Page 1
ECGATE2013 PAPER
1
Q. No. 1 – 25 Carry One Mark Each
1. A bulb in a staircase has two switches, one switch being at the ground floor
and the other one at the first floor. The bulb can be turned ON and also can
be turned OFF by any one of the switches irrespective of the state of the
other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Answer: (C)
Exp: (C)
Let Switches =
1 2
p , p
1 2
p , p Z(o / p)
OFF OFF OFF
OFF ON ON
ON OFF ON
ON ON OFF
From Truth Table, it can be verified that ExOR logic is implemented.
2. Consider a vector field ( ) A r
. The closed loop line integral A dl •
?
can be
expressed as
(A)
( )
A ds ?× •
??
over the closed surface bounded by the loop
(B)
( )
A dv ?•
???
over the closed volume bounded by the loop
(C)
( )
A dv ?•
???
over the open volume bounded by the loop
(D)
( )
A ds ?× •
??
over the closed surface bounded by the loop
Answer: (D)
Exp: (D)
Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is
equal to the integral of curl of A over the open surface S enclosed by the closed
path L”.
( )
? = ?×
? ??
A.dl A .ds
3. Two systems with impulse responses
( ) ( )
1 2
h t and h t are connected in cascade.
Then the overall impulse response of the cascaded system is given by
(A) Product of
( ) ( )
1 2
h t and h t
(B) Sum of
( ) ( )
1 2
h t and h t
(C) Convolution of
( ) ( )
1 2
h t and h t
(D) Subtraction of ( ) ( )
2 1
h t from h t
Page 2
ECGATE2013 PAPER
1
Q. No. 1 – 25 Carry One Mark Each
1. A bulb in a staircase has two switches, one switch being at the ground floor
and the other one at the first floor. The bulb can be turned ON and also can
be turned OFF by any one of the switches irrespective of the state of the
other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Answer: (C)
Exp: (C)
Let Switches =
1 2
p , p
1 2
p , p Z(o / p)
OFF OFF OFF
OFF ON ON
ON OFF ON
ON ON OFF
From Truth Table, it can be verified that ExOR logic is implemented.
2. Consider a vector field ( ) A r
. The closed loop line integral A dl •
?
can be
expressed as
(A)
( )
A ds ?× •
??
over the closed surface bounded by the loop
(B)
( )
A dv ?•
???
over the closed volume bounded by the loop
(C)
( )
A dv ?•
???
over the open volume bounded by the loop
(D)
( )
A ds ?× •
??
over the closed surface bounded by the loop
Answer: (D)
Exp: (D)
Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is
equal to the integral of curl of A over the open surface S enclosed by the closed
path L”.
( )
? = ?×
? ??
A.dl A .ds
3. Two systems with impulse responses
( ) ( )
1 2
h t and h t are connected in cascade.
Then the overall impulse response of the cascaded system is given by
(A) Product of
( ) ( )
1 2
h t and h t
(B) Sum of
( ) ( )
1 2
h t and h t
(C) Convolution of
( ) ( )
1 2
h t and h t
(D) Subtraction of ( ) ( )
2 1
h t from h t
ECGATE2013 PAPER
2
Answer: (C)
Exp:
4. In a forward biased pn junction diode, the sequence of events that best describes
the mechanism of current flow is
(A) injection, and subsequent diffusion and recombination of minority carriers
(B) injection, and subsequent drift and generation of minority carriers
(C) extraction, and subsequent diffusion and generation of minority carriers
(D) extraction, and subsequent drift and recombination of minority carriers
Answer: (A)
5. In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation
(using steam or water vapor) produces
(A) superior quality oxide with a higher growth rate
(B) inferior quality oxide with a higher growth rate
(C) inferior quality oxide with a lower growth rate
(D) superior quality oxide with a lower growth rate
Answer: (D)
6. The maximum value of ? until which the approximation sin? ˜ ? holds to within 10%
error is
(A)
o
10 (B)
o
18 (C)
