Download GATE (Graduate Aptitude Test in Engineering) Last 10 Years 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010 EC02 Electronics and Communication Engg Question Papers With Solutions And Answer Keys
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
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hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 6/14
Q.24 Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium
be expressed as ?? = ?? ? ?? ?? ?? ? ?? ( ???? ? ???? )
, where the propagation constant ?? is a function of the angular
frequency ?? . Assume that ?? ( ?? ) and ?? ?? are known and are real. From the information available,
which one of the following CANNOT be determined?
(A) The type of polarization of the wave.
(B) The group velocity of the wave.
(C) The phase velocity of the wave.
(D) The power flux through the ?? = 0 plane.
Q.25 Light from free space is incident at an angle ?? ?? to the normal of the facet of a step-index large core
optical fibre. The core and cladding refractive indices are ?? 1
= 1.5 and ?? 2
= 1.4, respectively.
The maximum value of ?? ?? (in degrees) for which the incident light will be guided in the core of the
fibre is ________
Q. 26 ? Q. 55 carry two marks each.
Q.26 The ordinary differential equation
????
????
= ?3 ?? + 2, with ?? (0) = 1
is to be solved using the forward Euler method. The largest time step that can be used to solve the
equation without making the numerical solution unstable is ________
Q.27 Suppose C is the closed curve defined as the circle ?? 2
+ ?? 2
= 1 with C oriented anti-clockwise.
The value of ?( ?? ?? 2
?? ?? + ?? 2
?? ?? ?? ) over the curve C equals ________
Q.28 Two random variables ?? and ?? are distributed according to
?? ?? , ?? ( ?? , ?? ) = ?
( ?? + ?? ), 0 ? ?? ? 1, 0 ? ?? ? 1
0, otherwise.
The probability ?? ( ?? + ?? ? 1) is ________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 6/14
Q.24 Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium
be expressed as ?? = ?? ? ?? ?? ?? ? ?? ( ???? ? ???? )
, where the propagation constant ?? is a function of the angular
frequency ?? . Assume that ?? ( ?? ) and ?? ?? are known and are real. From the information available,
which one of the following CANNOT be determined?
(A) The type of polarization of the wave.
(B) The group velocity of the wave.
(C) The phase velocity of the wave.
(D) The power flux through the ?? = 0 plane.
Q.25 Light from free space is incident at an angle ?? ?? to the normal of the facet of a step-index large core
optical fibre. The core and cladding refractive indices are ?? 1
= 1.5 and ?? 2
= 1.4, respectively.
The maximum value of ?? ?? (in degrees) for which the incident light will be guided in the core of the
fibre is ________
Q. 26 ? Q. 55 carry two marks each.
Q.26 The ordinary differential equation
????
????
= ?3 ?? + 2, with ?? (0) = 1
is to be solved using the forward Euler method. The largest time step that can be used to solve the
equation without making the numerical solution unstable is ________
Q.27 Suppose C is the closed curve defined as the circle ?? 2
+ ?? 2
= 1 with C oriented anti-clockwise.
The value of ?( ?? ?? 2
?? ?? + ?? 2
?? ?? ?? ) over the curve C equals ________
Q.28 Two random variables ?? and ?? are distributed according to
?? ?? , ?? ( ?? , ?? ) = ?
( ?? + ?? ), 0 ? ?? ? 1, 0 ? ?? ? 1
0, otherwise.
The probability ?? ( ?? + ?? ? 1) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 7/14
Q.29
The matrix
?
?
?
?
?
?
?
?
?
?
?
?
=
b
a
A
0 0 0
4 2 0 0
3 1 5 2
7 3 0
has det( ?? ) = 100 and trace( ?? ) = 14.
The value of | ?? ? ?? | is ________
Q.30 In the given circuit, each resistor has a value equal to 1 ?.
What is the equivalent resistance across the terminals ?? and ?? ?
(A) 1/6 ? (B) 1/3 ? (C) 9/20 ? (D) 8/15 ?
Q.31 In the circuit shown in the figure, the magnitude of the current (in amperes) through R
2
is ___
Q.32
A continuous-time filter with transfer function ?? ( ?? ) =
2 ?? + 6
?? 2
+ 6 ?? + 8
is converted to a discrete-
time filter with transfer function ?? ( ?? ) =
2 ?? 2
? 0.5 0 3 2 ?? ?? 2
? 0.5 0 3 2 ?? + ?? so that the impulse response of the
continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response
of the discrete time filter. The value of ?? is ________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
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cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
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In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
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ave become
ad a pre-colo
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(D)
en in a mirro
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What is the
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amorphous f
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or, the reflect
urrent time s
12:15
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20.61
on for leisure
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(D)
form until th
nded to furth
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statements?
sm.
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tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
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sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 6/14
Q.24 Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium
be expressed as ?? = ?? ? ?? ?? ?? ? ?? ( ???? ? ???? )
, where the propagation constant ?? is a function of the angular
frequency ?? . Assume that ?? ( ?? ) and ?? ?? are known and are real. From the information available,
which one of the following CANNOT be determined?
(A) The type of polarization of the wave.
(B) The group velocity of the wave.
(C) The phase velocity of the wave.
(D) The power flux through the ?? = 0 plane.
Q.25 Light from free space is incident at an angle ?? ?? to the normal of the facet of a step-index large core
optical fibre. The core and cladding refractive indices are ?? 1
= 1.5 and ?? 2
= 1.4, respectively.
The maximum value of ?? ?? (in degrees) for which the incident light will be guided in the core of the
fibre is ________
Q. 26 ? Q. 55 carry two marks each.
Q.26 The ordinary differential equation
????
????
= ?3 ?? + 2, with ?? (0) = 1
is to be solved using the forward Euler method. The largest time step that can be used to solve the
equation without making the numerical solution unstable is ________
Q.27 Suppose C is the closed curve defined as the circle ?? 2
+ ?? 2
= 1 with C oriented anti-clockwise.
The value of ?( ?? ?? 2
?? ?? + ?? 2
?? ?? ?? ) over the curve C equals ________
Q.28 Two random variables ?? and ?? are distributed according to
?? ?? , ?? ( ?? , ?? ) = ?
( ?? + ?? ), 0 ? ?? ? 1, 0 ? ?? ? 1
0, otherwise.
The probability ?? ( ?? + ?? ? 1) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 7/14
Q.29
The matrix
?
?
?
?
?
?
?
?
?
?
?
?
=
b
a
A
0 0 0
4 2 0 0
3 1 5 2
7 3 0
has det( ?? ) = 100 and trace( ?? ) = 14.
The value of | ?? ? ?? | is ________
Q.30 In the given circuit, each resistor has a value equal to 1 ?.
What is the equivalent resistance across the terminals ?? and ?? ?
(A) 1/6 ? (B) 1/3 ? (C) 9/20 ? (D) 8/15 ?
Q.31 In the circuit shown in the figure, the magnitude of the current (in amperes) through R
2
is ___
Q.32
A continuous-time filter with transfer function ?? ( ?? ) =
2 ?? + 6
?? 2
+ 6 ?? + 8
is converted to a discrete-
time filter with transfer function ?? ( ?? ) =
2 ?? 2
? 0.5 0 3 2 ?? ?? 2
? 0.5 0 3 2 ?? + ?? so that the impulse response of the
continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response
of the discrete time filter. The value of ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 8/14
Q.33 The Discrete Fourier Transform (DFT) of the 4-point sequence
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {3, 2, 3, 4} is
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {12, 2?? , 0, ?2?? }.
If X
1
[k] is the DFT of the 12-point sequence ?? 1
[ ?? ] = {3, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0},
the value of ?
?? 1
[ 8]
?? 1
[ 1 1]
? is ________
Q.34 The switch S in the circuit shown has been closed for a long time. It is opened at time ?? = 0 and
remains open after that. Assume that the diode has zero reverse current and zero forward voltage
drop.
The steady state magnitude of the capacitor voltage ?? C
(in volts) is ______
Q.35 A voltage ?? ?? is applied across a MOS capacitor with metal gate and p-type silicon substrate at
T=300 K. The inversion carrier density (in number of carriers per unit area) for ?? ?? = 0.8 V is
2 ? 10
1 1
cm
? 2
. For ?? ?? = 1.3 V, the inversion carrier density is 4 ? 10
1 1
cm
? 2
. What is the value
of the inversion carrier density for ?? ??
= 1.8 V?
(A) 4.5 ? 10
1 1
cm
? 2
(B) 6.0 ? 10
1 1
cm
? 2
(C) 7.2 ? 10
1 1
cm
? 2
(D) 8.4 ? 10
1 1
cm
? 2
Q.36 Consider avalanche breakdown in a silicon ?? +
?? junction. The ?? -region is uniformly doped with a
donor density ?? ?? . Assume that breakdown occurs when the magnitude of the electric field at any
point in the device becomes equal to the critical field ?? ?????? ?? . Assume ?? ?????? ?? to be independent of ?? ?? .
If the built-in voltage of the ?? +
?? junction is much smaller than the breakdown voltage, ?? ?? ?? , the
relationship between ?? ?? ?? and ?? ?? is given by
(A) ?? ?? ?? ? ? ?? ?? = constant (B) ?? ?? ? ? ?? ?? ?? = constant
(C) ?? ?? ? ?? ?? ?? = constant (D) ?? ?? / ?? ?? ?? = constant
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
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onial origin.
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urrent time s
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on for leisure
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(D)
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(D)
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stance (in km
(D)
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108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
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25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 6/14
Q.24 Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium
be expressed as ?? = ?? ? ?? ?? ?? ? ?? ( ???? ? ???? )
, where the propagation constant ?? is a function of the angular
frequency ?? . Assume that ?? ( ?? ) and ?? ?? are known and are real. From the information available,
which one of the following CANNOT be determined?
(A) The type of polarization of the wave.
(B) The group velocity of the wave.
