# GATE Mock Test Electronics Engineering (ECE)- 5

## 65 Questions MCQ Test GATE ECE (Electronics) 2023 Mock Test Series | GATE Mock Test Electronics Engineering (ECE)- 5

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Attempt GATE Mock Test Electronics Engineering (ECE)- 5 | 65 questions in 180 minutes | Mock test for GATE preparation | Free important questions MCQ to study GATE ECE (Electronics) 2023 Mock Test Series for GATE Exam | Download free PDF with solutions
QUESTION: 1

Solution:
QUESTION: 2

### The following question comprises two words that have a certain relationship between them followed by four pairs of words. Select the pair that has same relationship as the original pair of words             Fox : Cunning

Solution:

Fox is cunning animal similarly
Ants are Industrious.
The second word shows the quality of the first.

QUESTION: 3

### Replace the phrase printed in bold to make it grammatically correct ?     A twenty-first century economy "cannot be held" hostage by power cuts nor travel on nineteenth century roads.

Solution:
QUESTION: 4

Improve the sentence with suitable options by replacing the underlined word.

He "lay" on the grass enjoying the sunshine.

Solution:
QUESTION: 5

Fill in the blanks :

At times, we are all ______ to be mistaken.

Solution:

At times, we are all likely to be mistaken.

QUESTION: 6

There are two solutions of wine and water, the concentration of wine being 0.4 and 0.6 respectively. If five liters of the first solution be mixed with fifteen liters of the second, find the concentration of wine in the resultant solution.

Solution:

Resultant concentration of wine

QUESTION: 7

Rajiv bought some apples at the rate of 25 for Rs. 400 and an equal number at the rate of 30 for Rs. 270. He then sold all at the rate of 10 for Rs. 180. Find his profit/loss percentage

Solution:

Let Rajiv bought x apples of each kind.

Total cost price of Rajiv =

Total selling price of Rajiv =

SP > CP , Hence he makes profit;

Profit percentage =

QUESTION: 8

Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is alteast one graduate among them ?

Solution:

QUESTION: 9

2 men and 3 boys can do a piece of work in 10 days, while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work ?

Solution:

Let work done by 1 man in 1 day = x units

Let work done by 1 boy in 1 day = y units

2 men and 1 boy can finish work

No. of days taken by 2 men and 1 boy = = 12.5 days

QUESTION: 10

In an exam, 60% of the candidates passed in Maths and 70% candidates passed in English and 10% of the candidates failed in both the subjects, 300 candidates passed in both the subjects. Find the total number of candidates appeared in the exam, if they took test in only two subjects that is Math and English.

Solution:

Let total number of students appear be X.

X = 750

QUESTION: 11

In the figure, the value of resistor R is (I 5) ohms, where I is the current in amperes. The value of current I is

Solution:

150 – IR = 0

150 – I (I +5) = 0

150 – I2 - 5I = 0

I2 +5I – 150 = 0

I2 +15I – 10I - 150 = 0

I (I +15) – 10 (I +15) = 0

(I +15) (I-10) = 0

I = 10A & I = -15A

QUESTION: 12

The velocity of propagation of electromagnetic wave in an underground cable with relative permittivity of 9 is

Solution:

QUESTION: 13

The function shown in the figure can be represented as

Solution:
QUESTION: 14

Consider an LTI system with impulse response h(t) = e-5t u(t). Determine the output of the system for the input x(t) = 5 u(t)

Solution:

y(t)      = h(t) * x(t)

= e-5t u(t) * 5u(t)

y(t)      = (1 - e-5t) u(t)

QUESTION: 15

The value of integral   is

Solution:

= e0 ×  0

= 0

QUESTION: 16

A rectangular pulse x(t) is shown in the figure. Determine the value of

Solution:

According to Parswell’s theorem

QUESTION: 17

If   and f(t) is     as t → ∞ . Determine the value of K

Solution:

⇒K = 2

QUESTION: 18

In the signal flow graph shown in the given figure, the value of C/R ratio is

Solution:

There are three path

QUESTION: 19

What is the open-loop transfer function for an unity feedback system having root locus shown in the following figure ?

