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# Electronics And Communication - ECE 2013 GATE Paper (Practice Test)

## 65 Questions MCQ Test GATE ECE (Electronics) 2022 Mock Test Series | Electronics And Communication - ECE 2013 GATE Paper (Practice Test)

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This mock test of Electronics And Communication - ECE 2013 GATE Paper (Practice Test) for GATE helps you for every GATE entrance exam. This contains 65 Multiple Choice Questions for GATE Electronics And Communication - ECE 2013 GATE Paper (Practice Test) (mcq) to study with solutions a complete question bank. The solved questions answers in this Electronics And Communication - ECE 2013 GATE Paper (Practice Test) quiz give you a good mix of easy questions and tough questions. GATE students definitely take this Electronics And Communication - ECE 2013 GATE Paper (Practice Test) exercise for a better result in the exam. You can find other Electronics And Communication - ECE 2013 GATE Paper (Practice Test) extra questions, long questions & short questions for GATE on EduRev as well by searching above.
QUESTION: 1

Solution:
QUESTION: 2

Solution:
QUESTION: 3

### In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41ºC and of Tuesday to Thursday was 43ºC. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in ºC on Thursday was

Solution:

Let the temperature of Monday be TM
Sum of temperatures of Tuesday and Wednesday = T and
Temperature of Thursday =TTh
Now, Tm +T = 41x 3 =123
& Tth+ T= 43x 3= 129
Tth -Tm= 6, Also Tth= 1.15Tm
0.15Tm= 6 Tm =40
Temperature of thursday= 40+ 6= 46o C

QUESTION: 4

Complete the sentence:
Dare ____________ mistakes.

Solution:
QUESTION: 5

They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?

Solution:
QUESTION: 6

Q. No. 6 – 10 Carry Two Marks Each

Q.

A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16km in the third quarter. The average speed of the car in km per hour over the entire journey is

Solution:

Average speed = Total distance/Total Time

QUESTION: 7

Find the sum to n terms of the series 10 + 84 + 734 + …

Solution:

Explanations:-Using the answer options, substitute n = 2. The sum should add up to 94
Alternative Solution:
The given series is 10+84+734+………………………..+n terms

QUESTION: 8

Statement: There were different streams of freedom movements in colonial India
carried out by the moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?

Solution:
QUESTION: 9

The set of values of p for which the roots of the equation  3x2 + 2x + p( p − 1) = 0
are of opposite sign is

Solution:

QUESTION: 10

What is the chance that a leap year, selected at random, will contain 53
Sundays?

Solution:

There are 52 complete weeks in a calendar year  852 × 7 =364days
Number of days in a leap year = 366

Probability of 53 Saturdays 2/7

QUESTION: 11

Q. No. 11 – 35 Carry One Mark Each

Q.

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles

Solution:

From Truth Table, it can be verified that Ex-OR logic is implemented

QUESTION: 12

Consider a vector field  The closed loop line integral
can be expressed as

Solution:

Stoke’s Theorem: “ The Line Integral of a vector around a closed path L is
equal to the integral of curl of over the open surface S enclosed by the closed
path L”.

QUESTION: 13

In a forward biased pn junction diode, the sequence of events that best describes
the mechanism of current flow is

Solution:
QUESTION: 14

Two systems with impulse responses  h1(t) and h2(t) are connected in cascade.
Then the overall impulse response of the cascaded system is given by

Solution:

QUESTION: 15

In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation
(using steam or water vapor) produces

Solution:
QUESTION: 16

The maximum value of q until which the approximation sinθ ≈ θ holds to within 10%
error is

Solution:

Out of all possible options we need to go for max theta below 45° Hence it is
18°

QUESTION: 17

The divergence of the vector field

Solution:

QUESTION: 18

The impulse response of a system is h(t) = tu(t). For an input u(t − 1) , the output is

Solution:

For LTI system, if input gets delayed by one unit, output will also get delayed by
one unit.

QUESTION: 19

The Bode plot of a transfer function G (s) is shown in the figure below

The gain (20 log |G(s)| ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively.
The phase is negative for all ω. The G(s) is

Solution:

Any two paints on same line segment of Bode plot satisfies the equation of
straight line.

QUESTION: 20

In the circuit shown below what is the output voltage ( ) out V if a silicon transistor
Q and an ideal op-amp are used?

Solution:

QUESTION: 21

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding star equivalent will be scaled by a factor of

Solution:

Above expression shown that if Ra , Rb & Rc is scaled by k, Ra , Rb & Rc is scaled
by k only.

QUESTION: 22

For 8085 microprocessor, the following program is executed
MVI A, 05H;
MVIB, 05H;
DCR B;
JNZ PTR;
HLT;
At the end of program, accumulator contains

Solution:

Accumulator changes as follows (05 + 05 + 04 +03 +02 +01)H
At the end of Loop accumulator contains = 14H

QUESTION: 23

The bit rate of a digital communication system is R kbits/s. The modulation used is
32-QAM. The minimum bandwidth required for ISI free transmission is

Solution:

Bit rate given = R Kbits/second
Modulation = 32-QAM
No. of bits/symbol = 2 5 [log 32]
Symbol rate =R/5 k symbols / sec ond

Finally we are transmitting symbols.