(C) The phase velocity of the wave.
(D) The power flux through the ?? = 0 plane.
Q.25 Light from free space is incident at an angle ?? ?? to the normal of the facet of a step-index large core
optical fibre. The core and cladding refractive indices are ?? 1
= 1.5 and ?? 2
= 1.4, respectively.
The maximum value of ?? ?? (in degrees) for which the incident light will be guided in the core of the
fibre is ________
Q. 26 ? Q. 55 carry two marks each.
Q.26 The ordinary differential equation
????
????
= ?3 ?? + 2, with ?? (0) = 1
is to be solved using the forward Euler method. The largest time step that can be used to solve the
equation without making the numerical solution unstable is ________
Q.27 Suppose C is the closed curve defined as the circle ?? 2
+ ?? 2
= 1 with C oriented anti-clockwise.
The value of ?( ?? ?? 2
?? ?? + ?? 2
?? ?? ?? ) over the curve C equals ________
Q.28 Two random variables ?? and ?? are distributed according to
?? ?? , ?? ( ?? , ?? ) = ?
( ?? + ?? ), 0 ? ?? ? 1, 0 ? ?? ? 1
0, otherwise.
The probability ?? ( ?? + ?? ? 1) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 7/14
Q.29
The matrix
?
?
?
?
?
?
?
?
?
?
?
?
=
b
a
A
0 0 0
4 2 0 0
3 1 5 2
7 3 0
has det( ?? ) = 100 and trace( ?? ) = 14.
The value of | ?? ? ?? | is ________
Q.30 In the given circuit, each resistor has a value equal to 1 ?.
What is the equivalent resistance across the terminals ?? and ?? ?
(A) 1/6 ? (B) 1/3 ? (C) 9/20 ? (D) 8/15 ?
Q.31 In the circuit shown in the figure, the magnitude of the current (in amperes) through R
2
is ___
Q.32
A continuous-time filter with transfer function ?? ( ?? ) =
2 ?? + 6
?? 2
+ 6 ?? + 8
is converted to a discrete-
time filter with transfer function ?? ( ?? ) =
2 ?? 2
? 0.5 0 3 2 ?? ?? 2
? 0.5 0 3 2 ?? + ?? so that the impulse response of the
continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response
of the discrete time filter. The value of ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 8/14
Q.33 The Discrete Fourier Transform (DFT) of the 4-point sequence
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {3, 2, 3, 4} is
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {12, 2?? , 0, ?2?? }.
If X
1
[k] is the DFT of the 12-point sequence ?? 1
[ ?? ] = {3, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0},
the value of ?
?? 1
[ 8]
?? 1
[ 1 1]
? is ________
Q.34 The switch S in the circuit shown has been closed for a long time. It is opened at time ?? = 0 and
remains open after that. Assume that the diode has zero reverse current and zero forward voltage
drop.
The steady state magnitude of the capacitor voltage ?? C
(in volts) is ______
Q.35 A voltage ?? ?? is applied across a MOS capacitor with metal gate and p-type silicon substrate at
T=300 K. The inversion carrier density (in number of carriers per unit area) for ?? ?? = 0.8 V is
2 ? 10
1 1
cm
? 2
. For ?? ?? = 1.3 V, the inversion carrier density is 4 ? 10
1 1
cm
? 2
. What is the value
of the inversion carrier density for ?? ??
= 1.8 V?
(A) 4.5 ? 10
1 1
cm
? 2
(B) 6.0 ? 10
1 1
cm
? 2
(C) 7.2 ? 10
1 1
cm
? 2
(D) 8.4 ? 10
1 1
cm
? 2
Q.36 Consider avalanche breakdown in a silicon ?? +
?? junction. The ?? -region is uniformly doped with a
donor density ?? ?? . Assume that breakdown occurs when the magnitude of the electric field at any
point in the device becomes equal to the critical field ?? ?????? ?? . Assume ?? ?????? ?? to be independent of ?? ?? .
If the built-in voltage of the ?? +
?? junction is much smaller than the breakdown voltage, ?? ?? ?? , the
relationship between ?? ?? ?? and ?? ?? is given by
(A) ?? ?? ?? ? ? ?? ?? = constant (B) ?? ?? ? ? ?? ?? ?? = constant
(C) ?? ?? ? ?? ?? ?? = constant (D) ?? ?? / ?? ?? ?? = constant
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 9/14
Q.37 Consider a region of silicon devoid of electrons and holes, with an ionized donor density of
?? ?? +
= 10
1 7
cm
? 3
. The electric field at ?? = 0 is 0 V/cm and the electric field at ?? = ?? is
50 kV/cm in the positive ?? direction. Assume that the electric field is zero in the ?? and ?? directions
at all points.
Given ?? = 1.6 ? 10
? 1 9
coulomb, ?? 0
= 8.85 ? 10
? 1 4
F/cm, ?? ?? = 11.7 for silicon, the value of ?? in
nm is ________
Q.38 Consider a long-channel NMOS transistor with source and body connected together. Assume that
the electron mobility is independent of ?? ????
and ?? ???? . Given,
?? ?? = 0.5 ?? A/V for ?? ???? = 50 mV and ?? ????
= 2 V,
?? ?? = 8 ?? A/V for ?? ????
= 2 V and ?? ???? = 0 V,
where ?? ?? =
?? ?? ?? ?? ?? ????
and ?? ?? =
?? ?? ?? ?? ?? ????
The threshold voltage (in volts) of the transistor is ________
Q.39 The figure shows a half-wave rectifier with a 475 ?? F filter capacitor. The load draws a constant
current ?? ?? = 1 A from the rectifier. The figure also shows the input voltage ?? ?? , the output voltage
?? ?? and the peak-to-peak voltage ripple ?? on ?? ?? . The input voltage ?? ?? is a triangle-wave with an
amplitude of 10 V and a period of 1 ms.
The value of the ripple ?? (in volts) is ________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
Q.7 Soc
they
In t
way
Wh
(A)
(C)
Q.8 Tw
mar
(A)
Q.9 M
5 k
the
(A)
GATE 2016
10 carry tw
e Venn diagr
om the data g
) 44
cial science
y were instit
the time of g
ys of knowle
hich of the fo
(i) Soc
(ii) Soc
(iii) Soc
(iv) Soc
) (ii) only
) (ii) and (iv
wo and a quar
rkings seeme
) 8:15
and N start f
km South and
end of their
) 18.60
wo marks
ram shows th
given, the num
(B)
disciplines w
tutionalized.
globalization
edge product
ollowing can
cial science d
cial science d
cial science d
cial science m
v) only
rter hours ba
ed to show 1
(B)
from the sam
d then 4 km
travel?
(B)
each.
he preference
mber of stud
51
were in exist
In varying
and the econ
tion have bec
be logically
disciplines h
disciplines h
disciplines al
must maintai
ack, when see
:30. What is
11:15
me location. M
South-East.
22.50
e of the stude
dents who lik
(C)
tence in an a
degrees, they
nomic rise o
come obsolet
y inferred from
ave become
ad a pre-colo
lways promo
in disciplinar
(B)
(D)
en in a mirro
s the actual cu
(C)
M travels 10
What is the
(C)
ent populatio
ke to read boo
79
amorphous f
y were inten
f postcolonia
te.
m the above
obsolete.
onial origin.
ote colonialis
ry boundarie
(i) and (iii)
(iii) and (iv
or, the reflect
urrent time s
12:15
0 km East an
e shortest dis
20.61
on for leisure
oks or play s
(D)
form until th
nded to furth
al countries l
statements?
sm.
es.
) only
v) only
tion of a wal
shown by the
(D)
nd then 10 km
stance (in km
(D)
General Ap
e activities.
sports is ____
108
he colonial p
her the colon
like India, co
ll clock with
e clock?
12:45
m North-Eas
m) between M
25.00
ptitude - GA Set-
2/3
__.
eriod when
nial interest.
onventional
out number
st. N travels
M and N at
3
3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 6/14
Q.24 Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium
be expressed as ?? = ?? ? ?? ?? ?? ? ?? ( ???? ? ???? )
, where the propagation constant ?? is a function of the angular
frequency ?? . Assume that ?? ( ?? ) and ?? ?? are known and are real. From the information available,
which one of the following CANNOT be determined?
(A) The type of polarization of the wave.
(B) The group velocity of the wave.
(C) The phase velocity of the wave.
(D) The power flux through the ?? = 0 plane.
Q.25 Light from free space is incident at an angle ?? ?? to the normal of the facet of a step-index large core
optical fibre. The core and cladding refractive indices are ?? 1
= 1.5 and ?? 2
= 1.4, respectively.
The maximum value of ?? ?? (in degrees) for which the incident light will be guided in the core of the
fibre is ________
Q. 26 ? Q. 55 carry two marks each.
Q.26 The ordinary differential equation
????
????
= ?3 ?? + 2, with ?? (0) = 1
is to be solved using the forward Euler method. The largest time step that can be used to solve the
equation without making the numerical solution unstable is ________
Q.27 Suppose C is the closed curve defined as the circle ?? 2
+ ?? 2
= 1 with C oriented anti-clockwise.
The value of ?( ?? ?? 2
?? ?? + ?? 2
?? ?? ?? ) over the curve C equals ________
Q.28 Two random variables ?? and ?? are distributed according to
?? ?? , ?? ( ?? , ?? ) = ?
( ?? + ?? ), 0 ? ?? ? 1, 0 ? ?? ? 1
0, otherwise.
The probability ?? ( ?? + ?? ? 1) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 7/14
Q.29
The matrix
?
?
?
?
?
?
?
?
?
?
?
?
=
b
a
A
0 0 0
4 2 0 0
3 1 5 2
7 3 0
has det( ?? ) = 100 and trace( ?? ) = 14.
The value of | ?? ? ?? | is ________
Q.30 In the given circuit, each resistor has a value equal to 1 ?.