Solution:
QUESTION: 20

The digital circuit shown in the figure works as a

Solution:

For D flip-flop

Qn 1 = D

Here, D = X Qn

So Qn 1 = X Qn

So it becomes T flip-flop

QUESTION: 21

The simplified form of Boolean function F(A,B,C) implemented by the given 3 × 8 decoder is

Solution:

QUESTION: 22

The contents of the accumulator in an 8085 microprocessor is altered after the execution of the instruction

Solution:

Compare operation does not affect the accumulator and ORAA does not change the content of accumulator.

QUESTION: 23

Assuming that all the diodes are ideal in figure, the current in the diode D2 is

Solution:

Assume both the diodes are ON

So, I1 = -1A

But current can not flow from n to p side in a diode so D1 will be off and equivalent circuit becomes

Therefore,

QUESTION: 24

Determine the upper and lower threshold voltage of the schmitt trigger shown below :

Solution:

QUESTION: 25

The transistor in the given circuit, should always be in saturation region. Take VCE (sat) = 0V and VBE = 0.7V. the minimum value of RC is

Solution:

QUESTION: 26

A differential amplifier has input at non inverting terminal is 1050 μV and at inverting terminal 950 μV. What is the error in the differential output if CMRR is 1000.

Solution:

QUESTION: 27

Which one of the following type of negative feedback increases the input resistance and decreases the output resistance of an amplifier ?

Solution:
QUESTION: 28

The spectral density and auto correlation function of white noise are respectively.

Solution:

Auto corelation function and PSD are fourier transform pair

Here, PSD = N0

QUESTION: 29

For a random variable x having the probability density function is shown in the figure, what are the variance of random variable.

Solution:

=  4/3

QUESTION: 30

An amplitude modulated signal is given as, S(t) = 100 Cos 2pfct 50 Cos 2pfmt.Cos 2pfct, where f fm. and fc is the carrier frequency and fm is the modulating signal frequency. The power efficiency is.

Solution:

S(t) = 100 Cos 2pfct 50 Cos 2pfmt.Cos 2pfct

= 100 [1 0.5 Cos 2pfmt] Cos 2pfct

Here modulation index, μ = 0.5

= 11.11%

QUESTION: 31

Signal x(t) = 4Sinc2 100t. Sin 500pt .At what sampling frequency should this signal be sampled to avoid aliasing ?

Solution:

So, fm = f1 f2

= 350 Hz

So, fs  = 2fm

= 2 × 350

= 700 Hz

QUESTION: 32

The value of   is

Solution:

QUESTION: 33

The solution of differential equation dy = (1-y) dx is

Solution:

dy = (1 – y) dx

y = 1 ce-x

QUESTION: 34

The rank of the matrix A is 2, when K is

Solution:

= 2 {3k} - 3{2k} 4{2´15 - 3´16}

= 0 {for any value of k}

QUESTION: 35

Given    If C is a counter-clockwise path in the z-plane such that |z - i| = 1, the value of  is

Solution:

Poles are at z = -1, -2

There is no any pole inside the circle, so integration will be zero

QUESTION: 36

In the circuit shown in figure, determine the maximum power absorbed by the load resistance RL

Solution:

Rth  = 4 ohms

For Vth

V2 – V3 V2 – V1 12 = 0

But V1 = 2V

So,       2 V2 – V3 – V1 12 = 0

2 V2 – V3 – 2 12 = 0

2 V2 – V= -10…………....2

From equation 1 and 2

V3 – V= 12………………..1

-V3 2V= -10…………….2

V2 = 2 Volt

So V3 = 14 Volt

So Vth = 14V

QUESTION: 37

In the circuit shown below, the switch is closed at t = 0. What is the initial value of the current through the capacitor C.