o
50 (D)
o
90
Answer: (B)
Exp:
3 5
sin .......
3! 5!
? ?
? = ? + +
3
sin error
Error should 10% of
if 0.1
6
? = ?+
?
?
= ?
3
if 0.1
6
?
= ?
Then higher order terms also going to be less than 0.1?
So, sin? ˜ ? approximation is valid
3
2
0.1
6
0.6
0.6
?
< ?
? <
? <
Consider
max
0.6 0.7746 radians ? = =
180
(in degrees) 0.7746 45 ? = × °
p
Out of all possible options we need to go for max theta
below
45°
Hence it is
18°
x(t)
y(t)
1 2
h(t) *h(t)
x(t)
y(t) 1
h (t)
2
h (t)
Page 3
ECGATE2013 PAPER
1
Q. No. 1 – 25 Carry One Mark Each
1. A bulb in a staircase has two switches, one switch being at the ground floor
and the other one at the first floor. The bulb can be turned ON and also can
be turned OFF by any one of the switches irrespective of the state of the
other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Answer: (C)
Exp: (C)
Let Switches =
1 2
p , p
1 2
p , p Z(o / p)
OFF OFF OFF
OFF ON ON
ON OFF ON
ON ON OFF
From Truth Table, it can be verified that ExOR logic is implemented.
2. Consider a vector field ( ) A r
. The closed loop line integral A dl •
?
can be
expressed as
(A)
( )
A ds ?× •
??
over the closed surface bounded by the loop
(B)
( )
A dv ?•
???
over the closed volume bounded by the loop
(C)
( )
A dv ?•
???
over the open volume bounded by the loop
(D)
( )
A ds ?× •
??
over the closed surface bounded by the loop
Answer: (D)
Exp: (D)
Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is
equal to the integral of curl of A over the open surface S enclosed by the closed
path L”.
( )
? = ?×
? ??
A.dl A .ds
3. Two systems with impulse responses
( ) ( )
1 2
h t and h t are connected in cascade.
Then the overall impulse response of the cascaded system is given by
(A) Product of
( ) ( )
1 2
h t and h t
(B) Sum of
( ) ( )
1 2
h t and h t
(C) Convolution of
( ) ( )
1 2
h t and h t
(D) Subtraction of ( ) ( )
2 1
h t from h t
ECGATE2013 PAPER
2
Answer: (C)
Exp:
4. In a forward biased pn junction diode, the sequence of events that best describes
the mechanism of current flow is
(A) injection, and subsequent diffusion and recombination of minority carriers
(B) injection, and subsequent drift and generation of minority carriers
(C) extraction, and subsequent diffusion and generation of minority carriers
(D) extraction, and subsequent drift and recombination of minority carriers
Answer: (A)
5. In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation
(using steam or water vapor) produces
(A) superior quality oxide with a higher growth rate
(B) inferior quality oxide with a higher growth rate
(C) inferior quality oxide with a lower growth rate
(D) superior quality oxide with a lower growth rate
Answer: (D)
6. The maximum value of ? until which the approximation sin? ˜ ? holds to within 10%
error is
(A)
o
10 (B)
o
18 (C)
o
50 (D)
o
90
Answer: (B)
Exp:
3 5
sin .......
3! 5!
? ?
? = ? + +
3
sin error
Error should 10% of
if 0.1
6
? = ?+
?
?
= ?
3
if 0.1
6
?
= ?
Then higher order terms also going to be less than 0.1?
So, sin? ˜ ? approximation is valid
3
2
0.1
6
0.6
0.6
?
< ?
? <
? <
Consider
max
0.6 0.7746 radians ? = =
180
(in degrees) 0.7746 45 ? = × °
p
Out of all possible options we need to go for max theta
below
45°
Hence it is
18°
x(t)
y(t)
1 2
h(t) *h(t)
x(t)
y(t) 1
h (t)
2
h (t)
ECGATE2013 PAPER
3
7. The divergence of the vector field
x y z
ˆ ˆ ˆ A xa ya za = + +
is
(A) 0 (B) 1/3 (C) 1 (D) 3
Answer: (D)
Exp: Given
x y z
A xa ya za = + +
( ) ( ) ( )
( ) ( ) ( )
x y z
x y z
.A A A A
x y z
A x, A y, A z,
x y z
x y z
1 1 1 3
? ? ?
? = + +
? ? ?
= = =
? ? ?
= + +
? ? ?
= + + =
8. The impulse response of a system is
( ) ( )
h t tu t . = For an input
( )
u t 1  , the output
is
(A)
( )
2
t
u t
2
(B)
( )
( )
t t 1
u t 1
2

