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Delhi University Entrance Test (DUET) 2020 Previous Year Question Paper With Answer Key

This post was last modified on 27 December 2020

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Topic:- ELEC PHD S2

The complex number (1+i)(2+i)(4+1) can be expressed in a + ib form as follows
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(1-i)

[Question ID = 5438]
1. 5+7i
  
  [Option ID = 21746]
2. -6+4i
  
  [Option ID = 21747]
3. -6+7i
  
  [Option ID = 21748]
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4. -4+7i
  
  [Option ID = 21749]
Correct Answer :-
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•-6+7i

[Option ID = 21748]
If f(x) = (2x + 1)/(2x-1) and g(x) = (x + 5)/(2x-3) then g(f(x)) is

[Question ID = 5439]
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1. (5x+3)/(x+4)
  
  [Option ID = 21750]
2. (3x+7)/(4-x)
  
  [Option ID = 21751]
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3. (2x-5)/(2x-3)
  
  [Option ID = 21752]
4. (12x-4)/(-2x+5)
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  [Option ID = 21753]
Correct Answer :-

• (12x-4)/(-2x+5)

[Option ID = 21753]
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lim (1 + cos x) / (x→π tan² x)

[Question ID = 5440]
1. 1
  
  [Option ID = 21754]
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2. -1
  
  [Option ID = 21755]
3. 1/2
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  [Option ID = 21756]
4. -1/2
  
  [Option ID = 21757]
Correct Answer :-

• 1/2
For the given differential equation, d²y/dx² + dy/dx

[Question ID = 5441]
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1. y(x) = Ae2x - Be-x
  
  [Option ID = 21758]
2. y(x) = Ae-2x + Bex
  
  [Option ID = 21759]
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3. y(x) = Ae2x + Bex
  
  [Option ID = 21760]
4. y(x) = Ae-2x + Be-x
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  [Option ID = 21761]
Correct Answer :-

• y(x) = Ae-2x + Bex

[Option ID = 21759]
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Given x = ct/(1-4t), y = ct²/(1-4t)' where t is a parameter and c is a constant, then dy/dx in terms of t only is

[Question ID = 5442]
1. (2t(1-2t)(1-3t))/(1-4t)2
  
  [Option ID = 21762]
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2. (2(1-2t)(1-4t)2)/(1-3t)2
  
  [Option ID = 21763]
3. (2t(1-2t)(1+3t))/(1+7t)2
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  [Option ID = 21764]
4. ((1-2t)(1-3t))/(1-7t)2
  
  [Option ID = 21765]
Correct Answer :-

• (2t(1-2t)(1-3t))/(1-4t)2

[Option ID = 21762]
The eigen values of the matrix [[4, 0, 2], [2, 1, 2], [L1, 2, 6]] are
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[Question ID = 5443]
1. 2,-3,6
  
  [Option ID = 21766]
2. -2,-3,-6
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  [Option ID = 21767]
3. -2,3,6
  
  [Option ID = 21768]
4. 2,-3,-6
  
  [Option ID = 21769]
Correct Answer :-

• -2,3,6
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[Option ID = 21768]
For what value of k the matrix [[4, k, 0], [2, 1, 2], [L1, 2, 6]] become singular?

[Question ID = 5444]
1. 1
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  [Option ID = 21770]
2. 0
  
  [Option ID = 21771]
3. 4
  
  [Option ID = 21772]
4. 2
  
  [Option ID = 21773]
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Correct Answer :-

• 4

[Option ID = 21772]

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If A is orthogonal matrix and A = [[a, b], [-b, c]], the values of a and b are

[Question ID = 5445]
1. a = b = ± 1/√2
  
  [Option ID = 21774]
2. a = b = ± 1
  
  [Option ID = 21775]
3. a = ±0 b = 1
  
  [Option ID = 21776]
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4. a = 1 b = ±0
  
  [Option ID = 21777]
Correct Answer :-
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• a = ± 1/√2 b = ± 1/√2

