Download GATE (Graduate Aptitude Test in Engineering) Last 10 Years 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010 EC03 Electronics and Communication Engg Question Papers With Solutions And Answer Keys
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 11/19
Q.34
The z-parameter matrix
?
?
?
?
?
?
?
?
22 21
12 11
z z
z z
for the two-port network shown is
6 ?
3 ?
input port output port
(A)
?
?
?
?
?
?
?
?
?
?
2 2
2 2
(B)
?
?
?
?
?
?
?
?
2 2
2 2
(C)
?
?
?
?
?
?
?
? ?
9 6
3 9
(D)
?
?
?
?
?
?
?
?
9 6
3 9
Q.35 A continuous-time speech signal x
a
(t) is sampled at a rate of 8 kHz and the samples are
subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real
time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all
operations sequentially, and takes 20 ?s for computing each complex multiplication (including
multiplications by 1 and ?1) and the time required for addition/subtraction is negligible, then the
maximum value of N is __________
Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
Unit
Delay
Unit
Delay
x[n]
5 5
?
+
y[n]
The filter can be used to approximate a
(A) low-pass filter (B) high-pass filter
(C) band-pass filter (D) band-stop filter
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 11/19
Q.34
The z-parameter matrix
?
?
?
?
?
?
?
?
22 21
12 11
z z
z z
for the two-port network shown is
6 ?
3 ?
input port output port
(A)
?
?
?
?
?
?
?
?
?
?
2 2
2 2
(B)
?
?
?
?
?
?
?
?
2 2
2 2
(C)
?
?
?
?
?
?
?
? ?
9 6
3 9
(D)
?
?
?
?
?
?
?
?
9 6
3 9
Q.35 A continuous-time speech signal x
a
(t) is sampled at a rate of 8 kHz and the samples are
subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real
time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all
operations sequentially, and takes 20 ?s for computing each complex multiplication (including
multiplications by 1 and ?1) and the time required for addition/subtraction is negligible, then the
maximum value of N is __________
Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
Unit
Delay
Unit
Delay
x[n]
5 5
?
+
y[n]
The filter can be used to approximate a
(A) low-pass filter (B) high-pass filter
(C) band-pass filter (D) band-stop filter
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 12/19
Q.37 The injected excess electron concentration profile in the base region of an npn BJT, biased in the
active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm
2
,
?
n
= 800 cm
2
/(V-s) in the base region and depletion layer widths are negligible, then the collector
current I
C
(in mA) at room temperature is __________
(Given: thermal voltage V
T
= 26 mV at room temperature, electronic charge q = 1.6 ? 10
?19
C)
10
14
cm
-3
0
n p n
I
B
Excess electron
profile I
E
I
C
0.5?m
Q.38 Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator
materials X (of thickness t
1
= 1 nm and dielectric constant ?
1
= 4) and Y (of thickness t
2
= 3 nm
and
dielectric constant ?
2
= 20). The capacitor in Figure II has only insulator material X of thickness t
Eq
.
If the capacitors are of equal capacitance, then the value of t
Eq
(in nm) is __________
Si
t
1
t
2
?
2
?
1
Metal
Si
Si
t
Eq ?
1
Si
Figure I
Figure II
Metal
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 11/19
Q.34
The z-parameter matrix
?
?
?
?
?
?
?
?
22 21
12 11
z z
z z
for the two-port network shown is
6 ?
3 ?
input port output port
(A)
?
?
?
?
?
?
?
?
?
?
2 2
2 2
(B)
?
?
?
?
?
?
?
?
2 2
2 2
(C)
?
?
?
?
?
?
?
? ?
9 6
3 9
(D)
?
?
?
?
?
?
?
?
9 6
3 9
Q.35 A continuous-time speech signal x
a
(t) is sampled at a rate of 8 kHz and the samples are
subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real
time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all
operations sequentially, and takes 20 ?s for computing each complex multiplication (including
multiplications by 1 and ?1) and the time required for addition/subtraction is negligible, then the
maximum value of N is __________
Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
Unit
Delay
Unit
Delay
x[n]
5 5
?
+
y[n]
The filter can be used to approximate a
(A) low-pass filter (B) high-pass filter
(C) band-pass filter (D) band-stop filter
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 12/19
Q.37 The injected excess electron concentration profile in the base region of an npn BJT, biased in the
active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm
2
,
?
n
= 800 cm
2
/(V-s) in the base region and depletion layer widths are negligible, then the collector
current I
C
(in mA) at room temperature is __________
(Given: thermal voltage V
T
= 26 mV at room temperature, electronic charge q = 1.6 ? 10
?19
C)
10
14
cm
-3
0
n p n
I
B
Excess electron
profile I
E
I
C
0.5?m
Q.38 Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator
materials X (of thickness t
1
= 1 nm and dielectric constant ?
1
= 4) and Y (of thickness t
2
= 3 nm
and
dielectric constant ?
2
= 20). The capacitor in Figure II has only insulator material X of thickness t
Eq
.
If the capacitors are of equal capacitance, then the value of t
Eq
(in nm) is __________
Si
t
1
t
2
?
2
?
1
Metal
Si
Si
t
Eq ?
1
Si
Figure I
Figure II
Metal
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 13/19
Q.39 The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used
in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown
occurs in
I
V
-80V
-70V
D1
D2
D2
D1
0-100V
Figure I Figure II
(A) D1 only (B) D2 only
(C) both D1and D2 (D) none of D1 and D2
Q.40 For the circuit shown in the figure, R
1
= R
2
= R
3
= 1 ?, L = 1 ?H and C = 1 ?F. If the input
( ) t
6
in
10 cos V = , then the overall voltage gain (V
out
/V
in
) of the circuit is __________
R
2
R
1
R
3
L
C
V
out
-
+
+
-
V
in
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 11/19
Q.34
The z-parameter matrix
?
?
?
?
?
?
?
?
22 21
12 11
z z
z z
for the two-port network shown is
6 ?
3 ?
input port output port
(A)
?
?
?
?
?
?
?
?
?
?
2 2
2 2
(B)
?
?
?
?
?
?
?
?
2 2
2 2
(C)
?
?
?
?
?
?
?
? ?
9 6
3 9
(D)
?
?
?
?
?
?
?
?
9 6
3 9
Q.35 A continuous-time speech signal x
a
(t) is sampled at a rate of 8 kHz and the samples are
subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real
time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all
operations sequentially, and takes 20 ?s for computing each complex multiplication (including
multiplications by 1 and ?1) and the time required for addition/subtraction is negligible, then the
maximum value of N is __________
Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
Unit
Delay
Unit
Delay
x[n]
5 5
?
