EC Gate Solved Paper 2016 Session 1

Q. 1 – Q. 5 carry one mark each.

Q.1 Which of the following is CORRECT
with respect to grammar and usage?
Mount Everest is ____________.
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world

Answer:(A)


Q.2 The policeman asked the victim
of a theft, “What did you ?”
(A) loose (B) lose (C) loss (D) louse

Answer:(B)



Q.3 Despite the new medicine’s ______________ in treating
diabetes, it is not ______________widely.
(A) effectiveness --- prescribed (B) availability --- used
(C) prescription --- available (D) acceptance --- proscribed


Answer:(A)



Q.4 In a huge pile of apples and oranges, both ripe and unripe
mixed together, 15% are unripe fruits. Of
the unripe fruits, 45% are apples. Of the ripe ones, 66% are
oranges. If the pile contains a total of
5692000 fruits, how many of them are apples?
(A) 2029198 (B) 2467482
(C) 2789080 (D) 3577422

Answer:(A)



Q.5 Michael lives 10 km away from where I live. Ahmed
lives 5 km away and Susan lives 7 km away
from where I live. Arun is farther away than Ahmed
but closer than Susan from where I live. From
the information provided here, what is one possible
distance (in km) at which I live from Arun’s
place?
(A) 3.00 (B) 4.99 (C) 6.02 (D) 7.01

Answer:(C)


Q. 6 – Q. 10 carry two marks each.
Q.6 A person moving through a tuberculosis prone zone
has a 50% probability of becoming infected.
However, only 30% of infected people develop the
 disease. What percentage of people moving
through a tuberculosis prone zone remains infected
 but does not show symptoms of disease?
(A) 15 (B) 33 (C) 35 (D) 37

Answer:(C)

Q.7 In a world filled with uncertainty, he was glad
to have many good friends. He had always assisted
them in times of need and was confident that they
would reciprocate. However, the events of the
last week proved him wrong.
Which of the following inference(s) is/are
logically valid and can be inferred from the above
passage?
(i) His friends were always asking him to help them.
(ii) He felt that when in need of help, his friends would let him down.
(iii)He was sure that his friends would help him when in need.
(iv) His friends did not help him last week.
(A) (i) and (ii) (B) (iii) and (iv) (C) (iii) only (D) (iv) only

Answer:(B)



Q.8 Leela is older than her cousin Pavithra. Pavithra’s
brother Shiva is older than Leela. When Pavithra
and Shiva are visiting Leela, all three like to play chess.
Pavithra wins more often than Leela does.
Which one of the following statements must be
TRUE based on the above?
(A) When Shiva plays chess with Leela and Pavithra,
he often loses.
(B) Leela is the oldest of the three.
(C) Shiva is a better chess player than Pavithra.
(D) Pavithra is the youngest of the three.


Answer:(D)



















Answer:(C)


Q.10 P, Q, R and S are working on a project. Q can
 finish the task in 25 days, working alone for 12
hours a day. R can finish the task in 50 days, working
alone for 12 hours per day. Q worked 12
hours a day but took sick leave in the beginning for two
days. R worked 18 hours a day on all days.
What is the ratio of work done by Q and R after
7 days from the start of the project?
(A) 10:11 (B) 11:10 (C) 20:21 (D) 21:20


Answer:(C)


Q. 1 – Q. 25 carry one mark each.
















Answer:(C)


Q.2 The second moment of a
Poisson-distributed randomvariable is 2.
The mean of the random
variable is _______


Answer:(0.9:1.1)




















Answer:(B)










(A) The solutions have neither maxima nor minima
 anywhere except at the boundaries.
(B) The solutions are not separable in the coordinates.
(C) The solutions are not continuous.
(D) The solutions are not dependent on the boundary conditions.


Answer:(A)

















































Answer:(C)



Q.6 Which one of the following is an eigen function of the class
of all continuous-time, linear, time-invariant systems (u(t)
denotes the unit-step function)?










Answer:(C)
















Answer:(B)














Answer:(B)
















Answer:(D)


Q.10 A continuous-time sinusoid of frequency
33 Hz is multiplied with a periodic Dirac impulse train of
frequency 46 Hz. The resulting signal is passed through
an ideal analog low-pass filter with a cutoff
frequency of 23 Hz. The fundamental frequency
(in Hz) of the output is _________


Answer:(12:14)


Q.11 A small percentage of impurity is added to an intrinsic
semiconductor at 300 K. Which one of the
following statements is true for the energy band diagram
 shown in the following figure?















(A) Intrinsic semiconductor doped with pentavalent
atoms to form n-type semiconductor
(B) Intrinsic semiconductor doped with trivalent atoms
 to form n-type semiconductor
(C) Intrinsic semiconductor doped with pentavalent
atoms to form p-type semiconductor
(D) Intrinsic semiconductor doped with trivalent
atoms to form p-type semiconductor


Answer:(A)


Q.12 Consider the following statements for a
metal oxide semiconductor field effect transistor
(MOSFET):
P: As channel length reduces, OFF-state current increases.
Q: As channel length reduces, output resistance increases.
R: As channel length reduces, threshold voltage remains constant.
S: As channel length reduces, ON current increases.
Which of the above statements are INCORRECT?
(A) P and Q (B) P and S (C) Q and R (D) R and S


Answer:(C)











































Answer:(B)






































Answer:(2.9:3.1)



Q.15 Consider the oscillator circuit shown in the figure.
The function of the network (shown in dotted
lines) consisting of the 100 kΩ resistor in series with
 the two diodes connected back-to-back is to:




























(A) introduce amplitude stabilization by preventing the
op amp from saturating and thus producing
sinusoidal oscillations of fixed amplitude
(B) introduce amplitude stabilization by forcing the opamp to
swing between positive and negative
saturation and thus producing square wave oscillations
of fixed amplitude
(C) introduce frequency stabilization by forcing the
circuit to oscillate at a single frequency
(D) enable the loop gain to take on a value
that produces square wave oscillations



Answer:(A)


Q.16 The block diagram of a frequency synthesizer consisting
of a Phase Locked Loop (PLL) and a divide-by-N counter
(comprising ÷ 2 ,÷ 4, ÷ 8, ÷ 16 outputs) is sketched below. The
synthesizer is excited with a 5 kHz signal (Input 1). The free-
running frequency of the PLL is set to 20 kHz. Assume that
the commutator switch makes contacts repeatedly
 in the order 1-2-3-4.























The corresponding frequencies synthesized are:
(A) 10 kHz, 20 kHz, 40 kHz, 80 kHz
(B) 20 kHz, 40 kHz, 80 kHz, 160 kHz
(C) 80 kHz, 40 kHz, 20 kHz, 10 kHz
(D) 160 kHz, 80 kHz, 40 kHz, 20 kHz



Answer:(A)


Q.17 The output of the combinational circuit
given below is
















(A) A+B+C
(B) A(B+C)
(C) B(C+A)
(D) C(A+B)


Answer:(C)


Q.18 What is the voltage V - out in the following circuit?




























Answer:(C)



Q.19 Match the inferences X, Y, and Z, about a
 system, to the corresponding properties of the elements
of first column in Routh’s Table of the system characteristic equation.
X: The system is stable …
Y: The system is unstable …
Z: The test breaks down …
P: … when all elements are positive
Q: … when any one element is zero
R: … when there is a change in sign of coefficients
(A) X→P, Y→Q, Z→R (B) X→Q, Y→P, Z→R
(C) X→R, Y→Q, Z→P (D) X→P, Y→R, Z→Q




Answer:(D)





Q.20 A closed-loop control system is stable if the Nyquist
plot of the corresponding open-loop transfer
function
(A) encircles the s-plane point (−1 + j0) in the counterclockwise
direction as many times as the number of right-half s-plane poles.
(B) encircles the s-plane point (0 − j1) in the clockwise direction
 as many times as the number of right-half s-plane poles.
(C) encircles the s-plane point (−1 + j0) in the counterclockwise
direction as many times as the number of left-half s-plane poles.
(D) encircles the s-plane point (−1 + j0) in the counterclockwise
 direction as many times as the number of right-half s-plane zeros.



Answer:(A)


Q.21 Consider binary data transmission at a rate of 56 kbps
using baseband binary pulse amplitude
modulation (PAM) that is designed to have a raised-cosine
spectrum. The transmission bandwidth
(in kHz) required for a roll-off factor of 0.25 is ______


Answer:(34.5:35.5)


Q.22.A superheterodyne receiver operates in the frequency
range of 58 MHz − 68 MHz. The intermediate frequency













Answer:(4.9:5.1)



Q.23 The amplitude of a sinusoidal carrier is modulated
by a single sinusoid to obtain the amplitude
modulated signal













Answer:(0.49:0.51)














Answer:(-0.28 : -0.22)


Q.25 The propagation constant of a lossy
 transmission line is











(A) L = 200 µH/m, C = 0.1 µF/m, R = 50 Ω/m, G = 0.02 S/m
(B) L = 250 µH/m, C = 0.1 µF/m, R = 100 Ω/m, G = 0.04 S/m
(C) L = 200 µH/m, C = 0.2 µF/m, R = 100 Ω/m, G = 0.02 S/m
(D) L = 250 µH/m, C = 0.2 µF/m, R = 50 Ω/m, G = 0.04 S/m


Answer:(B)



Q. 26 – Q. 55 carry two marks each.










Answer:(18:22)








































Answer:(-136 : -132)




















Answer:(4.66:4.76)





Q.30 The Laplace transform of the causal periodic square
wave of period T shown in the figure below is




















Answer:(MTA)



Q.31 A network consisting of a finite number of linear resistor (R),
inductor (L), and capacitor (C) elements, connected all in
series or all in parallel, is excited with a source of the form





























Answer:(A)


Q.32 A first-order low-pass filter of time constant T is excited
 with different input signals (with zero initial conditions up to t = 0).
Match the excitation signals X, Y, Z with the corresponding time 
responses for t ≥ 0:










(A) X→R, Y→Q, Z→P (B) X→Q, Y→P, Z→R
(C) X→R, Y→P, Z→Q (D) X→P, Y→R, Z→Q


Answer:(C)
































Answer:(0.9:1.1)

Q.34 In the circuit shown in the figure, 
the maximum power (in watt) delivered to the
 resistor R is __________






















Answer:(0.78:0.82)



Q.35 Consider the signal















Answer:(7.9:8.1)


















Answer:(-5.0 : -4.6)



Q.37 Consider an n-channel metal oxide semiconductor field 
effect transistor (MOSFET) with a gate-to-source
 voltage of















Answer:(28:29)



Q.38 The figure below shows the doping distribution
 in a p-type semiconductor in log scale. 


















The magnitude of the electric field (in kV/cm) 
in the semiconductor due to non uniform doping 
is _________


Answer:(1.10:1.25)


Q.39 Consider a silicon sample at T = 300 K, 
with a uniform donor density





























Answer:(A)
















































Answer:(14.9:15.5)


Q41. A p-i-n photodiode of responsivity 0.8A/W
is connected to the inverting input of an ideal opamp as
shown in the figure, +Vcc = 15 V, −Vcc
= −15V, Load resistor












Answer:(790 : 810 ; -810 : -790)




Q.42 Identify the circuit below.





