QUESTION: 24

For a periodic signal v (t) = 30sin100t + 10cos300t + 6 sin(500t + π / 4) , the

Solution:

ωo =100 rad / sec fundamental

o = 300 rad / sec third harmonic

o = 500 rad / sec fifth harmonic

QUESTION: 25

In a voltage-voltage feedback as shown below, which one of the following
statements is TRUE if the gain k is increased?

Solution:

In voltage-voltage feedback

QUESTION: 26

A band-limited signal with a maximum frequency of 5 kHz is to be sampled.
According to the sampling theorem, the sampling frequency which is not valid is

Solution:

Given: fm = 5kHz
According to sampling frequency

fs2f
fs10 kHz

So, only in option (a) it is less than 10KHz ie., (5KHz)

QUESTION: 27

In a MOSFET operating in the saturation region, the channel length modulation
effect causes

Solution:

No channel length modulation

under the presence of channel length modulation

which is reduced from ∞ to finite value

QUESTION: 28

Which one of the following statements is NOT TRUE for a continuous time causal
and stable LTI system?

Solution:

For an LTI system to be stable and causal all poles or roots of characteristic
equation must lie on LHS of s-plane i.e., left hand side of jω− axis
[Refer Laplace transform].

QUESTION: 29

The minimum Eigen value of the following matrix is

Solution:

So the matrix is singular
Therefore atleast one of the Eigen value is ‘0’
As the choices are non negative, the minimum Eigen value is ‘0’

QUESTION: 30

A polynomial  f( x) = a4 x4 + a3 x3 + a2 x2 + a1 x − a0 with all coefficients positive has

Solution:

Use Routh Hurwitz Criteria to get the condition.

QUESTION: 31

Assuming zero initial condition, the response y(t) of the system given below to a
unit step input u(t) is

Solution:

Integration of unit step function is ramp output

Writing in time domain

QUESTION: 32

The transfer function V2(s) / V1(s) of the circuit shown below is

Solution:

QUESTION: 33

A source Vs (t) = V cos100πt has an internal impedance of (4 + j3)? . If a purely
resistive load connected to this source has to extract the maximum power out of the
source, its value in ? should be

Solution:

For maximum power Transfer

QUESTION: 34

The return loss of a device is found to be 20 dB. The voltage standing wave ratio
(VSWR) and magnitude of reflection coefficient are respectively

Solution:

QUESTION: 35

Let , and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t),
then the Fourier transform of the output is

Solution:

The concept of matched filter assumes that the input signal is of the same form
g(t) as the transmitted signal(except difference in amplitude).this requires that the
shape of the transmitted signal not change on reflection.

QUESTION: 36

Q. No. 36 – 65 Carry Two Marks Each

Q

Let U and V be two independent zero mean Gaussian random variables of variances1/4 and 1/9 respectively,. The probability P (3V 2U) is

Solution:

QUESTION: 37

Let A be an m x n matrix and B an n x m matrix. It is given that determinant
( Im + AB) = determinant (In + BA) , where Ik is the k × k identity matrix. Using the
above property, the determinant of the matrix given below is

Solution:

QUESTION: 38

In the circuit shown below, if the source voltage Vs =10053.13o V then the
Thevenin’s equivalent voltage in Volts as seen by the load resistance  RL is

Solution:

QUESTION: 39

The open-loop transfer function of a dc motor is given as when
connected in feedback as shown below, the approximate value of a K that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

Solution:

QUESTION: 40

In the circuit shown below, the knee current of the ideal Zener diode is 10mA. To
maintain 5V across RL , the minimum value of  RL in ? and the minimum power
rating of the Zener diode in mW, respectively, are

Solution:

Minimum power rating of Zener should = 50 mA x 5V
= 250 mW

QUESTION: 41

The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8 An ac voltage Vwx1 = 100V is applied across WX to get an open circuit voltage VYZ1 across YZ. Next, an ac voltage VYZ2 =100V is applied across YZ to get an open circuit voltage VWX2 across WX.
Then, VYZ1 / VWX1 , VWX2 / VYZ2 are respectively.

