Download GATE (Graduate Aptitude Test in Engineering) Last 10 Years 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010 IN Instrumentation Engineering Question Papers With Solutions And Answer Keys
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
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GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
GATE 2016 Instrumentation Engineering - IN
IN 4/12
Q.21 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 ? resistors and a 10 ?
slide wire of length 1000 mm in series. The potentiometer is standardized with the current
I
p
= 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11
(11 numbers of the fixed 10 ? resistor are included) and the slide wire is on the 234th mm position.
The unknown voltage (up to four decimal places) in volt is _______.
Q.22 In the circuit given below, each input terminal of the opamp draws a bias current of 10 nA.
The effect due to these input bias currents on the output voltage V
O
will be zero, if the
value of R chosen in kilo-ohm is _______.
Q.23 A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to
300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is
______.
Q.24
The signal m(t) = cos( ?
m
t) is SSB (single side-band) modulated with a carrier cos( ?
c
t) to get s(t).
The signal obtained by passing s(t) through an ideal envelope detector is
(A) cos( ?
m
t) (B) sin( ?
m
t)
(C) cos( ?
m
t) + sin( ?
m
t) (D) 1
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
GATE 2016 Instrumentation Engineering - IN
IN 4/12
Q.21 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 ? resistors and a 10 ?
slide wire of length 1000 mm in series. The potentiometer is standardized with the current
I
p
= 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11
(11 numbers of the fixed 10 ? resistor are included) and the slide wire is on the 234th mm position.
The unknown voltage (up to four decimal places) in volt is _______.
Q.22 In the circuit given below, each input terminal of the opamp draws a bias current of 10 nA.
The effect due to these input bias currents on the output voltage V
O
will be zero, if the
value of R chosen in kilo-ohm is _______.
Q.23 A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to
300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is
______.
Q.24
The signal m(t) = cos( ?
m
t) is SSB (single side-band) modulated with a carrier cos( ?
c
t) to get s(t).
The signal obtained by passing s(t) through an ideal envelope detector is
(A) cos( ?
m
t) (B) sin( ?
m
t)
(C) cos( ?
m
t) + sin( ?
m
t) (D) 1
GATE 2016 Instrumentation Engineering - IN
IN 5/12
Q.25 Let
3
( ) rect
3
t
st
?
??
=
??
??
be a signal passed through an AWGN (additive white Gaussian noise)
channel with noise power spectral density (PSD)
0
2
N
to get () vt . If () vt is passed through a
matched-filter that is matched to ( ), st then output signal-to noise ratio (SNR) of the matched-filter
is
(A)
0
1
N
(B)
0
2
N
(C)
0
3
N
(D)
0
4
N
Q. 26 ? Q. 55 carry two marks each.
Q.26 Let : [ 1, 1] f ?? ? , where
34
( ) 2 10. fx x x = ?? The minimum value of () fx is______.
Q.27
An urn contains 5
red and 7 green balls. A ball is drawn at random and its colour is noted. The
ball is placed back into the urn along with another ball of the same colour. The probability of
getting a red ball in the next draw is
(A)
65
156
(B)
67
156
(C)
79
156
(D)
89
156
Q.28 Consider the matrix A =
21 1
23 4
112
??
??
??
??
???
??
whose eigenvalues are 1, 1 ?
and 3.
Then Trace of
( )
3 2
3 ? AA is _______.
Q.29 The relationship between the force f(t) and the displacement x(t) of a spring-mass system (with a
mass M, viscous damping D and spring constant K) is
2
2
() ()
() () + +=
d x t d x t
M D Kx t f t
dt dt
.
X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D = 2, K =10
in appropriate units, the transfer function
()
()
()
Xs
Gs
Fs
= is
(A)
2
10
20 100 ss ++
(B)
2
20 100 ss ++ (C)
2
2
10
20 100
s
ss ++
(D)
2
20 100
s
ss ++
Q.30
The value of the integral
2
2
11
21
C
z
dz
jz ?
+
?
?
where z is a complex number and C
is a unit circle with
center at 10 j + in the complex plane is_____________.
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
GATE 2016 Instrumentation Engineering - IN
IN 4/12
Q.21 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 ? resistors and a 10 ?
slide wire of length 1000 mm in series. The potentiometer is standardized with the current
I
p
= 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11
(11 numbers of the fixed 10 ? resistor are included) and the slide wire is on the 234th mm position.
The unknown voltage (up to four decimal places) in volt is _______.
Q.22 In the circuit given below, each input terminal of the opamp draws a bias current of 10 nA.
The effect due to these input bias currents on the output voltage V
O
will be zero, if the
value of R chosen in kilo-ohm is _______.
Q.23 A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to
300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is
______.
Q.24
The signal m(t) = cos( ?
m
t) is SSB (single side-band) modulated with a carrier cos( ?
c
t) to get s(t).
The signal obtained by passing s(t) through an ideal envelope detector is
(A) cos( ?
m
t) (B) sin( ?
m
t)
(C) cos( ?
m
t) + sin( ?
m
t) (D) 1
GATE 2016 Instrumentation Engineering - IN
IN 5/12
Q.25 Let
3
( ) rect
3
t
st
?
??
=
??
??
be a signal passed through an AWGN (additive white Gaussian noise)
channel with noise power spectral density (PSD)
0
2
N
to get () vt . If () vt is passed through a
matched-filter that is matched to ( ), st then output signal-to noise ratio (SNR) of the matched-filter
is
(A)
0
1
N
(B)
0
2
N
(C)
0
3
N
(D)
0
4
N
Q. 26 ? Q. 55 carry two marks each.
Q.26 Let : [ 1, 1] f ?? ? , where
34
( ) 2 10. fx x x = ?? The minimum value of () fx is______.
Q.27
An urn contains 5
red and 7 green balls. A ball is drawn at random and its colour is noted. The
ball is placed back into the urn along with another ball of the same colour. The probability of
getting a red ball in the next draw is
(A)
65
156
(B)
67
156
(C)
79
156
(D)
89
156
Q.28 Consider the matrix A =
21 1
23 4
112
??
??
??
??
???
??
whose eigenvalues are 1, 1 ?
and 3.
Then Trace of
( )
3 2
3 ? AA is _______.
Q.29 The relationship between the force f(t) and the displacement x(t) of a spring-mass system (with a
mass M, viscous damping D and spring constant K) is
2
2
() ()
() () + +=
d x t d x t
M D Kx t f t
dt dt
.
X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D = 2, K =10
in appropriate units, the transfer function
()
()
()
Xs
Gs
Fs
= is
(A)
2
10
20 100 ss ++
(B)
2
20 100 ss ++ (C)
2
2
10
20 100
s
ss ++
(D)
2
20 100
s
ss ++
Q.30
The value of the integral
2
2
11
21
C
z
dz
jz ?
+
?
?
where z is a complex number and C
is a unit circle with
center at 10 j + in the complex plane is_____________.
GATE 2016 Instrumentation Engineering - IN
IN 6/12
Q.31 The current I
X
in the circuit given below in milliampere is __________.
Q.32
In the circuit shown below,
S
101 0 V = ? V , R = 10 ? and ?L= 100 ?. The current I
S
is in phase
with V
S
. The magnitude of I
S
in milliampere is _________.
Q.33 A symmetrical three-phase three-wire RYB system is connected to a balanced delta-connected load.
The RMS values of the line current and line-to-line voltage are 10 A and 400 V respectively. The
power in the system is measured using the two wattmeter method. The first wattmeter connected
between R-line and Y-line reads zero. The reading of the second wattmeter (connected between B-
line and Y-line) in watt is ______.
Q.34 In the strain gauge bridge circuit given below, R
1
= R
3
= R (1 ? x) and R
2
= R
4
= R (1 + x), where
R is 350 ?. The voltage sources v
s
and v
n
represent the dc excitation and the undesired
noise/interference, respectively. The value of capacitor C in microfarad that is required to ensure
that the output across a and b is low-pass filtered with a cutoff frequency of 150 Hz is ________.
