Electrical Engineering (EE) 2011 GATE Paper with solution (solved) GATE Notes | EduRev

GATE : Electrical Engineering (EE) 2011 GATE Paper with solution (solved) GATE Notes | EduRev

 Page 1


                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
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written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        1 
Q. No. 1 – 25 Carry One Mark Each 
 
1. Roots of the algebraic equation 
3 2
x x x 1 0 + + + = are  
 (A) ( ) 1, j, j + + - (B) ( ) 1, 1, 1 + - + (C) (0,0,0) (D) ( ) 1, j, j - + - 
Answer: - (D) 
Exp: -
( )( )
3 2 2
x x x 1 0 x 1 x 1 0 + + + = ? + + =
  
2
x 1 0; x 1 0 ? + = + =
  
x 1 x j ? = - = ± 
 
2. With K as a constant, the possible solution for the first order differential equation 
3x
dy
e
dx
-
= is  
 (A) 
3x
1
e K
3
-
- + (B) 
3x
1
e K
3
- + (C) 
3x
1
e K
3
-
- + (D) 
x
3e K
-
- + 
Answer: - (A) 
Exp: -
3x 3x
dy
e dy e dx
dx
- -
= ? = 
 Integrate on both sides 
 
3x
3x
e 1
y K e K
3 3
-
-
= + = - +
-
 
 
3. The r.m.s value of the current i(t) in the circuit shown below is  
 (A) 
1
A
2
 
 (B) 
1
A
2
 
 (C) 1A 
 (D) 2A 
Answer: - (B) 
Exp: - 1 rad /sec ? = 
L C
X 1 ; X 1 = O = O 
 
 
 
 
  
 
 
                  ( )
Sin t
I t Sin t;
1
= =
O
rms
1
I A
2
= 
1F 
1H 
~ 
1O 
( ) i t 
( ) 1.0sint V 
+
 
1O 
1Sint 
1O
 
+
 
-
 
Page 2


                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        1 
Q. No. 1 – 25 Carry One Mark Each 
 
1. Roots of the algebraic equation 
3 2
x x x 1 0 + + + = are  
 (A) ( ) 1, j, j + + - (B) ( ) 1, 1, 1 + - + (C) (0,0,0) (D) ( ) 1, j, j - + - 
Answer: - (D) 
Exp: -
( )( )
3 2 2
x x x 1 0 x 1 x 1 0 + + + = ? + + =
  
2
x 1 0; x 1 0 ? + = + =
  
x 1 x j ? = - = ± 
 
2. With K as a constant, the possible solution for the first order differential equation 
3x
dy
e
dx
-
= is  
 (A) 
3x
1
e K
3
-
- + (B) 
3x
1
e K
3
- + (C) 
3x
1
e K
3
-
- + (D) 
x
3e K
-
- + 
Answer: - (A) 
Exp: -
3x 3x
dy
e dy e dx
dx
- -
= ? = 
 Integrate on both sides 
 
3x
3x
e 1
y K e K
3 3
-
-
= + = - +
-
 
 
3. The r.m.s value of the current i(t) in the circuit shown below is  
 (A) 
1
A
2
 
 (B) 
1
A
2
 
 (C) 1A 
 (D) 2A 
Answer: - (B) 
Exp: - 1 rad /sec ? = 
L C
X 1 ; X 1 = O = O 
 
 
 
 
  
 
 
                  ( )
Sin t
I t Sin t;
1
= =
O
rms
1
I A
2
= 
1F 
1H 
~ 
1O 
( ) i t 
( ) 1.0sint V 
+
 
1O 
1Sint 
1O
 
+
 
-
 
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        2 
4. The fourier series expansion ( )
0 n n
n 1
f t a a cosn t b sin n t
8
=
= + ? + ?
?
 of the periodic 
signal shown below will contain the following nonzero terms 
 ( )
0 n
A a and b , n 1,3,5,... = 8 
 ( )
0 n
B a and a , n 1,2,3,... = 8 
 ( )
0 n n
C a a and b , n 1,2,3,... = 8  
 ( )
0 n
D a anda n 1,3,5,... = 8 
Answer: - (D) 
Exp: -  ? it satisfies the half wave symmetry, so that it contains only odd harmonics. 
 ? It satisfies the even symmetry. So 
n
b 0 = 
 
5. A 4 – point starter is used to start and control the speed of a 
 (A)  dc shunt motor with armature resistance control 
 (B)  dc shunt motor with field weakening control 
 (C)  dc series motor 
 (D)  dc compound motor 
Answer: - (A) 
 
