ii, 4 – iv


(D)     1 – iv, 2 – ii, 3 – iii, 4 – i




Q.13    What is the maximum number of free independent real parameters specifying an
        n-dimensional orthogonal matrix?




(A)     n(n − 2)


(B)     (n − 1)


(C)     n(n − 1)
           2


(D)     n(n + 1)
           2



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        An excited state of Ca atom is [Mg]3p54s23d1. The spectroscopic terms corresponding to
Q.14    the total orbital angular momentum are




(A)     S, P, and D


(B)     P, D, and F


(C)     P and D


(D)     S and P




Q.15    On the surface of a spherical shell enclosing a charge free region, the electrostatic
        potential values are as follows: One quarter of the area has potential φ , another
        quarter has potential 2φ and the rest has potential 4φ . The potential at the
        centre of the shell is

        (You can use a property of the solution of Laplace’s equation.)




(A)     11
           φ
        4


(B)     11
           φ
        2


(C)     7
          φ
        3


(D)     7
          φ
        4




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Q.16    A point charge q is performing simple harmonic oscillations of amplitude A at
        angular frequency ω. Using Larmor’s formula, the power radiated by the charge is
        proportional to




(A)     qω A


(B)     qω A


(C)     q ω A


(D)     q ω A




Q.17    Which of the following relationship between the internal energy U and the Helmholtz’s
        free energy F is true?




(A)                  F
                   ∂ T
        U = −T
                     ∂T



(B)                  F
                   ∂ T
        U = +T
                     ∂T



(C)               ∂F
        U = +T
                  ∂T


(D)               ∂F
        U = −T
                  ∂T




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Q.18    If nucleons in a nucleus are considered to be confined in a three-dimensional cubical box,
        then the first four magic numbers are




(A)     2, 8, 20, 28


(B)     2, 8, 16, 24


(C)     2, 8, 14, 20


(D)     2, 10, 16, 28




Q.19    Consider the ordinary differential equation

                                         y − 2xy + 4y = 0

        and its solution y(x) = a + bx + cx . Then




(A)     a = 0, c = −2b ≠ 0


(B)     c = −2a ≠ 0, b = 0


(C)     b = −2a ≠ 0, c = 0


(D)     c = 2a ≠ 0, b = 0




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Q.20    For an Op-Amp based negative feedback, non-inverting amplifier, which of the
        following statements are true?




(A)     Closed loop gain < Open loop gain


(B)     Closed loop bandwidth < Open loop bandwidth


(C)     Closed loop input impedance > Open loop input impedance


(D)     Closed loop output impedance < Open loop output impedance




Q.21    From the pairs of operators given below, identify the ones which commute. Here l
        and j correspond to the orbital angular momentum and the total angular
        momentum, respectively.




(A)     l ,j


(B)     j ,j


(C)     j ,l


(D)     l ,j




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Q.22    For normal Zeeman lines observed ∥ and ⊥ to the magnetic field applied to an
        atom, which of the following statements are true?




(A)     Only π-lines are observed ∥ to the field


(B)     σ-lines ⊥ to the field are plane polarized


(C)     π-lines ⊥ to the field are plane polarized


(D)     Only σ-lines are observed ∥ to the field




Q.23    Pauli spin matrices satisfy




(A)     σ σ − σ σ = iε         σ


(B)     σ σ − σ σ = 2iε           σ


(C)     σ σ +σ σ =ε           σ


(D)     σ σ + σ σ = 2δ




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Q.24    For the refractive index n = n (ω) + in (ω) of a material, which of the
        following statements are correct?




(A)     n can be obtained from n     and vice versa


(B)     n   could be zero


(C)     n is an analytic function in the upper half of the complex  plane


(D)     n is independent of ω for some materials




Q.25    Complex function f(z) = z + |z − a| (a is a real number) is




(A)     continuous at (a, a)


(B)     complex-differentiable at (a, a)


(C)     complex-differentiable at (a, 0)


(D)     analytic at (a, 0)




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Q.26    If g(k) is the Fourier transform of f(x), then which of the following are true?




(A)     g(−k) = +g∗ (k) implies f(x) is real


(B)     g(−k) = −g∗ (k) implies f(x) is purely imaginary


(C)     g(−k) = +g∗ (k) implies f(x) is purely imaginary


(D)     g(−k) = −g∗ (k) implies f(x) is real




Q.27    The ordinary differential equation

                                       (1 − x )y′′ − xy′ + 9y = 0

        has a regular singularity at




(A)     −1


(B)     0


(C)     +1


(D)     no finite value of x




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Q.28    For a bipolar junction transistor, which of the following statements are true?




