Download DUET Master 2018 DU PhD in informatics IIC Question Paper With Answer Key

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DU PhD in informatics IIC

Topic:- DU_J18_PHD_INFO

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1. Customers arrive at a one-man barber shop according to a Poisson process with a mean interarrival time of 12 min. Customers spend an average of 10 min in the barber's chair. What is the expected number of customers in the barber shop.
   [Question ID = 52631]
   1. 1.3 [Option ID = 90517]
   2. 2 [Option ID = 90516]
   3. 5 [Option ID = 90519]
   4. 4 [Option ID = 90518]

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   Correct Answer :- 5 [Option ID = 90519]
2. The mass of a rocket is M and the total mass of the rocket and the fuel is Mo. The average exhaust velocity of gases ejected from rocket motors is u and the final velocity attained by the rocket after using up all fuel is v. The final velocoti v is proportional to
   [Question ID = 52583]
   1. ^Mu/_Mo [Option ID = 90325]
   2. (Mo-M)^-1 [Option ID = 90327]
   3. (M-Mo) [Option ID = 90326]

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   4. log (^Mo/_M) [Option ID = 90324]
   Correct Answer :- log(^Mo/_M) [Option ID = 90324]
3. A signal is carrying data in which one data element is encoded as one signal element (r = 1). If the bit rate is 100kbps, what is the average value of the baud rate if c is between 0 and 1.
   [Question ID = 52611]
   1. 50kbaud [Option ID = 90438]
   2. 10kbaud [Option ID = 90436]

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   3. 100kbaud [Option ID = 90439]
   4. 20kbaud [Option ID = 90437]
   Correct Answer :- 50kbaud [Option ID = 90438]
4. The solution of the differential equation ^dy/_dx + y = x⁴ with the boundary condition that y = 1 at x = 1, is
   [Question ID = 52618]
   1. y = ^x5/₅ + ⁴/_5x [Option ID = 90467]

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   2. y = ^x5/₅ + ⁴/₅ [Option ID = 90466]
   3. y = 5x⁴-4 [Option ID = 90464]
   4. y = ^x4/₅ + ⁴/_5x [Option ID = 90465]
   Correct Answer :- y = ^x5/₅ + ⁴/_5x [Option ID = 90467]
5. Can the following scalar and vector potential describe an electromagnetic field?
   

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   φ(x,t) = 3xyz - 4t, A(x,t) = (2x - ωt)i + (y - 2z)j + (z - 2e^iωt)k where ω is constant.
   [Question ID = 52593]
   1. Yes, in the Coulomb gauge [Option ID = 90364]
   2. Yes, provided ω = 0 [Option ID = 90366]
   3. Yes, in the Lorentz gauge [Option ID = 90365]
   4. Yes, provided ω ≠ 0 [Option ID = 90367]

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   Correct Answer :- Yes, in the Lorentz gauge [Option ID = 90365]
6. If the standard deviation of the Poisson's distribution is √2, the probability for r = 2 is
   [Question ID = 52623]
   1. ²/_e [Option ID = 90487]
   2. ¹/_e [Option ID = 90485]
   3. ¹/_2e [Option ID = 90484]

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   4. ²/_e [Option ID = 90486]
   Correct Answer :- ²/_e [Option ID = 90486]
7. For a step index fiber, the normalized frequency V = 26.6 at a 1300nm wavelength. If the core radius is 25µm. Find out the numerical aperture.
   [Question ID = 52610]
   1. 0.33 [Option ID = 90433]
   2. 0.11 [Option ID = 90435]

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   3. 0.22 [Option ID = 90432]
   4. 0.66 [Option ID = 90434]
   Correct Answer :- 0.22 [Option ID = 90432]
8. The value of c for which P(X=k) = ck² can serve as the probability function of a random variable X that takes value 0, 1, 2, 3, 4 is
   [Question ID = 52624]
   1. 1/30 [Option ID = 90489]

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   2. 1/40 [Option ID = 90491]
   3. 1/15 [Option ID = 90488]
   4. 1/10 [Option ID = 90490]
   Correct Answer :- 1/30 [Option ID = 90489]
9. An arbitrary vector X is an eigen vector of the matrix
   

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   A=

     1 0 0 a 0 0 0 0 b  

   if (a, b) is
   [Question ID = 52613]
   1. (0,1) [Option ID = 90446]
   2. (1,-1) [Option ID = 90444]
   3. (1,0) [Option ID = 90445]
   4. (1,1) [Option ID = 90447]