What is the equivalent resistance across the terminals ?? and ?? ?
(A) 1/6 ? (B) 1/3 ? (C) 9/20 ? (D) 8/15 ?
Q.31 In the circuit shown in the figure, the magnitude of the current (in amperes) through R
2
is ___
Q.32
A continuous-time filter with transfer function ?? ( ?? ) =
2 ?? + 6
?? 2
+ 6 ?? + 8
is converted to a discrete-
time filter with transfer function ?? ( ?? ) =
2 ?? 2
? 0.5 0 3 2 ?? ?? 2
? 0.5 0 3 2 ?? + ?? so that the impulse response of the
continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response
of the discrete time filter. The value of ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 8/14
Q.33 The Discrete Fourier Transform (DFT) of the 4-point sequence
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {3, 2, 3, 4} is
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {12, 2?? , 0, ?2?? }.
If X
1
[k] is the DFT of the 12-point sequence ?? 1
[ ?? ] = {3, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0},
the value of ?
?? 1
[ 8]
?? 1
[ 1 1]
? is ________
Q.34 The switch S in the circuit shown has been closed for a long time. It is opened at time ?? = 0 and
remains open after that. Assume that the diode has zero reverse current and zero forward voltage
drop.
The steady state magnitude of the capacitor voltage ?? C
(in volts) is ______
Q.35 A voltage ?? ?? is applied across a MOS capacitor with metal gate and p-type silicon substrate at
T=300 K. The inversion carrier density (in number of carriers per unit area) for ?? ?? = 0.8 V is
2 ? 10
1 1
cm
? 2
. For ?? ?? = 1.3 V, the inversion carrier density is 4 ? 10
1 1
cm
? 2
. What is the value
of the inversion carrier density for ?? ??
= 1.8 V?
(A) 4.5 ? 10
1 1
cm
? 2
(B) 6.0 ? 10
1 1
cm
? 2
(C) 7.2 ? 10
1 1
cm
? 2
(D) 8.4 ? 10
1 1
cm
? 2
Q.36 Consider avalanche breakdown in a silicon ?? +
?? junction. The ?? -region is uniformly doped with a
donor density ?? ?? . Assume that breakdown occurs when the magnitude of the electric field at any
point in the device becomes equal to the critical field ?? ?????? ?? . Assume ?? ?????? ?? to be independent of ?? ?? .
If the built-in voltage of the ?? +
?? junction is much smaller than the breakdown voltage, ?? ?? ?? , the
relationship between ?? ?? ?? and ?? ?? is given by
(A) ?? ?? ?? ? ? ?? ?? = constant (B) ?? ?? ? ? ?? ?? ?? = constant
(C) ?? ?? ? ?? ?? ?? = constant (D) ?? ?? / ?? ?? ?? = constant
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 9/14
Q.37 Consider a region of silicon devoid of electrons and holes, with an ionized donor density of
?? ?? +
= 10
1 7
cm
? 3
. The electric field at ?? = 0 is 0 V/cm and the electric field at ?? = ?? is
50 kV/cm in the positive ?? direction. Assume that the electric field is zero in the ?? and ?? directions
at all points.
Given ?? = 1.6 ? 10
? 1 9
coulomb, ?? 0
= 8.85 ? 10
? 1 4
F/cm, ?? ?? = 11.7 for silicon, the value of ?? in
nm is ________
Q.38 Consider a long-channel NMOS transistor with source and body connected together. Assume that
the electron mobility is independent of ?? ????
and ?? ???? . Given,
?? ?? = 0.5 ?? A/V for ?? ???? = 50 mV and ?? ????
= 2 V,
?? ?? = 8 ?? A/V for ?? ????
= 2 V and ?? ???? = 0 V,
where ?? ?? =
?? ?? ?? ?? ?? ????
and ?? ?? =
?? ?? ?? ?? ?? ????
The threshold voltage (in volts) of the transistor is ________
Q.39 The figure shows a half-wave rectifier with a 475 ?? F filter capacitor. The load draws a constant
current ?? ?? = 1 A from the rectifier. The figure also shows the input voltage ?? ?? , the output voltage
?? ?? and the peak-to-peak voltage ripple ?? on ?? ?? . The input voltage ?? ?? is a triangle-wave with an
amplitude of 10 V and a period of 1 ms.
The value of the ripple ?? (in volts) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 10/14
Q.40 In the opamp circuit shown, the Zener diodes ?? 1 and ?? 2 clamp the output voltage ?? ?? to +5 V or
?5 V. The switch S is initially closed and is opened at time ?? = 0.
The time ?? = ?? 1
(in seconds) at which ?? ?? changes state is ________
Q.41 An opamp has a finite open loop voltage gain of 100. Its input offset voltage V
ios
(= +5mV) is
modeled as shown in the circuit below. The amplifier is ideal in all other respects. V
input
is 25 mV.
The output voltage (in millivolts) is ________
Q.42 An 8 Kbyte ROM with an active low Chip Select input (CS
? ? ?
) is to be used in an 8085
microprocessor based system. The ROM should occupy the address range 1000H to 2FFFH. The
address lines are designated as ?? 1 5
to ?? 0
, where ?? 1 5
is the most significant address bit.
Which one of the following logic expressions will generate the correct CS
? ? ?
signal for this ROM?
(A) ?? 1 5
+ ?? 1 4
+ ( ?? 1 3
? ?? 1 2
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
? ? ? ? ?
)
(B) ?? 1 5
? ?? 1 4
? ( ?? 1 3
+ ?? 1 2
)
(C) ?? 1 5
? ? ? ? ?
? ?? 1 4
? ? ? ? ?
? ( ?? 1 3
? ?? 1 2
? ? ? ? ?
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
)
(D) ?? 1 5
? ? ? ? ?
+ ?? 1 4
? ? ? ? ?
+ ?? 1 3
? ?? 1 2
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
Q. 6 ? Q.
Q.6 The
Fro
(A)
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they
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way
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(A)
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from the sam
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each.
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mber of stud
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and the econ
tion have bec
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dents who lik
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3
GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 6/14
Q.24 Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium
be expressed as ?? = ?? ? ?? ?? ?? ? ?? ( ???? ? ???? )
, where the propagation constant ?? is a function of the angular
frequency ?? . Assume that ?? ( ?? ) and ?? ?? are known and are real. From the information available,
which one of the following CANNOT be determined?
(A) The type of polarization of the wave.
(B) The group velocity of the wave.
(C) The phase velocity of the wave.
(D) The power flux through the ?? = 0 plane.
Q.25 Light from free space is incident at an angle ?? ?? to the normal of the facet of a step-index large core
optical fibre. The core and cladding refractive indices are ?? 1
= 1.5 and ?? 2
= 1.4, respectively.
The maximum value of ?? ?? (in degrees) for which the incident light will be guided in the core of the
fibre is ________
Q. 26 ? Q. 55 carry two marks each.
Q.26 The ordinary differential equation
????
????
= ?3 ?? + 2, with ?? (0) = 1
is to be solved using the forward Euler method. The largest time step that can be used to solve the
equation without making the numerical solution unstable is ________
Q.27 Suppose C is the closed curve defined as the circle ?? 2
+ ?? 2
= 1 with C oriented anti-clockwise.
The value of ?( ?? ?? 2
?? ?? + ?? 2
?? ?? ?? ) over the curve C equals ________
Q.28 Two random variables ?? and ?? are distributed according to
?? ?? , ?? ( ?? , ?? ) = ?
( ?? + ?? ), 0 ? ?? ? 1, 0 ? ?? ? 1
0, otherwise.
The probability ?? ( ?? + ?? ? 1) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 7/14
Q.29
The matrix
?
?
?
?
?
?
?
?
?
?
?
?
=
b
a
A
0 0 0
4 2 0 0
3 1 5 2
7 3 0
has det( ?? ) = 100 and trace( ?? ) = 14.
The value of | ?? ? ?? | is ________
Q.30 In the given circuit, each resistor has a value equal to 1 ?.
What is the equivalent resistance across the terminals ?? and ?? ?
(A) 1/6 ? (B) 1/3 ? (C) 9/20 ? (D) 8/15 ?
Q.31 In the circuit shown in the figure, the magnitude of the current (in amperes) through R
2
is ___
Q.32
A continuous-time filter with transfer function ?? ( ?? ) =
2 ?? + 6
?? 2
+ 6 ?? + 8
is converted to a discrete-
time filter with transfer function ?? ( ?? ) =
2 ?? 2
? 0.5 0 3 2 ?? ?? 2
? 0.5 0 3 2 ?? + ?? so that the impulse response of the
continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response
of the discrete time filter. The value of ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 8/14
Q.33 The Discrete Fourier Transform (DFT) of the 4-point sequence
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {3, 2, 3, 4} is
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {12, 2?? , 0, ?2?? }.
If X
1
[k] is the DFT of the 12-point sequence ?? 1
[ ?? ] = {3, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0},
the value of ?
?? 1
[ 8]
?? 1
[ 1 1]
? is ________
Q.34 The switch S in the circuit shown has been closed for a long time. It is opened at time ?? = 0 and
remains open after that. Assume that the diode has zero reverse current and zero forward voltage
drop.
The steady state magnitude of the capacitor voltage ?? C
(in volts) is ______
Q.35 A voltage ?? ?? is applied across a MOS capacitor with metal gate and p-type silicon substrate at
T=300 K. The inversion carrier density (in number of carriers per unit area) for ?? ?? = 0.8 V is
2 ? 10
1 1
cm
? 2
. For ?? ?? = 1.3 V, the inversion carrier density is 4 ? 10
1 1
cm
? 2
. What is the value
of the inversion carrier density for ?? ??
= 1.8 V?
