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

Download DUET (Delhi University Entrance Test conducted by the NTA) 2018 DU PhD in informatics IIC Question Paper With Solution Key

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DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA

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DU PhD in informatics IIC

Topic:- DU_J18_PHD_INFO

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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]
Correct Answer :- 5 [Option ID = 90519]
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]
4. log (^Mo/_M) [Option ID = 90324]
Correct Answer :- log(^Mo/_M) [Option ID = 90324]
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]
3. 100kbaud [Option ID = 90439]
4. 20kbaud [Option ID = 90437]
Correct Answer :- 50kbaud [Option ID = 90438]
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]
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]
Can the following scalar and vector potential describe an electromagnetic field?
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f(x,t) = 3xyz - 4t, A(x,t) = (2x - ?t)i + (y - 2z)j + (z - 2e^i?t)k where ? is constant.
[Question ID = 52593]
1. Yes, in the Coulomb gauge [Option ID = 90364]
2. Yes, provided ? = 0 [Option ID = 90366]
3. Yes, in the Lorentz gauge [Option ID = 90365]
4. Yes, provided ? ? 0 [Option ID = 90367]
Correct Answer :- Yes, in the Lorentz gauge [Option ID = 90365]
If the standard deviation of the Poisson's distribution is v2, 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]
4. ²/_e [Option ID = 90486]
Correct Answer :- ²/_e [Option ID = 90486]
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]
3. 0.22 [Option ID = 90432]
4. 0.66 [Option ID = 90434]
Correct Answer :- 0.22 [Option ID = 90432]
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]
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]
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]
Correct Answer :- (1,1) [Option ID = 90447]
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]
4. 2 x 10¹¹W/m² [Option ID = 90360]
Correct Answer :- 2 x 10¹³W/m² [Option ID = 90362]
If the magnetic monopole existed, then which of the following Maxwell's equations will be modified?
[Question ID = 52591]
1. divD = ? [Option ID = 90356]
2. divB = 0 [Option ID = 90358]
3. curH= J+ ^?D/_?t [Option ID = 90359]
4. curE = ^?B/_?t [Option ID = 90357]
Correct Answer :- div B = 0 [Option ID = 90358]
Evaluate ?^2p₀ ^d?/_{1 + asin²?}, a² < 1.
[Question ID = 52622]
1. ^2p/_v1+a² [Option ID = 90481]
2. ^p/_v1-a² [Option ID = 90482]
3. ^p/_v1+a² [Option ID = 90483]
4. ^2p/_v1-a² [Option ID = 90480]
Correct Answer :- ^2p/_v1-a² [Option ID = 90480]
A voltage signal V(t) has the following Fourier transform
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V(j?) = A e^-j?d, for |?| < 1
0, for |?| > 0
The energy that would be dissipated in a 1O resistor fed from V(t) is
[Question ID = 52609]
1. ^A²/_p J [Option ID = 90428]
2. ¹/_p J [Option ID = 90430]
3. ^A²/_2p J [Option ID = 90431]
4. ^{2e^-2d}/_p [Option ID = 90429]
Correct Answer :- ^A²/_2p [Option ID = 90431]
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]
2. ^4m/_r [Option ID = 90330]
3. ^2m/_vr [Option ID = 90329]
4. ^8m/_r [Option ID = 90331]
Correct Answer :- ^2m/_vr [Option ID = 90329]
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/_{3x_k²+4} [Option ID = 90511]
2. x_k+1 = ^3x_k²+4/_{2x_k²+9} [Option ID = 90509]
3. x_k+1 = ^x_k³+9/_{3x_k²+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/_{3x_k²+4} [Option ID = 90508]