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   Correct Answer :- (1,1) [Option ID = 90447]
10. LASER are light source which give almost perfectly parallel beam of high intensity. If a 2kW laser beam is concentrated by a lens into cross-sectional area about 10^-6cm², then the value of poynting vector is
    [Question ID = 52592]
    1. 2 x 10¹⁴W/m² [Option ID = 90363]
    2. 2 x 10¹³W/m² [Option ID = 90362]
    3. 2 x 10¹²W/m² [Option ID = 90361]

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    4. 2 x 10¹¹W/m² [Option ID = 90360]
    Correct Answer :- 2 x 10¹³W/m² [Option ID = 90362]
11. If the magnetic monopole existed, then which of the following Maxwell's equations will be modified?
    [Question ID = 52591]
    1. divD = ρ [Option ID = 90356]
    2. divB = 0 [Option ID = 90358]

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    3. curH= J+ ^∂D/_∂t [Option ID = 90359]
    4. curE = ^∂B/_∂t [Option ID = 90357]
    Correct Answer :- div B = 0 [Option ID = 90358]
12. Evaluate ∫^2π₀ ^dθ/_{1 + asin²θ}, a² < 1.
    [Question ID = 52622]
    1. ^2π/_√1+a² [Option ID = 90481]

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    2. ^π/_√1-a² [Option ID = 90482]
    3. ^π/_√1+a² [Option ID = 90483]
    4. ^2π/_√1-a² [Option ID = 90480]
    Correct Answer :- ^2π/_√1-a² [Option ID = 90480]
13. A voltage signal V(t) has the following Fourier transform
    

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    V(jω) = A e^-jωd,   for |ω| < 1
    0,   for |ω| > 0
    The energy that would be dissipated in a 1Ω resistor fed from V(t) is
    [Question ID = 52609]
    1. ^A2/_π J [Option ID = 90428]
    2. ¹/_π J [Option ID = 90430]

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    3. ^A2/_2π J [Option ID = 90431]
    4. ^2e-2d/_π [Option ID = 90429]
    Correct Answer :- ^A2/_2π [Option ID = 90431]
14. A particle describe a circle of radius r. The centripetal acceleration of the particle is 4/r². What will be the momentum of the particle?
    [Question ID = 52584]
    1. ^2m/_r [Option ID = 90328]

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    2. ^4m/_r [Option ID = 90330]
    3. ^2m/_√r [Option ID = 90329]
    4. ^8m/_r [Option ID = 90331]
    Correct Answer :- ^2m/_√r [Option ID = 90329]
15. The equation x³+4x-9=0 needs to be numerically solved using the Newton-Raphson method. The iterative equation for this purpose is
    

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    [Question ID = 52629]
    1. x_k+1 = ^4x_k2+9/_3xk²+4 [Option ID = 90511]
    2. x_k+1 = ^3x_k2+4/_2xk²+9 [Option ID = 90509]
    3. x_k+1 = ^x_k3+9/_3xk²+4 [Option ID = 90508]
    4. x_k+1 = x_k - ^3x_k2+4/₉ [Option ID = 90510]
    Correct Answer :- x_k+1 = ^x_k3+9/_3xk²+4 [Option ID = 90508]

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16. The ratio of the reverse resistance to the forward resistance of a good solid-state diode is about
    [Question ID = 52599]
    1. 1:10 [Option ID = 90389]
    2. 10:1 [Option ID = 90388]
    3. 1:100 [Option ID = 90390]
    4. 1:1000 [Option ID = 90391]

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    Correct Answer :- 1:1000 [Option ID = 90391]
17. During execution, OP code of an instruction is stored in the
    [Question ID = 52602]
    1. general purpose register [Option ID = 90400]
    2. instruction register [Option ID = 90402]
    3. accumulator register [Option ID = 90401]

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    4. temporary register [Option ID = 90403]
    Correct Answer :- instruction register [Option ID = 90402]
18. Find the complimentary function
    ^d2y/_dx² - ^dy/_dx - 6y = e^3x
    [Question ID = 52616]
    1. (x²-1)e^3x [Option ID = 90459]

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    2. xe^3x-1 [Option ID = 90457]
    3. e^3x+ e^2x [Option ID = 90456]
    4. (x-1)e^3x [Option ID = 90458]
    Correct Answer :- (x-1)e^3x [Option ID = 90458]
19. When an 8 bit serial in / serial out register is used for a 24µs time delay, the clock frequency must be
    

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    [Question ID = 52604]
    1. 8MHz [Option ID = 90411]
    2. 41.67kHz [Option ID = 90408]
    3. 333kHz [Option ID = 90409]
    4. 125kHz [Option ID = 90410]
    Correct Answer :- 333kHz [Option ID = 90409]

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20. Evaluate ∫ e^iz/z dz, where c is the circle |z| = 2.
    [Question ID = 52621]
    1. -iπ [Option ID = 90478]
    2. 2iπ [Option ID = 90479]
    3. iπ [Option ID = 90477]
    4. π [Option ID = 90476]