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
GATE 2016 Instrumentation Engineering - IN
IN 4/12
Q.21 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 ? resistors and a 10 ?
slide wire of length 1000 mm in series. The potentiometer is standardized with the current
I
p
= 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11
(11 numbers of the fixed 10 ? resistor are included) and the slide wire is on the 234th mm position.
The unknown voltage (up to four decimal places) in volt is _______.
Q.22 In the circuit given below, each input terminal of the opamp draws a bias current of 10 nA.
The effect due to these input bias currents on the output voltage V
O
will be zero, if the
value of R chosen in kilo-ohm is _______.
Q.23 A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to
300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is
______.
Q.24
The signal m(t) = cos( ?
m
t) is SSB (single side-band) modulated with a carrier cos( ?
c
t) to get s(t).
The signal obtained by passing s(t) through an ideal envelope detector is
(A) cos( ?
m
t) (B) sin( ?
m
t)
(C) cos( ?
m
t) + sin( ?
m
t) (D) 1
GATE 2016 Instrumentation Engineering - IN
IN 5/12
Q.25 Let
3
( ) rect
3
t
st
?
??
=
??
??
be a signal passed through an AWGN (additive white Gaussian noise)
channel with noise power spectral density (PSD)
0
2
N
to get () vt . If () vt is passed through a
matched-filter that is matched to ( ), st then output signal-to noise ratio (SNR) of the matched-filter
is
(A)
0
1
N
(B)
0
2
N
(C)
0
3
N
(D)
0
4
N
Q. 26 ? Q. 55 carry two marks each.
Q.26 Let : [ 1, 1] f ?? ? , where
34
( ) 2 10. fx x x = ?? The minimum value of () fx is______.
Q.27
An urn contains 5
red and 7 green balls. A ball is drawn at random and its colour is noted. The
ball is placed back into the urn along with another ball of the same colour. The probability of
getting a red ball in the next draw is
(A)
65
156
(B)
67
156
(C)
79
156
(D)
89
156
Q.28 Consider the matrix A =
21 1
23 4
112
??
??
??
??
???
??
whose eigenvalues are 1, 1 ?
and 3.
Then Trace of
( )
3 2
3 ? AA is _______.
Q.29 The relationship between the force f(t) and the displacement x(t) of a spring-mass system (with a
mass M, viscous damping D and spring constant K) is
2
2
() ()
() () + +=
d x t d x t
M D Kx t f t
dt dt
.
X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D = 2, K =10
in appropriate units, the transfer function
()
()
()
Xs
Gs
Fs
= is
(A)
2
10
20 100 ss ++
(B)
2
20 100 ss ++ (C)
2
2
10
20 100
s
ss ++
(D)
2
20 100
s
ss ++
Q.30
The value of the integral
2
2
11
21
C
z
dz
jz ?
+
?
?
where z is a complex number and C
is a unit circle with
center at 10 j + in the complex plane is_____________.
GATE 2016 Instrumentation Engineering - IN
IN 6/12
Q.31 The current I
X
in the circuit given below in milliampere is __________.
Q.32
In the circuit shown below,
S
101 0 V = ? V , R = 10 ? and ?L= 100 ?. The current I
S
is in phase
with V
S
. The magnitude of I
S
in milliampere is _________.
Q.33 A symmetrical three-phase three-wire RYB system is connected to a balanced delta-connected load.
The RMS values of the line current and line-to-line voltage are 10 A and 400 V respectively. The
power in the system is measured using the two wattmeter method. The first wattmeter connected
between R-line and Y-line reads zero. The reading of the second wattmeter (connected between B-
line and Y-line) in watt is ______.
Q.34 In the strain gauge bridge circuit given below, R
1
= R
3
= R (1 ? x) and R
2
= R
4
= R (1 + x), where
R is 350 ?. The voltage sources v
s
and v
n
represent the dc excitation and the undesired
noise/interference, respectively. The value of capacitor C in microfarad that is required to ensure
that the output across a and b is low-pass filtered with a cutoff frequency of 150 Hz is ________.
GATE 2016 Instrumentation Engineering - IN
IN 7/12
Q.35 The voltage ) (t v
shown below is applied to the given circuit. 3 ) ( = t v V for 0 < t
and 6 ) ( = t v V
for 0. t >
The value of current ) (t i
at 1 = t s, in ampere is _____ .
Q.36
For the periodic signal ) (t x
shown below with period 8 = T s, the power in the 10
th
harmonic is
(A) 0 (B)
2
1 2
2 10
??
??
?
??
(C)
2
1 4
2 10
??
??
?
??
(D)
2
5
4
2
1
?
?
?
?
?
?
?
Q.37 The fundamental period
0
N of the discrete-time sinusoid
301
[ ] sin
4
xn n ?
? ?
=
? ?
? ?
is _______.
Q.38 The transfer function G(s) of a system which has the asymptotic Bode plot shown below is
(A)
( )
( )
2
4
2
1
10
100
s
s
?
+
(B)
( )
( )
2
4
2
1
10
100
s
s
+
+
(C)
( )
( )
4
2
1
10
100
+
+
s
s
(D)
( )
( )
2
4
2
1
10
100
s
s
?
?
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
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n flagged by
g 70% of pet
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rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
GATE 2016 Instrumentation Engineering - IN
IN 4/12
Q.21 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 ? resistors and a 10 ?
slide wire of length 1000 mm in series. The potentiometer is standardized with the current
I
p
= 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11
(11 numbers of the fixed 10 ? resistor are included) and the slide wire is on the 234th mm position.
The unknown voltage (up to four decimal places) in volt is _______.
Q.22 In the circuit given below, each input terminal of the opamp draws a bias current of 10 nA.
The effect due to these input bias currents on the output voltage V
O
will be zero, if the
value of R chosen in kilo-ohm is _______.
Q.23 A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to
300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is
______.
Q.24
The signal m(t) = cos( ?
m
t) is SSB (single side-band) modulated with a carrier cos( ?
c
t) to get s(t).
The signal obtained by passing s(t) through an ideal envelope detector is
(A) cos( ?
m
t) (B) sin( ?
m
t)
(C) cos( ?
m
t) + sin( ?
m
t) (D) 1
GATE 2016 Instrumentation Engineering - IN
IN 5/12
Q.25 Let
3
( ) rect
3
t
st
?
??
=
??
??
be a signal passed through an AWGN (additive white Gaussian noise)
channel with noise power spectral density (PSD)
0
2
N
to get () vt . If () vt is passed through a
matched-filter that is matched to ( ), st then output signal-to noise ratio (SNR) of the matched-filter
is
(A)
0
1
N
(B)
0
2
N
(C)
0
3
N
(D)
0
4
N
Q. 26 ? Q. 55 carry two marks each.
Q.26 Let : [ 1, 1] f ?? ? , where
34
( ) 2 10. fx x x = ?? The minimum value of () fx is______.
Q.27
An urn contains 5
red and 7 green balls. A ball is drawn at random and its colour is noted. The
ball is placed back into the urn along with another ball of the same colour. The probability of
getting a red ball in the next draw is
(A)
65
156
(B)
67
156
(C)
79
156
(D)
89
156
Q.28 Consider the matrix A =
21 1
23 4
112
??
??
??
??
???
??
whose eigenvalues are 1, 1 ?
and 3.
Then Trace of
( )
3 2
3 ? AA is _______.
Q.29 The relationship between the force f(t) and the displacement x(t) of a spring-mass system (with a
mass M, viscous damping D and spring constant K) is
2
2
() ()
() () + +=
d x t d x t
M D Kx t f t
dt dt
.
X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D = 2, K =10
in appropriate units, the transfer function
()
()
()
Xs
Gs
Fs
= is
(A)
2
10
20 100 ss ++
(B)
2
20 100 ss ++ (C)
2
2
10
20 100
s
ss ++
(D)
2
20 100
s
ss ++
Q.30
The value of the integral
2
2
11
21
C
z
dz
jz ?