+
y[n]
The filter can be used to approximate a
(A) low-pass filter (B) high-pass filter
(C) band-pass filter (D) band-stop filter
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 12/19
Q.37 The injected excess electron concentration profile in the base region of an npn BJT, biased in the
active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm
2
,
?
n
= 800 cm
2
/(V-s) in the base region and depletion layer widths are negligible, then the collector
current I
C
(in mA) at room temperature is __________
(Given: thermal voltage V
T
= 26 mV at room temperature, electronic charge q = 1.6 ? 10
?19
C)
10
14
cm
-3
0
n p n
I
B
Excess electron
profile I
E
I
C
0.5?m
Q.38 Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator
materials X (of thickness t
1
= 1 nm and dielectric constant ?
1
= 4) and Y (of thickness t
2
= 3 nm
and
dielectric constant ?
2
= 20). The capacitor in Figure II has only insulator material X of thickness t
Eq
.
If the capacitors are of equal capacitance, then the value of t
Eq
(in nm) is __________
Si
t
1
t
2
?
2
?
1
Metal
Si
Si
t
Eq ?
1
Si
Figure I
Figure II
Metal
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 13/19
Q.39 The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used
in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown
occurs in
I
V
-80V
-70V
D1
D2
D2
D1
0-100V
Figure I Figure II
(A) D1 only (B) D2 only
(C) both D1and D2 (D) none of D1 and D2
Q.40 For the circuit shown in the figure, R
1
= R
2
= R
3
= 1 ?, L = 1 ?H and C = 1 ?F. If the input
( ) t
6
in
10 cos V = , then the overall voltage gain (V
out
/V
in
) of the circuit is __________
R
2
R
1
R
3
L
C
V
out
-
+
+
-
V
in
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 14/19
Q.41 In the circuit shown in the figure, the channel length modulation of all transistors is non-zero
(? ? 0). Also, all transistors operate in saturation and have negligible body effect. The ac small
signal voltage gain (V
o
/V
in
) of the circuit is
V
DD
V
G
v
in
v
o
M3
M2
M1
(A) ? ?? ?? 1
( ?? ?? 1
|| ?? ?? 2
|| ?? ?? 3
)
(B) ? ?? ?? 1
( ?? ?? 1
||
1
?? ?? 3
|| ?? ?? 3
)
(C) ? ?? ?? 1
? ?? ?? 1
|| ?
1
?? ?? 2
|| ?? ?? 2
? || ?? ?? 3
? (D) ? ?? ?? 1
( ?? ?? 1
|| ?
1
?? ?? 3
|| ?? ?? 3
? || ?? ?? 2
)
Q.42 In the circuit shown in the figure, transistor M1 is in saturation and has transconductance
g
m
= 0.01 siemens. Ignoring internal parasitic capacitances and assuming the channel length
modulation ? to be zero, the small signal input pole frequency (in kHz) is __________
1k?
V
DD
50pF
5k?
v
in
v
o
M1
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 11/19
Q.34
The z-parameter matrix
?
?
?
?
?
?
?
?
22 21
12 11
z z
z z
for the two-port network shown is
6 ?
3 ?
input port output port
(A)
?
?
?
?
?
?
?
?
?
?
2 2
2 2
(B)
?
?
?
?
?
?
?
?
2 2
2 2
(C)
?
?
?
?
?
?
?
? ?
9 6
3 9
(D)
?
?
?
?
?
?
?
?
9 6
3 9
Q.35 A continuous-time speech signal x
a
(t) is sampled at a rate of 8 kHz and the samples are
subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real
time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all
operations sequentially, and takes 20 ?s for computing each complex multiplication (including
multiplications by 1 and ?1) and the time required for addition/subtraction is negligible, then the
maximum value of N is __________
Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
Unit
Delay
Unit
Delay
x[n]
5 5
?
+
y[n]
The filter can be used to approximate a
(A) low-pass filter (B) high-pass filter
(C) band-pass filter (D) band-stop filter
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 12/19
Q.37 The injected excess electron concentration profile in the base region of an npn BJT, biased in the
active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm
2
,
?
n
= 800 cm
2
/(V-s) in the base region and depletion layer widths are negligible, then the collector
current I
C
(in mA) at room temperature is __________
(Given: thermal voltage V
T
= 26 mV at room temperature, electronic charge q = 1.6 ? 10
?19
C)
10
14
cm
-3
0
n p n
I
B
Excess electron
profile I
E
I
C
0.5?m
Q.38 Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator
materials X (of thickness t
1
= 1 nm and dielectric constant ?
1
= 4) and Y (of thickness t
2
= 3 nm
and
dielectric constant ?
2
= 20). The capacitor in Figure II has only insulator material X of thickness t
Eq
.
If the capacitors are of equal capacitance, then the value of t
Eq
(in nm) is __________
Si
t
1
t
2
?
2
?
1
Metal
Si
Si
t
Eq ?
1
Si
Figure I
Figure II
Metal
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 13/19
Q.39 The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used
in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown
occurs in
I
V
-80V
-70V
D1
D2
D2
D1
0-100V
Figure I Figure II
(A) D1 only (B) D2 only
(C) both D1and D2 (D) none of D1 and D2
Q.40 For the circuit shown in the figure, R
1
= R
2
= R
3
= 1 ?, L = 1 ?H and C = 1 ?F. If the input
( ) t
6
in
10 cos V = , then the overall voltage gain (V
out
/V
in
) of the circuit is __________
R
2
R
1
R
3
L
C
V
out
-
+
+
-
V
in
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 14/19
Q.41 In the circuit shown in the figure, the channel length modulation of all transistors is non-zero
(? ? 0). Also, all transistors operate in saturation and have negligible body effect. The ac small
signal voltage gain (V
o
/V
in
) of the circuit is
V
DD
V
G
v
in
v
o
M3
M2
M1
(A) ? ?? ?? 1
( ?? ?? 1
|| ?? ?? 2
|| ?? ?? 3
)
(B) ? ?? ?? 1
( ?? ?? 1
||
1
?? ?? 3
|| ?? ?? 3
)
(C) ? ?? ?? 1
? ?? ?? 1
|| ?
1
?? ?? 2
|| ?? ?? 2
? || ?? ?? 3
? (D) ? ?? ?? 1
( ?? ?? 1
|| ?
1
?? ?? 3
|| ?? ?? 3
? || ?? ?? 2
)
Q.42 In the circuit shown in the figure, transistor M1 is in saturation and has transconductance
g
m
= 0.01 siemens. Ignoring internal parasitic capacitances and assuming the channel length
modulation ? to be zero, the small signal input pole frequency (in kHz) is __________
1k?