6. A three-phase, salient pole synchronous motor is connected to an infinite bus. Ig 
is operated at no load a normal excitation. The field excitation of the motor is 
first reduced to zero and then increased in reverse direction gradually. Then the 
armature current 
 (A) Increases continuously 
 (B) First increases and then decreases steeply 
 (C) First decreases and then increases steeply 
 (D) Remains constant 
Answer: - (B) 
 
7. A nuclear power station of 500 MW capacity  is located at 300 km away from a 
load center. Select the most suitable power evacuation transmission configuration 
among the following options 
 
 (A)  
 
 
 (B)  
 
 
 (C)  
 
 
 (D)  
Answer: - (A) 
( ) f t 
0 
t 
~
 
132kV,300km doublecircuit 
Load center 
~
 
132kv,300 km single circuitwith40%seriescapacitor compensation 
Load center 
~
 
400kV,300kmsinglecircuit 
Load center 
~
 
400kV,300km doublecircuit 
Load center 
Page 3


                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        1 
Q. No. 1 – 25 Carry One Mark Each 
 
1. Roots of the algebraic equation 
3 2
x x x 1 0 + + + = are  
 (A) ( ) 1, j, j + + - (B) ( ) 1, 1, 1 + - + (C) (0,0,0) (D) ( ) 1, j, j - + - 
Answer: - (D) 
Exp: -
( )( )
3 2 2
x x x 1 0 x 1 x 1 0 + + + = ? + + =
  
2
x 1 0; x 1 0 ? + = + =
  
x 1 x j ? = - = ± 
 
2. With K as a constant, the possible solution for the first order differential equation 
3x
dy
e
dx
-
= is  
 (A) 
3x
1
e K
3
-
- + (B) 
3x
1
e K
3
- + (C) 
3x
1
e K
3
-
- + (D) 
x
3e K
-
- + 
Answer: - (A) 
Exp: -
3x 3x
dy
e dy e dx
dx
- -
= ? = 
 Integrate on both sides 
 
3x
3x
e 1
y K e K
3 3
-
-
= + = - +
-
 
 
3. The r.m.s value of the current i(t) in the circuit shown below is  
 (A) 
1
A
2
 
 (B) 
1
A
2
 
 (C) 1A 
 (D) 2A 
Answer: - (B) 
Exp: - 1 rad /sec ? = 
L C
X 1 ; X 1 = O = O 
 
 
 
 
  
 
 
                  ( )
Sin t
I t Sin t;
1
= =
O
rms
1
I A
2
= 
1F 
1H 
~ 
1O 
( ) i t 
( ) 1.0sint V 
+
 
1O 
1Sint 
1O
 
+
 
-
 
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        2 
4. The fourier series expansion ( )
0 n n
n 1
f t a a cosn t b sin n t
8
=
= + ? + ?
?
 of the periodic 
signal shown below will contain the following nonzero terms 
 ( )
0 n
A a and b , n 1,3,5,... = 8 
 ( )
0 n
B a and a , n 1,2,3,... = 8 
 ( )
0 n n
C a a and b , n 1,2,3,... = 8  
 ( )
0 n
D a anda n 1,3,5,... = 8 
Answer: - (D) 
Exp: -  ? it satisfies the half wave symmetry, so that it contains only odd harmonics. 
 ? It satisfies the even symmetry. So 
n
b 0 = 
 
5. A 4 – point starter is used to start and control the speed of a 
 (A)  dc shunt motor with armature resistance control 
 (B)  dc shunt motor with field weakening control 
 (C)  dc series motor 
 (D)  dc compound motor 
Answer: - (A) 
 
6. A three-phase, salient pole synchronous motor is connected to an infinite bus. Ig 
is operated at no load a normal excitation. The field excitation of the motor is 
first reduced to zero and then increased in reverse direction gradually. Then the 
armature current 
 (A) Increases continuously 
 (B) First increases and then decreases steeply 
 (C) First decreases and then increases steeply 
 (D) Remains constant 
Answer: - (B) 
 
7. A nuclear power station of 500 MW capacity  is located at 300 km away from a 
load center. Select the most suitable power evacuation transmission configuration 
among the following options 
 
 (A)  
 
 
 (B)  
 
 
 (C)  
 