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    Correct Answer :- -iπ [Option ID = 90478]
21. Solve ^dy/_dx - y = (x-1)e^x.
    [Question ID = 52615]
    1. ^x/₂ e^x + c, c=const. [Option ID = 90452]
    2. ^x/₂ e^-x + c, c= const. [Option ID = 90453]
    3. ^x/₃ e^x + c, c=const. [Option ID = 90454]

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    4. ^x/₃ e^-x + c, c=const. [Option ID = 90455]
    Correct Answer :- ^x/₂ e^-x + c, c= const. [Option ID = 90453]
22. The eigen values of the matrix
    A=[

      cos θ -sin θ sin θ cos θ  

    ] are
    [Question ID = 52614]
    1. e^iθ [Option ID = 90450]

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    2. 3 e^tiθ [Option ID = 90451]
    3. e^iθ [Option ID = 90449]
    4. e^iθ [Option ID = 90448]
    Correct Answer :- e^iθ [Option ID = 90449]
23. Consider the following assembly language program

      MVI B,87H MOV A, B START: JMP NEXT MVI B, 00H XRA B OUT PORT 1 HLT NEXT: XRA B JP START 1 OUT PORT 2 HLT  

    [Question ID = 52608]
    1. infinite looping of the program execution with accumulator data alternaing between 00H and 87H [Option ID = 90427]

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    2. an output of 87H at PORT 2 [Option ID = 90425]
    3. an output of 87H at PORT 1 [Option ID = 90424]
    4. infinite looping of the program execution with accumulator data remaining at 00H [Option ID = 90426]
    Correct Answer :- an output of 87H at PORT 2 [Option ID = 90425]
24. The contribution of Coulomb energy in the sem-empirical mass formula of a nucleus of mass number A and atomic number Z is of the form (a is a constant)
    

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    [Question ID = 52596]
    1. ^aZ(Z+1)/_A [Option ID = 90377]
    2. ^aZ(Z-1)/_A [Option ID = 90378]
    3. ^aZ(Z+1)/_2A [Option ID = 90379]
    4. ^aZA2/3/_A [Option ID = 90376]
    Correct Answer :- ^aZ(Z-1)/_A [Option ID = 90378]

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25. The following programme is run on an 8085 microprocessor

      2000 LXI SP, 1000 2003 PUSH H 2004 PUSH D 2005 CALL 2050 2008 POP 2050 2009 HIT  

    As the completion of execution of the program, the program counter of the 8085 contains 2056, and the stack pointer contains.......
    [Question ID = 52606]
    1. 2251, OFFC [Option ID = 90417]
    2. 1025, OCCF [Option ID = 90418]
    3. 2050, OFFC [Option ID = 90416]
    4. 1025 [Option ID = 90419]

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    Correct Answer :- 2050, OFFC [Option ID = 90416]
26. When a transistor amplifier having current gain of 75 is given an input signal
    V_i = 2sin (157t+^π/₄),
    the output signal is found to be
    V_o = 200sin (157t+^3π/₂).
    

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    The transistor is connected as
    [Question ID = 52600]
    1. a common base amplifier [Option ID = 90393]
    2. a common collector amplifier [Option ID = 90392]
    3. a oscillator [Option ID = 90395]
    4. a common emitter amplifier [Option ID = 90394]

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    Correct Answer :- a common emitter amplifier [Option ID = 90394]
27. If a group is defined as
    a*b=a+b-1
    then inverse of the group is
    [Question ID = 52630]
    1. a [Option ID = 90512]

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    2. 1-a [Option ID = 90513]
    3. 2-a [Option ID = 90514]
    4. a-5 [Option ID = 90515]
    Correct Answer :- 2-a [Option ID = 90514]
28. A 10MHz clock frequency is applied in cascaded counter consisting of a modulus counter , a modulus-8 counter, and two two modulus-10 counters. The lowest output frequency possible is
    

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    [Question ID = 52603]
    1. 5kHz [Option ID = 90406]
    2. 25kHz [Option ID = 90407]
    3. 2.5kHz [Option ID = 90405]
    4. 10kHz [Option ID = 90404]
    Correct Answer :- 25kHz [Option ID = 90407]

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29. The equation of motion of a bead sliding on a uniform rod rotating in a force free space is
    [Question ID = 52585]
    1. r̈ - rω² = 0 [Option ID = 90332]
    2. r̈ - rω = 0 [Option ID = 90334]
    3. r̈ - rω² = 0 [Option ID = 90333]
    4. r̈ - rω + rω² = 0 [Option ID = 90335]