(A) Binary to Gray code converter 
(B) Binary to XS3 converter
(C) Gray to Binary converter 
(D) XS3 to Binary converter

Answer:(MTA)



Q.43 The functionality implemented 
by the circuit below is




















(A) 2-to-1 multiplexer 
(B) 4-to-1 multiplexer
(C) 7-to-1 multiplexer 
(D) 6-to-1 multiplexer

Answer:(B)


Q.44 In an 8085 system, a PUSH operation requires more 
clock cycles than a POP operation. Which one 
of the following options is the correct reason for this?
(A) For POP, the data transceivers remain in the same direction 
as for instruction fetch (memory to 
processor), whereas for PUSH their direction has to be reversed.
(B) Memory write operations are slower than memory read 
operations in an 8085 based system.
(C) The stack pointer needs to be pre-decremented before 
writing registers in a PUSH, whereas a
POP operation uses the address already in the stack pointer.
(D) Order of registers has to be interchanged for a PUSH 
operation, whereas POP uses their natural 
order.


Answer:(C)



Q.45 The open-loop transfer function of a unity-feedback 
control system is 







The value of K at the breakaway point of the feedback 
control system’s root-locus plot is ________

Answer:(1.2 : 1.3 ; -1.3 : -1.2)

Q.46 The open-loop transfer function of a unity-feedback 
control system is given by







For the peak overshoot of the closed-loop system to a unit
 step input to be 10%, the value of K is 
____________

Answer:(2.7 : 3.0)



Q.47 The transfer function of a linear time invariant 
system is given by






The number of zeros in the right half of the 
s-plane is ________

Answer:( 3 : 3)


Q.48 Consider a discrete memoryless source 
with alphabet S =









 The entropy of the source (in bits) is _______ 


Answer:( 1.8 : 2.2)


Q.49 A digital communication system uses a repetition code 
for channel encoding/decoding. During transmission, each 
bit is repeated three times (0 is transmitted as 000, and 1 is 
transmitted as 111). It is assumed that the source puts out 
symbols independently and with equal probability. The 
decoder operates as follows: In a block of three received bits,
 if the number of zeros exceeds the number of ones, the 
decoder decides in favor of a 0, and if the number of ones 
exceeds the number of zeros, the decoder decides in 
favor of a 1. Assuming a binary symmetric channel with 
crossover probability p = 0.1, 
the average probability of error is ________


Answer:(0.025 : 0.030 )



Q.50 An analog pulse s(t) is transmitted over an additive
white Gaussian noise (AWGN) channel. The
received signal is r(t) = s(t) + n(t), where n(t)
is additive white Gaussian noise with power spectral
























Answer:(A)



Q.51 The current density in a medium is given by
































Answer:(MTA)



Q.52 An antenna pointing in a certain direction has a
 noise temperature of 50 K. The ambient 
temperature is 290 K. The antenna is connected to a pre-
amplifier that has a noise figure of 2 dB and an available gain 
    of 40 dB over an effective bandwidth of 12 MHz. 
    The effective input noise temperature


















Answer:(A)

Q.53 Two lossless X-band horn antennas are separated
 by a distance of 200λ. The amplitude reflection coefficients 
at the terminals of the transmitting and receiving antennas 
are 0.15 and 0.18, respectively. The maximum directivities 
of the transmitting and receiving antennas (over the 
isotropic antenna) are 18 dB and 22 dB, respectively. 
Assuming that the input power in the lossless 
transmission line connected to the antenna is 2 W, 
and that the antennas are perfectly aligned and 
polarization matched, the power ( in mW) delivered to 
the load at the receiver is ________


Answer:(2.7 : 3.3)

Q.54 The electric field of a uniform plane wave travelling 
along the negative z direction is given by the following equation:






This wave is incident upon a receiving antenna placed at the 
origin and whose radiated electric field towards the incident 
wave is given by the following equation:









The polarization of the incident wave, the polarization 
of the antenna and losses due to the 
polarization mismatch are, respectively,
(A) Linear, Circular (clockwise), −5dB 
(B) Circular (clockwise), Linear, −5dB
(C) Circular (clockwise), Linear, −3dB
(D) Circular (anti clockwise), Linear, −3dB

Answer:(C ; D)




Q.55 The far-zone power density radiated by a 
helical antenna is approximated as:





Answer:(B)



End of Question Paper 

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