V
DD
50pF
5k?
v
in
v
o
M1
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 15/19
Q.43 Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum
sum-of-product (SOP) expression for the function is
PQ
RS
00 01 11 10
00
01
11
10
PQ
00 01 11
10
00
01
11
10
RS
X=0
X=1
1
1
1
1
1 1
1 1 0 0 0 0
0 0 0 0
0
0 0
0 0 0 0
0 0 0
0
0
0
0 0
0
(A) P QS X + P QS X + QR S X + QR S X
(B) QS X + Q S X
(C) QS X + Q S X
(D) QS + Q S
Q.44 For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns,
1.5 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant,
the maximum propagation delay (in ns) of the circuit is __________
P
Q
R
S
T
Y
0
1
0
1
S
0
S
0
MUX MUX
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 11/19
Q.34
The z-parameter matrix
?
?
?
?
?
?
?
?
22 21
12 11
z z
z z
for the two-port network shown is
6 ?
3 ?
input port output port
(A)
?
?
?
?
?
?
?
?
?
?
2 2
2 2
(B)
?
?
?
?
?
?
?
?
2 2
2 2
(C)
?
?
?
?
?
?
?
? ?
9 6
3 9
(D)
?
?
?
?
?
?
?
?
9 6
3 9
Q.35 A continuous-time speech signal x
a
(t) is sampled at a rate of 8 kHz and the samples are
subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real
time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all
operations sequentially, and takes 20 ?s for computing each complex multiplication (including
multiplications by 1 and ?1) and the time required for addition/subtraction is negligible, then the
maximum value of N is __________
Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
Unit
Delay
Unit
Delay
x[n]
5 5
?
+
y[n]
The filter can be used to approximate a
(A) low-pass filter (B) high-pass filter
(C) band-pass filter (D) band-stop filter
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 12/19
Q.37 The injected excess electron concentration profile in the base region of an npn BJT, biased in the
active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm
2
,
?
n
= 800 cm
2
/(V-s) in the base region and depletion layer widths are negligible, then the collector
current I
C
(in mA) at room temperature is __________
(Given: thermal voltage V
T
= 26 mV at room temperature, electronic charge q = 1.6 ? 10
?19
C)
10
14
cm
-3
0
n p n
I
B
Excess electron
profile I
E
I
C
0.5?m
Q.38 Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator
materials X (of thickness t
1
= 1 nm and dielectric constant ?
1
= 4) and Y (of thickness t
2
= 3 nm
and
dielectric constant ?
2
= 20). The capacitor in Figure II has only insulator material X of thickness t
Eq
.
If the capacitors are of equal capacitance, then the value of t
Eq
(in nm) is __________
Si
t
1
t
2
?
2
?
1
Metal
Si
Si
t
Eq ?
1
Si
Figure I
Figure II
Metal
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 13/19
Q.39 The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used
in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown
occurs in
I
V
-80V
-70V
D1
D2
D2
D1
0-100V
Figure I Figure II
(A) D1 only (B) D2 only
(C) both D1and D2 (D) none of D1 and D2
Q.40 For the circuit shown in the figure, R
1
= R
2
= R
3
= 1 ?, L = 1 ?H and C = 1 ?F. If the input
( ) t
6
in
10 cos V = , then the overall voltage gain (V
out
/V
in
) of the circuit is __________
R
2
R
1
R
3
L
C
V
out
-
+
+
-
V
in
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 14/19
Q.41 In the circuit shown in the figure, the channel length modulation of all transistors is non-zero
(? ? 0). Also, all transistors operate in saturation and have negligible body effect. The ac small
signal voltage gain (V
o
/V
in
) of the circuit is
V
DD
V
G
v
in
v
o
M3
M2
M1
(A) ? ?? ?? 1
( ?? ?? 1
|| ?? ?? 2
|| ?? ?? 3
)
(B) ? ?? ?? 1
( ?? ?? 1
||
1
?? ?? 3
|| ?? ?? 3
)
(C) ? ?? ?? 1
? ?? ?? 1
|| ?
1
?? ?? 2
|| ?? ?? 2
? || ?? ?? 3
? (D) ? ?? ?? 1
( ?? ?? 1
|| ?
1
?? ?? 3
|| ?? ?? 3
? || ?? ?? 2
)
Q.42 In the circuit shown in the figure, transistor M1 is in saturation and has transconductance
g
m
= 0.01 siemens. Ignoring internal parasitic capacitances and assuming the channel length
modulation ? to be zero, the small signal input pole frequency (in kHz) is __________
1k?
V
DD
50pF
5k?
v
in
v
o
M1
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 15/19
Q.43 Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum
sum-of-product (SOP) expression for the function is
PQ
RS
00 01 11 10
00
01
11
10
PQ
00 01 11
10
00
01
11
10
RS
X=0
X=1
1
1
1
1
1 1
1 1 0 0 0 0
0 0 0 0
0
0 0
0 0 0 0
0 0 0
0
0
0
0 0
0
(A) P QS X + P QS X + QR S X + QR S X
(B) QS X + Q S X
(C) QS X + Q S X
(D) QS + Q S
Q.44 For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns,
1.5 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant,
the maximum propagation delay (in ns) of the circuit is __________
P
Q
R
S
T
Y
0
1
0
1
S
0
S
0
MUX MUX
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 16/19
Q.45 For the circuit shown in the figure, the delay of the bubbled NAND gate is 2 ns and that of the
counter is assumed to be zero.
Q
0
(LSB)
Q1
Q
2
(MSB)
3-bit
Synchronous
Counter
RESET
Clk
If the clock (Clk) frequency is 1 GHz, then the counter behaves as a
(A) mod-5 counter (B) mod-6 counter (C) mod-7 counter (D) mod-8 counter
Q.46 The first two rows in the Routh table for the characteristic equation of a certain closed-loop control
system are given as
s
3
1 (2K + 3)
s
2
2K 4
The range of K for which the system is stable is
(A) ?2.0 < K < 0.5 (B) 0 < K < 0.5 (C) 0 < K < ? (D) 0.5 < K < ?
Q.47 A second-order linear time-invariant system is described by the following state equations
( ) ( ) ( ) t u t x t x
dt
d
3 2
1 1
= +
( ) ( ) ( ) t u t x t x
dt
d
= +
2 2
where x
1
(t) and x
2
(t) are the two state variables and u(t) denotes the input. If the output c(t) = x
1
(t),
then the system is
(A) controllable but not observable
(B) observable but not controllable
(C) both controllable and observable
(D) neither controllable nor observable
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 11/19
Q.34
The z-parameter matrix
?
?
?
?
?
?
?
?
22 21
12 11
z z
z z
for the two-port network shown is
6 ?
3 ?
input port output port
(A)
?
?
?
?
?
?
?
?
?
?
2 2
2 2
(B)
?
?
?
?
?
?
?
?
2 2
2 2
(C)
?
?
?
?
?