+
?
?
where z is a complex number and C
is a unit circle with
center at 10 j + in the complex plane is_____________.
GATE 2016 Instrumentation Engineering - IN
IN 6/12
Q.31 The current I
X
in the circuit given below in milliampere is __________.
Q.32
In the circuit shown below,
S
101 0 V = ? V , R = 10 ? and ?L= 100 ?. The current I
S
is in phase
with V
S
. The magnitude of I
S
in milliampere is _________.
Q.33 A symmetrical three-phase three-wire RYB system is connected to a balanced delta-connected load.
The RMS values of the line current and line-to-line voltage are 10 A and 400 V respectively. The
power in the system is measured using the two wattmeter method. The first wattmeter connected
between R-line and Y-line reads zero. The reading of the second wattmeter (connected between B-
line and Y-line) in watt is ______.
Q.34 In the strain gauge bridge circuit given below, R
1
= R
3
= R (1 ? x) and R
2
= R
4
= R (1 + x), where
R is 350 ?. The voltage sources v
s
and v
n
represent the dc excitation and the undesired
noise/interference, respectively. The value of capacitor C in microfarad that is required to ensure
that the output across a and b is low-pass filtered with a cutoff frequency of 150 Hz is ________.
GATE 2016 Instrumentation Engineering - IN
IN 7/12
Q.35 The voltage ) (t v
shown below is applied to the given circuit. 3 ) ( = t v V for 0 < t
and 6 ) ( = t v V
for 0. t >
The value of current ) (t i
at 1 = t s, in ampere is _____ .
Q.36
For the periodic signal ) (t x
shown below with period 8 = T s, the power in the 10
th
harmonic is
(A) 0 (B)
2
1 2
2 10
??
??
?
??
(C)
2
1 4
2 10
??
??
?
??
(D)
2
5
4
2
1
?
?
?
?
?
?
?
Q.37 The fundamental period
0
N of the discrete-time sinusoid
301
[ ] sin
4
xn n ?
? ?
=
? ?
? ?
is _______.
Q.38 The transfer function G(s) of a system which has the asymptotic Bode plot shown below is
(A)
( )
( )
2
4
2
1
10
100
s
s
?
+
(B)
( )
( )
2
4
2
1
10
100
s
s
+
+
(C)
( )
( )
4
2
1
10
100
+
+
s
s
(D)
( )
( )
2
4
2
1
10
100
s
s
?
?
GATE 2016 Instrumentation Engineering - IN
IN 8/12
Q.39 For the feedback system given below, the transfer function
2
1
()
( 1)
Gs
s
=
+
. The system CANNOT
be stabilized with
(A)
3
() 1 Cs
s
= + (B)
7
() 3 = + Cs
s
(C)
9
() 3 = + Cs
s
(D)
1
() = Cs
s
Q.40 Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given
below.
(A) P(s) ? (3), Q(s) ? (2), R(s) ? (1) (B) P(s) ? (1), Q(s) ? (2), R(s) ? (3)
(C) P(s) ? (2), Q(s) ? (1), R(s) ? (3) (D) P(s) ? (1), Q(s) ? (3), R(s) ? (2)
Q.41 An ideal opamp is used to realize a difference amplifier circuit given below having a gain of 10. If
x = 0.025, the CMRR of the circuit in dB is _______.
P(s) =
( )
1
1
?
+ s
Q(s) =
( )
( )
21
10 ( 2)
?
++
s
s s
R(s) =
( )
2
1
1 + s
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
GATE 2016 Instrumentation Engineering - IN
IN 4/12
Q.21 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 ? resistors and a 10 ?
slide wire of length 1000 mm in series. The potentiometer is standardized with the current
I
p
= 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11
(11 numbers of the fixed 10 ? resistor are included) and the slide wire is on the 234th mm position.
The unknown voltage (up to four decimal places) in volt is _______.
Q.22 In the circuit given below, each input terminal of the opamp draws a bias current of 10 nA.
The effect due to these input bias currents on the output voltage V
O
will be zero, if the
value of R chosen in kilo-ohm is _______.
Q.23 A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to
300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is
______.
Q.24
The signal m(t) = cos( ?
m
t) is SSB (single side-band) modulated with a carrier cos( ?
c
t) to get s(t).
The signal obtained by passing s(t) through an ideal envelope detector is
(A) cos( ?
m
t) (B) sin( ?
m
t)
(C) cos( ?
m
t) + sin( ?
m
t) (D) 1
GATE 2016 Instrumentation Engineering - IN
IN 5/12
Q.25 Let
3
( ) rect
3
t
st
?
??
=
??
??
be a signal passed through an AWGN (additive white Gaussian noise)
channel with noise power spectral density (PSD)
0
2
N
to get () vt . If () vt is passed through a
matched-filter that is matched to ( ), st then output signal-to noise ratio (SNR) of the matched-filter
is
(A)
0
1
N
(B)
0
2
N
(C)
0
3
N
(D)
0
4
N
Q. 26 ? Q. 55 carry two marks each.
Q.26 Let : [ 1, 1] f ?? ? , where
34
( ) 2 10. fx x x = ?? The minimum value of () fx is______.
Q.27
An urn contains 5
red and 7 green balls. A ball is drawn at random and its colour is noted. The
ball is placed back into the urn along with another ball of the same colour. The probability of
getting a red ball in the next draw is
(A)
65
156
(B)
67
156
(C)
79
156
(D)
89
156
Q.28 Consider the matrix A =
21 1
23 4
112
??
??
??
??
???
??
whose eigenvalues are 1, 1 ?
and 3.
Then Trace of
( )
3 2
3 ? AA is _______.
Q.29 The relationship between the force f(t) and the displacement x(t) of a spring-mass system (with a
mass M, viscous damping D and spring constant K) is
2
2
() ()
() () + +=
d x t d x t
M D Kx t f t
dt dt
.
X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D = 2, K =10
in appropriate units, the transfer function
()
()
()
Xs
Gs
Fs
= is
(A)
2
10
20 100 ss ++
(B)
2
20 100 ss ++ (C)
2
2
10
20 100
s
ss ++
(D)
2
20 100
s
ss ++
Q.30
The value of the integral
2
2
11
21
C
z
dz
jz ?
+
?
?
where z is a complex number and C
is a unit circle with
center at 10 j + in the complex plane is_____________.
GATE 2016 Instrumentation Engineering - IN
IN 6/12
Q.31 The current I
X
in the circuit given below in milliampere is __________.
Q.32
In the circuit shown below,
S
101 0 V = ? V , R = 10 ? and ?L= 100 ?. The current I
S
is in phase
with V
S
. The magnitude of I
S
in milliampere is _________.
Q.33 A symmetrical three-phase three-wire RYB system is connected to a balanced delta-connected load.
The RMS values of the line current and line-to-line voltage are 10 A and 400 V respectively. The
power in the system is measured using the two wattmeter method. The first wattmeter connected
between R-line and Y-line reads zero. The reading of the second wattmeter (connected between B-
line and Y-line) in watt is ______.
Q.34 In the strain gauge bridge circuit given below, R
1
= R
3
= R (1 ? x) and R
2
= R
4
= R (1 + x), where
R is 350 ?. The voltage sources v
s
and v
n
represent the dc excitation and the undesired
noise/interference, respectively. The value of capacitor C in microfarad that is required to ensure
that the output across a and b is low-pass filtered with a cutoff frequency of 150 Hz is ________.
GATE 2016 Instrumentation Engineering - IN
IN 7/12
Q.35 The voltage ) (t v
shown below is applied to the given circuit. 3 ) ( = t v V for 0 < t
and 6 ) ( = t v V
for 0. t >
The value of current ) (t i
at 1 = t s, in ampere is _____ .
Q.36
For the periodic signal ) (t x
shown below with period 8 = T s, the power in the 10
th
harmonic is
(A) 0 (B)
2
1 2
2 10
??
??
?
??
(C)
2
1 4
2 10
??