(A)     Doping concentration of emitter region is more than that in collector and base
        region


(B)     Only electrons participate in current conduction


(C)     The current gain β depends on temperature


(D)     Collector current is less than the emitter current




Q.29    Potassium metal has electron concentration of 1.4 × 10 m3 and the
        corresponding density of states at Fermi level is 6.2 × 10 Joule1 m3. If the
        Pauli paramagnetic susceptibility of Potassium is n × 10 in standard scientific
        form, then the value of k (an integer) is __________ (Magnetic moment of
        electron is 9. 3 × 10    Joule T1; permeability of free space is 4π × 10 T m
        A1)




Q.30    A power supply has internal resistance R and open load voltage V = 5 V. When
        a load resistance R is connected to the power supply, a voltage drop of V = 4 V
        is measured across the load. The value of   is __________ (Round off to the
        nearest integer)




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Q.31    Electric field is measured along the axis of a uniformly charged disc of radius 25
        cm. At a distance d from the centre, the field differs by 10% from that of an
        infinite plane having the same charge density. The value of d is _______cm.
        (Round off to one decimal place)




Q.32    In a solid, a Raman line observed at 300 cm1 has intensity of Stokes line four
        times that of the anti-Stokes line. The temperature of the sample is _______K.
        (Round off to the nearest integer) (1 cm1 ≡ 1.44 K)




Q.33    An electromagnetic pulse has a pulse width of 103 s. The uncertainty in the
        momentum of the corresponding photon is of the order of 10 kg m s1, where N
        is an integer. The value of N is ____________ (speed of light = 3 × 10 m s1,
        ℎ = 6.6 × 10       J s)




Q.34    The wavefunction of a particle in a one-dimensional infinite well of size 2a at a
        certain time is ψ(x) =     √2sin       + √3cos      + cos         . Probability of
                                √
        finding the particle in n = 2 state at that time is ______% (Round off to the nearest
        integer)




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Q.35    A spectrometer is used to detect plasma oscillations in a sample. The spectrometer
        can work in the range of 3 × 10 rad s1 to 30 × 10 rad s1. The minimum
        carrier concentration that can be detected by using this spectrometer is n × 10
        m. The value of n is _____________ (Round off to two decimal places)

        (Charge of an electron = −1.6 × 10     C, mass of an electron = 9.1 × 10     kg
        and ε = 8.85 × 10       C2 N1 m2)




Q.36 – Q.65 Carry TWO marks Each

Q.36    Consider a non-interacting gas of spin 1 particles, each with magnetic moment μ,
        placed in a weak magnetic field B, such that    ≪ 1. The average magnetic
        moment of a particle is




(A)     2μ μ B
         3 k T


(B)     μ μB
        2 k T


(C)     μ μB
        3 k T


(D)     3μ μ B
         4 k T




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Q.37    Water at 300 K can be brought to 320 K using one of the following processes.

        Process 1: Water is brought in equilibrium with a reservoir at 320 K directly.

        Process 2: Water is first brought in equilibrium with a reservoir at 310 K and then
        with the reservoir at 320 K.

        Process 3: Water is first brought in equilibrium with a reservoir at 350 K and then
        with the reservoir at 320 K.

        The corresponding changes in the entropy of the universe for these processes are
        ∆S , ∆S and ∆S , respectively. Then




(A)     ∆S > ∆S > ∆S


(B)     ∆S > ∆S > ∆S


(C)     ∆S > ∆S > ∆S


(D)     ∆S > ∆S > ∆S




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Q.38    A student sets up Young’s double slit experiment with electrons of momentum p
        incident normally on the slits of width w separated by distance d. In order to
        observe interference fringes on a screen at a distance D from the slits, which of the
        following conditions should be satisfied?




(A)     ℏ Dw
          >
        p   d


(B)     ℏ dw
          >
        p   D


(C)     ℏ d
         >
        p D


(D)     ℏ   d
          >
        p √Dw




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Q.39    Consider a particle in three different boxes of width L. The potential inside the
                                                                    ℏ
        boxes vary as shown in figures (i), (ii) and (iii) with V ≪   . The
        corresponding ground-state energies of the particle are E , E and E ,
        respectively. Then




(A)     E >E >E


(B)     E >E >E


(C)     E >E >E


(D)     E >E >E




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Q.40    In cylindrical coordinates (s, φ, z), which of the following is a Hermitian
        operator?