?
?
? ?
9 6
3 9
(D)
?
?
?
?
?
?
?
?
9 6
3 9
Q.35 A continuous-time speech signal x
a
(t) is sampled at a rate of 8 kHz and the samples are
subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real
time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all
operations sequentially, and takes 20 ?s for computing each complex multiplication (including
multiplications by 1 and ?1) and the time required for addition/subtraction is negligible, then the
maximum value of N is __________
Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
Unit
Delay
Unit
Delay
x[n]
5 5
?
+
y[n]
The filter can be used to approximate a
(A) low-pass filter (B) high-pass filter
(C) band-pass filter (D) band-stop filter
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 12/19
Q.37 The injected excess electron concentration profile in the base region of an npn BJT, biased in the
active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm
2
,
?
n
= 800 cm
2
/(V-s) in the base region and depletion layer widths are negligible, then the collector
current I
C
(in mA) at room temperature is __________
(Given: thermal voltage V
T
= 26 mV at room temperature, electronic charge q = 1.6 ? 10
?19
C)
10
14
cm
-3
0
n p n
I
B
Excess electron
profile I
E
I
C
0.5?m
Q.38 Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator
materials X (of thickness t
1
= 1 nm and dielectric constant ?
1
= 4) and Y (of thickness t
2
= 3 nm
and
dielectric constant ?
2
= 20). The capacitor in Figure II has only insulator material X of thickness t
Eq
.
If the capacitors are of equal capacitance, then the value of t
Eq
(in nm) is __________
Si
t
1
t
2
?
2
?
1
Metal
Si
Si
t
Eq ?
1
Si
Figure I
Figure II
Metal
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 13/19
Q.39 The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used
in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown
occurs in
I
V
-80V
-70V
D1
D2
D2
D1
0-100V
Figure I Figure II
(A) D1 only (B) D2 only
(C) both D1and D2 (D) none of D1 and D2
Q.40 For the circuit shown in the figure, R
1
= R
2
= R
3
= 1 ?, L = 1 ?H and C = 1 ?F. If the input
( ) t
6
in
10 cos V = , then the overall voltage gain (V
out
/V
in
) of the circuit is __________
R
2
R
1
R
3
L
C
V
out
-
+
+
-
V
in
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 14/19
Q.41 In the circuit shown in the figure, the channel length modulation of all transistors is non-zero
(? ? 0). Also, all transistors operate in saturation and have negligible body effect. The ac small
signal voltage gain (V
o
/V
in
) of the circuit is
V
DD
V
G
v
in
v
o
M3
M2
M1
(A) ? ?? ?? 1
( ?? ?? 1
|| ?? ?? 2
|| ?? ?? 3
)
(B) ? ?? ?? 1
( ?? ?? 1
||
1
?? ?? 3
|| ?? ?? 3
)
(C) ? ?? ?? 1
? ?? ?? 1
|| ?
1
?? ?? 2
|| ?? ?? 2
? || ?? ?? 3
? (D) ? ?? ?? 1
( ?? ?? 1
|| ?
1
?? ?? 3
|| ?? ?? 3
? || ?? ?? 2
)
Q.42 In the circuit shown in the figure, transistor M1 is in saturation and has transconductance
g
m
= 0.01 siemens. Ignoring internal parasitic capacitances and assuming the channel length
modulation ? to be zero, the small signal input pole frequency (in kHz) is __________
1k?
V
DD
50pF
5k?
v
in
v
o
M1
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 15/19
Q.43 Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum
sum-of-product (SOP) expression for the function is
PQ
RS
00 01 11 10
00
01
11
10
PQ
00 01 11
10
00
01
11
10
RS
X=0
X=1
1
1
1
1
1 1
1 1 0 0 0 0
0 0 0 0
0
0 0
0 0 0 0
0 0 0
0
0
0
0 0
0
(A) P QS X + P QS X + QR S X + QR S X
(B) QS X + Q S X
(C) QS X + Q S X
(D) QS + Q S
Q.44 For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns,
1.5 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant,
the maximum propagation delay (in ns) of the circuit is __________
P
Q
R
S
T
Y
0
1
0
1
S
0
S
0
MUX MUX
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 16/19
Q.45 For the circuit shown in the figure, the delay of the bubbled NAND gate is 2 ns and that of the
counter is assumed to be zero.
Q
0
(LSB)
Q1
Q
2
(MSB)
3-bit
Synchronous
Counter
RESET
Clk
If the clock (Clk) frequency is 1 GHz, then the counter behaves as a
(A) mod-5 counter (B) mod-6 counter (C) mod-7 counter (D) mod-8 counter
Q.46 The first two rows in the Routh table for the characteristic equation of a certain closed-loop control
system are given as
s
3
1 (2K + 3)
s
2
2K 4
The range of K for which the system is stable is
(A) ?2.0 < K < 0.5 (B) 0 < K < 0.5 (C) 0 < K < ? (D) 0.5 < K < ?
Q.47 A second-order linear time-invariant system is described by the following state equations
( ) ( ) ( ) t u t x t x
dt
d
3 2
1 1
= +
( ) ( ) ( ) t u t x t x
dt
d
= +
2 2
where x
1
(t) and x
2
(t) are the two state variables and u(t) denotes the input. If the output c(t) = x
1
(t),
then the system is
(A) controllable but not observable
(B) observable but not controllable
(C) both controllable and observable
(D) neither controllable nor observable
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 17/19
Q.48 The forward-path transfer function and the feedback-path transfer function of a single loop negative
feedback control system are given as
2 2
) 2 (
) (
2
+ +
+
=
s s
s K
s G and 1 ) ( = s H ,
respectively. If the variable parameter K is real positive, then the location of the breakaway point on
the root locus diagram of the system is __________
Q.49 A wide sense stationary random process ?? ( ?? ) passes through the LTI system shown in the figure. If
the autocorrelation function of ?? ( ?? ) is ?? ?? ( ?? ), then the autocorrelation function ?? ?? ( ?? ) of the output
?? ( ?? ) is equal to
Delay = T
0
X(t) Y(t)
(A) 2 ?? ?? ( ?? ) + ?? ?? ( ?? ? ?? 0
) + ?? ?? ( ?? + ?? 0
) (B) 2 ?? ?? ( ?? ) ? ?? ?? ( ?? ? ?? 0
) ? ?? ?? ( ?? + ?? 0
)
(C) 2 ?? ?? ( ?? ) + 2 ?? ?? ( ?? ? 2 ?? 0
) (D) 2 ?? ?? ( ?? ) ? 2 ?? ?? ( ?? ? 2 ?? 0
)
Q.50 A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of
4.0 kHz and two-sided noise power spectral density
5
10 5 . 2
2
?
? =
?