[Option ID = 21774]
The particular solution for Y''' - Y' = ex + e-x is

[Question ID = 5446]
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1. x(ex+e-x)/2
  
  [Option ID = 21778]
2. (ex+e-x)/2
  
  [Option ID = 21779]
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3. -x(ex+e-x)/2
  
  [Option ID = 21780]
4. -(ex + e-x)/2
  --- Content provided by FirstRanker.com ---
  
  [Option ID = 21781]
Correct Answer :-

x(ex+e-x)/2

[Option ID = 21778]
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The partial differential equation (∂²z/∂x²) + (∂²z/∂y²) = xy can be classified as

[Question ID = 5447]
1. parabolic
  
  [Option ID = 21782]
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2. hyperbolic
  
  [Option ID = 21783]
3. none of these
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  [Option ID = 21784]
4. elliptic
  
  [Option ID = 21785]
Correct Answer :-

• elliptic

[Option ID = 21785]
Consider an ordinary differential equation dx/dt = 4t+ 4. if x = x0 at t=0, the increment in x calculated using Runge-Kutta fourth order multi-step method with a step size of At = 0.2 is
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[Question ID = 5448]
1. 0.66 [Option ID = 21786]
2. 0.44 [Option ID = 21787]
3. 0.88 [Option ID = 21788]
4. 0.22 [Option ID = 21789]
Correct Answer :-
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• 0.88 [Option ID = 21788]
The velocity v(in kilometre/minute) of a motorbike which starts from rest, is given at fixed intervals of time t(in minutes) as follows:

t 2 4 6 8 10 12 14 16 18 20

V 10 18 25 29 32 20 11 5 2 0
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The approximate distance (in kilometres) rounded to two places of decimals covered in 20 minutes using Simpson's 1/3rd rule is

[Question ID = 5449]
1. 200
  
  [Option ID = 21790]
2. 309
  
  [Option ID = 21791]
3. 119
  
  [Option ID = 21792]
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4. 234
  
  [Option ID = 21793]
Correct Answer :-
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• 309

[Option ID = 21791]
Consider p(s) = s³ + a2s² + a₁s + ao with all real coefficients. It is known that its derivative p’(s) has no real roots. The number of real roots of p(s) is

[Question ID = 5450]
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1. 0
  
  [Option ID = 21794]
2. 1
  
  [Option ID = 21795]
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3. 2
  
  [Option ID = 21796]
4. 3
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  [Option ID = 21797]
Gauss Seidel method is used to solve the following equations (as per the given order):

X1+ 2x2+ 3x3= 5;
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2x1+ 3X2+ X3= 1;

3X1+ 2X2+ X3= 3;

Assuming initial guess as X1=X2=X3=0, the value of x3 after the first iteration is

[Question ID = 5451]
1. 1.55
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  [Option ID = 21798]
2. 2.55
  
  [Option ID = 21799]
3. 1.00
  
  [Option ID = 21800]
4. 3.67
  
  [Option ID = 21801]
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Correct Answer :-

• 1.55

[Option ID = 21798]

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The function f(x)=ex - 1 is to be solved using Newton-Raphson method, an initial guess of xo is taken as 1.0, then the absolute error observed at 2nd iteration is

[Question ID = 5452]
1. 0.50 [Option ID = 21802]
2. 1.25 [Option ID = 21803]
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3. 0.25 [Option ID = 21804]
4. 0.33 [Option ID = 21805]
Correct Answer :-

• 0.25 [Option ID = 21804]
IF F(s) is the Fourier transform of f(x) then the Fourier transform of e5xf(x) is

[Question ID = 5453]
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1. F(s)
  
  [Option ID = 21806]
2. F(5s)
  
  [Option ID = 21807]
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3. F(s + 5)
  
  [Option ID = 21808]
4. F(s-5)
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  [Option ID = 21809]
Correct Answer :-

• F(s + 5)