 (C)
( )
( )
2
t 1
u t 1
2

 (D)
( )
2
t 1
u t 1
2


Answer: (C)
Exp:
For LTI system, if input gets delayed by one unit, output will also get delayed by
one unit.
2
(t 1)
u(t 1) u(t 1)
2

 ? 
9. The Bode plot of a transfer function G (s) is shown in the figure below
The gain
( ) ( )
20 log G s is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively.
The phase is negative for all ?. The G(s) is
(A)
39.8
s
(B)
2
39.8
s
(C)
32
s
(D)
2
32
s
40
32
20
1
0
10
8 
100
( ) rad / s ?
Gain (dB)
U(t) t u (t)
2
t
u(t)
2
LTI system
Page 4
ECGATE2013 PAPER
1
Q. No. 1 – 25 Carry One Mark Each
1. A bulb in a staircase has two switches, one switch being at the ground floor
and the other one at the first floor. The bulb can be turned ON and also can
be turned OFF by any one of the switches irrespective of the state of the
other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Answer: (C)
Exp: (C)
Let Switches =
1 2
p , p
1 2
p , p Z(o / p)
OFF OFF OFF
OFF ON ON
ON OFF ON
ON ON OFF
From Truth Table, it can be verified that ExOR logic is implemented.
2. Consider a vector field ( ) A r
. The closed loop line integral A dl •
?
can be
expressed as
(A)
( )
A ds ?× •
??
over the closed surface bounded by the loop
(B)
( )
A dv ?•
???
over the closed volume bounded by the loop
(C)
( )
A dv ?•
???
over the open volume bounded by the loop
(D)
( )
A ds ?× •
??
over the closed surface bounded by the loop
Answer: (D)
Exp: (D)
Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is
equal to the integral of curl of A over the open surface S enclosed by the closed
path L”.
( )
? = ?×
? ??
A.dl A .ds
3. Two systems with impulse responses
( ) ( )
1 2
h t and h t are connected in cascade.
Then the overall impulse response of the cascaded system is given by
(A) Product of
( ) ( )
1 2
h t and h t
(B) Sum of
( ) ( )
1 2
h t and h t
(C) Convolution of
( ) ( )
1 2
h t and h t
(D) Subtraction of ( ) ( )
2 1
h t from h t
ECGATE2013 PAPER
2
Answer: (C)
Exp:
4. In a forward biased pn junction diode, the sequence of events that best describes
the mechanism of current flow is
(A) injection, and subsequent diffusion and recombination of minority carriers
(B) injection, and subsequent drift and generation of minority carriers
(C) extraction, and subsequent diffusion and generation of minority carriers
(D) extraction, and subsequent drift and recombination of minority carriers
Answer: (A)
5. In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation
(using steam or water vapor) produces
(A) superior quality oxide with a higher growth rate
(B) inferior quality oxide with a higher growth rate
(C) inferior quality oxide with a lower growth rate
(D) superior quality oxide with a lower growth rate
Answer: (D)
6. The maximum value of ? until which the approximation sin? ˜ ? holds to within 10%
error is
(A)
o
10 (B)
o
18 (C)
o
50 (D)
o
90
Answer: (B)
Exp:
3 5
sin .......
3! 5!
? ?
? = ? + +
3
sin error
Error should 10% of
if 0.1
6
? = ?+
?
?
= ?
3
if 0.1
6
?
= ?
Then higher order terms also going to be less than 0.1?
So, sin? ˜ ? approximation is valid
3
2
0.1
6
0.6
0.6
?
< ?
? <
? <
Consider
max
0.6 0.7746 radians ? = =
180
(in degrees) 0.7746 45 ? = × °
p
Out of all possible options we need to go for max theta
below
45°
Hence it is
18°
x(t)
y(t)
1 2
h(t) *h(t)
x(t)
y(t) 1
h (t)
2
h (t)
ECGATE2013 PAPER
3
7. The divergence of the vector field
x y z
ˆ ˆ ˆ A xa ya za = + +
is
(A) 0 (B) 1/3 (C) 1 (D) 3
Answer: (D)
Exp: Given
x y z
A xa ya za = + +
( ) ( ) ( )
( ) ( ) ( )
x y z
x y z
.A A A A
x y z
A x, A y, A z,
x y z
x y z
1 1 1 3
? ? ?
? = + +
? ? ?
= = =
? ? ?
= + +
? ? ?
= + + =
8. The impulse response of a system is
( ) ( )
h t tu t . = For an input
( )
u t 1  , the output
is
(A)
( )
2
t
u t
2
(B)
( )
( )
t t 1
u t 1
2