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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]
Correct Answer :- 1:1000 [Option ID = 90391]
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]
4. temporary register [Option ID = 90403]
Correct Answer :- instruction register [Option ID = 90402]
Find the complimentary function
^d²y/_dx² - ^dy/_dx - 6y = e^3x
[Question ID = 52616]
1. (x²-1)e^3x [Option ID = 90459]
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]
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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Evaluate ? e^iz/z dz, where c is the circle |z| = 2.
[Question ID = 52621]
1. -ip [Option ID = 90478]
2. 2ip [Option ID = 90479]
3. ip [Option ID = 90477]
4. p [Option ID = 90476]
Correct Answer :- -ip [Option ID = 90478]
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]
4. ^x/₃ e^-x + c, c=const. [Option ID = 90455]
Correct Answer :- ^x/₂ e^-x + c, c= const. [Option ID = 90453]
The eigen values of the matrix
A=[
```
  cos ? -sin ? sin ? cos ?  
```
] are
[Question ID = 52614]
1. e^i? [Option ID = 90450]
2. 3 e^ti? [Option ID = 90451]
3. e^i? [Option ID = 90449]
4. e^i? [Option ID = 90448]
Correct Answer :- e^i? [Option ID = 90449]
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]
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]
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. ^{aZA^2/3}/_A [Option ID = 90376]
Correct Answer :- ^aZ(Z-1)/_A [Option ID = 90378]

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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]
Correct Answer :- 2050, OFFC [Option ID = 90416]
When a transistor amplifier having current gain of 75 is given an input signal
V_i = 2sin (157t+^p/₄),
the output signal is found to be
V_o = 200sin (157t+^3p/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]
Correct Answer :- a common emitter amplifier [Option ID = 90394]
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]
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]
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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The equation of motion of a bead sliding on a uniform rod rotating in a force free space is
[Question ID = 52585]
1. r¨ - r?² = 0 [Option ID = 90332]
2. r¨ - r? = 0 [Option ID = 90334]
3. r¨ - r?² = 0 [Option ID = 90333]
4. r¨ - r? + r?² = 0 [Option ID = 90335]
Correct Answer :- r¨ - r?² = 0 [Option ID = 90333]
A particle is described by a wavefunction ?(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]
4. e^-2a [Option ID = 90374]
Correct Answer :- 1-e^-2a [Option ID = 90375]
The wavefunction in the ground state of H-atom is given by ? = ¹/_vpa³ e^-r/a. Find the average value of r.
[Question ID = 52594]
1. 0 [Option ID = 90368]
2. ³/₂ a [Option ID = 90369]
3. ⁵/₂ a [Option ID = 90370]
4. ^a/₂ [Option ID = 90371]
Correct Answer :- ³/₂ a [Option ID = 90369]
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]
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]
The Lagrangian of a particle of mass m moving in a plane is given by
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L = ¹/₂m(x?²+y?²) + a(xy?+yx?)
The canonical momenta are given by
[Question ID = 52586]
1. p_x = mx? - ay?, p_y = my? + ax? [Option ID = 90338]
2. p_x = mx? + ay?, p_y = my? - ax? [Option ID = 90339]
3. p_x = mx? + ay?, p_y = my? + ax? [Option ID = 90337]
4. p_x = mx?, p_y = my? [Option ID = 90336]
Correct Answer :- p_x = mx? + ay?, p_y = my? + ax? [Option ID = 90337]
Magnetic field in a region is B = ßtz^, the induced electric field due to this time varying magnetic field is
[Question ID = 52590]
1. ^ßr/₂(f^) [Option ID = 90354]
2. ^ßr/₂(-f^) [Option ID = 90353]
3. ^ßr/₂(f^) [Option ID = 90352]
4. ßr(-f^) [Option ID = 90355]
Correct Answer :- ^ßr/₂(-f^) [Option ID = 90353]
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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The Lagrangian for an harmonic oscillator is given by L = ¹/₂x?² - ¹/₂?²x³. Find the Hamiltonian.
[Question ID = 52587]
1. H = -¹/₂p² - ¹/₂?²x³ [Option ID = 90341]
2. H = ¹/₂p² + ¹/₂?²x³ [Option ID = 90342]
3. H = ¹/₂p² + ¹/₂?²x³ [Option ID = 90343]
4. H = -¹/₂p² - ¹/₂?²x³ [Option ID = 90340]
Correct Answer :- H = ¹/₂p² + ¹/₂?²x³ [Option ID = 90342]
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]
4. ¹/₅[4P₂ + 3P₁ + 11P₀] [Option ID = 90463]
Correct Answer :- ¹/₅[4P₂ - 3P₁ + 11P₀] [Option ID = 90462]
In an n-type semiconductor, the Fermi level lies 0.3eV below the conduction band at 300K. If the temperature is
This download link is referred from the post: DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA

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This post was last modified on 29 January 2020

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