(A) 4.5 ? 10
1 1
cm
? 2
(B) 6.0 ? 10
1 1
cm
? 2
(C) 7.2 ? 10
1 1
cm
? 2
(D) 8.4 ? 10
1 1
cm
? 2
Q.36 Consider avalanche breakdown in a silicon ?? +
?? junction. The ?? -region is uniformly doped with a
donor density ?? ?? . Assume that breakdown occurs when the magnitude of the electric field at any
point in the device becomes equal to the critical field ?? ?????? ?? . Assume ?? ?????? ?? to be independent of ?? ?? .
If the built-in voltage of the ?? +
?? junction is much smaller than the breakdown voltage, ?? ?? ?? , the
relationship between ?? ?? ?? and ?? ?? is given by
(A) ?? ?? ?? ? ? ?? ?? = constant (B) ?? ?? ? ? ?? ?? ?? = constant
(C) ?? ?? ? ?? ?? ?? = constant (D) ?? ?? / ?? ?? ?? = constant
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 9/14
Q.37 Consider a region of silicon devoid of electrons and holes, with an ionized donor density of
?? ?? +
= 10
1 7
cm
? 3
. The electric field at ?? = 0 is 0 V/cm and the electric field at ?? = ?? is
50 kV/cm in the positive ?? direction. Assume that the electric field is zero in the ?? and ?? directions
at all points.
Given ?? = 1.6 ? 10
? 1 9
coulomb, ?? 0
= 8.85 ? 10
? 1 4
F/cm, ?? ?? = 11.7 for silicon, the value of ?? in
nm is ________
Q.38 Consider a long-channel NMOS transistor with source and body connected together. Assume that
the electron mobility is independent of ?? ????
and ?? ???? . Given,
?? ?? = 0.5 ?? A/V for ?? ???? = 50 mV and ?? ????
= 2 V,
?? ?? = 8 ?? A/V for ?? ????
= 2 V and ?? ???? = 0 V,
where ?? ?? =
?? ?? ?? ?? ?? ????
and ?? ?? =
?? ?? ?? ?? ?? ????
The threshold voltage (in volts) of the transistor is ________
Q.39 The figure shows a half-wave rectifier with a 475 ?? F filter capacitor. The load draws a constant
current ?? ?? = 1 A from the rectifier. The figure also shows the input voltage ?? ?? , the output voltage
?? ?? and the peak-to-peak voltage ripple ?? on ?? ?? . The input voltage ?? ?? is a triangle-wave with an
amplitude of 10 V and a period of 1 ms.
The value of the ripple ?? (in volts) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 10/14
Q.40 In the opamp circuit shown, the Zener diodes ?? 1 and ?? 2 clamp the output voltage ?? ?? to +5 V or
?5 V. The switch S is initially closed and is opened at time ?? = 0.
The time ?? = ?? 1
(in seconds) at which ?? ?? changes state is ________
Q.41 An opamp has a finite open loop voltage gain of 100. Its input offset voltage V
ios
(= +5mV) is
modeled as shown in the circuit below. The amplifier is ideal in all other respects. V
input
is 25 mV.
The output voltage (in millivolts) is ________
Q.42 An 8 Kbyte ROM with an active low Chip Select input (CS
? ? ?
) is to be used in an 8085
microprocessor based system. The ROM should occupy the address range 1000H to 2FFFH. The
address lines are designated as ?? 1 5
to ?? 0
, where ?? 1 5
is the most significant address bit.
Which one of the following logic expressions will generate the correct CS
? ? ?
signal for this ROM?
(A) ?? 1 5
+ ?? 1 4
+ ( ?? 1 3
? ?? 1 2
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
? ? ? ? ?
)
(B) ?? 1 5
? ?? 1 4
? ( ?? 1 3
+ ?? 1 2
)
(C) ?? 1 5
? ? ? ? ?
? ?? 1 4
? ? ? ? ?
? ( ?? 1 3
? ?? 1 2
? ? ? ? ?
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
)
(D) ?? 1 5
? ? ? ? ?
+ ?? 1 4
? ? ? ? ?
+ ?? 1 3
? ?? 1 2
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 11/14
Q.43 In an N bit flash ADC, the analog voltage is fed simultaneously to 2
?? ? 1 comparators. The output
of the comparators is then encoded to a binary format using digital circuits. Assume that the analog
voltage source V
in
(whose output is being converted to digital format) has a source resistance of
75 ? as shown in the circuit diagram below and the input capacitance of each comparator is 8 pF.
The input must settle to an accuracy of 1/2 LSB even for a full scale input change for proper
conversion. Assume that the time taken by the thermometer to binary encoder is negligible.
If the flash ADC has 8 bit resolution, which one of the following alternatives is closest to the
maximum sampling rate ?
(A) 1 megasamples per second
(B) 6 megasamples per second
(C) 64 megasamples per second
(D) 256 megasamples per second
Q.44 The state transition diagram for a finite state machine with states A, B and C, and binary inputs X,
Y and Z, is shown in the figure.
Which one of the following statements is correct?
(A) Transitions from State A are ambiguously defined.
(B) Transitions from State B are ambiguously defined.
(C) Transitions from State C are ambiguously defined.
(D) All of the state transitions are defined unambiguously.
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
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GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 6/14
Q.24 Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium
be expressed as ?? = ?? ? ?? ?? ?? ? ?? ( ???? ? ???? )
, where the propagation constant ?? is a function of the angular
frequency ?? . Assume that ?? ( ?? ) and ?? ?? are known and are real. From the information available,
which one of the following CANNOT be determined?
(A) The type of polarization of the wave.
(B) The group velocity of the wave.
(C) The phase velocity of the wave.
(D) The power flux through the ?? = 0 plane.
Q.25 Light from free space is incident at an angle ?? ?? to the normal of the facet of a step-index large core
optical fibre. The core and cladding refractive indices are ?? 1
= 1.5 and ?? 2
= 1.4, respectively.
The maximum value of ?? ?? (in degrees) for which the incident light will be guided in the core of the
fibre is ________
Q. 26 ? Q. 55 carry two marks each.
Q.26 The ordinary differential equation
????
????
= ?3 ?? + 2, with ?? (0) = 1
is to be solved using the forward Euler method. The largest time step that can be used to solve the
equation without making the numerical solution unstable is ________
Q.27 Suppose C is the closed curve defined as the circle ?? 2
+ ?? 2
= 1 with C oriented anti-clockwise.
The value of ?( ?? ?? 2
?? ?? + ?? 2
?? ?? ?? ) over the curve C equals ________
Q.28 Two random variables ?? and ?? are distributed according to
?? ?? , ?? ( ?? , ?? ) = ?
( ?? + ?? ), 0 ? ?? ? 1, 0 ? ?? ? 1
0, otherwise.
The probability ?? ( ?? + ?? ? 1) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 7/14
Q.29
The matrix
?
?
?
?
?
?
?
?
?
?
?
?
=
b
a
A
0 0 0
4 2 0 0
3 1 5 2
7 3 0
has det( ?? ) = 100 and trace( ?? ) = 14.
The value of | ?? ? ?? | is ________
Q.30 In the given circuit, each resistor has a value equal to 1 ?.
What is the equivalent resistance across the terminals ?? and ?? ?
(A) 1/6 ? (B) 1/3 ? (C) 9/20 ? (D) 8/15 ?
Q.31 In the circuit shown in the figure, the magnitude of the current (in amperes) through R
2
is ___
Q.32
A continuous-time filter with transfer function ?? ( ?? ) =
2 ?? + 6
?? 2
+ 6 ?? + 8
is converted to a discrete-
time filter with transfer function ?? ( ?? ) =
2 ?? 2
? 0.5 0 3 2 ?? ?? 2
? 0.5 0 3 2 ?? + ?? so that the impulse response of the
continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response
of the discrete time filter. The value of ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 8/14
Q.33 The Discrete Fourier Transform (DFT) of the 4-point sequence
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {3, 2, 3, 4} is
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {12, 2?? , 0, ?2?? }.
If X
1
[k] is the DFT of the 12-point sequence ?? 1
[ ?? ] = {3, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0},
the value of ?
?? 1
[ 8]
?? 1
[ 1 1]
? is ________
Q.34 The switch S in the circuit shown has been closed for a long time. It is opened at time ?? = 0 and
remains open after that. Assume that the diode has zero reverse current and zero forward voltage
drop.
The steady state magnitude of the capacitor voltage ?? C
(in volts) is ______
Q.35 A voltage ?? ?? is applied across a MOS capacitor with metal gate and p-type silicon substrate at
T=300 K. The inversion carrier density (in number of carriers per unit area) for ?? ?? = 0.8 V is
2 ? 10
1 1
cm
? 2
. For ?? ?? = 1.3 V, the inversion carrier density is 4 ? 10
1 1
cm
? 2
. What is the value
of the inversion carrier density for ?? ??
= 1.8 V?
(A) 4.5 ? 10
1 1
cm
? 2
(B) 6.0 ? 10
1 1
cm
? 2
(C) 7.2 ? 10
1 1
cm
? 2
(D) 8.4 ? 10
1 1
cm
? 2
Q.36 Consider avalanche breakdown in a silicon ?? +
?? junction. The ?? -region is uniformly doped with a
donor density ?? ?? . Assume that breakdown occurs when the magnitude of the electric field at any
point in the device becomes equal to the critical field ?? ?????? ?? . Assume ?? ?????? ?? to be independent of ?? ?? .
If the built-in voltage of the ?? +
?? junction is much smaller than the breakdown voltage, ?? ?? ?? , the
relationship between ?? ?? ?? and ?? ?? is given by
(A) ?? ?? ?? ? ? ?? ?? = constant (B) ?? ?? ? ? ?? ?? ?? = constant
(C) ?? ?? ? ?? ?? ?? = constant (D) ?? ?? / ?? ?? ?? = constant
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 9/14
Q.37 Consider a region of silicon devoid of electrons and holes, with an ionized donor density of
?? ?? +
= 10
1 7
cm
? 3
. The electric field at ?? = 0 is 0 V/cm and the electric field at ?? = ?? is
50 kV/cm in the positive ?? direction. Assume that the electric field is zero in the ?? and ?? directions
at all points.