Solution:

At t = 0-, the equivalent circuit is shown below :

At t = 0 , the equivalent circuit

So, ic = 4 – 3.2 = 0.8A

QUESTION: 38

Determine the z-parameter for the network shown below.

Solution:

Since it is symmetrical ladder network

QUESTION: 39

At which frequency (in rad/sec) the thevenins equivalent impedance looking at terminals AB becomes purely resistive?

Solution:

From the circuit it is clear, that ZAB becomes real when circuit is in resonance and resonance frequency of this circuit is given as

QUESTION: 40

Consider  if  y(t) = Ae-t  for    then value of A is

Solution:
QUESTION: 41

The 4-point DFT of sequence x[n] = [1,2,2,1] is

Solution:

QUESTION: 42

The output y(t) of a continuous-time system for the input x(t) is given by . Which one of the following is correct ?

Solution:

It is an integrator that generally an unstable system because integrator produces an unbounded output and for causal

Let at t = 2

It means y(2) is depends on x(4) that means present output is depends on future input, so it is non-causal

QUESTION: 43

For the NMOS and PMOS shown in the figure are matched and   = 1mA/V2  and V n = -V p = 1 V. Determine V0

Solution:

For the circuit, it is clear that since QN and QP are perfectly matched and are operating at |VGS| equal values of  i.e. are 2.5V, the symmetrical which dictates that V0 = 0V

QUESTION: 44

Determine the region of operation of BJT in the given circuit.

Solution:

Since, VEB = 0.7

Here VB = 0, So, VE = 0.7 V

So, VC = -10 4.6 × 1

= - 5.4 V

Since, VEC = 0.7 5.4 = 6.1V

That is greater than 0.2V So BJT is in active region.

QUESTION: 45

In the silicon BJT circuit shown below. Assume the emitter area of transistor Q2 is two time of area of Q1. The value of Io { Let b of the transistors are very large}

Solution:

= 2mA

Since β is very large,

So, Iref = Ic1

i.e. Ic1 = 2mA

Also the emitter current area of transistor Q2 is times of Q1

So, Ic2 = 2 Ic1

= 2 × 2 mA

= 4 mA

So, I0 = +4 mA

QUESTION: 46

Determine the current io in the given circuit.

Solution:

Circuit can be redrawn

QUESTION: 47

Consider a bar of silicon in which a hole concentration profile describe by P(x) = P0.e-x/Lp. Find the current at x = 0, given P0 = 1016/cm3, Lp = 1 mm and cross-sectional area of the bar is 100 mm2 and Dp = 12 cm2/sec.

Solution:

= 192 A/cm2

So the current Ip,

Ip = Jp × A

= 192 × 10-8

= 192 mA

QUESTION: 48

A system with the open loop transfer function   is connected in a negative feedback gain of unity. What is the value of K for which the system is unstable.

Solution:

The characteristic equation

S (S3 8S2 24S 32) K = 0

Routh – Hurwitz array

S4                1             24        K

S3                8             32        O

S2                20           K

S' (20×32-8K) 0

S0                K

So for stable system,

K > 0

and 20×32 - 8K > 0

K < 80

So for unstable system    K > 80

i.e. K = 90

QUESTION: 49

In the system shown below x(t) = e-2t u(t). Determine the output y(t) in steady state.

Solution:

Here, x(t) = e-2t u(t)

QUESTION: 50

The polar diagram of a conditionally stable system for open loop gain K = 1 is shown in the figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for

Solution:

System is stable in the region 0.1 to 5 on the left side of 10 as number of enrichment there is zero

0.1K < 1 ⇒ K < 10

5K > 1    ⇒ K > 0.2

0.2 < K < 10

Also 1 > 10 K

K < 0.1

So for the stable system 0.2 < K < 10 and K < 0.1

QUESTION: 51

The sensitivity of transfer function  with respect to the parameter K is -0.5, Determine the value of K