(A)     1∂
        i ∂s

(B)     1 ∂ 1
            +
        i ∂s s

(C)     1 ∂   1
            +
        i ∂s 2s

(D)      ∂ 1
           +
         ∂s s




Q.41    A particle of mass 1 kg is released from a height of 1 m above the ground. When
        it reaches the ground, what is the value of Hamilton’s action for this motion in J s?
        (g is the acceleration due to gravity; take gravitation potential to be zero on the
        ground)




(A)         2
        −     2g
            3

(B)     5
          2g
        3

(C)     3 2g


(D)         1
        −     2g
            3




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Q.42    If (ẋ ẏ + αxy) is a constant of motion of a two-dimensional isotropic harmonic
        oscillator with Lagrangian

                                          m(ẋ + ẏ ) k(x + y )
                                     L=              −
                                               2          2
        then α is




(A)         k
        +
            m

(B)         k
        −
            m

(C)         2k
        −
            m

(D)     0




Q.43    In a two-dimensional square lattice, frequency ω of phonons in the long
        wavelength limit changes linearly with the wave vector k. Then the density of
        states of phonons is proportional to




(A)     ω


(B)     ω


(C)     √ω


(D)      1
        √ω




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Q.44    At T = 0 K, which of the following diagram represents the occupation probability
        P(E) of energy states of electrons in a BCS type superconductor?




(A)       P(E)

             1



                                            EF                          E




(B)       P(E)

             1


                                            EF                          E




(C)     P(E)

            1



                                           EF                          E



(D)      P(E)


               1


                                            EF                          E




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Q.45    For a one-dimensional harmonic oscillator, the creation operator (a ) acting on the
        nth state |ψ ⟩, where n = 0, 1, 2, …, gives a |ψ ⟩ = √n + 1|ψ ⟩. The matrix
                                                       ℏ
        representation of the position operator x =        (a + a ) for the first three rows
        and columns is




(A)          1       0  0
          ℏ
             0       √2 0
         2mω
             0       0 √3


(B)          0 1         0
          ℏ
             1 0         1
         2mω
             0 1         0

(C)          0       1  0
          ℏ
             1       0 √2
         2mω
             0       √2 0


(D)               1 0        √3
          ℏ
                  0 0         0
         2mω
                 √3 0         1




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Q.46    A piston of mass m is fitted to an airtight horizontal cylindrical jar. The cylinder
        and piston have identical unit area of cross-section. The gas inside the jar has
        volume V and is held at pressure P = P              . The piston is pushed inside the
        jar very slowly over a small distance. On releasing, the piston performs an
        undamped simple harmonic motion of low frequency. Assuming that the gas is
        ideal and no heat is exchanged with the atmosphere, the frequency of the small
        oscillations is proportional to




(A)
          P
         γmV


(B)
         Pγ
         Vm


(C)
          P
         mV


(D)
          γP
         mV




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Q.47    A paramagnetic salt of mass m is held at temperature T in a magnetic field H. If S
        is the entropy of the salt and M is its magnetization, then dG = −SdT − MdH,
        where G is the Gibbs free energy. If the magnetic field is changed adiabatically by
        ΔH → 0 and the corresponding infinitesimal changes in entropy and temperature
        are ΔS and ΔT, then which of the following statements are correct




(A)              1 ∂G
        ΔS = −            ΔT
                 T ∂T


(B)     ΔS = 0


(C)            ∂M
               ∂T
        ΔT = −           ΔH
               ∂S
               ∂T


(D)     ΔT = 0




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Q.48    A particle of mass m is moving inside a hollow spherical shell of radius a so that
        the potential is


                                                   0 for r < a
                                          V(r) =
                                                   ∞ for r ≥ a


        The ground state energy and wavefunction of the particle are E and R(r),
        respectively. Then which of the following options are correct?




(A)           ℏ π
        E =
              2ma


(B)         ℏ 1 d     dR
        −           r    =E R           (r < a)
            2m r dr   dr


(C)         ℏ 1d R
        −           =E R        (r < a)
            2m r dr

(D)              1     πr
        R(r) =     sin        (r < a)
                 r     a




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Q.49    A particle of unit mass moves in a potential V(r) = −V e . If the angular
        momentum of the particle is L = 0.5 V , then which of the following statements
        are true?




(A)     There are two equilibrium points along the radial coordinate


(B)     There is one stable equilibrium point at r and one unstable equilibrium point at
        r >r


(C)     There are two stable equilibrium points along the radial coordinate


(D)     There is only one equilibrium point along the radial coordinate




Q.50    In a diatomic molecule of mass M, electronic, rotational and vibrational energy
        scales are of magnitude E , E and E , respectively. The spring constant for the
        vibrational energy is determined by E . If the electron mass is m then




(A)           m
        E ~     E
              M

(B)            m
        E ~      E
               M


(C)            m
        E ~      E
               M


(D)            m     ⁄
        E ~              E
               M




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Q.51    Electronic specific heat of a solid at temperature T is C = γT, where γ is a
        constant related to the thermal effective mass m        of the electrons. Then which
        of the following statements are correct?