 
 (D)  
Answer: - (A) 
( ) f t 
0 
t 
~
 
132kV,300km doublecircuit 
Load center 
~
 
132kv,300 km single circuitwith40%seriescapacitor compensation 
Load center 
~
 
400kV,300kmsinglecircuit 
Load center 
~
 
400kV,300km doublecircuit 
Load center 
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        3 
8. The frequency response of a linear system ( ) G j? is provided in the tubular form 
below 
( ) G j? 
1.3 1.2 1.0 0.8 0.5 0.3 
( ) G j ? ? 
O
130 - 
O
140 - 
O
150 - 
O
160 - 
O
180 - 
O
200 - 
 ( )
O
A 6 dB and 30   ( )
O
B 6 dB and 30 - 
 ( )
O
C 6 dB and 30 -   ( )
O
D 6 dB and 30 - - 
Answer: - (A) 
Exp: - At ( ) G jw 180 ? = - magnitude M=0.5 
 So G.M = 20 log 
1
6dB
0.5
? ?
=
? ?
? ?
 
 At ( ) G jw 1 = phase angle ( ) G jw 150 ? = - 
 So P.M = ( )
0
180 150 30 + - = 
 
9. The steady state error of a unity feedback linear system for a unit step input is 
0.1. The steady state error of the same system, for a pulse input r(t) having a 
magnitude of 10 and a duration of one second, as shown in the figure is 
 
 
 
 
 (A) 0 (B) 0.1 (C) 1 (D) 10 
Answer: - (A) 
Exp: - For step input 
ss
1
e 0.1 k 9
1 k
= = ? =
+
 
 ( )
9
G S
S 1
=
+
 
 Now the input is pulse ( ) ( ) ( ) r t 10 u t u t 1 ? ? = - -
? ?
 
 ( )
s
1 e
r s 10
s
-
? ? -
=
? ?
? ?
 
 
( )
( ) ( )
s
ss
S 0 S 0
S 10 1 e
S.R s
S
e Lt Lt
S 10 1 G S H S
S 1
-
? ?
? ? -
? ?
= =
+ +
+
 
0
0
10
= = 
 
10. Consider the following statement 
 (i)  The compensating coil of a low power factor wattmeter compensates the 
effect of the impedance of the current coil. 
 (ii) The compensating coil of a low power factor wattmeter compensates the 
effect 0of the impedance of the voltage coil circuit. 
( ) r t 
10 
1s 
t 
Page 4


                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        1 
Q. No. 1 – 25 Carry One Mark Each 
 
1. Roots of the algebraic equation 
3 2
x x x 1 0 + + + = are  
 (A) ( ) 1, j, j + + - (B) ( ) 1, 1, 1 + - + (C) (0,0,0) (D) ( ) 1, j, j - + - 
Answer: - (D) 
Exp: -
( )( )
3 2 2
x x x 1 0 x 1 x 1 0 + + + = ? + + =
  
2
x 1 0; x 1 0 ? + = + =
  
x 1 x j ? = - = ± 
 
2. With K as a constant, the possible solution for the first order differential equation 
3x
dy
e
dx
-
= is  
 (A) 
3x
1
e K
3
-
- + (B) 
3x
1
e K
3
- + (C) 
3x
1
e K
3
-
- + (D) 
x
3e K
-
- + 
Answer: - (A) 
Exp: -
3x 3x
dy
e dy e dx
dx
- -
= ? = 
 Integrate on both sides 
 
3x
3x
e 1
y K e K
3 3
-
-
= + = - +
-
 
 
3. The r.m.s value of the current i(t) in the circuit shown below is  
 (A) 
1
A
2
 
 (B) 
1
A
2
 
 (C) 1A 
 (D) 2A 
Answer: - (B) 
Exp: - 1 rad /sec ? = 
L C
X 1 ; X 1 = O = O 
 
 
 
 
  
 
 
                  ( )
Sin t
I t Sin t;
1
= =
O
rms
1
I A
2
= 
1F 
1H 
~ 
1O 
( ) i t 
( ) 1.0sint V 
+
 
1O 
1Sint 
1O
 
+
 
-
 
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        2 
4. The fourier series expansion ( )
0 n n
n 1
f t a a cosn t b sin n t
8
=
= + ? + ?
?
 of the periodic 
signal shown below will contain the following nonzero terms 
 ( )
0 n
A a and b , n 1,3,5,... = 8 
 ( )
0 n
B a and a , n 1,2,3,... = 8 
 ( )
0 n n
C a a and b , n 1,2,3,... = 8  
 ( )
0 n
D a anda n 1,3,5,... = 8 
Answer: - (D) 
Exp: -  ? it satisfies the half wave symmetry, so that it contains only odd harmonics. 
 ? It satisfies the even symmetry. So 
n
b 0 = 
 
5. A 4 – point starter is used to start and control the speed of a 
 (A)  dc shunt motor with armature resistance control 
 (B)  dc shunt motor with field weakening control 
 (C)  dc series motor 
 (D)  dc compound motor 
Answer: - (A) 
 
6. A three-phase, salient pole synchronous motor is connected to an infinite bus. Ig 
is operated at no load a normal excitation. The field excitation of the motor is 
first reduced to zero and then increased in reverse direction gradually. Then the 
armature current 
 (A) Increases continuously 
 (B) First increases and then decreases steeply 
 (C) First decreases and then increases steeply 
 (D) Remains constant 
Answer: - (B) 
 
7. A nuclear power station of 500 MW capacity  is located at 300 km away from a 
load center. Select the most suitable power evacuation transmission configuration 
among the following options 
 
 (A)  
 
 
 (B)  
 
 
 (C)  
 
 
 (D)  
Answer: - (A) 
( ) f t 
0 
t 
~
 
132kV,300km doublecircuit 
Load center 
~
 
132kv,300 km single circuitwith40%seriescapacitor compensation 
Load center 
~
 
400kV,300kmsinglecircuit 
Load center 
~
 
400kV,300km doublecircuit 
Load center 
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        3 
8. The frequency response of a linear system ( ) G j? is provided in the tubular form 
below 
( ) G j? 
1.3 1.2 1.0 0.8 0.5 0.3 
( ) G j ? ? 
O
130 - 
O
140 - 
O
150 - 
O
160 - 
O
180 - 
O
200 - 
 ( )
O
A 6 dB and 30   ( )
O
B 6 dB and 30 - 
 ( )
O
C 6 dB and 30 -   ( )
O
D 6 dB and 30 - - 
Answer: - (A) 
Exp: - At ( ) G jw 180 ? = - magnitude M=0.5 
 So G.M = 20 log 
1
6dB
0.5
? ?
=
? ?
? ?
 
 At ( ) G jw 1 = phase angle ( ) G jw 150 ? = - 
 So P.M = ( )
0
180 150 30 + - = 
 
9. The steady state error of a unity feedback linear system for a unit step input is 
0.1. The steady state error of the same system, for a pulse input r(t) having a 
magnitude of 10 and a duration of one second, as shown in the figure is 
 
 
 
 
 (A) 0 (B) 0.1 (C) 1 (D) 10 
Answer: - (A) 
Exp: - For step input 
ss
1
e 0.1 k 9
1 k
= = ? =
+
 
 ( )
9
G S
S 1
=
+
 
 Now the input is pulse ( ) ( ) ( ) r t 10 u t u t 1 ? ? = - -
? ?
 
 ( )
s
1 e
r s 10
s
-
? ? -
=
? ?
? ?
 
 
( )
( ) ( )
s
ss
S 0 S 0
S 10 1 e
S.R s
S
e Lt Lt
S 10 1 G S H S
S 1
-
? ?
? ? -
? ?
= =
+ +
+
 
0
0
10
= = 
 
10. Consider the following statement 
 (i)  The compensating coil of a low power factor wattmeter compensates the 
effect of the impedance of the current coil. 
 (ii) The compensating coil of a low power factor wattmeter compensates the 
effect 0of the impedance of the voltage coil circuit. 
( ) r t 
10 
1s 
t 
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        4 
 (A)  (i) is true but (ii) is false (B) (i) is false but (ii) is true 
 (C)  both (i) and (ii) are true (D) both (i) and (ii) are false 
Answer: - (B) 
 
11. A low – pass filter with a cut-off frequency of 30Hz is cascaded with a high-pass 
filter with a cut-off frequency of 20Hz. The resultant system of filters will function 
as 
 (A)  an all-pass filter  (B)  an all-stop filter  
 (B)  an band stop (band-reject) filter (D)  a band – pass filter 
Answer: - (D) 
Exp: -  
  
 
 
 
 So it is a band pass filter 
 
12.  
 
 
 
 
 
 
 
 
 The CORRECT transfer characteristic is 
 
 
 (A)    (B)  
 
 
 
 
 
  
 
 
 
 (C)    (D)  
 
 
R 
12V + 
12V + 
O
V 
12V - 
12V - 
R R 
R 
R 
vi 
- 
+ 
- 
+ 
Vo 
6v - 
12v - 
Vi 
12v + 12V + 
6v - 
12v - 
Vi 
O
V 
6v + 
Vo 
Vi 
6v + 6v - 
12v + 
Vo 
Vi 
6v + 6v - 
12v + 
20 30
Page 5


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© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        1 
Q. No. 1 – 25 Carry One Mark Each 
 
1. Roots of the algebraic equation 
3 2
x x x 1 0 + + + = are  
 (A) ( ) 1, j, j + + - (B) ( ) 1, 1, 1 + - + (C) (0,0,0) (D) ( ) 1, j, j - + - 
Answer: - (D) 
Exp: -
( )( )
3 2 2
x x x 1 0 x 1 x 1 0 + + + = ? + + =
  
2
x 1 0; x 1 0 ? + = + =
  
x 1 x j ? = - = ± 
 
2. With K as a constant, the possible solution for the first order differential equation 
3x
dy
e
dx
-
= is  
 (A) 
3x
1
e K
3
-
- + (B) 
3x
1
e K
3
- + (C) 
3x
1
e K
3
-
- + (D) 
x
3e K
-
- + 
Answer: - (A) 
Exp: -
3x 3x
dy
e dy e dx
dx
- -
= ? = 
 Integrate on both sides 
 
3x
3x
e 1
y K e K
3 3
-
-
= + = - +
-
 
 
3. The r.m.s value of the current i(t) in the circuit shown below is  
 (A) 
1
A
2
 
 (B) 
1
A
2
 
 (C) 1A 
 (D) 2A 
Answer: - (B) 
Exp: - 1 rad /sec ? = 
L C
X 1 ; X 1 = O = O 
 
 
 
 
  
 
 
                  ( )
Sin t
I t Sin t;
1
= =
O
rms
1
I A
2
= 
1F 
1H 
~ 
1O 
( ) i t 
( ) 1.0sint V 
+
 
1O 
1Sint 
1O
 
+
 
-
 
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        2 
4. The fourier series expansion ( )
0 n n
n 1
f t a a cosn t b sin n t
8
=
= + ? + ?
?
 of the periodic 
signal shown below will contain the following nonzero terms 
 ( )
0 n
A a and b , n 1,3,5,... = 8 
 ( )
0 n
B a and a , n 1,2,3,... = 8 
 ( )
0 n n
C a a and b , n 1,2,3,... = 8  
 ( )
0 n
D a anda n 1,3,5,... = 8 
Answer: - (D) 
Exp: -  ? it satisfies the half wave symmetry, so that it contains only odd harmonics. 
 ? It satisfies the even symmetry. So 
n
b 0 = 
 
5. A 4 – point starter is used to start and control the speed of a 
 (A)  dc shunt motor with armature resistance control 
 (B)  dc shunt motor with field weakening control 
 (C)  dc series motor 
 (D)  dc compound motor 
Answer: - (A) 
 
6. A three-phase, salient pole synchronous motor is connected to an infinite bus. Ig 
is operated at no load a normal excitation. The field excitation of the motor is 
first reduced to zero and then increased in reverse direction gradually. Then the 
armature current 
 (A) Increases continuously 
 (B) First increases and then decreases steeply 
 (C) First decreases and then increases steeply 
 (D) Remains constant 
Answer: - (B) 
 
7. A nuclear power station of 500 MW capacity  is located at 300 km away from a 
load center. Select the most suitable power evacuation transmission configuration 
among the following options 
 
 (A)  
 
 
 (B)  
 
 
 (C)  
 
 
 (D)  
Answer: - (A) 
( ) f t 
0 
t 
~
 
132kV,300km doublecircuit 
Load center 
~
 
132kv,300 km single circuitwith40%seriescapacitor compensation 
Load center 
~
 
400kV,300kmsinglecircuit 
Load center 
~
 
400kV,300km doublecircuit 
Load center 
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        3 
8. The frequency response of a linear system ( ) G j? is provided in the tubular form 
below 
( ) G j? 
1.3 1.2 1.0 0.8 0.5 0.3 
( ) G j ? ? 
O
130 - 
O
140 - 
O
150 - 
O
160 - 
O
180 - 
O
200 - 
 ( )
O
A 6 dB and 30   ( )
O
B 6 dB and 30 - 
 ( )
O
C 6 dB and 30 -   ( )
O
D 6 dB and 30 - - 
Answer: - (A) 
Exp: - At ( ) G jw 180 ? = - magnitude M=0.5 
 So G.M = 20 log 
1
6dB
0.5
? ?
=
? ?
? ?
 
 At ( ) G jw 1 = phase angle ( ) G jw 150 ? = - 
 So P.M = ( )
0
180 150 30 + - = 
 
9. The steady state error of a unity feedback linear system for a unit step input is 
0.1. The steady state error of the same system, for a pulse input r(t) having a 
magnitude of 10 and a duration of one second, as shown in the figure is 
 
 
 
 
 (A) 0 (B) 0.1 (C) 1 (D) 10 
Answer: - (A) 
Exp: - For step input 
ss
1
e 0.1 k 9
1 k
= = ? =
+
 
 ( )
9
G S
S 1
=
+
 
 Now the input is pulse ( ) ( ) ( ) r t 10 u t u t 1 ? ? = - -
? ?
 
 ( )
s
1 e
r s 10
s
-
? ? -
=
? ?
? ?
 
 
( )
( ) ( )
s
ss
S 0 S 0
S 10 1 e
S.R s
S
e Lt Lt
S 10 1 G S H S
S 1
-
? ?
? ? -
? ?
= =
+ +
+
 
0
0
10
= = 
 
10. Consider the following statement 
 (i)  The compensating coil of a low power factor wattmeter compensates the 
effect of the impedance of the current coil. 
 (ii) The compensating coil of a low power factor wattmeter compensates the 
effect 0of the impedance of the voltage coil circuit. 
( ) r t 
10 
1s 
t 
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        4 
 (A)  (i) is true but (ii) is false (B) (i) is false but (ii) is true 
 (C)  both (i) and (ii) are true (D) both (i) and (ii) are false 
Answer: - (B) 
 
11. A low – pass filter with a cut-off frequency of 30Hz is cascaded with a high-pass 
filter with a cut-off frequency of 20Hz. The resultant system of filters will function 
as 
 (A)  an all-pass filter  (B)  an all-stop filter  
 (B)  an band stop (band-reject) filter (D)  a band – pass filter 
Answer: - (D) 
Exp: -  
  
 
 
 
 So it is a band pass filter 
 
12.  
 
 
 
 
 
 
 
 
 The CORRECT transfer characteristic is 
 
 
 (A)    (B)  
 
 
 
 
 
  
 
 
 
 (C)    (D)  
 
 
R 
12V + 
12V + 
O
V 
12V - 
12V - 
R R 
R 
R 
vi 
- 
+ 
- 
+ 
Vo 
6v - 
12v - 
Vi 
12v + 12V + 
6v - 
12v - 
Vi 
O
V 
6v + 
Vo 
Vi 
6v + 6v - 
12v + 
Vo 
Vi 
6v + 6v - 
12v + 
20 30
                                          ?EE-Paper Code-A? GATE 2011                          www.gateforum.com  
 
© All rights reserved by Gateforum Educational Services Pvt. Ltd.  No part of this document may be reproduced or utilized in any form without the 
written permission. Discuss GATE 2011 question paper at www.gatementor.com.                                                                                        5 
Answer: - (D) 
Exp: -  It is a Schmitt trigger and phase shift is zero. 
 
13. A three-phase current source inverter used for the speed control of an induction 
motor is to be realized using MOSFET switches as shown below. Switches S
1
 to S
6
 
are identical switches. 
 
 
 
 
 
 
 
 
 
 The proper configuration for realizing switches S
1
 to S
6
 is 
 
 
 
 (A)  (B)  (C)  (D) 
 
 
Answer: - (C) 
 
14. A point Z has been plotted in the complex plane, as shown in figure below. 
 
 
 
 
 
 
 The plot of the complex number 
1
y is
z
= 
 
 
 
 
 
 
 
 
 
 
d
I 
A 
1
S 
B 
2
S 
3
S 
A 
B 
4
S 
6
S 
2
S 
l.M. 
A 
B 
A 
B 
A 
B 
A 
B 
Im unit circle 
o
Z 
Re 
Im unit circle 
y
•
 
Re 
( ) A Im unit circle 
y
•
 
Re 
( ) B 
Im unit circle 
y
•
 
Re 
( ) C Im unit circle 
y
•
 
Re 
( ) D 
Read More
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