??
?
??
(D)
2
5
4
2
1
?
?
?
?
?
?
?
Q.37 The fundamental period
0
N of the discrete-time sinusoid
301
[ ] sin
4
xn n ?
? ?
=
? ?
? ?
is _______.
Q.38 The transfer function G(s) of a system which has the asymptotic Bode plot shown below is
(A)
( )
( )
2
4
2
1
10
100
s
s
?
+
(B)
( )
( )
2
4
2
1
10
100
s
s
+
+
(C)
( )
( )
4
2
1
10
100
+
+
s
s
(D)
( )
( )
2
4
2
1
10
100
s
s
?
?
GATE 2016 Instrumentation Engineering - IN
IN 8/12
Q.39 For the feedback system given below, the transfer function
2
1
()
( 1)
Gs
s
=
+
. The system CANNOT
be stabilized with
(A)
3
() 1 Cs
s
= + (B)
7
() 3 = + Cs
s
(C)
9
() 3 = + Cs
s
(D)
1
() = Cs
s
Q.40 Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given
below.
(A) P(s) ? (3), Q(s) ? (2), R(s) ? (1) (B) P(s) ? (1), Q(s) ? (2), R(s) ? (3)
(C) P(s) ? (2), Q(s) ? (1), R(s) ? (3) (D) P(s) ? (1), Q(s) ? (3), R(s) ? (2)
Q.41 An ideal opamp is used to realize a difference amplifier circuit given below having a gain of 10. If
x = 0.025, the CMRR of the circuit in dB is _______.
P(s) =
( )
1
1
?
+ s
Q(s) =
( )
( )
21
10 ( 2)
?
++
s
s s
R(s) =
( )
2
1
1 + s
GATE 2016 Instrumentation Engineering - IN
IN 9/12
Q.42 In the circuit given below, the opamp is ideal. The input v
x
is a sinusoid. To ensure v
y
= v
x
, the
value of C
N
in picofarad is _____.
Q.43 In the circuit given below, the opamp is ideal. The value of current I
L
in microampere is ______.
Q.44 A 4 to 1 multiplexer to realize a Boolean function F (X, Y, Z) is shown in the figure below. The
inputs Y and Z are connected to the selectors of the MUX (Y is more significant). The canonical
sum-of-product expression for F ( X, Y, Z ) is
(A) ? m ( 2, 3, 4, 7 ) (B) ? m ( 1, 3, 5, 7)
(C) ? m ( 0, 2, 4, 6 ) (D) ? m (2, 3, 5, 6 )
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
GATE 2016 Instrumentation Engineering - IN
IN 4/12
Q.21 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 ? resistors and a 10 ?
slide wire of length 1000 mm in series. The potentiometer is standardized with the current
I
p
= 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11
(11 numbers of the fixed 10 ? resistor are included) and the slide wire is on the 234th mm position.
The unknown voltage (up to four decimal places) in volt is _______.
Q.22 In the circuit given below, each input terminal of the opamp draws a bias current of 10 nA.
The effect due to these input bias currents on the output voltage V
O
will be zero, if the
value of R chosen in kilo-ohm is _______.
Q.23 A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to
300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is
______.
Q.24
The signal m(t) = cos( ?
m
t) is SSB (single side-band) modulated with a carrier cos( ?
c
t) to get s(t).
The signal obtained by passing s(t) through an ideal envelope detector is
(A) cos( ?
m
t) (B) sin( ?
m
t)
(C) cos( ?
m
t) + sin( ?
m
t) (D) 1
GATE 2016 Instrumentation Engineering - IN
IN 5/12
Q.25 Let
3
( ) rect
3
t
st
?
??
=
??
??
be a signal passed through an AWGN (additive white Gaussian noise)
channel with noise power spectral density (PSD)
0
2
N
to get () vt . If () vt is passed through a
matched-filter that is matched to ( ), st then output signal-to noise ratio (SNR) of the matched-filter
is
(A)
0
1
N
(B)
0
2
N
(C)
0
3
N
(D)
0
4
N
Q. 26 ? Q. 55 carry two marks each.
Q.26 Let : [ 1, 1] f ?? ? , where
34
( ) 2 10. fx x x = ?? The minimum value of () fx is______.
Q.27
An urn contains 5
red and 7 green balls. A ball is drawn at random and its colour is noted. The
ball is placed back into the urn along with another ball of the same colour. The probability of
getting a red ball in the next draw is
(A)
65
156
(B)
67
156
(C)
79
156
(D)
89
156
Q.28 Consider the matrix A =
21 1
23 4
112
??
??
??
??
???
??
whose eigenvalues are 1, 1 ?
and 3.
Then Trace of
( )
3 2
3 ? AA is _______.
Q.29 The relationship between the force f(t) and the displacement x(t) of a spring-mass system (with a
mass M, viscous damping D and spring constant K) is
2
2
() ()
() () + +=
d x t d x t
M D Kx t f t
dt dt
.
X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D = 2, K =10
in appropriate units, the transfer function
()
()
()
Xs
Gs
Fs
= is
(A)
2
10
20 100 ss ++
(B)
2
20 100 ss ++ (C)
2
2
10
20 100
s
ss ++
(D)
2
20 100
s
ss ++
Q.30
The value of the integral
2
2
11
21
C
z
dz
jz ?
+
?
?
where z is a complex number and C
is a unit circle with
center at 10 j + in the complex plane is_____________.
GATE 2016 Instrumentation Engineering - IN
IN 6/12
Q.31 The current I
X
in the circuit given below in milliampere is __________.
Q.32
In the circuit shown below,
S
101 0 V = ? V , R = 10 ? and ?L= 100 ?. The current I
S
is in phase
with V
S
. The magnitude of I
S
in milliampere is _________.
Q.33 A symmetrical three-phase three-wire RYB system is connected to a balanced delta-connected load.
The RMS values of the line current and line-to-line voltage are 10 A and 400 V respectively. The
power in the system is measured using the two wattmeter method. The first wattmeter connected
between R-line and Y-line reads zero. The reading of the second wattmeter (connected between B-
line and Y-line) in watt is ______.
Q.34 In the strain gauge bridge circuit given below, R
1
= R
3
= R (1 ? x) and R
2
= R
4
= R (1 + x), where
R is 350 ?. The voltage sources v
s
and v
n
represent the dc excitation and the undesired
noise/interference, respectively. The value of capacitor C in microfarad that is required to ensure
that the output across a and b is low-pass filtered with a cutoff frequency of 150 Hz is ________.
GATE 2016 Instrumentation Engineering - IN
IN 7/12
Q.35 The voltage ) (t v
shown below is applied to the given circuit. 3 ) ( = t v V for 0 < t
and 6 ) ( = t v V
for 0. t >
The value of current ) (t i
at 1 = t s, in ampere is _____ .
Q.36
For the periodic signal ) (t x
shown below with period 8 = T s, the power in the 10
th
harmonic is
(A) 0 (B)
2
1 2
2 10
??
??
?
??
(C)
2
1 4
2 10
??
??
?
??
(D)
2
5
4
2
1
?
?
?
?
?
?
?
Q.37 The fundamental period
0
N of the discrete-time sinusoid
301
[ ] sin
4
xn n ?
? ?
=
? ?
? ?
is _______.
Q.38 The transfer function G(s) of a system which has the asymptotic Bode plot shown below is
(A)
( )
( )
2
4
2
1
10
100
s
s
?
+
(B)
( )
( )
2
4
2
1
10
100
s
s
+
+
(C)
( )
( )
4
2
1
10
100
+
+
s
s
(D)
( )
( )
2
4
2
1
10
100
s
s
?
?
GATE 2016 Instrumentation Engineering - IN
IN 8/12
Q.39 For the feedback system given below, the transfer function
2
1
()
( 1)
Gs
s
=
+
. The system CANNOT
be stabilized with
(A)
3
() 1 Cs
s
= + (B)
7
() 3 = + Cs
s
(C)
9
() 3 = + Cs
s
(D)
1
() = Cs
s
Q.40 Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given
below.