[Option ID = 21808]
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The Fourier cosine transform of 7e-x + e-5x is

[Question ID = 5454]
1. 7/(π(s²+1)(s²+25))
  
  [Option ID = 21810]
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2. 7/(s²+1) + 1/(s²+25)
  
  [Option ID = 21811]
3. 7/s²+1 + 5/s²+25
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  [Option ID = 21812]
4. 27/s² + 1/s²
  
  [Option ID = 21813]
Correct Answer :-

• 7/(s²+1) + 1/(s²+25)

[Option ID = 21811]
Using Laplace transform evaluate the given integral
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∫-∞ te-2t sin3t dt

[Question ID = 5455]
1. 12/169
  
  [Option ID = 21814]
2. 1
  
  [Option ID = 21815]
3. 9/225
  
  [Option ID = 21816]
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4. 0
  
  [Option ID = 21817]
Correct Answer :-
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• 12/169

[Option ID = 21814]
If Laplace transform of the function f(t) is given by ∫0 f(t)e-stdt then Laplace transform of the function shown in the figure is

f(t)
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5

1

[Question ID = 5456]
1. (5-e)/S
  
  [Option ID = 21818]
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2. 5/S
  
  [Option ID = 21819]
3. (5+e)/S
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  [Option ID = 21820]
4. (5+ es)/S
  
  [Option ID = 21821]
Correct Answer :-

5/S

[Option ID = 21819]
[Question ID = 5457]
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1. 15/√(2t) e^(2)
  
  [Option ID = 21822]
2. 15/2 √(2)
  
  [Option ID = 21823]
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3. 1/√π
  
  [Option ID = 21824]
4. 5/√(2τπ) e^(2)
  --- Content provided by FirstRanker.com ---
  
  [Option ID = 21825]
Correct Answer :-

• 5/√(2τπ) e^(2)

[Option ID = 21825]
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Which MATLAB command will return the corner elements of a 5-by-5 matrix A?

[Question ID = 5458]
1. A([1,1], [end, end]) [Option ID = 21826]
2. A({[1,1], [1, end], [end, 1], [end, end]}) [Option ID = 21827]
3. A(1:end, 1:end) [Option ID = 21828]
4. A([1, end], [1, end]) [Option ID = 21829]
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Correct Answer :-

• A([1, end], [1, end]) [Option ID = 21829]
Two vectors created in MATLAB as
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>> X = [7 7 7];

>> Y=6:9;

The output of the command X == Y is

[Question ID = 5459]
1. 0 1 0 0
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  [Option ID = 21830]
2. 6 7 8 9
  
  [Option ID = 21831]
3. 7 7 7 7
  
  [Option ID = 21832]
4. 0 1 0 1
  
  [Option ID = 21833]
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Correct Answer :-

• 0 1 0 0

[Option ID = 21830]

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Consider the following MATLAB vectors:

x = [ 1 2 ];

y = [ 3 4 ];

z = [x' [y;y]]';

What is the value of z after this program executes?
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[Question ID = 5460]
1. [[1, 2], [3, 4], [3, 4]]
  
  [Option ID = 21834]
2. [[1, 2], [3, 4]]
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  [Option ID = 21835]
3. [[1, 3, 3], [2, 4, 4]]
  
  [Option ID = 21836]
4. [[1, 2], [3, 3], [4, 4]]
  
  [Option ID = 21837]
Correct Answer :-

• [[1, 2], [3, 3], [4, 4]]
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[Option ID = 21837]
In C language, what is the output of the following code?

int main() { int j = 4; printf("%d%d",j,j++); }

[Question ID = 5461]
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1. 4 4
  
  [Option ID = 21838]
2. 4 5
  
  [Option ID = 21839]
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3. 5 4
  
  [Option ID = 21840]
4. 5 5
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  [Option ID = 21841]
Correct Answer :-

• 5 4

[Option ID = 21840]
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In C language, what is the output of the following code?