Given ?? = 1.6 ? 10
? 1 9
coulomb, ?? 0
= 8.85 ? 10
? 1 4
F/cm, ?? ?? = 11.7 for silicon, the value of ?? in
nm is ________
Q.38 Consider a long-channel NMOS transistor with source and body connected together. Assume that
the electron mobility is independent of ?? ????
and ?? ???? . Given,
?? ?? = 0.5 ?? A/V for ?? ???? = 50 mV and ?? ????
= 2 V,
?? ?? = 8 ?? A/V for ?? ????
= 2 V and ?? ???? = 0 V,
where ?? ?? =
?? ?? ?? ?? ?? ????
and ?? ?? =
?? ?? ?? ?? ?? ????
The threshold voltage (in volts) of the transistor is ________
Q.39 The figure shows a half-wave rectifier with a 475 ?? F filter capacitor. The load draws a constant
current ?? ?? = 1 A from the rectifier. The figure also shows the input voltage ?? ?? , the output voltage
?? ?? and the peak-to-peak voltage ripple ?? on ?? ?? . The input voltage ?? ?? is a triangle-wave with an
amplitude of 10 V and a period of 1 ms.
The value of the ripple ?? (in volts) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 10/14
Q.40 In the opamp circuit shown, the Zener diodes ?? 1 and ?? 2 clamp the output voltage ?? ?? to +5 V or
?5 V. The switch S is initially closed and is opened at time ?? = 0.
The time ?? = ?? 1
(in seconds) at which ?? ?? changes state is ________
Q.41 An opamp has a finite open loop voltage gain of 100. Its input offset voltage V
ios
(= +5mV) is
modeled as shown in the circuit below. The amplifier is ideal in all other respects. V
input
is 25 mV.
The output voltage (in millivolts) is ________
Q.42 An 8 Kbyte ROM with an active low Chip Select input (CS
? ? ?
) is to be used in an 8085
microprocessor based system. The ROM should occupy the address range 1000H to 2FFFH. The
address lines are designated as ?? 1 5
to ?? 0
, where ?? 1 5
is the most significant address bit.
Which one of the following logic expressions will generate the correct CS
? ? ?
signal for this ROM?
(A) ?? 1 5
+ ?? 1 4
+ ( ?? 1 3
? ?? 1 2
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
? ? ? ? ?
)
(B) ?? 1 5
? ?? 1 4
? ( ?? 1 3
+ ?? 1 2
)
(C) ?? 1 5
? ? ? ? ?
? ?? 1 4
? ? ? ? ?
? ( ?? 1 3
? ?? 1 2
? ? ? ? ?
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
)
(D) ?? 1 5
? ? ? ? ?
+ ?? 1 4
? ? ? ? ?
+ ?? 1 3
? ?? 1 2
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 11/14
Q.43 In an N bit flash ADC, the analog voltage is fed simultaneously to 2
?? ? 1 comparators. The output
of the comparators is then encoded to a binary format using digital circuits. Assume that the analog
voltage source V
in
(whose output is being converted to digital format) has a source resistance of
75 ? as shown in the circuit diagram below and the input capacitance of each comparator is 8 pF.
The input must settle to an accuracy of 1/2 LSB even for a full scale input change for proper
conversion. Assume that the time taken by the thermometer to binary encoder is negligible.
If the flash ADC has 8 bit resolution, which one of the following alternatives is closest to the
maximum sampling rate ?
(A) 1 megasamples per second
(B) 6 megasamples per second
(C) 64 megasamples per second
(D) 256 megasamples per second
Q.44 The state transition diagram for a finite state machine with states A, B and C, and binary inputs X,
Y and Z, is shown in the figure.
Which one of the following statements is correct?
(A) Transitions from State A are ambiguously defined.
(B) Transitions from State B are ambiguously defined.
(C) Transitions from State C are ambiguously defined.
(D) All of the state transitions are defined unambiguously.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 12/14
Q.45
In the feedback system shown below ?? ( ?? ) =
1
( ?? 2
+ 2 ?? )
.
The step response of the closed-loop system should have minimum settling time and have no
overshoot.
The required value of gain ?? to achieve this is ________
Q.46
In the feedback system shown below ?? ( ?? ) =
1
( ?? + 1)( ?? + 2)( ?? + 3)
.
The positive value of ?? for which the gain margin of the loop is exactly 0 dB and the phase margin
of the loop is exactly zero degree is ________
Q.47
The asymptotic Bode phase plot of ?? ( ?? ) =
?? ( ?? + 0. 1)( ?? + 1 0)( ?? + ?? 1
)
, with ?? and ?? 1
both positive,
is shown below.
The value of ?? 1
is ________
Q.48 An information source generates a binary sequence { ?? ?? }. ?? ?? can take one of the two possible
values ?1 and +1 with equal probability and are statistically independent and identically
distributed. This sequence is precoded to obtain another sequence { ?? ?? }, as ?? ?? = ?? ?? + ?? ?? ?? ? 3
.
The sequence { ?? ?? } is used to modulate a pulse ?? ( ?? ) to generate the baseband signal
?? ( ?? ) = ? ?? ?? ?? ( ?? ? ???? )
?
?? = ? ?
, where ?? ( ?? ) = ?
1, 0 ? ?? ? ??
0, otherwise.
If there is a null at ?? =
1
3 ?? in the power spectral density of ?? ( ?? ), then ?? is ________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
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GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 6/14
Q.24 Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium
be expressed as ?? = ?? ? ?? ?? ?? ? ?? ( ???? ? ???? )
, where the propagation constant ?? is a function of the angular
frequency ?? . Assume that ?? ( ?? ) and ?? ?? are known and are real. From the information available,
which one of the following CANNOT be determined?
(A) The type of polarization of the wave.
(B) The group velocity of the wave.
(C) The phase velocity of the wave.
(D) The power flux through the ?? = 0 plane.
Q.25 Light from free space is incident at an angle ?? ?? to the normal of the facet of a step-index large core
optical fibre. The core and cladding refractive indices are ?? 1
= 1.5 and ?? 2
= 1.4, respectively.
The maximum value of ?? ?? (in degrees) for which the incident light will be guided in the core of the
fibre is ________
Q. 26 ? Q. 55 carry two marks each.
Q.26 The ordinary differential equation
????
????
= ?3 ?? + 2, with ?? (0) = 1
is to be solved using the forward Euler method. The largest time step that can be used to solve the
equation without making the numerical solution unstable is ________
Q.27 Suppose C is the closed curve defined as the circle ?? 2
+ ?? 2
= 1 with C oriented anti-clockwise.
The value of ?( ?? ?? 2
?? ?? + ?? 2
?? ?? ?? ) over the curve C equals ________
Q.28 Two random variables ?? and ?? are distributed according to
?? ?? , ?? ( ?? , ?? ) = ?
( ?? + ?? ), 0 ? ?? ? 1, 0 ? ?? ? 1
0, otherwise.
The probability ?? ( ?? + ?? ? 1) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 7/14
Q.29
The matrix
?
?
?
?
?
?
?
?
?
?
?
?
=
b
a
A
0 0 0
4 2 0 0
3 1 5 2
7 3 0
has det( ?? ) = 100 and trace( ?? ) = 14.
The value of | ?? ? ?? | is ________
Q.30 In the given circuit, each resistor has a value equal to 1 ?.
What is the equivalent resistance across the terminals ?? and ?? ?
(A) 1/6 ? (B) 1/3 ? (C) 9/20 ? (D) 8/15 ?
Q.31 In the circuit shown in the figure, the magnitude of the current (in amperes) through R
2
is ___
Q.32
A continuous-time filter with transfer function ?? ( ?? ) =
2 ?? + 6
?? 2
+ 6 ?? + 8
is converted to a discrete-
time filter with transfer function ?? ( ?? ) =
2 ?? 2
? 0.5 0 3 2 ?? ?? 2
? 0.5 0 3 2 ?? + ?? so that the impulse response of the
continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response
of the discrete time filter. The value of ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 8/14
Q.33 The Discrete Fourier Transform (DFT) of the 4-point sequence
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {3, 2, 3, 4} is
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {12, 2?? , 0, ?2?? }.
If X
1
[k] is the DFT of the 12-point sequence ?? 1
[ ?? ] = {3, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0},
the value of ?
?? 1
[ 8]
?? 1
[ 1 1]
? is ________
Q.34 The switch S in the circuit shown has been closed for a long time. It is opened at time ?? = 0 and
remains open after that. Assume that the diode has zero reverse current and zero forward voltage
drop.
The steady state magnitude of the capacitor voltage ?? C
(in volts) is ______
Q.35 A voltage ?? ?? is applied across a MOS capacitor with metal gate and p-type silicon substrate at
T=300 K. The inversion carrier density (in number of carriers per unit area) for ?? ?? = 0.8 V is
2 ? 10
1 1
cm
? 2
. For ?? ?? = 1.3 V, the inversion carrier density is 4 ? 10
1 1
cm
? 2
. What is the value
of the inversion carrier density for ?? ??
= 1.8 V?
(A) 4.5 ? 10
1 1
cm
? 2
(B) 6.0 ? 10
1 1
cm
? 2
(C) 7.2 ? 10
1 1
cm
? 2
(D) 8.4 ? 10
1 1
cm
? 2
Q.36 Consider avalanche breakdown in a silicon ?? +
?? junction. The ?? -region is uniformly doped with a
donor density ?? ?? . Assume that breakdown occurs when the magnitude of the electric field at any
point in the device becomes equal to the critical field ?? ?????? ?? . Assume ?? ?????? ?? to be independent of ?? ?? .