Solution:

8K2 10K 3 = -4K

8K2 14K 3 = 0

4K (2K 3) 1 (2K 3) = 0

(2K 3) (4K 1) = 0

K = -1.5 and K = -0.25

QUESTION: 52

Given two binary FSK signals    i = 1, 2.The minimum frequency separation of these two signals such that they are orthogonal is

Solution:

For the two signals to be orthogonal

QUESTION: 53

A block code is transmitted in NRZ invent-one-one format with voltage levels

6V → ‘1’

-6V → ‘0’

Three code words are sent : 10010, 11110, 01001. Over these three transmitted code words the average voltage is

Solution:

There are total 15 digits so, In which 8 are 1’s and 7 are 0’s

So average value = = 0.4V

QUESTION: 54

A signal is given by,

γ(t) = s(t) n(t)

where s(t) = 20 Cos2π4000t 40 Cos2π2000t and the noise n(t) is white with power spectral density η0 = 1 W/Hz. The total received signal is put through a band pass filter with pass band between 100 to 110 Hz. The value of SNR at the output of filter is

Solution:

Signal power

= 200 800

= 1000

and noise power, Pn = n0 × (BW)

= 1 × 10

= 10W

So, SNR = 1000/10 = 100

In dB = 10log100 = 20dB

QUESTION: 55

The base band signal m(t) is recovered from the DSB-Sc signal s(t) = m(t). Cos2πfct, by multiplying s(t) by the locally generated carrier Cos (2πfct φ). The product is passed through a LPF which rejects the double frequency signal. If the base band signal is band limited to 4KHz, what is the minimum value of fc for which m(t) can be recovered by filtering ?

Solution:

In order to recover m(t) from s(t) by filter method it is necessary that the lowest frequency contained in the first term of s(t) must be greater than the highest frequency contained in the second term that is

So minimum value of fc = 4 KHz

QUESTION: 56

A plane wave in free space  is incident normally on a large block of material  . which occupies z > 0. If the incident electric field is = 10 Cos (ωt z)     V/m, the reflected magnetic field is :

Solution:

QUESTION: 57

A plane wave with    is incident normally on a thick plane conductor lying in the X-Y plane. Its conductivity is 6 × 106 s/m and surface impedance is 5 × 10-4

?.  The skin depth of conductor is

Solution:

QUESTION: 58

The volume of the paralleopipe whose sides are given by  is

Solution:

Volume of paralleopipe

2 {-1} 2 {-1 3} 0 = -2 4 = 2

QUESTION: 59

A number in 4 bit 2 5 complement representation is 1101. This number when stored using 8-bits will beA number in 4 bit 2’5 complement representation is 1101. This number when stored using 8-bits will be

Solution:

The number in 4 bit 1101

So original number, 0011

Now the original number in 8-bit,

00000011

So, in 2s complement, 11111101

QUESTION: 60

Four variable K-map is shown in the figure. The essential prime implicants are

Solution:

QUESTION: 61

An 8085 microprocessor is interfaced to a 8KB RAM as shown below. The address range of the RAM is

Solution:

The RAM will be active when   is 0

when, A13 A14 A15 = 011 as decoder is active low.

So the range of RAM address is from COOOH to DFFFH

QUESTION: 62

If z = x – iy and   = p iq, then     is

Solution:

= P iq

Z = P3 (iq)3 3P (iq) (P iq)

x – iy = P3 – 3Pq2 i (3P2q – q3)

X = P3 – 3Pq2

QUESTION: 63

The Newton – Raphson method is used to find the roots of the equation f(x) = x - cosπx   If the initial guess for the root is 0.5, then the value of x after the first iteration is

Solution:

f(x)    = X - Cosπx

f(0.5) = 0.5 – Cos 0.5π

= 0.5

= 0.38

QUESTION: 64

The eign value of the matrix     are,

Solution:

QUESTION: 65

The value of     is

Solution:

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