int main() { int a=52; printf("%0 %x",a,a); }

[Question ID = 5462]
1. 052 0x52
  --- Content provided by FirstRanker.com ---
  
  [Option ID = 21842]
2. 64 34
  
  [Option ID = 21843]
3. 62 43
  
  [Option ID = 21844]
4. error
  
  [Option ID = 21845]
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Correct Answer :-

• 64 34

[Option ID = 21843]

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The length and cross sectional area of n-type photo conductor are 150 µm and 10-7 cm² respectively. What is the transit time if the device is illuminated with an optical power of 10 µW and an applied voltage of 15 V? (Assume mobility of electron µη = 950 cm²/V.s)

[Question ID = 5463]
1. 15.8 ns
  
  [Option ID = 21846]
2. 10.5 ns
  
  [Option ID = 21847]
3. 7.4 ns
  
  [Option ID = 21848]
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4. 3.1 ns
  
  [Option ID = 21849]
Correct Answer :-
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• 15.8 ns

[Option ID = 21846]
If the number density of a free electron gas changes from 1027 to 1025 electrons/m³ then the value of plasma frequency (in Hz) changes from 9.85 × 1014 to

[Question ID = 5464]
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1. 9.85 × 1010 [Option ID = 21850]
2. 9.85 × 109 [Option ID = 21851]
3. 9.85 x 1013 [Option ID = 21852]
  --- Content provided by FirstRanker.com ---
4. 9.85 × 107 [Option ID = 21853]
Correct Answer :-

• 9.85 x 1013 [Option ID = 21852]
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Match List I with List II typical spectroscopic regions type of transitions

List I List II

A. Infrared region I. Electron transition involving valance electrons

B. Ultraviolet visible region II. Nuclear transitions
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C. X-ray region III. Vibrational transitions of molecules

D. y-ray region IV. Transitions involving inner shell electrons

Choose the correct answer from the options given below:

[Question ID = 5465]
1. A III, BI, C - IV, D - II
  --- Content provided by FirstRanker.com ---
  
  [Option ID = 21854]
2. AIV, B II, CI, D - III
  
  [Option ID = 21855]
3. AI, BII, C - III, D - IV
  
  [Option ID = 21856]
4. A III, BIV, CI, D - II
  
  [Option ID = 21857]
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Correct Answer :-

AIII, BI, C - IV, D - II

[Option ID = 21854]

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The value of at which the first order peak in X-ray (λ = 1.53 Å) diffraction corresponding to (1 1 1) plane of a single cubic structure with the lattice constant a = 2.65 Å is proximately

[Question ID = 5466]
1. 15°
  
  [Option ID = 21858]
2. 45°
  
  [Option ID - 21859]
3. 30°
  
  [Option ID = 21860]
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4. 90°
  
  [Option ID = 21861]
Correct Answer :-
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30°

[Option ID = 21860]
If an IMPATT diode amplifier has negative resistance Rd = -15Ω and load resistance R₁ = 25 Ω the power gain is

[Question ID = 5467]
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1. 25 [Option ID = 21862]
2. 0 [Option ID = 21863]
3. 3.00 [Option ID = 21864]
  --- Content provided by FirstRanker.com ---
4. 16 [Option ID = 21865]
Correct Answer :-

• 16 [Option ID = 21865]
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How many AND gates are required for 1 to 16 de-multiplexer?

[Question ID = 5468]
1. 8 [Option ID = 21866]
2. 16 [Option ID = 21867]
3. 14 [Option ID = 21868]
4. 20 [Option ID = 21869]
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Correct Answer :-

• 16 [Option ID = 21867]
A 12 bit ADC is used to convert analog voltage of 0 to 10 V into digital. The resolution is
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[Question ID = 5469]
1. 24.4 mV [Option ID = 21870]
2. 2.44 mV [Option ID = 21871]
3. 1.2 V [Option ID = 21872]
4. none of these [Option ID = 21873]
Correct Answer :-
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• 2.44 mV [Option ID = 21871]
The value of x for the given system: (√2^2)^x = 6 is