(A) P(s) ? (3), Q(s) ? (2), R(s) ? (1) (B) P(s) ? (1), Q(s) ? (2), R(s) ? (3)
(C) P(s) ? (2), Q(s) ? (1), R(s) ? (3) (D) P(s) ? (1), Q(s) ? (3), R(s) ? (2)
Q.41 An ideal opamp is used to realize a difference amplifier circuit given below having a gain of 10. If
x = 0.025, the CMRR of the circuit in dB is _______.
P(s) =
( )
1
1
?
+ s
Q(s) =
( )
( )
21
10 ( 2)
?
++
s
s s
R(s) =
( )
2
1
1 + s
GATE 2016 Instrumentation Engineering - IN
IN 9/12
Q.42 In the circuit given below, the opamp is ideal. The input v
x
is a sinusoid. To ensure v
y
= v
x
, the
value of C
N
in picofarad is _____.
Q.43 In the circuit given below, the opamp is ideal. The value of current I
L
in microampere is ______.
Q.44 A 4 to 1 multiplexer to realize a Boolean function F (X, Y, Z) is shown in the figure below. The
inputs Y and Z are connected to the selectors of the MUX (Y is more significant). The canonical
sum-of-product expression for F ( X, Y, Z ) is
(A) ? m ( 2, 3, 4, 7 ) (B) ? m ( 1, 3, 5, 7)
(C) ? m ( 0, 2, 4, 6 ) (D) ? m (2, 3, 5, 6 )
GATE 2016 Instrumentation Engineering - IN
IN 10/12
Q.45 A synchronous counter using two J - K flip flops that goes through the sequence of states:
Q
1
Q
2
= 00 ? 10 ? 01? 11? 00 ? ? ? is required. To achieve this, the inputs to the flip flops are
(A) J
1
= Q
2
, K
1
= 0 ; J
2
= Q
1
?, K
2
= Q
1
(B) J
1
= 1, K
1
= 1 ; J
2
= Q
1
, K
2
= Q
1
(C) J
1
= Q
2
, K
1
= Q
2
? ; J
2
= 1 , K
2
= 1 (D) J
1
= Q
2
?, K
1
= Q
2
; J
2
= Q
1
, K
2
= Q
1
?
Q.46 A 1 Kbyte memory module has to be interfaced with an 8-bit microprocessor that has 16 address
lines. The address lines A
0
to A
9
of the processor are connected to the corresponding address lines
of the memory module. The active low chip select CS of the memory module is connected to the y
5
output of a 3 to 8 decoder with active low outputs. S
0
, S
1
, and S
2
are the input lines to the decoder,
with S
2
as the MSB. The decoder has one active low 1 EN and one active high
2
EN enable lines as
shown below. The address range(s) that gets mapped onto this memory module is (are)
(A) 3000
H
to 33FF
H
and E000
H
to E3FF
H
(B) 1400
H
to 17FF
H
(C) 5300
H
to 53FF
H
and A300
H
to A3FF
H
(D) 5800
H
to 5BFF
H
and D800
H
to DBFF
H
Q.47 A coil is tested with a series type Q-meter. Resonance at a particular frequency is obtained with a
capacitance of 110 pF. When the frequency is doubled, the capacitance required for resonance is
20 pF. The distributed capacitance of the coil in pico farad is ______.
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
) Rabies can
) Stray dogs
flat is shared
oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
Sravan
he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
Trideep
y=5 in the fir
15.70
in m/s and
w much will
(D)
ndia has been
t inoculating
mber of peopl
sentences?
nfected with
ray dogs.
agreed to allo
r than Sravan
Who should oc
(D)
rst quadrant.
(D)
General Ap
plotted as s
l the odome
5
n flagged by
g 70% of pet
le infected w
rabies is low
ow the oldest
n, who is th
ccupy the ex
Pavan
20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
GATE 2016 Instrumentation Engineering - IN
IN 4/12
Q.21 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 ? resistors and a 10 ?
slide wire of length 1000 mm in series. The potentiometer is standardized with the current
I
p
= 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11
(11 numbers of the fixed 10 ? resistor are included) and the slide wire is on the 234th mm position.
The unknown voltage (up to four decimal places) in volt is _______.
Q.22 In the circuit given below, each input terminal of the opamp draws a bias current of 10 nA.
The effect due to these input bias currents on the output voltage V
O
will be zero, if the
value of R chosen in kilo-ohm is _______.
Q.23 A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to
300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is
______.
Q.24
The signal m(t) = cos( ?
m
t) is SSB (single side-band) modulated with a carrier cos( ?
c
t) to get s(t).
The signal obtained by passing s(t) through an ideal envelope detector is
(A) cos( ?
m
t) (B) sin( ?
m
t)
(C) cos( ?
m
t) + sin( ?
m
t) (D) 1
GATE 2016 Instrumentation Engineering - IN
IN 5/12
Q.25 Let
3
( ) rect
3
t
st
?
??
=
??
??
be a signal passed through an AWGN (additive white Gaussian noise)
channel with noise power spectral density (PSD)
0
2
N
to get () vt . If () vt is passed through a
matched-filter that is matched to ( ), st then output signal-to noise ratio (SNR) of the matched-filter
is
(A)
0
1
N
(B)
0
2
N
(C)
0
3
N
(D)
0
4
N
Q. 26 ? Q. 55 carry two marks each.
Q.26 Let : [ 1, 1] f ?? ? , where
34
( ) 2 10. fx x x = ?? The minimum value of () fx is______.
Q.27
An urn contains 5
red and 7 green balls. A ball is drawn at random and its colour is noted. The
ball is placed back into the urn along with another ball of the same colour. The probability of
getting a red ball in the next draw is
(A)
65
156
(B)
67
156
(C)
79
156
(D)
89
156
Q.28 Consider the matrix A =
21 1
23 4
112
??
??
??
??
???
??
whose eigenvalues are 1, 1 ?
and 3.
Then Trace of
( )
3 2
3 ? AA is _______.
Q.29 The relationship between the force f(t) and the displacement x(t) of a spring-mass system (with a
mass M, viscous damping D and spring constant K) is
2
2
() ()
() () + +=
d x t d x t
M D Kx t f t
dt dt
.
X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D = 2, K =10
in appropriate units, the transfer function
()
()
()
Xs
Gs
Fs
= is
(A)
2
10
20 100 ss ++
(B)
2
20 100 ss ++ (C)
2
2
10
20 100
s
ss ++
(D)
2
20 100
s
ss ++
Q.30
The value of the integral
2
2
11
21
C
z
dz
jz ?
+
?
?
where z is a complex number and C
is a unit circle with
center at 10 j + in the complex plane is_____________.
GATE 2016 Instrumentation Engineering - IN
IN 6/12
Q.31 The current I
X
in the circuit given below in milliampere is __________.
Q.32
In the circuit shown below,
S
101 0 V = ? V , R = 10 ? and ?L= 100 ?. The current I
S
is in phase
with V
S
. The magnitude of I
S
in milliampere is _________.
Q.33 A symmetrical three-phase three-wire RYB system is connected to a balanced delta-connected load.
The RMS values of the line current and line-to-line voltage are 10 A and 400 V respectively. The
power in the system is measured using the two wattmeter method. The first wattmeter connected
between R-line and Y-line reads zero. The reading of the second wattmeter (connected between B-
line and Y-line) in watt is ______.
Q.34 In the strain gauge bridge circuit given below, R
1
= R
3
= R (1 ? x) and R
2
= R
4
= R (1 + x), where
R is 350 ?. The voltage sources v
s
and v
n
represent the dc excitation and the undesired
noise/interference, respectively. The value of capacitor C in microfarad that is required to ensure
that the output across a and b is low-pass filtered with a cutoff frequency of 150 Hz is ________.