Watt per Hz. If information at
the rate of 52 kbps is to be transmitted over this channel with arbitrarily small bit error rate, then the
minimum bit-energy E
b
(in mJ/bit) necessary is __________
Q.51 The bit error probability of a memoryless binary symmetric channel is 10
?5
. If 10
5
bits are sent over
this channel, then the probability that not more than one bit will be in error is __________
Q.52 Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. At
10 GHz operating frequency, the value of the propagation constant (per meter) of the corresponding
propagating mode is __________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 11/19
Q.34
The z-parameter matrix
?
?
?
?
?
?
?
?
22 21
12 11
z z
z z
for the two-port network shown is
6 ?
3 ?
input port output port
(A)
?
?
?
?
?
?
?
?
?
?
2 2
2 2
(B)
?
?
?
?
?
?
?
?
2 2
2 2
(C)
?
?
?
?
?
?
?
? ?
9 6
3 9
(D)
?
?
?
?
?
?
?
?
9 6
3 9
Q.35 A continuous-time speech signal x
a
(t) is sampled at a rate of 8 kHz and the samples are
subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real
time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all
operations sequentially, and takes 20 ?s for computing each complex multiplication (including
multiplications by 1 and ?1) and the time required for addition/subtraction is negligible, then the
maximum value of N is __________
Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
Unit
Delay
Unit
Delay
x[n]
5 5
?
+
y[n]
The filter can be used to approximate a
(A) low-pass filter (B) high-pass filter
(C) band-pass filter (D) band-stop filter
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 12/19
Q.37 The injected excess electron concentration profile in the base region of an npn BJT, biased in the
active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm
2
,
?
n
= 800 cm
2
/(V-s) in the base region and depletion layer widths are negligible, then the collector
current I
C
(in mA) at room temperature is __________
(Given: thermal voltage V
T
= 26 mV at room temperature, electronic charge q = 1.6 ? 10
?19
C)
10
14
cm
-3
0
n p n
I
B
Excess electron
profile I
E
I
C
0.5?m
Q.38 Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator
materials X (of thickness t
1
= 1 nm and dielectric constant ?
1
= 4) and Y (of thickness t
2
= 3 nm
and
dielectric constant ?
2
= 20). The capacitor in Figure II has only insulator material X of thickness t
Eq
.
If the capacitors are of equal capacitance, then the value of t
Eq
(in nm) is __________
Si
t
1
t
2
?
2
?
1
Metal
Si
Si
t
Eq ?
1
Si
Figure I
Figure II
Metal
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 13/19
Q.39 The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used
in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown
occurs in
I
V
-80V
-70V
D1
D2
D2
D1
0-100V
Figure I Figure II
(A) D1 only (B) D2 only
(C) both D1and D2 (D) none of D1 and D2
Q.40 For the circuit shown in the figure, R
1
= R
2
= R
3
= 1 ?, L = 1 ?H and C = 1 ?F. If the input
( ) t
6
in
10 cos V = , then the overall voltage gain (V
out
/V
in
) of the circuit is __________
R
2
R
1
R
3
L
C
V
out
-
+
+
-
V
in
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 14/19
Q.41 In the circuit shown in the figure, the channel length modulation of all transistors is non-zero
(? ? 0). Also, all transistors operate in saturation and have negligible body effect. The ac small
signal voltage gain (V
o
/V
in
) of the circuit is
V
DD
V
G
v
in
v
o
M3
M2
M1
(A) ? ?? ?? 1
( ?? ?? 1
|| ?? ?? 2
|| ?? ?? 3
)
(B) ? ?? ?? 1
( ?? ?? 1
||
1
?? ?? 3
|| ?? ?? 3
)
(C) ? ?? ?? 1
? ?? ?? 1
|| ?
1
?? ?? 2
|| ?? ?? 2
? || ?? ?? 3
? (D) ? ?? ?? 1
( ?? ?? 1
|| ?
1
?? ?? 3
|| ?? ?? 3
? || ?? ?? 2
)
Q.42 In the circuit shown in the figure, transistor M1 is in saturation and has transconductance
g
m
= 0.01 siemens. Ignoring internal parasitic capacitances and assuming the channel length
modulation ? to be zero, the small signal input pole frequency (in kHz) is __________
1k?
V
DD
50pF
5k?
v
in
v
o
M1
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 15/19
Q.43 Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum
sum-of-product (SOP) expression for the function is
PQ
RS
00 01 11 10
00
01
11
10
PQ
00 01 11
10
00
01
11
10
RS
X=0
X=1
1
1
1
1
1 1
1 1 0 0 0 0
0 0 0 0
0
0 0
0 0 0 0
0 0 0
0
0
0
0 0
0
(A) P QS X + P QS X + QR S X + QR S X
(B) QS X + Q S X
(C) QS X + Q S X
(D) QS + Q S
Q.44 For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns,
1.5 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant,
the maximum propagation delay (in ns) of the circuit is __________
P
Q
R
S
T
Y
0
1
0
1
S
0
S
0
MUX MUX
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 16/19
Q.45 For the circuit shown in the figure, the delay of the bubbled NAND gate is 2 ns and that of the
counter is assumed to be zero.
Q
0
(LSB)
Q1
Q
2
(MSB)
3-bit
Synchronous
Counter
RESET
Clk
If the clock (Clk) frequency is 1 GHz, then the counter behaves as a
(A) mod-5 counter (B) mod-6 counter (C) mod-7 counter (D) mod-8 counter
Q.46 The first two rows in the Routh table for the characteristic equation of a certain closed-loop control
system are given as
s
3
1 (2K + 3)
s
2
2K 4
The range of K for which the system is stable is
(A) ?2.0 < K < 0.5 (B) 0 < K < 0.5 (C) 0 < K < ? (D) 0.5 < K < ?
Q.47 A second-order linear time-invariant system is described by the following state equations
( ) ( ) ( ) t u t x t x
dt
d
3 2
1 1
= +
( ) ( ) ( ) t u t x t x
dt
d
= +
2 2
where x
1
(t) and x
2
(t) are the two state variables and u(t) denotes the input. If the output c(t) = x
1
(t),
then the system is
(A) controllable but not observable
(B) observable but not controllable
(C) both controllable and observable
(D) neither controllable nor observable
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 17/19
Q.48 The forward-path transfer function and the feedback-path transfer function of a single loop negative
feedback control system are given as
2 2
) 2 (
) (
2
+ +
+
=
s s
s K
s G and 1 ) ( = s H ,
respectively. If the variable parameter K is real positive, then the location of the breakaway point on
the root locus diagram of the system is __________
Q.49 A wide sense stationary random process ?? ( ?? ) passes through the LTI system shown in the figure. If
the autocorrelation function of ?? ( ?? ) is ?? ?? ( ?? ), then the autocorrelation function ?? ?? ( ?? ) of the output
?? ( ?? ) is equal to
Delay = T
0
X(t) Y(t)
(A) 2 ?? ?? ( ?? ) + ?? ?? ( ?? ? ?? 0
) + ?? ?? ( ?? + ?? 0
) (B) 2 ?? ?? ( ?? ) ? ?? ?? ( ?? ? ?? 0
) ? ?? ?? ( ?? + ?? 0
)
(C) 2 ?? ?? ( ?? ) + 2 ?? ?? ( ?? ? 2 ?? 0
) (D) 2 ?? ?? ( ?? ) ? 2 ?? ?? ( ?? ? 2 ?? 0
)
Q.50 A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of
4.0 kHz and two-sided noise power spectral density
5
10 5 . 2
2
?