[Question ID = 5470]
1. 17 [Option ID = 21874]
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2. 15 [Option ID = 21875]
3. 16 [Option ID = 21876]
4. none of these [Option ID = 21877]
Correct Answer :-

• 17 [Option ID = 21874]

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The input impedance of the following circuit

[Diagram of a circuit with 10k, 100k, and 10k resistors]

[Question ID = 5471]
1. 120 ΚΩ [Option ID = 21878]
2. 110 ΚΩ [Option ID = 21879]
3. 10 ΚΩ [Option ID = 21880]
4. Infinity [Option ID = 21881]
  --- Content provided by FirstRanker.com ---
Correct Answer :-

• 10 ΚΩ [Option ID = 21880]
What is the bandwidth of single stage amplifier if its rise time is 0.35 microseconds?
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[Question ID = 5472]
1. 2 MHz [Option ID = 21882]
2. 5 KHz [Option ID = 21883]
3. 1 MHz [Option ID = 21884]
4. 2 KHz [Option ID = 21885]
Correct Answer :-
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• 1 MHz [Option ID = 21884]
If the electric field strength E of an electromagnetic wave in free space is given by E = 2cos w(t-z/no) ay V/m. The magnetic flux density B is calculated as

[Question ID = 5473]
1. 2/vo cosw(t-z/no) -axA/m
  --- Content provided by FirstRanker.com ---
  
  [Option ID = 21886]
2. -cosw(t-z/no) ayA/m
  
  [Option ID = 21887]
3. 2/vo - sinw (t-z/no) -axA/m
  
  [Option ID = 21888]
4. 2/vo---sinw (t-z/no)ayA/m
  
  [Option ID = 21889]
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Correct Answer :-

• 2/vo cosw(t-z/no) -axA/m

[Option ID = 21886]

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The electric field acting on an electron (charge -1.6 x 10-19 C) which is 1 µm away from a perfectly conducting plane

[Question ID = 5474]
1. 181 V/m [Option ID = 21890]
2. 360 V/m [Option ID = 21891]
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3. 543 V/m [Option ID = 21892]
4. 271 V/m [Option ID = 21893]
Correct Answer :-

• 360 V/m [Option ID = 21891]
An electron starts with zero velocity from a cathode which is at a potential of -5 kV and then moves into a region where the potential is zero. The velocity of this electron is

[Question ID = 5475]
--- Content provided by FirstRanker.com ---
1. 32.65 x 106 m/s [Option ID = 21894]
2. 31.55 x 107 m/s [Option ID = 21895]
3. 41.95 x 106 m/s [Option ID = 21896]
  --- Content provided by FirstRanker.com ---
4. 52.65 x 107 m/s [Option ID = 21897]
Correct Answer :-

--- Content provided by FirstRanker.com ---

power generator whosesource impedance is 50 W. is connected to an oscilloscope by 1 m of 75 W polythene (er=2.5) filled coaxial cable. The VSWR and phase velocity respective

[Question ID = 5476]
1. 2.0 and 0.70 × 108 m/s [Option ID = 21898]
2. 1.3 and 3.65 × 108 m/s [Option ID = 21899]
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3. 1.5 and 1.90 × 108 m/s [Option ID = 21900]
4. 2.5 and 2.50 x 107 m/s [Option ID = 21901]
Correct Answer :-

• 1.5 and 1.90 × 108 m/s [Option ID = 21900]
A transmission line is terminated by a resistance load which is less than the characteristic impedance and VSWR on the line is 1.5. The ratio of reflected wave to the incident wave in decibels is

[Question ID = 5477]
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1. 0 dB [Option ID = 21902]
2. 1.5 Db [Option ID = 21903]
3. -13.98 dB [Option ID = 21904]
  --- Content provided by FirstRanker.com ---
4. -1.5 dB [Option ID = 21905]
Correct Answer :-