 (C)
( )
( )
2
t 1
u t 1
2

 (D)
( )
2
t 1
u t 1
2


Answer: (C)
Exp:
For LTI system, if input gets delayed by one unit, output will also get delayed by
one unit.
2
(t 1)
u(t 1) u(t 1)
2

 ? 
9. The Bode plot of a transfer function G (s) is shown in the figure below
The gain
( ) ( )
20 log G s is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively.
The phase is negative for all ?. The G(s) is
(A)
39.8
s
(B)
2
39.8
s
(C)
32
s
(D)
2
32
s
40
32
20
1
0
10
8 
100
( ) rad / s ?
Gain (dB)
U(t) t u (t)
2
t
u(t)
2
LTI system
ECGATE2013 PAPER
4
Answer: (B)
Exp: Any two paints on same line segment of Bode plot satisfies the equation of
straight line.
2 1
2 1
G G
i.e, slope of the line segment.
log log

=
?  ?
For the initial straight line
( )
2 1
2 1
1
N
1
2
2
G G
dB
40
dec
log log
0 32 40log
1
6.309 k ;Where N is type of system here initial slope is
dB
40 Hence N = 2
dec
6.309 k
k 6.309
k 39.8

? = 
?  ?
? ? ?
?  = 
? ?
? ?
? ? = =

? =
? =
=
Hence ( )
2
39.8
G s
s
=
10. In the circuit shown below what is the output voltage
( )
out
V if a silicon transistor
Q and an ideal opamp are used?
(A) –15V (B) –0.7V (C) +0.7V (D) +15V
+