GATE 2016 Instrumentation Engineering - IN
IN 7/12
Q.35 The voltage ) (t v
shown below is applied to the given circuit. 3 ) ( = t v V for 0 < t
and 6 ) ( = t v V
for 0. t >
The value of current ) (t i
at 1 = t s, in ampere is _____ .
Q.36
For the periodic signal ) (t x
shown below with period 8 = T s, the power in the 10
th
harmonic is
(A) 0 (B)
2
1 2
2 10
??
??
?
??
(C)
2
1 4
2 10
??
??
?
??
(D)
2
5
4
2
1
?
?
?
?
?
?
?
Q.37 The fundamental period
0
N of the discrete-time sinusoid
301
[ ] sin
4
xn n ?
? ?
=
? ?
? ?
is _______.
Q.38 The transfer function G(s) of a system which has the asymptotic Bode plot shown below is
(A)
( )
( )
2
4
2
1
10
100
s
s
?
+
(B)
( )
( )
2
4
2
1
10
100
s
s
+
+
(C)
( )
( )
4
2
1
10
100
+
+
s
s
(D)
( )
( )
2
4
2
1
10
100
s
s
?
?
GATE 2016 Instrumentation Engineering - IN
IN 8/12
Q.39 For the feedback system given below, the transfer function
2
1
()
( 1)
Gs
s
=
+
. The system CANNOT
be stabilized with
(A)
3
() 1 Cs
s
= + (B)
7
() 3 = + Cs
s
(C)
9
() 3 = + Cs
s
(D)
1
() = Cs
s
Q.40 Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given
below.
(A) P(s) ? (3), Q(s) ? (2), R(s) ? (1) (B) P(s) ? (1), Q(s) ? (2), R(s) ? (3)
(C) P(s) ? (2), Q(s) ? (1), R(s) ? (3) (D) P(s) ? (1), Q(s) ? (3), R(s) ? (2)
Q.41 An ideal opamp is used to realize a difference amplifier circuit given below having a gain of 10. If
x = 0.025, the CMRR of the circuit in dB is _______.
P(s) =
( )
1
1
?
+ s
Q(s) =
( )
( )
21
10 ( 2)
?
++
s
s s
R(s) =
( )
2
1
1 + s
GATE 2016 Instrumentation Engineering - IN
IN 9/12
Q.42 In the circuit given below, the opamp is ideal. The input v
x
is a sinusoid. To ensure v
y
= v
x
, the
value of C
N
in picofarad is _____.
Q.43 In the circuit given below, the opamp is ideal. The value of current I
L
in microampere is ______.
Q.44 A 4 to 1 multiplexer to realize a Boolean function F (X, Y, Z) is shown in the figure below. The
inputs Y and Z are connected to the selectors of the MUX (Y is more significant). The canonical
sum-of-product expression for F ( X, Y, Z ) is
(A) ? m ( 2, 3, 4, 7 ) (B) ? m ( 1, 3, 5, 7)
(C) ? m ( 0, 2, 4, 6 ) (D) ? m (2, 3, 5, 6 )
GATE 2016 Instrumentation Engineering - IN
IN 10/12
Q.45 A synchronous counter using two J - K flip flops that goes through the sequence of states:
Q
1
Q
2
= 00 ? 10 ? 01? 11? 00 ? ? ? is required. To achieve this, the inputs to the flip flops are
(A) J
1
= Q
2
, K
1
= 0 ; J
2
= Q
1
?, K
2
= Q
1
(B) J
1
= 1, K
1
= 1 ; J
2
= Q
1
, K
2
= Q
1
(C) J
1
= Q
2
, K
1
= Q
2
? ; J
2
= 1 , K
2
= 1 (D) J
1
= Q
2
?, K
1
= Q
2
; J
2
= Q
1
, K
2
= Q
1
?
Q.46 A 1 Kbyte memory module has to be interfaced with an 8-bit microprocessor that has 16 address
lines. The address lines A
0
to A
9
of the processor are connected to the corresponding address lines
of the memory module. The active low chip select CS of the memory module is connected to the y
5
output of a 3 to 8 decoder with active low outputs. S
0
, S
1
, and S
2
are the input lines to the decoder,
with S
2
as the MSB. The decoder has one active low 1 EN and one active high
2
EN enable lines as
shown below. The address range(s) that gets mapped onto this memory module is (are)
(A) 3000
H
to 33FF
H
and E000
H
to E3FF
H
(B) 1400
H
to 17FF
H
(C) 5300
H
to 53FF
H
and A300
H
to A3FF
H
(D) 5800
H
to 5BFF
H
and D800
H
to DBFF
H
Q.47 A coil is tested with a series type Q-meter. Resonance at a particular frequency is obtained with a
capacitance of 110 pF. When the frequency is doubled, the capacitance required for resonance is
20 pF. The distributed capacitance of the coil in pico farad is ______.
GATE 2016 Instrumentation Engineering - IN
IN 11/12
Q.48 The comparators (output = ?1?, when input ? 0 and output =?0?, when input < 0), exclusive-OR gate
and the unity gain low-pass filter given in the circuit are ideal. The logic output voltages of the
exclusive-OR gate are 0 V and 5 V. The cutoff frequency of the low-pass filter is 0.1 Hz. For
V
1
= 1 sin (3000t + 36
o
) V and V
2
= 1 sin (3000t) V, the value of V
O
in volt is ______.
Q.49 A 200 mV full scale dual-slope 3 ? digit DMM has a reference voltage of 100 mV and a first
integration time of 100 ms. For an input of [100 + 10 Cos(100?t)] mV, the conversion time
(without taking the auto-zero phase time into consideration) in millisecond is ______.
Q.50 In the circuit below, the opamp is ideal and the sensor is an RTD whose resistance
R
?
= 1000 (1 + 0.004 ?) ?
, where ? is temperature in ?C. The output sensitivity in mV/ ?C is ___.
Q.51 The photo diode in the figure below has an active sensing area of 10 mm
2
, a sensitivity of 0.5 A/W
and a dark current of 1 ?A. The i-to-v converter has a sensitivity of 100 mV/ ?A. For an input light
intensity of 4 W/m
2
, the output V
O
in volt is ____.
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-4
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 An apple costs Rs. 10. An onion costs Rs. 8.
Select the most suitable sentence with respect to grammar and usage.
(A) The price of an apple is greater than an onion.
(B) The price of an apple is more than onion.
(C) The price of an apple is greater than that of an onion.
(D) Apples are more costlier than onions.
Q.2 The Buddha said, ?Holding on to anger is like grasping a hot coal with the intent of throwing it at
someone else; you are the one who gets burnt.?
Select the word below which is closest in meaning to the word underlined above.
(A) burning (B) igniting (C) clutching (D) flinging
Q.3 M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-
law of M. How is P related to M?
(A) P is the son-in-law of M. (B) P is the grandchild of M.
(C) P is the daughter-in law of M. (D) P is the grandfather of M.
Q.4 The number that least fits this set: (324, 441, 97 and 64) is ________.
(A) 324 (B) 441 (C) 97 (D) 64
Q.5 It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to
completely pass a telegraph post. The length of the first train is 120 m and that of the second train is
150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________.
(A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0
Q. 6 ? Q.
Q.6 The
resp
incr
(A)
Q.7 The
Hea
dog
Wh
(A)
(B)
(C)
(D)
Q.8 A f
enj
you
the
(A)
Q.9 Fin
(A)
GATE 2016
10 carry tw
e velocity V
pect to time
rease by (in
) 0
e overwhelm
alth Organiz
gs against rab
hich of the fo
) The numb
) The numb
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oy some ext
unger than Tr
flat?
) Manu
nd the area bo
) 14.95
wo marks
V of a vehicl
e in seconds
m)?