Solution:

The potentiometer gives an attenuation factor of 0.8 over v2

Since potentiometer and transformer are bilateral elements. Hence

QUESTION: 42

Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, their effective Q factor at the same operating frequency is

Solution:

When such two coils are connected in series individual inductances and

QUESTION: 43

The impulse response of a continuous time system is given by
h(t) = δ (t − 1) + δ (t − 3) . The value of the step response at t = 2 is

Solution:

h(t) =δd (t − 1) + δ (t −)

y(t) =u(t-1)+u(t-3)

y(2)=u(1)+u(-1) =1

QUESTION: 44

The small-signal resistance (  i.e dVB/dID) in k? offered by the n-channel MOSFET M shown in the figure below, at a bias point of VB = 2 V is (device data for M: device Transconductance parameter  kN = μ Cox (W / L0 = 40μA / Vthreshold voltage VTN = 1V, and neglect body effect and channel length
modulation effects)

Solution:

QUESTION: 45

The ac schematic of an NMOS common-source stage is shown in the figure below, where part of the biasing circuits has been omitted for simplicity. For the nchannel MOSFET M, the Transconductance gm = 1mA / V, and body effect and channel length modulation effect are to be neglected. The lower cutoff frequency
in Hz of the circuit is approximately at

Solution:

QUESTION: 46

A system is described by the differential equation

Let x(t) be a rectangular pulse given by

Assuming that y(0)=0 and dy/dt =0 at t = 0, the Laplace transform of y(t) is

Solution:

QUESTION: 47

A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes -2y(t) for t>0, we need to

Solution:

So if we want −2y (t) as a solution both x(t) and y(0) has to be doubled and
multiplied by –ve sign

x(t) → -2x(t)

y(0) → -2x(0)

QUESTION: 48

Consider two identically distributed zero-mean random variables U and V. Let the
cumulative distribution functions of U and 2V be F(x) and G(x) respectively.
Then, for all values of x

Solution:

F (x) = P{X x}
G (x) = P {2X x}
=P{ X x/2}

For positive value of x,
F (x) − G(x) is always greater than zero
For negative value of x.
F (x) − G(x) is − ve
but . F (x) − G(x) . x 0

QUESTION: 49

The DFT of vector  [ a b c d]  is the vector[ α β γ δ]  . Consider the product

The DFT of the vector [ p q r s] is a scaled version of

Solution:

QUESTION: 50

The signal flow graph for a system is given below. The transfer function Y(s)/U(s) for this system is

Solution:

QUESTION: 51

In the circuit shown below the op-amps are ideal. The Vout in Volts is

Solution:

V1 = 1(1+ 1)- 2(-1) =4V
Vout  =2V1= 8V

QUESTION: 52

In the circuit shown below,  Q1 has negligible collector-to-emitter saturation
voltage and the diode drops negligible voltage across it under forward bias. If
Vcc is + 5V,X and Y are digital signals with 0 V as logic 0 and VCC as logic 1,
then the Boolean expression for Z is

Solution:

QUESTION: 53

A voltage 1000sin ωt Volts is applied across YZ. Assuming ideal diodes, the
voltage measured across WX in Volts, is

Solution:

QUESTION: 54

Three capacitors  C1 ,C2 and C3 whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe voltage in Volts that can be applied across the combination, and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively.

Solution:

From (3), V 10 Volts
To operate Circuit safe, V should be minimum of those =2.8V

QUESTION: 55

There are four chips each of 1024 bytes connected to a 16 bit address bus as
shown in the figure below. RAMs 1,2,3 and 4 respectively are mapped to

Solution:

QUESTION: 56

In the circuit shown below, the silicon npn transistor Q has a very high value of
b . The required value of R2 in k? to produce IC = 1mA is

Solution:

QUESTION: 57

Let U and V be two independent and identically distributed random variables such
that P(U= 1+) = P(U= -1)=1/2 The entropy H(U + V) in bits is

Solution:

QUESTION: 58

Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the
respective received signals for both bits are as shown below.

Q.

If the detection threshold is 1, the BER will be

Solution:

QUESTION: 59

Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the
respective received signals for both bits are as shown below.

Q.

The optimum threshold to achieve minimum bit error rate (BER) is

Solution:

Optimum threshold = The point of intersection of two pdf’s

QUESTION: 60

Consider the following figure

The current IS in Amps in the voltage source, and voltage VS in Volts across the
current source respectively, are

Solution:

Is+8+5 =0

Is =13A

QUESTION: 61

Consider the following figure

Q.

The current in the 1? resistor in Amps is

Solution:

I ? 10A = we can use principle of superposition to determine the current across 1 ohm resistance.

QUESTION: 62

A monochromatic plane wave of wavelength λ = 600μm is propagating in the direction as shown in the figure below.  denote incident, reflected, and transmitted electric field vectors associated with the wave.

The angle of incidence θ1 and the expression for  are

Solution:

The given oblique incidence is an vertical polarization ie., is parallel to the
plane of incidence, is perpendicular to the plane of incident

QUESTION: 63

A monochromatic plane wave of wavelength l = 600μm is propagating in the  direction as shown in the figure below.  denote incident, reflected, and transmitted electric field vectors associated with the wave.

Q.

The expression for  is

Solution:

The reflection co-efficient for parallel polarization is given by

But  θr = θsince reflected ray and incident ray lies in the same medium by using
snell’s law

QUESTION: 64

The state diagram of a system is shown below. A system is described by the state-variable equations

Q. The state-variable equations of the system shown in the figure above are

Solution:

QUESTION: 65

The state diagram of a system is shown below. A system is described by the
state-variable equations

Q.

The state transition matrix eAt of the system shown in the figure above is

Solution: