Instrumentation (IN) 2011 GATE Paper without solution - GATE Past Year Papers for Practice (All Branches)

 Page 1


?IN? GATE 2011  
Q. No. 1 – 25 Carry One Mark Each 
1. The matrix
2 2 3
M 2 1 6
1 2 0
- - ? ?
? ?
= -
? ?
? ?
- -
? ?
has Eigen values -3,-3,5. An Eigen vector 
corresponding to the Eigen value 5 is
T
1 2 1 - ? ?
? ?
. One of the eigenvectors of the
matrix M
3
 is 
(A) 
T
1 8 1 - ? ?
? ?
(B) 
T
1 2 1 - ? ?
? ?
(C) 
T
3
1 2 1
? ?
-
? ?
(D) 
T
1 1 1 - ? ?
? ?
2. The contour integral
1/ z
C
e dz
? 

 with C as the counter-clockwise unit circle in the
Z-plane is equal to 
(A) 0 (B) 2p (C) 2 1 p - (D) 8
3. Consider the signal ( )
t
e , t 0
x t
0, t<0
-
?
= ?
=
?
?
?
.Let ( ) X ? denote the Fourier transform of
this signal. The integral ( )
1
X d
2
8
-8
? ?
p
?
 is 
(A) 0 (B) 1/2 (C) 1 (D) 8
4. The continuous-time signal ( )
0
x t sin t = ? is a periodic signal. However, for its
discrete-time counterpart
0
x n sin n = ? ? ?
? ?
to be periodic, the necessary condition is
(A) 
0
0 2 = ? < p (B) 
0
2
 to be an integer
p
?
(C) 
0
2
 to be a ratio of integers
p
?
(D) none of these 
5. Consider a periodic signal ( ) x t as shown below.
( ) x t
t
1
1 -
0 1
3 6 3 - 2 - 1 - 2 4 5
Page 2


?IN? GATE 2011  
Q. No. 1 – 25 Carry One Mark Each 
1. The matrix
2 2 3
M 2 1 6
1 2 0
- - ? ?
? ?
= -
? ?
? ?
- -
? ?
has Eigen values -3,-3,5. An Eigen vector 
corresponding to the Eigen value 5 is
T
1 2 1 - ? ?
? ?
. One of the eigenvectors of the
matrix M
3
 is 
(A) 
T
1 8 1 - ? ?
? ?
(B) 
T
1 2 1 - ? ?
? ?
(C) 
T
3
1 2 1
? ?
-
? ?
(D) 
T
1 1 1 - ? ?
? ?
2. The contour integral
1/ z
C
e dz
? 

 with C as the counter-clockwise unit circle in the
Z-plane is equal to 
(A) 0 (B) 2p (C) 2 1 p - (D) 8
3. Consider the signal ( )
t
e , t 0
x t
0, t<0
-
?
= ?
=
?
?
?
.Let ( ) X ? denote the Fourier transform of
this signal. The integral ( )
1
X d
2
8
-8
? ?
p
?
 is 
(A) 0 (B) 1/2 (C) 1 (D) 8
4. The continuous-time signal ( )
0
x t sin t = ? is a periodic signal. However, for its
discrete-time counterpart
0
x n sin n = ? ? ?
? ?
to be periodic, the necessary condition is
(A) 
0
0 2 = ? < p (B) 
0
2
 to be an integer
p
?
(C) 
0
2
 to be a ratio of integers
p
?
(D) none of these 
5. Consider a periodic signal ( ) x t as shown below.
( ) x t
t
1
1 -
0 1
3 6 3 - 2 - 1 - 2 4 5
?IN? GATE 2011  
It has a Fourier series representation ( )
( ) j 2 / T kt
k
k
x t a e
8
p
=-8
=
?
. Which one of the 
following statements is TRUE? 
(A) 
k
a 0, for k odd integer and T=3 =
(B) 
k
a 0, for k even integer and T=3 =
(C) 
k
a 0, for k even integer and T=6 =
(D) 
k
a 0, for k odd integer and T=6 =
6. The integral ( )
2
2 t / 2
1
t e 1 2t dt
2
8
-
-8
d -
p
?
 is equal to 
(A) 
1 / 8
1
e
8 2
-
p
(B) 
1 / 8
1
e
4 2
-
p
(C) 
1 /2
1
e
2
-
p
(D) 1 
7. Shown below is a pole zero plot of a digital filter
Which one of the following statements is TRUE? 
(A) This is a low pass filter (B) This is a high pass filter 
(C) This is an IIR filter (D) This is an FIR filter 
8. The continuous time signal ( ) ( ) ( ) x t cos 100 t sin 300 t = p + p is sampled at the rate
of 100Hz to get the signal 
( ) ( ) ( )
s s s s
n=-
x t x nT t nT ; T = sampling period
8
8
= d -
?
 
The signal ( )
s
x t is passed through an ideal low pass filter with cutoff frequency 
100Hz. The output of the filter is proportional to 
(A) ( ) cos 100 t p (B) ( ) ( ) cos 100 t sin 100 t p + p
(C) ( ) ( ) cos 100 t sin 100 t p - p (D) ( ) sin 100 t p
Re
Im
th
6 order pole
at the origin
1 2
1
2
1
2
-
1 - 2 -
Z plane -
Page 3


?IN? GATE 2011  
Q. No. 1 – 25 Carry One Mark Each 
1. The matrix
2 2 3
M 2 1 6
1 2 0
- - ? ?
? ?
= -
? ?
? ?
- -
? ?
has Eigen values -3,-3,5. An Eigen vector 
corresponding to the Eigen value 5 is
T
1 2 1 - ? ?
? ?
. One of the eigenvectors of the
matrix M
3
 is 
(A) 
T
1 8 1 - ? ?
? ?
(B) 
T
1 2 1 - ? ?
? ?
(C) 
T
3
1 2 1
? ?
-
? ?
(D) 
T
1 1 1 - ? ?
? ?
2. The contour integral
1/ z
C
e dz
? 

 with C as the counter-clockwise unit circle in the
Z-plane is equal to 
(A) 0 (B) 2p (C) 2 1 p - (D) 8
3. Consider the signal ( )
t
e , t 0
x t
0, t<0
-
?
= ?
=
?
?
?
.Let ( ) X ? denote the Fourier transform of
this signal. The integral ( )
1
X d
2
8
-8
? ?
p
?
 is 
(A) 0 (B) 1/2 (C) 1 (D) 8
4. The continuous-time signal ( )
0
x t sin t = ? is a periodic signal. However, for its
discrete-time counterpart
0
x n sin n = ? ? ?
? ?
to be periodic, the necessary condition is
(A) 
0
0 2 = ? < p (B) 
0
2
 to be an integer
p
?
(C) 
0
2
 to be a ratio of integers
p
?
(D) none of these 
5. Consider a periodic signal ( ) x t as shown below.
( ) x t
t
1
1 -
0 1
3 6 3 - 2 - 1 - 2 4 5
?IN? GATE 2011  
It has a Fourier series representation ( )
( ) j 2 / T kt
k
k
x t a e
8
p
=-8
=
?
. Which one of the 
following statements is TRUE? 
(A) 
k
a 0, for k odd integer and T=3 =
(B) 
k
a 0, for k even integer and T=3 =
(C) 
k
a 0, for k even integer and T=6 =
(D) 
k
a 0, for k odd integer and T=6 =
6. The integral ( )
2
2 t / 2
1
t e 1 2t dt
2
8
-
-8
d -
p
?
 is equal to 
(A) 
1 / 8
1
e
8 2
-
p
(B) 
1 / 8
1
e
4 2
-
p
(C) 
1 /2
1
e
2
-
p
(D) 1 
7. Shown below is a pole zero plot of a digital filter
Which one of the following statements is TRUE? 
(A) This is a low pass filter (B) This is a high pass filter 
(C) This is an IIR filter (D) This is an FIR filter 
8. The continuous time signal ( ) ( ) ( ) x t cos 100 t sin 300 t = p + p is sampled at the rate
of 100Hz to get the signal 
( ) ( ) ( )
s s s s
n=-
x t x nT t nT ; T = sampling period
8
8
= d -
?
 
The signal ( )
s
x t is passed through an ideal low pass filter with cutoff frequency 
100Hz. The output of the filter is proportional to 
(A) ( ) cos 100 t p (B) ( ) ( ) cos 100 t sin 100 t p + p
(C) ( ) ( ) cos 100 t sin 100 t p - p (D) ( ) sin 100 t p
Re
Im
th
6 order pole
at the origin
1 2
1
2
1
2
-
1 - 2 -
Z plane -
?IN? GATE 2011  
9. Consider a system with input x(t) and y(t) related as follows
( ) ( ) { }
t
d
y t e x t
dt
-
=
Which one of the following statements is TRUE? 
(A) The system is nonlinear (B) The system is time-invariant 
(C) The system is stable  (D) The system has memory 
10. The first two rows of Routh’s table of a third-order characteristic equation are
3
2
s 3 3
s 4 4
It can be inferred that the system has 
(A) one real pole in right half of s-plane 
(B) a pair of complex conjugate poles in the right half of s-plane 
(C) a pair of real poles symmetrically placed around s=0 
(D) a pair of complex conjugate poles on the imaginary axis of the s-plane 
11. The amplifier shown below has a voltage gain of -2.5, an input resistance of
10kO and a lower 3-dB cutoff frequency of 20Hz. Which one of following
statements is TRUE when the emitter resistance R
E
 is doubled?
(A) Magnitude of voltage gain will decrease 
(B) Input resistance will decrease 
(C) Collector bias current will increase 
(D) Lower 3-dB cut-off frequency will increase 
12. Figure below shows a circuit for implementing an 8-bit Digital-to-Analog
converter (DAC) using two identical 4-bit DAC’s with equal reference voltages.
Assume that b
0
 represents LSB, b
7
 MSB and the op-amp is ideal. To obtain
correct analog values corresponding to an 8-bit DAC at the output V
O
, the value
of resistor R is
~
1
R
C
R
CC
V
C
C
o
v
L
R
E
R
2
R
B
C
s
v
Page 4


?IN? GATE 2011  
Q. No. 1 – 25 Carry One Mark Each 
1. The matrix
2 2 3
M 2 1 6
1 2 0
- - ? ?
? ?
= -
? ?
? ?
- -
? ?
has Eigen values -3,-3,5. An Eigen vector 
corresponding to the Eigen value 5 is
T
1 2 1 - ? ?
? ?
. One of the eigenvectors of the
matrix M
3
 is 
(A) 
T
1 8 1 - ? ?
? ?
(B) 
T
1 2 1 - ? ?
? ?
(C) 
T
3
1 2 1
? ?
-
? ?
(D) 
T
1 1 1 - ? ?
? ?
2. The contour integral
1/ z
C
e dz
? 

 with C as the counter-clockwise unit circle in the
Z-plane is equal to 
(A) 0 (B) 2p (C) 2 1 p - (D) 8
3. Consider the signal ( )
t
e , t 0
x t
0, t<0
-
?
= ?
=
?
?
?
.Let ( ) X ? denote the Fourier transform of
this signal. The integral ( )
1
X d
2
8
-8
? ?
p
?
 is 
(A) 0 (B) 1/2 (C) 1 (D) 8
4. The continuous-time signal ( )
0
x t sin t = ? is a periodic signal. However, for its
discrete-time counterpart
0
x n sin n = ? ? ?
? ?
to be periodic, the necessary condition is
(A) 
0
0 2 = ? < p (B) 
0
2
 to be an integer
p
?
(C) 
0
2
 to be a ratio of integers
p
?
(D) none of these 
5. Consider a periodic signal ( ) x t as shown below.
( ) x t
t
1
1 -
0 1
3 6 3 - 2 - 1 - 2 4 5
?IN? GATE 2011  
It has a Fourier series representation ( )
( ) j 2 / T kt
k
k
x t a e
8
p
=-8
=
?
. Which one of the 
following statements is TRUE? 
(A) 
k
a 0, for k odd integer and T=3 =
(B) 
k
a 0, for k even integer and T=3 =
(C) 
k
a 0, for k even integer and T=6 =
(D) 
k
a 0, for k odd integer and T=6 =
6. The integral ( )
2
2 t / 2
1
t e 1 2t dt
2
8
-
-8
d -
p
?
 is equal to 
(A) 
1 / 8
1
e
8 2
-
p
(B) 
1 / 8
1
e
4 2
-
p
(C) 
1 /2
1
e
2
-
p
(D) 1 
7. Shown below is a pole zero plot of a digital filter
Which one of the following statements is TRUE? 
(A) This is a low pass filter (B) This is a high pass filter 
(C) This is an IIR filter (D) This is an FIR filter 
8. The continuous time signal ( ) ( ) ( ) x t cos 100 t sin 300 t = p + p is sampled at the rate
of 100Hz to get the signal 
( ) ( ) ( )
s s s s
n=-
x t x nT t nT ; T = sampling period
8
8
= d -
?
 
The signal ( )
s
x t is passed through an ideal low pass filter with cutoff frequency 
100Hz. The output of the filter is proportional to 
(A) ( ) cos 100 t p (B) ( ) ( ) cos 100 t sin 100 t p + p
(C) ( ) ( ) cos 100 t sin 100 t p - p (D) ( ) sin 100 t p
Re
Im
th
6 order pole
at the origin
1 2
1
2
1
2
-
1 - 2 -
Z plane -
?IN? GATE 2011  
9. Consider a system with input x(t) and y(t) related as follows
( ) ( ) { }
t
d
y t e x t
dt
-
=
Which one of the following statements is TRUE? 
(A) The system is nonlinear (B) The system is time-invariant 
(C) The system is stable  (D) The system has memory 
10. The first two rows of Routh’s table of a third-order characteristic equation are
3
2
s 3 3
s 4 4
It can be inferred that the system has 
(A) one real pole in right half of s-plane 
(B) a pair of complex conjugate poles in the right half of s-plane 
(C) a pair of real poles symmetrically placed around s=0 
(D) a pair of complex conjugate poles on the imaginary axis of the s-plane 
11. The amplifier shown below has a voltage gain of -2.5, an input resistance of
10kO and a lower 3-dB cutoff frequency of 20Hz. Which one of following
statements is TRUE when the emitter resistance R
E
 is doubled?
(A) Magnitude of voltage gain will decrease 
(B) Input resistance will decrease 
(C) Collector bias current will increase 
(D) Lower 3-dB cut-off frequency will increase 
12. Figure below shows a circuit for implementing an 8-bit Digital-to-Analog
converter (DAC) using two identical 4-bit DAC’s with equal reference voltages.
Assume that b
0
 represents LSB, b
7
 MSB and the op-amp is ideal. To obtain
correct analog values corresponding to an 8-bit DAC at the output V
O
, the value
of resistor R is
~
1
R
C
R
CC
V
C
C
o
v
L
R
E
R
2
R
B
C
s
v
?IN? GATE 2011  
(A) 0.25kO (B) 0.5kO (C) 1kO (D) 8kO
13. In the circuit, the switch, initially at position 1 for a long time, is changed to
position 2 at t=0.
The current i through the inductor for t 0 = is
(A) 
20t
1 e
-
- A (B) 
20t
1 e
-
+ A (C) 
20t
1 2e
-
+ A (D) 
20t
2 e
-
- A 
14. The current I shown in the circuit given below is equal to
(A) 3A (B) 2.67A (C) 6A (D) 9A 
15. The signal flow graph of a system is given below
The transfer function (C/R) of the system is 
4 bit DAC - 4 bit DAC -
o
V
8kO
R
8kO O1
V O2
V
-
+
3 0
b ...b
7 4
b ...b
-
+
1
t 0 =
2
1H
10O
10V
10O 4A
i
10O
10A
10O 10V
I
+
-
10O
R
C
3
G
1
G
2
G
1
H
2
H -
1 1 1
Page 5


?IN? GATE 2011  
Q. No. 1 – 25 Carry One Mark Each 
1. The matrix
2 2 3
M 2 1 6
1 2 0
- - ? ?
? ?
= -
? ?
? ?
- -
? ?
has Eigen values -3,-3,5. An Eigen vector 
corresponding to the Eigen value 5 is
T
1 2 1 - ? ?
? ?
. One of the eigenvectors of the
matrix M
3
 is 
(A) 
T
1 8 1 - ? ?
? ?
(B) 
T
1 2 1 - ? ?
? ?
(C) 
T
3
1 2 1
? ?
-
? ?
(D) 
T
1 1 1 - ? ?
? ?
2. The contour integral
1/ z
C
e dz
? 

 with C as the counter-clockwise unit circle in the
Z-plane is equal to 
(A) 0 (B) 2p (C) 2 1 p - (D) 8
3. Consider the signal ( )
t
e , t 0
x t
0, t<0
-
?
= ?
=
?
?
?
.Let ( ) X ? denote the Fourier transform of
this signal. The integral ( )
1
X d
2
8
-8
? ?
p
?
 is 
(A) 0 (B) 1/2 (C) 1 (D) 8
4. The continuous-time signal ( )
0
x t sin t = ? is a periodic signal. However, for its
discrete-time counterpart
0
x n sin n = ? ? ?
? ?
to be periodic, the necessary condition is
(A) 
0
0 2 = ? < p (B) 
0
2
 to be an integer
p
?
(C) 
0
2
 to be a ratio of integers
p
?
(D) none of these 
5. Consider a periodic signal ( ) x t as shown below.
( ) x t
t
1
1 -
0 1
3 6 3 - 2 - 1 - 2 4 5
?IN? GATE 2011  
It has a Fourier series representation ( )
( ) j 2 / T kt
k
k
x t a e
8
p
=-8
=
?
. Which one of the 
following statements is TRUE? 
(A) 
k
a 0, for k odd integer and T=3 =
(B) 
k
a 0, for k even integer and T=3 =
(C) 
k
a 0, for k even integer and T=6 =
(D) 
k
a 0, for k odd integer and T=6 =
6. The integral ( )
2
2 t / 2
1
t e 1 2t dt
2
8
-
-8
d -
p
?
 is equal to 
(A) 
1 / 8
1
e
8 2
-
p
(B) 
1 / 8
1
e
4 2
-
p
(C) 
1 /2
1
e
2
-
p
(D) 1 
7. Shown below is a pole zero plot of a digital filter
Which one of the following statements is TRUE? 
(A) This is a low pass filter (B) This is a high pass filter 
(C) This is an IIR filter (D) This is an FIR filter 
8. The continuous time signal ( ) ( ) ( ) x t cos 100 t sin 300 t = p + p is sampled at the rate
of 100Hz to get the signal 
( ) ( ) ( )
s s s s
n=-
x t x nT t nT ; T = sampling period
8
8
= d -
?
 