If the built-in voltage of the ?? +
?? junction is much smaller than the breakdown voltage, ?? ?? ?? , the
relationship between ?? ?? ?? and ?? ?? is given by
(A) ?? ?? ?? ? ? ?? ?? = constant (B) ?? ?? ? ? ?? ?? ?? = constant
(C) ?? ?? ? ?? ?? ?? = constant (D) ?? ?? / ?? ?? ?? = constant
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 9/14
Q.37 Consider a region of silicon devoid of electrons and holes, with an ionized donor density of
?? ?? +
= 10
1 7
cm
? 3
. The electric field at ?? = 0 is 0 V/cm and the electric field at ?? = ?? is
50 kV/cm in the positive ?? direction. Assume that the electric field is zero in the ?? and ?? directions
at all points.
Given ?? = 1.6 ? 10
? 1 9
coulomb, ?? 0
= 8.85 ? 10
? 1 4
F/cm, ?? ?? = 11.7 for silicon, the value of ?? in
nm is ________
Q.38 Consider a long-channel NMOS transistor with source and body connected together. Assume that
the electron mobility is independent of ?? ????
and ?? ???? . Given,
?? ?? = 0.5 ?? A/V for ?? ???? = 50 mV and ?? ????
= 2 V,
?? ?? = 8 ?? A/V for ?? ????
= 2 V and ?? ???? = 0 V,
where ?? ?? =
?? ?? ?? ?? ?? ????
and ?? ?? =
?? ?? ?? ?? ?? ????
The threshold voltage (in volts) of the transistor is ________
Q.39 The figure shows a half-wave rectifier with a 475 ?? F filter capacitor. The load draws a constant
current ?? ?? = 1 A from the rectifier. The figure also shows the input voltage ?? ?? , the output voltage
?? ?? and the peak-to-peak voltage ripple ?? on ?? ?? . The input voltage ?? ?? is a triangle-wave with an
amplitude of 10 V and a period of 1 ms.
The value of the ripple ?? (in volts) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 10/14
Q.40 In the opamp circuit shown, the Zener diodes ?? 1 and ?? 2 clamp the output voltage ?? ?? to +5 V or
?5 V. The switch S is initially closed and is opened at time ?? = 0.
The time ?? = ?? 1
(in seconds) at which ?? ?? changes state is ________
Q.41 An opamp has a finite open loop voltage gain of 100. Its input offset voltage V
ios
(= +5mV) is
modeled as shown in the circuit below. The amplifier is ideal in all other respects. V
input
is 25 mV.
The output voltage (in millivolts) is ________
Q.42 An 8 Kbyte ROM with an active low Chip Select input (CS
? ? ?
) is to be used in an 8085
microprocessor based system. The ROM should occupy the address range 1000H to 2FFFH. The
address lines are designated as ?? 1 5
to ?? 0
, where ?? 1 5
is the most significant address bit.
Which one of the following logic expressions will generate the correct CS
? ? ?
signal for this ROM?
(A) ?? 1 5
+ ?? 1 4
+ ( ?? 1 3
? ?? 1 2
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
? ? ? ? ?
)
(B) ?? 1 5
? ?? 1 4
? ( ?? 1 3
+ ?? 1 2
)
(C) ?? 1 5
? ? ? ? ?
? ?? 1 4
? ? ? ? ?
? ( ?? 1 3
? ?? 1 2
? ? ? ? ?
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
)
(D) ?? 1 5
? ? ? ? ?
+ ?? 1 4
? ? ? ? ?
+ ?? 1 3
? ?? 1 2
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 11/14
Q.43 In an N bit flash ADC, the analog voltage is fed simultaneously to 2
?? ? 1 comparators. The output
of the comparators is then encoded to a binary format using digital circuits. Assume that the analog
voltage source V
in
(whose output is being converted to digital format) has a source resistance of
75 ? as shown in the circuit diagram below and the input capacitance of each comparator is 8 pF.
The input must settle to an accuracy of 1/2 LSB even for a full scale input change for proper
conversion. Assume that the time taken by the thermometer to binary encoder is negligible.
If the flash ADC has 8 bit resolution, which one of the following alternatives is closest to the
maximum sampling rate ?
(A) 1 megasamples per second
(B) 6 megasamples per second
(C) 64 megasamples per second
(D) 256 megasamples per second
Q.44 The state transition diagram for a finite state machine with states A, B and C, and binary inputs X,
Y and Z, is shown in the figure.
Which one of the following statements is correct?
(A) Transitions from State A are ambiguously defined.
(B) Transitions from State B are ambiguously defined.
(C) Transitions from State C are ambiguously defined.
(D) All of the state transitions are defined unambiguously.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 12/14
Q.45
In the feedback system shown below ?? ( ?? ) =
1
( ?? 2
+ 2 ?? )
.
The step response of the closed-loop system should have minimum settling time and have no
overshoot.
The required value of gain ?? to achieve this is ________
Q.46
In the feedback system shown below ?? ( ?? ) =
1
( ?? + 1)( ?? + 2)( ?? + 3)
.
The positive value of ?? for which the gain margin of the loop is exactly 0 dB and the phase margin
of the loop is exactly zero degree is ________
Q.47
The asymptotic Bode phase plot of ?? ( ?? ) =
?? ( ?? + 0. 1)( ?? + 1 0)( ?? + ?? 1
)
, with ?? and ?? 1
both positive,
is shown below.
The value of ?? 1
is ________
Q.48 An information source generates a binary sequence { ?? ?? }. ?? ?? can take one of the two possible
values ?1 and +1 with equal probability and are statistically independent and identically
distributed. This sequence is precoded to obtain another sequence { ?? ?? }, as ?? ?? = ?? ?? + ?? ?? ?? ? 3
.
The sequence { ?? ?? } is used to modulate a pulse ?? ( ?? ) to generate the baseband signal
?? ( ?? ) = ? ?? ?? ?? ( ?? ? ???? )
?
?? = ? ?
, where ?? ( ?? ) = ?
1, 0 ? ?? ? ??
0, otherwise.
If there is a null at ?? =
1
3 ?? in the power spectral density of ?? ( ?? ), then ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 13/14
Q.49 An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communication. A modem is
designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with
a raised cosine spectrum that utilizes the entire frequency band is ________
Q.50 Consider a random process ?? ( ?? ) = 3 ?? ( ?? ) ? 8, where ?? ( ?? ) is a zero mean stationary random
process with autocorrelation ?? ?? ( ?? ) = 4 ?? ? 5| ?? |
. The power in ?? ( ?? ) is ________
Q.51 A binary communication system makes use of the symbols ?zero? and ?one?. There are channel
errors. Consider the following events:
?? 0
: a "zero" is transmitted
?? 1
: a "one" is transmitted
?? 0
: a "zero" is received
?? 1
: a "one" is received
The following probabilities are given: ?? ( ?? 0
) =
1
2
, ?? ( ?? 0
| ?? 0
) =
3
4
, and ?? ( ?? 0
| ?? 1
) =
1
2
. The
information in bits that you obtain when you learn which symbol has been received (while you
know that a ?zero? has been transmitted) is ________
Q.52 The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that
the energy stored in it is ?? when the plate separation is ?? . The capacitor is then isolated electrically
and the plates are moved such that the plate separation becomes 2?? .
At this new plate separation, what is the energy stored in the capacitor, neglecting fringing effects?
(A) 2 ??
(B) ?2 ??
(C) ?? (D) ?? 2 ?
Q.53 A lossless microstrip transmission line consists of a trace of width ?? . It is drawn over a practically
infinite ground plane and is separated by a dielectric slab of thickness ?? and relative permittivity
?? ?? > 1. The inductance per unit length and the characteristic impedance of this line are ?? and ?? 0
,
respectively.
Which one of the following inequalities is always satisfied?
(A) ?? 0
> ?
????
?? 0
?? ?? ?? (B) ?? 0
< ?
????
?? 0
?? ?? ??
(C) ?? 0
> ?
????
?? 0
?? ?? ?? (D) ?? 0
< ?
????
?? 0
?? ?? ??
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-3
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Based on the given statements, select the appropriate option with respect to grammar and usage.
Statements
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
Q.2 The students ___________ the teacher on teachers? day for twenty years of dedicated teaching.
(A) facilitated (B) felicitated (C) fantasized (D) facillitated
Q.3 After India?s cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket
till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
(A) history will rest in peace (B) rest is recorded in history books
(C) rest is well known (D) rest is archaic
Q.4
Given (9 inches)
?
= (0.25 yards)
?
, which one of the following statements is TRUE?
(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards
(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards
Q.5 S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency
of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E
and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the
project?
(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1
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GATE 2016 General Aptitude - GA Set-3
3/3
Q.10 A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and
the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the
square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
(A) 30 (B) 40 (C) 120 (D) 180
END OF THE QUESTION PAPER
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
The value of ?? for which the matrix ?? = ?
3 2 4
9 7 13
?6 ?4 ?9 + ?? ?
has zero as an eigenvalue is ________
Q.2 Consider the complex valued function ?? ( ?? ) = 2 ?? 3
+ ?? | ?? |
3
where ?? is a complex variable.
The value of ?? for which the function ?? ( ?? ) is analytic is ________
Q.3 As ?? varies from ?1 to +3, which one of the following describes the behaviour of the function
?? ( ?? ) = ?? 3
? 3 ?? 2
+ 1?
(A) ?? ( ?? ) increases monotonically.
(B) ?? ( ?? ) increases, then decreases and increases again.
(C) ?? ( ?? ) decreases, then increases and decreases again.
(D) ?? ( ?? ) increases and then decreases.
Q.4 How many distinct values of ?? satisfy the equation sin( ?? ) = ?? /2, where ?? is in radians?