(A)     γ ∝ m


(B)     m     is greater than free electron mass for all solids


(C)     Temperature dependence of C depends on the dimensionality of the solid


(D)     The linear temperature dependence of C is observed at T ≪ Debye temperature




Q.52    In a Hall effect experiment on an intrinsic semiconductor, which of the following
        statements are correct?




(A)     Hall voltage is always zero


(B)     Hall voltage is negative if the effective mass of holes is larger than those of
        electrons


(C)     Hall coefficient can be used to estimate the carrier concentration in the
        semiconductor


(D)     Hall voltage depends on the mobility of the carriers




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Q.53    A parallel plate capacitor with spacing d and area of cross-section A is connected
        to a source of voltage V. If the plates are pulled apart quasistatically to a spacing
        of 2d, then which of the following statements are correct?




(A)     The force between the plates at spacing 2d is


(B)     The work done in moving the plates is


(C)     The energy transferred to the voltage source is


(D)     The energy of the capacitor reduces by




Q.54    A system with time independent Hamiltonian H(q, p) has two constants of motion
        f(q, p) and g(q, p). Then which of the following Poisson brackets are always
        zero?




(A)     {H, f + g}


(B)      H, {f, g}


(C)     {H + f, g}


(D)     {H, H + fg}




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Q.55    In the action-angle variables (I , I , θ , θ ), consider the Hamiltonian H = 4I I
        and 0 ≤ θ , θ < 2π. Let = . Which of the following are possible plots of the
        trajectories with different initial conditions in θ -θ plane?




(A)




(B)




(C)




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(D)




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Q.56    A particle of mass m in the x-y plane is confined in an infinite two-dimensional
        well with vertices at (0, 0), (0, L), (L, L), (L, 0). The eigenfunctions of this particle
        are ψ , = sin                sin         . If perturbation of the form V = Cxy, where
        C is a real constant, is applied, then which of the following statements are correct
        for the first excited state?




(A)     The unperturbed energy is
                                        ℏ




(B)     The unperturbed energy is
                                        ℏ




(C)     First order energy shift due to the applied perturbation is zero


(D)     The shift () in energy due to the applied perturbation is determined by an
                               a−δ        b
        equation of the form                   = 0, where a and b are real, non-zero
                                 b      a−δ
        constants




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Q.57    A junction is formed between a metal on the left and an n-type semiconductor on
        the right. Before forming the junction, the Fermi level EF of the metal lies below
        that of the semiconductor. Then which of the following schematics are correct for
        the bands and the I-V characteristics of the junction?




(A)
                                   Conduction Band
        EF
                                                   EF
                   Metal         n-type semiconductor

                                   Valence Band


(B)                              Conduction Band

          EF                                       EF
                  Metal          n-type semiconductor


                                  Valence Band


(C)                                       I



                           -V0
                                                        V




(D)                                      I



                           -V0
                                                        V




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Q.58    A plane polarized electromagnetic wave propagating in y-z plane is incident at the
        interface of two media at Brewster’s angle. Taking z = 0 as the boundary
        between the two media, the electric field of the reflected wave is given by

                                                  √3    1
                              E⃗ = A cos k           y − z − ωt x
                                                  2     2

        then which among the following statements are correct?




(A)     The angle of refraction is


(B)     Ratio of permittivity of the medium of refraction (ε ) with respect to the medium
        on incidence (ε ),    =3


(C)     The incident wave can have components of its electric field in y-z plane


(D)     The angle of reflection is




Q.59    The minimum number of two-input NAND gates required to implement the
        following Boolean expression is ________________

                                     Y = [AB (C + BD) + A̅B ]C




Q.60    In a nucleus, the interaction V l⃗ ⋅ s⃗ is responsible for creating spin-orbit doublets.
                                                                               ℏ
        The energy difference between p / and p / states in units of V             is
        ____________ (Round off to the nearest integer)




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Q.61    Two identical particles of rest mass m approach each other with equal and
        opposite velocity v = 0.5c, where c is the speed of light. The total energy of one
        particle as measured in the rest frame of the other is E = αm c . The value of α
        is _______________ (Round off to two decimal places)




Q.62    In an X-Ray diffraction experiment on a solid with FCC structure, five diffraction
        peaks corresponding to (111), (200), (220), (311) and (222) planes are observed
        using 1.54 Å X-rays. On using 3 Å X-rays on the same solid, the number of
        observed peaks will be ________________




Q.63    For 1 mole of Nitrogen gas, the ratio          of entropy change of the gas in
        processes (I) and (II) mentioned below is ______________ (Round off to one
        decimal place)

           (I)     The gas is held at 1 atm and is cooled from 300 K to 77 K.