The signal ( )
s
x t is passed through an ideal low pass filter with cutoff frequency 
100Hz. The output of the filter is proportional to 
(A) ( ) cos 100 t p (B) ( ) ( ) cos 100 t sin 100 t p + p
(C) ( ) ( ) cos 100 t sin 100 t p - p (D) ( ) sin 100 t p
Re
Im
th
6 order pole
at the origin
1 2
1
2
1
2
-
1 - 2 -
Z plane -
?IN? GATE 2011  
9. Consider a system with input x(t) and y(t) related as follows
( ) ( ) { }
t
d
y t e x t
dt
-
=
Which one of the following statements is TRUE? 
(A) The system is nonlinear (B) The system is time-invariant 
(C) The system is stable  (D) The system has memory 
10. The first two rows of Routh’s table of a third-order characteristic equation are
3
2
s 3 3
s 4 4
It can be inferred that the system has 
(A) one real pole in right half of s-plane 
(B) a pair of complex conjugate poles in the right half of s-plane 
(C) a pair of real poles symmetrically placed around s=0 
(D) a pair of complex conjugate poles on the imaginary axis of the s-plane 
11. The amplifier shown below has a voltage gain of -2.5, an input resistance of
10kO and a lower 3-dB cutoff frequency of 20Hz. Which one of following
statements is TRUE when the emitter resistance R
E
 is doubled?
(A) Magnitude of voltage gain will decrease 
(B) Input resistance will decrease 
(C) Collector bias current will increase 
(D) Lower 3-dB cut-off frequency will increase 
12. Figure below shows a circuit for implementing an 8-bit Digital-to-Analog
converter (DAC) using two identical 4-bit DAC’s with equal reference voltages.
Assume that b
0
 represents LSB, b
7
 MSB and the op-amp is ideal. To obtain
correct analog values corresponding to an 8-bit DAC at the output V
O
, the value
of resistor R is
~
1
R
C
R
CC
V
C
C
o
v
L
R
E
R
2
R
B
C
s
v
?IN? GATE 2011  
(A) 0.25kO (B) 0.5kO (C) 1kO (D) 8kO
13. In the circuit, the switch, initially at position 1 for a long time, is changed to
position 2 at t=0.
The current i through the inductor for t 0 = is
(A) 
20t
1 e
-
- A (B) 
20t
1 e
-
+ A (C) 
20t
1 2e
-
+ A (D) 
20t
2 e
-
- A 
14. The current I shown in the circuit given below is equal to
(A) 3A (B) 2.67A (C) 6A (D) 9A 
15. The signal flow graph of a system is given below
The transfer function (C/R) of the system is 
4 bit DAC - 4 bit DAC -
o
V
8kO
R
8kO O1
V O2
V
-
+
3 0
b ...b
7 4
b ...b
-
+
1
t 0 =
2
1H
10O
10V
10O 4A
i
10O
10A
10O 10V
I
+
-
10O
R
C
3
G
1
G
2
G
1
H
2
H -
1 1 1
?IN? GATE 2011  
(A) ( ) ( )
1 2 1 3 1 2 2
G G G G / 1 G G H + +
(B) ( ) ( )
1 2 1 3 1 1 1 2 2
G G G G / 1 G H G G H + - +
(C) ( ) ( )
1 2 1 3 1 1 1 2 2 1 3 2
G G G G / 1 G H G G H G G H + - + +
(D) ( ) ( )
1 2 1 3 1 1 1 2 2 1 3 2 1 2 3 1
G G G G / 1 G H G G H G G H G G G H + - + + +
16. For the Boolean expression f abc a bc abc abc abc = + + + + , the minimized Product
of Sum (PoS) expression is
(A) 
( ) ( )
f b c . a c = + + (B) 
( ) ( )
f b c . a c = + +
(C) 
( ) ( )
f b c . a c = + + (D) f c abc = +
17. The base of the number system for the addition operation 24+14=41 to be true
is
(A) 8 (B) 7 (C) 6 (D) 5
18. An 8Kx8 bit RAM is interfaced to an 8085 microprocessor. In a fully decoded
scheme, if the address of the last memory location of this RAM is 4FFFH, the
address of the first memory location of the RAM will be
(A) 1000H (B) 2000H (C) 3000H (D) 4000H 
19. The Treadmill Test is used to diagnose
(A) the balancing style during walk of the patient
(B) the auditory activity of the patient
(C) the visual activity of the patient
(D) the cardiac activity of the patient
20. The characteristics of a thermometer measuring ambient temperature is
i
i a
dT
2 T T 0
dt
+ - = where T
i
 and T
a
 are the indicated and ambient temperatures, 
respectively, both in ºC and time is in seconds. The -3dB cut-off frequency in the 
frequency response of the thermometer is 
(A) 1/4p Hz (B) 1/2Hz (C) 1Hz (D) 2p Hz
21. For a copper-constantan (Type T) thermocouple, the junction potential E (in µV)
at ºC ? is given by
2 2 4 3 6 4
E 38.74 3.3 10 2.07 10 2.2 10 higher order terms
- - -
= ?+ × ? + × ? - × ? + ,