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    Correct Answer :- r̈ - rω² = 0 [Option ID = 90333]
30. A particle is described by a wavefunction ψ(x) = e^-|x|/a in one dimension. What is the probability that it will be found in the region |x| ≤ a, a > 0?
    [Question ID = 52595]
    1. 1-e^-2a [Option ID = 90375]
    2. e^-a [Option ID = 90372]
    3. 1-e^-a [Option ID = 90373]

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    4. e^-2a [Option ID = 90374]
    Correct Answer :- 1-e^-2a [Option ID = 90375]
31. The wavefunction in the ground state of H-atom is given by ψ = ¹/_√πα³ e^-r/a. Find the average value of r.
    [Question ID = 52594]
    1. 0 [Option ID = 90368]
    2. ³/₂ a [Option ID = 90369]

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    3. ⁵/₂ a [Option ID = 90370]
    4. ^a/₂ [Option ID = 90371]
    Correct Answer :- ³/₂ a [Option ID = 90369]
32. The correct sequence of the band -gaps of germanium (E_g1), silicon (E_g2) and gallium arsenide (E_g3) will be
    [Question ID = 52597]
    1. E_g1 < E_g2 < E_g3 [Option ID = 90381]

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    2. E_g2 < E_g1 < E_g3 [Option ID = 90382]
    3. E_g2 > E_g1 > E_g3 [Option ID = 90383]
    4. E_g1 < E_g3 < E_g2 [Option ID = 90380]
    Correct Answer :- E_g2 < E_g1 < E_g3 [Option ID = 90382]
33. The Lagrangian of a particle of mass m moving in a plane is given by
    

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    L = ¹/₂m(ẋ²+ẏ²) + a(xẏ+yẋ)
    The canonical momenta are given by
    [Question ID = 52586]
    1. p_x = mẋ - aẏ, p_y = mẏ + aẋ [Option ID = 90338]
    2. p_x = mẋ + aẏ, p_y = mẏ - aẋ [Option ID = 90339]
    3. p_x = mẋ + aẏ, p_y = mẏ + aẋ [Option ID = 90337]

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    4. p_x = mẋ, p_y = mẏ [Option ID = 90336]
    Correct Answer :- p_x = mẋ + aẏ, p_y = mẏ + aẋ [Option ID = 90337]
34. Magnetic field in a region is B = βtẑ, the induced electric field due to this time varying magnetic field is
    [Question ID = 52590]
    1. ^βr/₂(φ̂) [Option ID = 90354]
    2. ^βr/₂(-φ̂) [Option ID = 90353]

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    3. ^βr/₂(φ̂) [Option ID = 90352]
    4. βr(-φ̂) [Option ID = 90355]
    Correct Answer :- ^βr/₂(-φ̂) [Option ID = 90353]
35. The transition probability matrix of a Markov chain X_n, n = 1,2,3,... having 3 states 1, 2 and 3 is
    P=

      [ 0.1 0.5 0.4 0.6 0.2 0.2 0.3 0.4 0.3 ]  

    and the initial distribution is p(0) = (0.7, 0.2, 0.1). Find P(X₂ = 3)
    

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    [Question ID = 52625]
    1. 0.0046 [Option ID = 90495]
    2. 0.012 [Option ID = 90493]
    3. 0.279 [Option ID = 90492]
    4. 0.0048 [Option ID = 90494]
    Correct Answer :- 0.279 [Option ID = 90492]

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36. The Lagrangian for an harmonic oscillator is given by L = ¹/₂ẋ² - ¹/₂ω²x³. Find the Hamiltonian.
    [Question ID = 52587]
    1. H = -¹/₂p² - ¹/₂ω²x³ [Option ID = 90341]
    2. H = ¹/₂p² + ¹/₂ω²x³ [Option ID = 90342]
    3. H = ¹/₂p² + ¹/₂ω²x³ [Option ID = 90343]
    4. H = -¹/₂p² - ¹/₂ω²x³ [Option ID = 90340]

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    Correct Answer :- H = ¹/₂p² + ¹/₂ω²x³ [Option ID = 90342]
37. The polynomial 2x² + x + 3 in terms of Legendre's polynomial is
    [Question ID = 52617]
    1. ¹/₅[4P₂ - 3P₁ - 11P₀] [Option ID = 90461]
    2. ¹/₅[4P₂ + 3P₁ - 11P₀] [Option ID = 90460]
    3. ¹/₅[4P₂ - 3P₁ + 11P₀] [Option ID = 90462]

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    4. ¹/₅[4P₂ + 3P₁ + 11P₀] [Option ID = 90463]
    Correct Answer :- ¹/₅[4P₂ - 3P₁ + 11P₀] [Option ID = 90462]
38. In an n-type semiconductor, the Fermi level lies 0.3eV below the conduction band at 300K. If the temperature is
    

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