(A) 1 (B) 2 (C) 3 (D) 4 or more
Q.5 Consider the time-varying vector ?? = ?? ? 15 cos( ?? ?? ) + ?? ? 5 sin( ?? ?? ) in Cartesian coordinates, where
?? > 0 is a constant. When the vector magnitude | ?? | is at its minimum value, the angle ?? that ??
makes with the ?? axis (in degrees, such that 0 ? ?? ? 180) is ________
Q.6 In the circuit shown below, ?? ?? is a constant voltage source and ?? ?? is a constant current load.
The value of ?? ?? that maximizes the power absorbed by the constant current load is
(A)
?? ?? 4 ?? (B)
?? ?? 2 ?? (C)
?? ?? ??
(D) ?
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 2/14
Q.7 The switch has been in position 1 for a long time and abruptly changes to position 2 at ?? = 0.
If time ?? is in seconds, the capacitor voltage V
C
(in volts) for ?? > 0 is given by
(A) 4(1 ? exp( ? ?? /0.5))
(B) 10 ? 6 exp( ? ?? /0.5)
(C) 4(1 ? exp( ? ?? /0.6))
(D) 10 ? 6 exp( ? ?? /0.6)
Q.8 The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio | ?? ?? |/| ?? ?? |, i.e., the ratio of the magnitudes of the inductor current phasor and
the resistor current phasor, is ________
Q.9 The z-parameter matrix for the two-port network shown is
?
2???? ???? ???? 3 + 2???? ?,
where the entries are in ?. Suppose ?? ?? ( ???? ) = ?? ?? + ???? .
Then the value of ?? ?? (in ?) equals ________
Q.10
The energy of the signal ?? ( ?? ) =
sin( 4 ???? )
4 ????
is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 3/14
Q.11 The Ebers-Moll model of a BJT is valid
(A) only in active mode
(B) only in active and saturation modes
(C) only in active and cut-off modes
(D) in active, saturation and cut-off modes
Q.12 A long-channel NMOS transistor is biased in the linear region with ?? ???? =50 mV and is used as a
resistance. Which one of the following statements is NOT correct?
(A) If the device width ?? is increased, the resistance decreases.
(B) If the threshold voltage is reduced, the resistance decreases.
(C) If the device length ?? is increased, the resistance increases.
(D) If ?? ????
is increased, the resistance increases.
Q.13 Assume that the diode in the figure has ?? ????
= 0.7 ?? , but is otherwise ideal.
The magnitude of the current i
2
(in mA) is equal to ________
Q.14 Resistor R
1
in the circuit below has been adjusted so that I
1
= 1 mA. The bipolar transistors Q1 and
Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The
supply voltage V
cc
is 6 V. The thermal voltage ?? ?? / ?? is 26 mV.
The value of R
2
(in ?) for which I
2
=100 ?A is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 4/14
Q.15 Which one of the following statements is correct about an ac-coupled common-emitter amplifier
operating in the mid-band region?
(A) The device parasitic capacitances behave like open circuits, whereas coupling and bypass
capacitances behave like short circuits.
(B) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
open circuits.
(C) The device parasitic capacitances, coupling capacitances and bypass capacitances behave like
short circuits.
(D) The device parasitic capacitances behave like short circuits, whereas coupling and bypass
capacitances behave like open circuits.
Q.16 Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst
case charge and discharge times for driving a load capacitor C. This design is to be converted to
that of a NOR circuit in the same technology, so that its worst case charge and discharge times
while driving the same capacitor are similar. The channel lengths of all transistors are to be kept
unchanged. Which one of the following statements is correct?
(A) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should be
halved.
(B) Widths of PMOS transistors should be doubled, while widths of NMOS transistors should not
be changed.
(C) Widths of PMOS transistors should be halved, while widths of NMOS transistors should not be
changed.
(D) Widths of PMOS transistors should be unchanged, while widths of NMOS transistors should be
halved.
Q.17 Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor ?? = 10 ?? ?
and the supply voltage is 5 ?? . The D flip-flops D
1
, D
2
, D
3
, D
4
and D
5
are initialized with logic
values 0,1,0,1 and 0, respectively. The clock has a 30% duty cycle.
The average power dissipated (in mW) in the resistor ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 5/14
Q.18 A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits
to be added while ?? in
is the input carry and ?? out
is the output carry. A and B are to be used as the
select bits with A being the more significant select bit.
Which one of the following statements correctly describes the choice of signals to be connected to
the inputs I
0
, I
1
, I
2
and I
3
so that the output is C
out
?
(A) I
0
=0, I
1
=C
in
, I
2
=C
in
and I
3
=1
(B) I
0
=1, I
1
=C
in
, I
2
=C
in
and I
3
=1
(C) I
0
=C
in
, I
1
=0, I
2
=1 and I
3
=C
in
(D) I
0
=0, I
1
=C
in
, I
2
=1 and I
3
=C
in
Q.19
The response of the system ?? ( ?? ) =
?? ? 2
( ?? + 1)( ?? + 3)
to the unit step input ?? ( ?? ) is ?? ( ?? ).
The value of
????
????
at ?? = 0
+
is _________
Q.20 The number and direction of encirclements around the point ?1 + ?? 0 in the complex plane by the
Nyquist plot of ?? ( ?? ) =
1 ? ?? 4+2 ?? is
(A) zero. (B) one, anti-clockwise.
(C) one, clockwise. (D) two, clockwise.
Q.21 A discrete memoryless source has an alphabet { ?? 1
, ?? 2
, ?? 3
, ?? 4
} with corresponding probabilities
?
1
2
,
1
4
,
1
8
,
1
8
?. The minimum required average codeword length in bits to represent this source for
error-free reconstruction is ________
Q.22 A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM
data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz)
required for transmission is ________
Q.23 A uniform and constant magnetic field ?? = ?? ? ?? exists in the ?? ? direction in vacuum. A particle of
mass ?? with a small charge ?? is introduced into this region with an initial velocity ?? = ?? ? ?? ?? + ?? ? ?? ?? .
Given that ?? , ?? , ?? , ?? ?? and ?? ?? are all non-zero, which one of the following describes the eventual
trajectory of the particle?
(A) Helical motion in the ?? ? direction.
(B) Circular motion in the ?? ?? plane.
(C) Linear motion in the ?? ? direction.
(D) Linear motion in the ?? ? direction.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 6/14
Q.24 Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium
be expressed as ?? = ?? ? ?? ?? ?? ? ?? ( ???? ? ???? )
, where the propagation constant ?? is a function of the angular
frequency ?? . Assume that ?? ( ?? ) and ?? ?? are known and are real. From the information available,
which one of the following CANNOT be determined?
(A) The type of polarization of the wave.
(B) The group velocity of the wave.
(C) The phase velocity of the wave.
(D) The power flux through the ?? = 0 plane.
Q.25 Light from free space is incident at an angle ?? ?? to the normal of the facet of a step-index large core
optical fibre. The core and cladding refractive indices are ?? 1
= 1.5 and ?? 2
= 1.4, respectively.
The maximum value of ?? ?? (in degrees) for which the incident light will be guided in the core of the
fibre is ________
Q. 26 ? Q. 55 carry two marks each.
Q.26 The ordinary differential equation
????
????
= ?3 ?? + 2, with ?? (0) = 1
is to be solved using the forward Euler method. The largest time step that can be used to solve the
equation without making the numerical solution unstable is ________
Q.27 Suppose C is the closed curve defined as the circle ?? 2
+ ?? 2
= 1 with C oriented anti-clockwise.
The value of ?( ?? ?? 2
?? ?? + ?? 2
?? ?? ?? ) over the curve C equals ________
Q.28 Two random variables ?? and ?? are distributed according to
?? ?? , ?? ( ?? , ?? ) = ?
( ?? + ?? ), 0 ? ?? ? 1, 0 ? ?? ? 1
0, otherwise.
The probability ?? ( ?? + ?? ? 1) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 7/14
Q.29
The matrix
?
?
?
?
?
?
?
?
?
?
?
?
=
b
a
A
0 0 0
4 2 0 0
3 1 5 2
7 3 0
has det( ?? ) = 100 and trace( ?? ) = 14.
The value of | ?? ? ?? | is ________
Q.30 In the given circuit, each resistor has a value equal to 1 ?.
What is the equivalent resistance across the terminals ?? and ?? ?
(A) 1/6 ? (B) 1/3 ? (C) 9/20 ? (D) 8/15 ?
Q.31 In the circuit shown in the figure, the magnitude of the current (in amperes) through R
2
is ___
Q.32
A continuous-time filter with transfer function ?? ( ?? ) =
2 ?? + 6
?? 2
+ 6 ?? + 8
is converted to a discrete-
time filter with transfer function ?? ( ?? ) =
2 ?? 2
? 0.5 0 3 2 ?? ?? 2
? 0.5 0 3 2 ?? + ?? so that the impulse response of the
continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response
of the discrete time filter. The value of ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 8/14
Q.33 The Discrete Fourier Transform (DFT) of the 4-point sequence
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {3, 2, 3, 4} is
?? [ ?? ] = { ?? [0], ?? [1], ?? [2], ?? [3]} = {12, 2?? , 0, ?2?? }.
If X
1
[k] is the DFT of the 12-point sequence ?? 1
[ ?? ] = {3, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0},
the value of ?
?? 1
[ 8]
?? 1
[ 1 1]
? is ________
Q.34 The switch S in the circuit shown has been closed for a long time. It is opened at time ?? = 0 and
remains open after that. Assume that the diode has zero reverse current and zero forward voltage
drop.
The steady state magnitude of the capacitor voltage ?? C
(in volts) is ______
Q.35 A voltage ?? ?? is applied across a MOS capacitor with metal gate and p-type silicon substrate at
T=300 K. The inversion carrier density (in number of carriers per unit area) for ?? ?? = 0.8 V is
2 ? 10
1 1
cm
? 2
. For ?? ?? = 1.3 V, the inversion carrier density is 4 ? 10
1 1
cm
? 2
. What is the value
of the inversion carrier density for ?? ??