? =
?
Watt per Hz. If information at
the rate of 52 kbps is to be transmitted over this channel with arbitrarily small bit error rate, then the
minimum bit-energy E
b
(in mJ/bit) necessary is __________
Q.51 The bit error probability of a memoryless binary symmetric channel is 10
?5
. If 10
5
bits are sent over
this channel, then the probability that not more than one bit will be in error is __________
Q.52 Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. At
10 GHz operating frequency, the value of the propagation constant (per meter) of the corresponding
propagating mode is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 18/19
Q.53 Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The
increasing order of the cut-off frequencies for different modes is
(A) TE
01
< TE
10
< TE
11
< TE
20
(B) TE
20
< TE
11
< TE
10
< TE
01
(C) TE
10
< TE
20
< TE
01
< TE
11
(D) TE
10
< TE
11
< TE
20
< TE
01
Q.54 A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has
a gain of 150 and is aligned for maximum directional radiation and reception to a target 1 km away
having radar cross-section of 3 m
2
. If it transmits 100 kW, then the received power (in ?W) is
__________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 1/19
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a 2 ? 2 square matrix
?
?
?
?
?
?
?
?
=
? ?
? x
A ,
where x is unknown. If the eigenvalues of the matrix A are ) ( ? ? j +
and ) ( ? ? j ? , then x is
equal to
(A) ? j + (B) j? ? (C) ? + (D) ? ?
Q.2
For ( )
( )
2
sin
z
z
z f = , the residue of the pole at z = 0 is __________
Q.3 The probability of getting a ?head? in a single toss of a biased coin is 0.3. The coin is tossed
repeatedly till a ?head? is obtained. If the tosses are independent, then the probability of getting
?head? for the first time in the fifth toss is __________
Q.4
The integral
?
?
1
0
) 1 ( x
dx
is equal to __________
Q.5 Consider the first order initial value problem
y' = y + 2x ? x
2
, y(0) = 1, (0 ? x < ?)
with exact solution y(x) = x
2
+ e
x
. For x = 0.1, the percentage difference between the exact solution
and the solution obtained using a single iteration of the second-order Runge-Kutta method with
step-size h = 0.1is __________
Q.6 Consider the signal ?? ( ?? ) = cos(6 ???? ) + sin(8???? ), where ?? is in seconds. The Nyquist sampling
rate (in samples/second) for the signal ?? ( ?? ) = ?? (2 ?? + 5) is
(A) 8 (B) 12 (C) 16 (D) 32
Q.7
If the signal ?? ( ?? ) =
s in( ?? )
????
?
s in( ?? )
????
with ? denoting the convolution operation, then x(t) is equal to
(A)
s in( ?? )
????
(B)
s in( 2 ?? )
2 ????
(C)
2 s in( ?? )
????
(D) ?
s in( ?? )
????
?
2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 2/19
Q.8 A discrete-time signal ?? [ ?? ] = ?? [ ?? ? 3] + 2 ?? [ ?? ? 5] has z-transform X(z). If ?? ( ?? ) = ?? ( ? ?? ) is the
z-transform of another signal y[n], then
(A) ?? [ ?? ] = ?? [ ?? ] (B) ?? [ ?? ] = ?? [ ? ?? ]
(C) ?? [ ?? ] = ? ?? [ ?? ] (D) ?? [ ?? ] = ? ?? [ ? ?? ]
Q.9 In the RLC circuit shown in the figure, the input voltage is given by
?? ?? ( ?? ) = 2 cos(200 ?? ) + 4 sin(500 ?? ).
The output voltage ?? ?? ( ?? ) is
+
-
0.25 H
100 ?F
2 ?
0.4 H 10 ?F
2 ?
v
o
(t)
+
-
v
i
(t)
(A) cos(200 ?? ) + 2 sin(500 ?? ) (B) 2cos(200 ?? ) + 4 sin(500 ?? )
(C) sin(200 ?? ) + 2 cos(500 ?? ) (D) 2sin(200 ?? ) + 4 cos(500 ?? )
Q.10 The I-V characteristics of three types of diodes at the room temperature, made of semiconductors
X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in
all respects except their materials. If E
gX
, E
gY
and E
gZ
are the band gaps of X, Y and Z, respectively,
then
X Y
Z
V
I
(A) E
gX
> E
gY
> E
gZ
(B) E
gX
= E
gY
= E
gZ
(C) E
gX
< E
gY
< E
gZ
(D) no relationship among these band gaps exists.
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 3/19
Q.11 The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in
E
C
E
V
E
i
E
FS
SiO
2
E
M
?
B
?
B
(A) inversion (B) accumulation (C) depletion (D) flat band
Q.12 The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm
2
. The solar cell has an area of 3 cm
2
and a fill factor of 0.7. The maximum
efficiency (in %) of the device is __________
I
V
I
SC
= 180mA
V
OC
=0.5V
(0, 0)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 4/19
Q.13 The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is
very large compared to the time period of the ac voltage. Assuming that the diodes do not
breakdown in the reverse bias, the output voltage V
O
(in volt) at the steady state is __________
ac
C
R
+
-
V
o
10sin?t
D1
D2
C
Q.14 Consider the circuit shown in the figure. Assuming V
BE1
= V
EB2
= 0.7 volt, the value of the dc
voltage V
C2
(in volt) is __________
10 k?
1 k?
?
1
=100
?
2
= 50
V
CC
= 2.5V
Q1
Q2
1V
V
C2
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 5/19
Q.15 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the
output pin 3 is __________
Gnd
Trig
Thresh
Disch
Vcc
Res
Out
R
B
= 4.7 k?
R
A
= 2.2 k?