(B)
ming number
zation as a so
bies can lead
ollowing can
ber of people
er of people
n be eradicat
s are the mai
by four first
tra space in
rideep. Pava
(B)
ounded by th
(B)
each.
le along a st
. At the end
3
r of people in
ource of con
d to a signific
be logically
in India infe
in other part
ed in India b
n source of r
t year underg
the flat. Ma
an is one mon
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he lines 3x+2
15.25
traight line i
d of the 7 s
(C)
nfected with
ncern. It is es
cant reductio
y inferred from
ected with ra
ts of the wor
by vaccinatin
rabies worldw
graduate stud
anu is two m
nth older than
(C)
2y=14, 2x-3y
(C)
is measured
seconds, how
4
h rabies in In
stimated that
on in the num
m the above
abies is high.
ld who are in
ng 70% of str
wide.
dents. They a
months older
n Sravan. W
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y=5 in the fir
15.70
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w much will
(D)
ndia has been
t inoculating
mber of peopl
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nfected with
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Who should oc
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20.35
ptitude - GA Set-4
2/3
shown with
eter reading
y the World
ts and stray
with rabies.
w.
t of them to
hree months
xtra space in
4
3
GATE 2016 General Aptitude - GA Set-4
3/3
Q.10 A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a
slope of ?0.02. What is the value of y at x = 5 from the fit?
(A) ?0.030 (B) ?0.014 (C) 0.014 (D) 0.030
END OF THE QUESTION PAPER
GATE 2016 Instrumentation Engineering - IN
IN 1/12
Q. 1 ? Q. 25 carry one mark each.
Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The
value of m is ________ .
Q.2
( )
22
lim 1
n
nn n
??
+ ? + is __________________.
Q.3 A voltage V
1
is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
is computed as: V
3
= V
1
+ V
2
.
Then the standard deviation of V
3
in volt is ____.
Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.
(A) (i ?2j + k) (B) (?i + 2j ?k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k)
Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
???? ( ???? ) =1+(1 ? ???? )+(1 ? ???? )
2
+ ????
Then f(z) is
(A)
1
z
(B)
1
2 z
?
?
(C)
1
1
z
z
?
+
(D)
1
21 z ?
Q.6 Three currents i
1
, i
2
and i
3
meet at a node as shown in the figure below. If i
1
= 3 cos( ?t) ampere,
i
2
= 4 sin( ?t) ampere and i
3
= I
3
cos( ?t + ?) ampere, the value of I
3
in ampere is __________.
Q.7 An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting
skin effect) will be ________.
Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial
charge. The voltage across the capacitor for t > 2 s in volt is _________
GATE 2016 Instrumentation Engineering - IN
IN 2/12
Q.9
The signal ] [n x shown in the figure below is convolved with itself to get y[n]. The value of ] 1 [ ? y
is ________ .
Q.10 In the circuit shown below (v
1
+ v
2
) = [1 sin(2 ?10000t) + 1 sin(2 ?30000t)] V. The RMS value of
the current through the resistor R will be minimum if the value of the capacitor C in microfarad is
______.
Q.11 If ) (s X , the Laplace transform of signal ) (t x
is given by
2
) 3 )( 1 (
) 2 (
) (
+ +
+
=
s s
s
s X , then the value
of ) (t x
as ? ? t
is ______.
Q.12 The number of times the Nyquist plot of
1
()
1
s
G s
s
?
=
+
will encircle the origin clockwise is ______.
Q.13 The value of a
0
which will ensure that the polynomial s
3
+ 3s
2
+ 2s + a
0
has roots on the left half of
the s-plane is
(A) 11 (B) 9 (C) 7 (D) 5
Q.14 The input ( ) 2sin(3 ) it t ? = + is applied to a system whose transfer function
( )
2
8
() .
10
G s
s
=
+
The amplitude of the output of the system is______.
Q.15
The diode D used in the circuit below is ideal. The voltage drop V
ab
across the 1 k ? resistor in volt
is _________.
GATE 2016 Instrumentation Engineering - IN
IN 3/12
Q.16 In the circuit given below, the opamp is ideal. The output voltage V
O
in volt is ____.
Q.17 In the circuit given below, the diodes D
1
and D
2
have a forward voltage drop of 0.6 V. The opamp
used is ideal. The magnitude of the negative peak value of the output V
O
in volt is ________.
Q.18 The Boolean expression XY + ( X ?+ Y ? )Z is equivalent to
(A) XYZ ? + X ?Y ?Z (B) X ?Y ?Z ? + XYZ
(C) ( X + Z )( Y+Z ) (D) ( X ? + Z )( Y ? + Z )
Q.19 In the digital circuit given below, F is
(A) XY YZ + (B) XY YZ +
(C) XY YZ + (D) XZ Y +
Q.20 A 3 ? digit DMM has an accuracy specification of ? 1 % of full scale (accuracy class 1). A reading
of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in
milliampere is ?______ .
GATE 2016 Instrumentation Engineering - IN
IN 4/12
Q.21 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 ? resistors and a 10 ?
slide wire of length 1000 mm in series. The potentiometer is standardized with the current
I
p
= 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11
(11 numbers of the fixed 10 ? resistor are included) and the slide wire is on the 234th mm position.
The unknown voltage (up to four decimal places) in volt is _______.
Q.22 In the circuit given below, each input terminal of the opamp draws a bias current of 10 nA.
The effect due to these input bias currents on the output voltage V
O
will be zero, if the
value of R chosen in kilo-ohm is _______.
Q.23 A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to
300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is
______.
Q.24
The signal m(t) = cos( ?
m
t) is SSB (single side-band) modulated with a carrier cos( ?
c
t) to get s(t).
The signal obtained by passing s(t) through an ideal envelope detector is
(A) cos( ?
m
t) (B) sin( ?
m
t)
(C) cos( ?
m
t) + sin( ?
m
t) (D) 1
GATE 2016 Instrumentation Engineering - IN
IN 5/12
Q.25 Let
3
( ) rect
3
t
st
?
??
=
??
??
be a signal passed through an AWGN (additive white Gaussian noise)
channel with noise power spectral density (PSD)
0
2
N
to get () vt . If () vt is passed through a
matched-filter that is matched to ( ), st then output signal-to noise ratio (SNR) of the matched-filter
is
(A)
0
1
N
(B)
0
2
N
(C)
0
3
N
(D)
0
4
N
Q. 26 ? Q. 55 carry two marks each.
Q.26 Let : [ 1, 1] f ?? ? , where
34
( ) 2 10. fx x x = ?? The minimum value of () fx is______.
Q.27
An urn contains 5
red and 7 green balls. A ball is drawn at random and its colour is noted. The
ball is placed back into the urn along with another ball of the same colour. The probability of
getting a red ball in the next draw is
(A)
65
156
(B)
67
156
(C)
79
156
(D)
89
156
Q.28 Consider the matrix A =
21 1
23 4
112
??
??
??
??
???
??
whose eigenvalues are 1, 1 ?
and 3.
Then Trace of
( )
3 2
3 ? AA is _______.
Q.29 The relationship between the force f(t) and the displacement x(t) of a spring-mass system (with a
mass M, viscous damping D and spring constant K) is
2
2
() ()
() () + +=
d x t d x t
M D Kx t f t
dt dt
.
X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D = 2, K =10
in appropriate units, the transfer function
()
()
()
Xs
Gs
Fs
= is
(A)
2
10
20 100 ss ++
(B)
2
20 100 ss ++ (C)
2
2
10
20 100
s
ss ++
(D)
2
20 100
s
ss ++
Q.30
The value of the integral
2
2
11
21
C
z
dz
jz ?
+
?
?
where z is a complex number and C
is a unit circle with
center at 10 j + in the complex plane is_____________.
GATE 2016 Instrumentation Engineering - IN
IN 6/12
Q.31 The current I
X
in the circuit given below in milliampere is __________.
Q.32
In the circuit shown below,
S
101 0 V = ? V , R = 10 ? and ?L= 100 ?. The current I
S
is in phase
with V
S
. The magnitude of I
S
in milliampere is _________.
Q.33 A symmetrical three-phase three-wire RYB system is connected to a balanced delta-connected load.
The RMS values of the line current and line-to-line voltage are 10 A and 400 V respectively. The
power in the system is measured using the two wattmeter method. The first wattmeter connected
between R-line and Y-line reads zero. The reading of the second wattmeter (connected between B-
line and Y-line) in watt is ______.