• -13.98 dB [Option ID = 21904]
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The power internally generated within a double-hetero junction LED if it has internal quantum efficiency of 54.5% and drive current of 50 mA with a peak emission wavelength of 0.72 µm is

[Question ID = 5478]
1. 0.09 W [Option ID = 21906]
2. 0.047 W [Option ID = 21907]
3. 0.01 W [Option ID = 21908]
4. 0.6 W [Option ID = 21909]
  --- Content provided by FirstRanker.com ---
Correct Answer :-

• 0.047 W [Option ID = 21907]
For a phototransistor having gain of 116.5, wavelength of 1.28 µm, optical power 123µW. The collector current is
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[Question ID = 5479]
1. 7.46 mA [Option ID = 21910]
2. 1.23 mA [Option ID = 21911]
3. 5.24 mA [Option ID = 21912]
4. 14.76 mA [Option ID = 21913]
Correct Answer :-
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• 14.76 mA [Option ID = 21913]
In 8086 microprocessor the overflow flag is set when

[Question ID = 5480]
1. the sum is more than 16 bits [Option ID = 21914]
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2. carry and sign flags are set. [Option ID = 21915]
3. Subtraction [Option ID = 21916]
4. signed numbers go out of their range after an arithmetic operation [Option ID = 21917]
Correct Answer :-

• signed numbers go out of their range after an arithmetic operation [Option ID = 21917]

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What is the bit size of the 8051 microcontroller?

[Question ID = 5481]
1. 4 bit [Option ID = 21918]
2. 16 bit [Option ID = 21919]
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3. 128 bit [Option ID = 21920]
4. 8 bit [Option ID = 21921]
Correct Answer :-

• 8 bit [Option ID = 21921]
Α 50 Ω lossless transmission line has a pure reactance of j100 Q as its load. The VSWR in the line is

[Question ID = 5482]
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1. ∞ (infinity)
  
  [Option ID = 21922]
2. 1/2 (half)
  
  [Option ID = 21923]
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3. 1 [Option ID = 21924]
4. 0 [Option ID = 21925]
Correct Answer :-

• ∞ (infinity)

[Option ID = 21922]
The bit stream 01001 is differentially encoded using 'Delay and EX-OR' scheme for DPSK transmission. Assuming the reference bit as '1' and assigning phases of '0' and π for 1's and O's respectively in the encoded sequence, the transmitted phase sequence becomes
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[Question ID = 5483]
1. Οπππο [Option ID = 21926]
2. ποππο [Option ID = 21927]
3. Οππ00 [Option ID = 21928]
4. ππποπ [Option ID = 21929]
Correct Answer :-
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• Οπππο [Option ID = 21926]
An AM modulator has output xc (t) = Acos(400πt)+ Bcos(380πt)+ Bcos(420πt). The carrier power is 100W and the efficiency is 40%. The value of A and B are

[Question ID = 5484]
1. 14.14, 8.16 [Option ID = 21930]
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2. 50, 10 [Option ID = 21931]
3. 22.36, 13.46 [Option ID = 21932]
4. None of these [Option ID = 21933]
Correct Answer :-

• 14.14, 8.16 [Option ID = 21930]

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To prevent overloading of the last IF amplifier in a receiver, one should use

[Question ID = 5485]
1. Squelch [Option ID = 21934]
2. Variable sensitivity [Option ID = 21935]
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3. Variable selectivity [Option ID = 21936]
4. Double conversion [Option ID = 21937]
Correct Answer :-

• Variable sensitivity [Option ID = 21935]
A base band PCM system with a matched filter at receiver is implemented with ±5V bipolar pulse with pulse duration of 72usec. If the noise power spectral density is 1.0 x 10-4 V2/Hz, the probability of error for this system is given by

[Question ID = 5486]
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1. 1.15 x 10-5 [Option ID = 21938]
2. 1.85 x 10-5 [Option ID

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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 27 December 2020

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