V
cc
4
8
7
6
2
1
3
555 Timer
C = 0.022 ?F
Q.16 In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0,
respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and
the carry flag, respectively, will be
(A) 4E and 0 (B) 4E and 1 (C) 4F and 0 (D) 4F and 1
Q.17 The logic functionality realized by the circuit shown below is
(A) OR (B) XOR (C) NAND (D) AND
Q.18 The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is
(A) 4 (B) 5 (C) 6 (D) 7
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 6/19
Q.19 The block diagram of a feedback control system is shown in the figure. The overall closed-loop
gain G of the system is
G
1
G
2
H
1
+
?
+
?
X Y
(A)
1 1
2 1
1 H G
G G
G
+
= (B)
1 1 2 1
2 1
1 H G G G
G G
G
+ +
=
(C)
1 2 1
2 1
1 H G G
G G
G
+
= (D)
1 2 1 2 1
2 1
1 H G G G G
G G
G
+ +
=
Q.20 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as
) 1 (
2
) (
+
=
s s
s G .
The steady state error e
ss
due to a unit step input is
G(s)
e(t)
y(t) x(t)
+
?
(A) 0 (B) 0.5 (C) 1.0 (D) ?
Q.21 For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator
frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator
frequency, then the image frequency (in MHz) is __________
Q.22 An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are
quantized into four message symbols that occur independently with probabilities p
1
= p
4
= 0.125
and p
2
= p
3
. The information rate (bits/sec) of the message source is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 7/19
Q.23 A binary baseband digital communication system employs the signal
?
?
?
?
?
? ?
=
otherwise , 0
T t 0 ,
T
1
) t (
S
S
p
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal
will be
(A)
0
1/T
s
T
s
2T
s
y(t)
t
(B)
0
T
s
2T
s
0.5
y(t)
t
(C)
1
0
T
s
2T
s
y(t)
t
(D)
1
0
T
s
/2 T
s
y(t)
t
Q.24 If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then
the reflected wave will be
(A) right-handed circularly polarized
(B) left-handed circularly polarized
(C) elliptically polarized with a tilt angle of 45
0
(D) horizontally polarized
Q.25 Faraday?s law of electromagnetic induction is mathematically described by which one of the
following equations?
(A) 0 = ? ? B
?
(B)
V
D ? = ? ?
?
(C)
t
B
E
?
?
? = ? ?
?
?
(D)
t
D
E H
?
?
+ = ? ?
?
? ?
?
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 8/19
Q. 26 ? Q. 55 carry two marks each.
Q.26 The particular solution of the initial value problem given below is
2
2
0
12 36 0 with (0) 3 and 36
x
d y dy dy
yy
dx dx dx
=
+ += = = ?
(A) (3 ? 18x) e
?6x
(B) (3 + 25x) e
?6x
(C) (3 + 20x) e
?6x
(D) (3 ? 12x) e
?6x
Q.27 If the vectors e
1
= (1, 0, 2), e
2
= (0, 1, 0) and e
3
= (?2, 0, 1) form an orthogonal basis of the three-
dimensional real space ?
3
, then the vector u = (4, 3,?3) ? ?
3
can be expressed as
(A)
3 2 1
5
11
3
5
2
e e e u ? ? ? = (B)
3 2 1
5
11
3
5
2
e e e u + ? ? =
(C)
3 2 1
5
11
3
5
2
e e e u + + ? = (D)
3 2 1
5
11
3
5
2
e e e u ? + ? =
Q.28 A triangle in the xy-plane is bounded by the straight lines 2x = 3y, y = 0 and x = 3. The volume
above the triangle and under the plane x + y + z = 6 is __________
Q.29
The values of the integral
1
22
z
c
e
dz
jz ? ?
? ?
along a closed contour c in anti-clockwise direction for
(i) the point z
0
= 2 inside the contour c, and
(ii) the point z
0
= 2 outside the contour c,
respectively, are
(A) (i) 2.72, (ii) 0 (B) (i) 7.39, (ii) 0
(C) (i) 0, (ii) 2.72 (D) (i) 0, (ii) 7.39
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 9/19
Q.30
A signal 2 cos ?
2 ?? 3
?? ? ? cos (???? ) is the input to an LTI system with the transfer function
?? ( ?? ) = ?? ?? + ?? ? ?? .
If ?? ?? denotes the k
th
coefficient in the exponential Fourier series of the output signal, then ?? 3
is
equal to
(A) 0 (B) 1 (C) 2 (D) 3
Q.31 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the
shaded region in the z-plane. If the signal ( ) [ ] 2.0 ,
n
xn n = ??<<+?, then the ROC of its
z-transform is represented by
(A)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(B)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(C)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(D)
Im
Re
Unit circle
z-plane
?
0.5
?
2
(ROC does not exist)
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 10/19
Q.32 Assume that the circuit in the figure has reached the steady state before time ?? = 0 when the 3 ?
resistor suddenly burns out, resulting in an open circuit. The current ?? ( ?? ) (in ampere) at ?? = 0
+
is
__________
12 V
1 ?
3 F
2 ?
2 F
3 ?
2 ?
i(t)
Q.33 In the figure shown, the current ?? (in ampere) is __________
5 ?
1 ?
1 ? 1 ?
1 ?
i
8 V
1 A
8 V
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 11/19
Q.34
The z-parameter matrix
?
?
?
?
?
?
?
?
22 21
12 11
z z
z z
for the two-port network shown is
6 ?
3 ?
input port output port
(A)
?
?
?
?
?
?
?
?
?
?
2 2
2 2
(B)
?
?
?
?
?
?
?
?
2 2
2 2
(C)
?
?
?
?
?
?
?
? ?
9 6
3 9
(D)
?
?
?
?
?
?
?
?
9 6
3 9
Q.35 A continuous-time speech signal x
a
(t) is sampled at a rate of 8 kHz and the samples are
subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real
time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all
operations sequentially, and takes 20 ?s for computing each complex multiplication (including
multiplications by 1 and ?1) and the time required for addition/subtraction is negligible, then the
maximum value of N is __________
Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
Unit
Delay
Unit
Delay
x[n]
5 5
?
+
y[n]
The filter can be used to approximate a
(A) low-pass filter (B) high-pass filter
(C) band-pass filter (D) band-stop filter
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 12/19
Q.37 The injected excess electron concentration profile in the base region of an npn BJT, biased in the
active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.001 cm
2
,
?
n
= 800 cm
2
/(V-s) in the base region and depletion layer widths are negligible, then the collector
current I
C
(in mA) at room temperature is __________
(Given: thermal voltage V
T
= 26 mV at room temperature, electronic charge q = 1.6 ? 10
?19
C)
10
14
cm
-3
0
n p n
I
B
Excess electron
profile I
E
I
C
0.5?m
Q.38 Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator
materials X (of thickness t
1
= 1 nm and dielectric constant ?
1
= 4) and Y (of thickness t
2
= 3 nm
and
dielectric constant ?
2
= 20). The capacitor in Figure II has only insulator material X of thickness t
Eq
.