= 1.8 V?
(A) 4.5 ? 10
1 1
cm
? 2
(B) 6.0 ? 10
1 1
cm
? 2
(C) 7.2 ? 10
1 1
cm
? 2
(D) 8.4 ? 10
1 1
cm
? 2
Q.36 Consider avalanche breakdown in a silicon ?? +
?? junction. The ?? -region is uniformly doped with a
donor density ?? ?? . Assume that breakdown occurs when the magnitude of the electric field at any
point in the device becomes equal to the critical field ?? ?????? ?? . Assume ?? ?????? ?? to be independent of ?? ?? .
If the built-in voltage of the ?? +
?? junction is much smaller than the breakdown voltage, ?? ?? ?? , the
relationship between ?? ?? ?? and ?? ?? is given by
(A) ?? ?? ?? ? ? ?? ?? = constant (B) ?? ?? ? ? ?? ?? ?? = constant
(C) ?? ?? ? ?? ?? ?? = constant (D) ?? ?? / ?? ?? ?? = constant
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 9/14
Q.37 Consider a region of silicon devoid of electrons and holes, with an ionized donor density of
?? ?? +
= 10
1 7
cm
? 3
. The electric field at ?? = 0 is 0 V/cm and the electric field at ?? = ?? is
50 kV/cm in the positive ?? direction. Assume that the electric field is zero in the ?? and ?? directions
at all points.
Given ?? = 1.6 ? 10
? 1 9
coulomb, ?? 0
= 8.85 ? 10
? 1 4
F/cm, ?? ?? = 11.7 for silicon, the value of ?? in
nm is ________
Q.38 Consider a long-channel NMOS transistor with source and body connected together. Assume that
the electron mobility is independent of ?? ????
and ?? ???? . Given,
?? ?? = 0.5 ?? A/V for ?? ???? = 50 mV and ?? ????
= 2 V,
?? ?? = 8 ?? A/V for ?? ????
= 2 V and ?? ???? = 0 V,
where ?? ?? =
?? ?? ?? ?? ?? ????
and ?? ?? =
?? ?? ?? ?? ?? ????
The threshold voltage (in volts) of the transistor is ________
Q.39 The figure shows a half-wave rectifier with a 475 ?? F filter capacitor. The load draws a constant
current ?? ?? = 1 A from the rectifier. The figure also shows the input voltage ?? ?? , the output voltage
?? ?? and the peak-to-peak voltage ripple ?? on ?? ?? . The input voltage ?? ?? is a triangle-wave with an
amplitude of 10 V and a period of 1 ms.
The value of the ripple ?? (in volts) is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 10/14
Q.40 In the opamp circuit shown, the Zener diodes ?? 1 and ?? 2 clamp the output voltage ?? ?? to +5 V or
?5 V. The switch S is initially closed and is opened at time ?? = 0.
The time ?? = ?? 1
(in seconds) at which ?? ?? changes state is ________
Q.41 An opamp has a finite open loop voltage gain of 100. Its input offset voltage V
ios
(= +5mV) is
modeled as shown in the circuit below. The amplifier is ideal in all other respects. V
input
is 25 mV.
The output voltage (in millivolts) is ________
Q.42 An 8 Kbyte ROM with an active low Chip Select input (CS
? ? ?
) is to be used in an 8085
microprocessor based system. The ROM should occupy the address range 1000H to 2FFFH. The
address lines are designated as ?? 1 5
to ?? 0
, where ?? 1 5
is the most significant address bit.
Which one of the following logic expressions will generate the correct CS
? ? ?
signal for this ROM?
(A) ?? 1 5
+ ?? 1 4
+ ( ?? 1 3
? ?? 1 2
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
? ? ? ? ?
)
(B) ?? 1 5
? ?? 1 4
? ( ?? 1 3
+ ?? 1 2
)
(C) ?? 1 5
? ? ? ? ?
? ?? 1 4
? ? ? ? ?
? ( ?? 1 3
? ?? 1 2
? ? ? ? ?
+ ?? 1 3
? ? ? ? ?
? ?? 1 2
)
(D) ?? 1 5
? ? ? ? ?
+ ?? 1 4
? ? ? ? ?
+ ?? 1 3
? ?? 1 2
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 11/14
Q.43 In an N bit flash ADC, the analog voltage is fed simultaneously to 2
?? ? 1 comparators. The output
of the comparators is then encoded to a binary format using digital circuits. Assume that the analog
voltage source V
in
(whose output is being converted to digital format) has a source resistance of
75 ? as shown in the circuit diagram below and the input capacitance of each comparator is 8 pF.
The input must settle to an accuracy of 1/2 LSB even for a full scale input change for proper
conversion. Assume that the time taken by the thermometer to binary encoder is negligible.
If the flash ADC has 8 bit resolution, which one of the following alternatives is closest to the
maximum sampling rate ?
(A) 1 megasamples per second
(B) 6 megasamples per second
(C) 64 megasamples per second
(D) 256 megasamples per second
Q.44 The state transition diagram for a finite state machine with states A, B and C, and binary inputs X,
Y and Z, is shown in the figure.
Which one of the following statements is correct?
(A) Transitions from State A are ambiguously defined.
(B) Transitions from State B are ambiguously defined.
(C) Transitions from State C are ambiguously defined.
(D) All of the state transitions are defined unambiguously.
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 12/14
Q.45
In the feedback system shown below ?? ( ?? ) =
1
( ?? 2
+ 2 ?? )
.
The step response of the closed-loop system should have minimum settling time and have no
overshoot.
The required value of gain ?? to achieve this is ________
Q.46
In the feedback system shown below ?? ( ?? ) =
1
( ?? + 1)( ?? + 2)( ?? + 3)
.
The positive value of ?? for which the gain margin of the loop is exactly 0 dB and the phase margin
of the loop is exactly zero degree is ________
Q.47
The asymptotic Bode phase plot of ?? ( ?? ) =
?? ( ?? + 0. 1)( ?? + 1 0)( ?? + ?? 1
)
, with ?? and ?? 1
both positive,
is shown below.
The value of ?? 1
is ________
Q.48 An information source generates a binary sequence { ?? ?? }. ?? ?? can take one of the two possible
values ?1 and +1 with equal probability and are statistically independent and identically
distributed. This sequence is precoded to obtain another sequence { ?? ?? }, as ?? ?? = ?? ?? + ?? ?? ?? ? 3
.
The sequence { ?? ?? } is used to modulate a pulse ?? ( ?? ) to generate the baseband signal
?? ( ?? ) = ? ?? ?? ?? ( ?? ? ???? )
?
?? = ? ?
, where ?? ( ?? ) = ?
1, 0 ? ?? ? ??
0, otherwise.
If there is a null at ?? =
1
3 ?? in the power spectral density of ?? ( ?? ), then ?? is ________
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 13/14
Q.49 An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communication. A modem is
designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with
a raised cosine spectrum that utilizes the entire frequency band is ________
Q.50 Consider a random process ?? ( ?? ) = 3 ?? ( ?? ) ? 8, where ?? ( ?? ) is a zero mean stationary random
process with autocorrelation ?? ?? ( ?? ) = 4 ?? ? 5| ?? |
. The power in ?? ( ?? ) is ________
Q.51 A binary communication system makes use of the symbols ?zero? and ?one?. There are channel
errors. Consider the following events:
?? 0
: a "zero" is transmitted
?? 1
: a "one" is transmitted
?? 0
: a "zero" is received
?? 1
: a "one" is received
The following probabilities are given: ?? ( ?? 0
) =
1
2
, ?? ( ?? 0
| ?? 0
) =
3
4
, and ?? ( ?? 0
| ?? 1
) =
1
2
. The
information in bits that you obtain when you learn which symbol has been received (while you
know that a ?zero? has been transmitted) is ________
Q.52 The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that
the energy stored in it is ?? when the plate separation is ?? . The capacitor is then isolated electrically
and the plates are moved such that the plate separation becomes 2?? .
At this new plate separation, what is the energy stored in the capacitor, neglecting fringing effects?
(A) 2 ??
(B) ?2 ??
(C) ?? (D) ?? 2 ?
Q.53 A lossless microstrip transmission line consists of a trace of width ?? . It is drawn over a practically
infinite ground plane and is separated by a dielectric slab of thickness ?? and relative permittivity
?? ?? > 1. The inductance per unit length and the characteristic impedance of this line are ?? and ?? 0
,
respectively.
Which one of the following inequalities is always satisfied?
(A) ?? 0
> ?
????
?? 0
?? ?? ?? (B) ?? 0
< ?
????
?? 0
?? ?? ??
(C) ?? 0
> ?
????
?? 0
?? ?? ?? (D) ?? 0
< ?
????
?? 0
?? ?? ??
GATE 2016 Electronics and Communication Engineering (Set 2)
EC (2) 14/14
Q.54 A microwave circuit consisting of lossless transmission lines T
1
and T
2
is shown in the figure.
The plot shows the magnitude of the input reflection coefficient ? as a function of frequency ?? .
The phase velocity of the signal in the transmission lines is 2 ? 10
8
m/s.
The length ?? (in meters) of T
2
is ________
Q.55 A positive charge ?? is placed at ?? = 0 between two infinite metal plates placed at ?? = ? ?? and at
?? = + ?? respectively. The metal plates lie in the ?? ?? plane.
The charge is at rest at ?? = 0, when a voltage + ?? is applied to the plate at ? ?? and voltage ? ?? is
applied to the plate at ?? = + ?? . Assume that the quantity of the charge ?? is small enough that it does
not perturb the field set up by the metal plates. The time that the charge ?? takes to reach the right
plate is proportional to
(A) ?? / ??
(B) ? ?? / ?? (C) ?? / ? ?? (D) ? ?? / ??
END OF THE QUESTION PAPER
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This post was last modified on 18 December 2019