Q.34 In the strain gauge bridge circuit given below, R
1
= R
3
= R (1 ? x) and R
2
= R
4
= R (1 + x), where
R is 350 ?. The voltage sources v
s
and v
n
represent the dc excitation and the undesired
noise/interference, respectively. The value of capacitor C in microfarad that is required to ensure
that the output across a and b is low-pass filtered with a cutoff frequency of 150 Hz is ________.
GATE 2016 Instrumentation Engineering - IN
IN 7/12
Q.35 The voltage ) (t v
shown below is applied to the given circuit. 3 ) ( = t v V for 0 < t
and 6 ) ( = t v V
for 0. t >
The value of current ) (t i
at 1 = t s, in ampere is _____ .
Q.36
For the periodic signal ) (t x
shown below with period 8 = T s, the power in the 10
th
harmonic is
(A) 0 (B)
2
1 2
2 10
??
??
?
??
(C)
2
1 4
2 10
??
??
?
??
(D)
2
5
4
2
1
?
?
?
?
?
?
?
Q.37 The fundamental period
0
N of the discrete-time sinusoid
301
[ ] sin
4
xn n ?
? ?
=
? ?
? ?
is _______.
Q.38 The transfer function G(s) of a system which has the asymptotic Bode plot shown below is
(A)
( )
( )
2
4
2
1
10
100
s
s
?
+
(B)
( )
( )
2
4
2
1
10
100
s
s
+
+
(C)
( )
( )
4
2
1
10
100
+
+
s
s
(D)
( )
( )
2
4
2
1
10
100
s
s
?
?
GATE 2016 Instrumentation Engineering - IN
IN 8/12
Q.39 For the feedback system given below, the transfer function
2
1
()
( 1)
Gs
s
=
+
. The system CANNOT
be stabilized with
(A)
3
() 1 Cs
s
= + (B)
7
() 3 = + Cs
s
(C)
9
() 3 = + Cs
s
(D)
1
() = Cs
s
Q.40 Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given
below.
(A) P(s) ? (3), Q(s) ? (2), R(s) ? (1) (B) P(s) ? (1), Q(s) ? (2), R(s) ? (3)
(C) P(s) ? (2), Q(s) ? (1), R(s) ? (3) (D) P(s) ? (1), Q(s) ? (3), R(s) ? (2)
Q.41 An ideal opamp is used to realize a difference amplifier circuit given below having a gain of 10. If
x = 0.025, the CMRR of the circuit in dB is _______.
P(s) =
( )
1
1
?
+ s
Q(s) =
( )
( )
21
10 ( 2)
?
++
s
s s
R(s) =
( )
2
1
1 + s
GATE 2016 Instrumentation Engineering - IN
IN 9/12
Q.42 In the circuit given below, the opamp is ideal. The input v
x
is a sinusoid. To ensure v
y
= v
x
, the
value of C
N
in picofarad is _____.
Q.43 In the circuit given below, the opamp is ideal. The value of current I
L
in microampere is ______.
Q.44 A 4 to 1 multiplexer to realize a Boolean function F (X, Y, Z) is shown in the figure below. The
inputs Y and Z are connected to the selectors of the MUX (Y is more significant). The canonical
sum-of-product expression for F ( X, Y, Z ) is
(A) ? m ( 2, 3, 4, 7 ) (B) ? m ( 1, 3, 5, 7)
(C) ? m ( 0, 2, 4, 6 ) (D) ? m (2, 3, 5, 6 )
GATE 2016 Instrumentation Engineering - IN
IN 10/12
Q.45 A synchronous counter using two J - K flip flops that goes through the sequence of states:
Q
1
Q
2
= 00 ? 10 ? 01? 11? 00 ? ? ? is required. To achieve this, the inputs to the flip flops are
(A) J
1
= Q
2
, K
1
= 0 ; J
2
= Q
1
?, K
2
= Q
1
(B) J
1
= 1, K
1
= 1 ; J
2
= Q
1
, K
2
= Q
1
(C) J
1
= Q
2
, K
1
= Q
2
? ; J
2
= 1 , K
2
= 1 (D) J
1
= Q
2
?, K
1
= Q
2
; J
2
= Q
1
, K
2
= Q
1
?
Q.46 A 1 Kbyte memory module has to be interfaced with an 8-bit microprocessor that has 16 address
lines. The address lines A
0
to A
9
of the processor are connected to the corresponding address lines
of the memory module. The active low chip select CS of the memory module is connected to the y
5
output of a 3 to 8 decoder with active low outputs. S
0
, S
1
, and S
2
are the input lines to the decoder,
with S
2
as the MSB. The decoder has one active low 1 EN and one active high
2
EN enable lines as
shown below. The address range(s) that gets mapped onto this memory module is (are)
(A) 3000
H
to 33FF
H
and E000
H
to E3FF
H
(B) 1400
H
to 17FF
H
(C) 5300
H
to 53FF
H
and A300
H
to A3FF
H
(D) 5800
H
to 5BFF
H
and D800
H
to DBFF
H
Q.47 A coil is tested with a series type Q-meter. Resonance at a particular frequency is obtained with a
capacitance of 110 pF. When the frequency is doubled, the capacitance required for resonance is
20 pF. The distributed capacitance of the coil in pico farad is ______.
GATE 2016 Instrumentation Engineering - IN
IN 11/12
Q.48 The comparators (output = ?1?, when input ? 0 and output =?0?, when input < 0), exclusive-OR gate
and the unity gain low-pass filter given in the circuit are ideal. The logic output voltages of the
exclusive-OR gate are 0 V and 5 V. The cutoff frequency of the low-pass filter is 0.1 Hz. For
V
1
= 1 sin (3000t + 36
o
) V and V
2
= 1 sin (3000t) V, the value of V
O
in volt is ______.
Q.49 A 200 mV full scale dual-slope 3 ? digit DMM has a reference voltage of 100 mV and a first
integration time of 100 ms. For an input of [100 + 10 Cos(100?t)] mV, the conversion time
(without taking the auto-zero phase time into consideration) in millisecond is ______.
Q.50 In the circuit below, the opamp is ideal and the sensor is an RTD whose resistance
R
?
= 1000 (1 + 0.004 ?) ?
, where ? is temperature in ?C. The output sensitivity in mV/ ?C is ___.
Q.51 The photo diode in the figure below has an active sensing area of 10 mm
2
, a sensitivity of 0.5 A/W
and a dark current of 1 ?A. The i-to-v converter has a sensitivity of 100 mV/ ?A. For an input light
intensity of 4 W/m
2
, the output V
O
in volt is ____.
GATE 2016 Instrumentation Engineering - IN
IN 12/12
Q.52 The velocity of flow of water (density 1000 kg/m
3
) in a horizontal pipe is measured using the
PITOT tube shown below. The fluid in the U-tube manometer is mercury with a density of
13534 kg/m
3
. Assume g = 9.81 m/s
2
. If the height difference (h) is measured as 94.1 mm, the
velocity of flow of water in m/s is ______.
Q.53 The bandgap in eV of a semiconductor material required to construct an LED that emits peak power
at the wavelength of 620 nm is ______.
(Plank constant h = 4.13567 ?10
-15
eV s and speed of light c = 2.998 ?10
8
m/s).
Q.54 The signal
sin(100 )
()
100
t
m t
t
=
?
?
is frequency modulated (FM) with an FM modulator of frequency
deviation constant of 30 kHz/V. Using Carson?s rule, the approximate bandwidth of the modulated
wave in kilohertz is ________.
Q.55
A signal m(t) varies from 3.5 V ? to 3.5 V + with an average power of 3 W. The signal is
quantized using a midtread type quantizer and subsequently binary encoded. With the codeword of
length 3, the signal to quantization noise ratio in dB is _______.
END OF THE QUESTION PAPER
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This post was last modified on 18 December 2019