If the capacitors are of equal capacitance, then the value of t
Eq
(in nm) is __________
Si
t
1
t
2
?
2
?
1
Metal
Si
Si
t
Eq ?
1
Si
Figure I
Figure II
Metal
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 13/19
Q.39 The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used
in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown
occurs in
I
V
-80V
-70V
D1
D2
D2
D1
0-100V
Figure I Figure II
(A) D1 only (B) D2 only
(C) both D1and D2 (D) none of D1 and D2
Q.40 For the circuit shown in the figure, R
1
= R
2
= R
3
= 1 ?, L = 1 ?H and C = 1 ?F. If the input
( ) t
6
in
10 cos V = , then the overall voltage gain (V
out
/V
in
) of the circuit is __________
R
2
R
1
R
3
L
C
V
out
-
+
+
-
V
in
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 14/19
Q.41 In the circuit shown in the figure, the channel length modulation of all transistors is non-zero
(? ? 0). Also, all transistors operate in saturation and have negligible body effect. The ac small
signal voltage gain (V
o
/V
in
) of the circuit is
V
DD
V
G
v
in
v
o
M3
M2
M1
(A) ? ?? ?? 1
( ?? ?? 1
|| ?? ?? 2
|| ?? ?? 3
)
(B) ? ?? ?? 1
( ?? ?? 1
||
1
?? ?? 3
|| ?? ?? 3
)
(C) ? ?? ?? 1
? ?? ?? 1
|| ?
1
?? ?? 2
|| ?? ?? 2
? || ?? ?? 3
? (D) ? ?? ?? 1
( ?? ?? 1
|| ?
1
?? ?? 3
|| ?? ?? 3
? || ?? ?? 2
)
Q.42 In the circuit shown in the figure, transistor M1 is in saturation and has transconductance
g
m
= 0.01 siemens. Ignoring internal parasitic capacitances and assuming the channel length
modulation ? to be zero, the small signal input pole frequency (in kHz) is __________
1k?
V
DD
50pF
5k?
v
in
v
o
M1
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 15/19
Q.43 Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum
sum-of-product (SOP) expression for the function is
PQ
RS
00 01 11 10
00
01
11
10
PQ
00 01 11
10
00
01
11
10
RS
X=0
X=1
1
1
1
1
1 1
1 1 0 0 0 0
0 0 0 0
0
0 0
0 0 0 0
0 0 0
0
0
0
0 0
0
(A) P QS X + P QS X + QR S X + QR S X
(B) QS X + Q S X
(C) QS X + Q S X
(D) QS + Q S
Q.44 For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns,
1.5 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant,
the maximum propagation delay (in ns) of the circuit is __________
P
Q
R
S
T
Y
0
1
0
1
S
0
S
0
MUX MUX
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 16/19
Q.45 For the circuit shown in the figure, the delay of the bubbled NAND gate is 2 ns and that of the
counter is assumed to be zero.
Q
0
(LSB)
Q1
Q
2
(MSB)
3-bit
Synchronous
Counter
RESET
Clk
If the clock (Clk) frequency is 1 GHz, then the counter behaves as a
(A) mod-5 counter (B) mod-6 counter (C) mod-7 counter (D) mod-8 counter
Q.46 The first two rows in the Routh table for the characteristic equation of a certain closed-loop control
system are given as
s
3
1 (2K + 3)
s
2
2K 4
The range of K for which the system is stable is
(A) ?2.0 < K < 0.5 (B) 0 < K < 0.5 (C) 0 < K < ? (D) 0.5 < K < ?
Q.47 A second-order linear time-invariant system is described by the following state equations
( ) ( ) ( ) t u t x t x
dt
d
3 2
1 1
= +
( ) ( ) ( ) t u t x t x
dt
d
= +
2 2
where x
1
(t) and x
2
(t) are the two state variables and u(t) denotes the input. If the output c(t) = x
1
(t),
then the system is
(A) controllable but not observable
(B) observable but not controllable
(C) both controllable and observable
(D) neither controllable nor observable
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 17/19
Q.48 The forward-path transfer function and the feedback-path transfer function of a single loop negative
feedback control system are given as
2 2
) 2 (
) (
2
+ +
+
=
s s
s K
s G and 1 ) ( = s H ,
respectively. If the variable parameter K is real positive, then the location of the breakaway point on
the root locus diagram of the system is __________
Q.49 A wide sense stationary random process ?? ( ?? ) passes through the LTI system shown in the figure. If
the autocorrelation function of ?? ( ?? ) is ?? ?? ( ?? ), then the autocorrelation function ?? ?? ( ?? ) of the output
?? ( ?? ) is equal to
Delay = T
0
X(t) Y(t)
(A) 2 ?? ?? ( ?? ) + ?? ?? ( ?? ? ?? 0
) + ?? ?? ( ?? + ?? 0
) (B) 2 ?? ?? ( ?? ) ? ?? ?? ( ?? ? ?? 0
) ? ?? ?? ( ?? + ?? 0
)
(C) 2 ?? ?? ( ?? ) + 2 ?? ?? ( ?? ? 2 ?? 0
) (D) 2 ?? ?? ( ?? ) ? 2 ?? ?? ( ?? ? 2 ?? 0
)
Q.50 A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of
4.0 kHz and two-sided noise power spectral density
5
10 5 . 2
2
?
? =
?
Watt per Hz. If information at
the rate of 52 kbps is to be transmitted over this channel with arbitrarily small bit error rate, then the
minimum bit-energy E
b
(in mJ/bit) necessary is __________
Q.51 The bit error probability of a memoryless binary symmetric channel is 10
?5
. If 10
5
bits are sent over
this channel, then the probability that not more than one bit will be in error is __________
Q.52 Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. At
10 GHz operating frequency, the value of the propagation constant (per meter) of the corresponding
propagating mode is __________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 18/19
Q.53 Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The
increasing order of the cut-off frequencies for different modes is
(A) TE
01
< TE
10
< TE
11
< TE
20
(B) TE
20
< TE
11
< TE
10
< TE
01
(C) TE
10
< TE
20
< TE
01
< TE
11
(D) TE
10
< TE
11
< TE
20
< TE
01
Q.54 A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has
a gain of 150 and is aligned for maximum directional radiation and reception to a target 1 km away
having radar cross-section of 3 m
2
. If it transmits 100 kW, then the received power (in ?W) is
__________
GATE 2016 Electronics and Communication Engineering (Set 3)
EC (3) 19/19
Q.55 Consider the charge profile shown in the figure. The resultant potential distribution is best
described by
(A)
(B)
(C)
(D)
END OF THE QUESTION PAPER
FirstRanker.com - FirstRanker's Choice
This post was last modified on 18 December 2019