           (II)    The gas is liquified at 77 K.

        (Take Cp = 7.0 cal mol1 K1, Latent heat L = 1293.6 cal mol1)




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Q.64    Frequency bandwidth ∆ν of a gas laser of frequency ν Hz is

                                                   2ν α
                                            Δν =
                                                    c A

        where α = 3.44 × 106 m2 s2 at room temperature and A is the atomic mass of the
        lasing atom. For 4He - 20Ne laser (wavelength = 633 nm), Δν = n × 10 Hz. The
        value of n is ________ (Round off to one decimal place)




Q.65    A current of 1 A is flowing through a very long solenoid made of winding density
        3000 turns/m. As shown in the figure, a parallel plate capacitor, with plates
        oriented parallel to the solenoid axis and carrying surface charge density
        6ε C m2, is placed at the middle of the solenoid. The momentum density of the
        electromagnetic field at the midpoint X of the capacitor is n × 10     N s m3. The
        value of n is ______________ (Round off to the nearest integer)

        (speed of light c = 3 × 10 m s1)




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Q. No.   Session Question   Subject   Key/Range      Mark
                 Type       Name
1        5       MCQ        GA        D              1
2        5       MCQ        GA        A              1
3        5       MCQ        GA        D              1
4        5       MCQ        GA        B              1
5        5       MCQ        GA        B              1
6        5       MCQ        GA        B              2
7        5       MCQ        GA        B              2
8        5       MCQ        GA        B              2
9        5       MCQ        GA        B              2
10       5       MCQ        GA        MTA            2
11       5       MCQ        PH        A              1
12       5       MCQ        PH        B              1
13       5       MCQ        PH        C              1
14       5       MCQ        PH        B              1
15       5       MCQ        PH        A              1
16       5       MCQ        PH        D              1
17       5       MCQ        PH        A              1
18       5       MCQ        PH        C              1
19       5       MCQ        PH        B              1
20       5       MSQ        PH        A, C, D        1
21       5       MSQ        PH        A, B, D        1
22       5       MSQ        PH        B,C,D          1
23       5       MSQ        PH        B,D            1
24       5       MSQ        PH        A,C            1
25       5       MSQ        PH        A,C            1
26       5       MSQ        PH        A,B            1
27       5       MSQ        PH        A,C            1
28       5       MSQ        PH        A, C, D        1
29       5       NAT        PH        6 to 6         1
30       5       NAT        PH        4 to 4         1
31       5       NAT        PH        2.4 to 2.6     1
32       5       NAT        PH        311 to 312     1
33       5       NAT        PH        39 to 40       1
34       5       NAT        PH        33 to 34       1
35       5       NAT        PH        2.70 to 2.96   1
36       5       MCQ        PH        A              2
37       5       MCQ        PH        B              2
38       5       MCQ        PH        B              2
39       5       MCQ        PH        A              2
40       5       MCQ        PH        C              2
41       5       MCQ        PH        D              2
42       5       MCQ        PH        A              2
43       5       MCQ        PH        A              2
44       5       MCQ        PH        A              2

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45   5   MCQ   PH   C              2
46   5   MCQ   PH   B              2
47   5   MSQ   PH   B,C            2
48   5   MSQ   PH   A,B,D          2
49   5   MSQ   PH   A,B            2
50   5   MSQ   PH   A,C            2
51   5   MSQ   PH   A,D            2
52   5   MSQ   PH   D              2
53   5   MSQ   PH   A,C,D          2
54   5   MSQ   PH   A,B,D          2
55   5   MSQ   PH   B,C            2
56   5   MSQ   PH   B,D            2
57   5   MSQ   PH   A,C            2
58   5   MSQ   PH   A,B,C          2
59   5   NAT   PH   3 to 3         2
60   5   NAT   PH   3 to 3         2
61   5   NAT   PH   1.65 to 1.70   2
62   5   NAT   PH   1 to 1         2
63   5   NAT   PH   0.5 to 0.7     2
64   5   NAT   PH   1.2 to 1.4     2
65   5   NAT   PH   2 to 2         2

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Source: GATE. Question paper published by GATE.