1 kO
5V
15V +
15V 
Q
out
V +

( ) 20log G j?
40
32
20
8 
w
10
( ) w rad
1
Page 5
ECGATE2013 PAPER
1
Q. No. 1 – 25 Carry One Mark Each
1. A bulb in a staircase has two switches, one switch being at the ground floor
and the other one at the first floor. The bulb can be turned ON and also can
be turned OFF by any one of the switches irrespective of the state of the
other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Answer: (C)
Exp: (C)
Let Switches =
1 2
p , p
1 2
p , p Z(o / p)
OFF OFF OFF
OFF ON ON
ON OFF ON
ON ON OFF
From Truth Table, it can be verified that ExOR logic is implemented.
2. Consider a vector field ( ) A r
. The closed loop line integral A dl •
?
can be
expressed as
(A)
( )
A ds ?× •
??
over the closed surface bounded by the loop
(B)
( )
A dv ?•
???
over the closed volume bounded by the loop
(C)
( )
A dv ?•
???
over the open volume bounded by the loop
(D)
( )
A ds ?× •
??
over the closed surface bounded by the loop
Answer: (D)
Exp: (D)
Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is
equal to the integral of curl of A over the open surface S enclosed by the closed
path L”.
( )
? = ?×
? ??
A.dl A .ds
3. Two systems with impulse responses
( ) ( )
1 2
h t and h t are connected in cascade.
Then the overall impulse response of the cascaded system is given by
(A) Product of
( ) ( )
1 2
h t and h t
(B) Sum of
( ) ( )
1 2
h t and h t
(C) Convolution of
( ) ( )
1 2
h t and h t
(D) Subtraction of ( ) ( )
2 1
h t from h t
ECGATE2013 PAPER
2
Answer: (C)
Exp:
4. In a forward biased pn junction diode, the sequence of events that best describes
the mechanism of current flow is
(A) injection, and subsequent diffusion and recombination of minority carriers
(B) injection, and subsequent drift and generation of minority carriers
(C) extraction, and subsequent diffusion and generation of minority carriers
(D) extraction, and subsequent drift and recombination of minority carriers
Answer: (A)
5. In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation
(using steam or water vapor) produces
(A) superior quality oxide with a higher growth rate
(B) inferior quality oxide with a higher growth rate
(C) inferior quality oxide with a lower growth rate
(D) superior quality oxide with a lower growth rate
Answer: (D)
6. The maximum value of ? until which the approximation sin? ˜ ? holds to within 10%
error is
(A)
o
10 (B)
o
18 (C)
o
50 (D)
o
90
Answer: (B)
Exp:
3 5
sin .......
3! 5!
? ?
? = ? + +
3
sin error
Error should 10% of
if 0.1
6
? = ?+
?
?
= ?
3
if 0.1
6
?
= ?
Then higher order terms also going to be less than 0.1?
So, sin? ˜ ? approximation is valid
3
2
0.1
6
0.6
0.6
?
< ?
? <
? <
Consider
max
0.6 0.7746 radians ? = =
180
(in degrees) 0.7746 45 ? = × °
p
Out of all possible options we need to go for max theta
below
45°
Hence it is
18°
x(t)
y(t)
1 2
h(t) *h(t)
x(t)
y(t) 1
h (t)
2
h (t)
ECGATE2013 PAPER
3
7. The divergence of the vector field
x y z
ˆ ˆ ˆ A xa ya za = + +
is
(A) 0 (B) 1/3 (C) 1 (D) 3
Answer: (D)
Exp: Given
x y z
A xa ya za = + +
( ) ( ) ( )
( ) ( ) ( )
x y z
x y z
.A A A A
x y z
A x, A y, A z,
x y z
x y z
1 1 1 3
? ? ?
? = + +
? ? ?
= = =
? ? ?
= + +
? ? ?
= + + =
8. The impulse response of a system is
( ) ( )
h t tu t . = For an input
( )
u t 1  , the output
is
(A)
( )
2
t
u t
2
(B)
( )
( )
t t 1
u t 1
2

 (C)
( )
( )
2
t 1
u t 1
2

 (D)
( )
2
t 1
u t 1
2


Answer: (C)
Exp:
For LTI system, if input gets delayed by one unit, output will also get delayed by
one unit.
2
(t 1)
u(t 1) u(t 1)
2

 ? 
9. The Bode plot of a transfer function G (s) is shown in the figure below
The gain
( ) ( )
20 log G s is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively.
The phase is negative for all ?. The G(s) is
(A)
39.8
s
(B)
2
39.8
s
(C)
32
s
(D)
2
32
s
40
32
20
1
0
10
8 
100
( ) rad / s ?
Gain (dB)
U(t) t u (t)
2
t
u(t)
2
LTI system
ECGATE2013 PAPER
4
Answer: (B)
Exp: Any two paints on same line segment of Bode plot satisfies the equation of
straight line.
2 1
2 1
G G
i.e, slope of the line segment.
log log

=
?  ?
For the initial straight line
( )
2 1
2 1
1
N
1
2
2
G G
dB
40
dec
log log
0 32 40log
1
6.309 k ;Where N is type of system here initial slope is
dB
40 Hence N = 2
dec
6.309 k
k 6.309
k 39.8

? = 
?  ?
? ? ?
?  = 
? ?
? ?
? ? = =

? =
? =
=
Hence ( )
2
39.8
G s
s
=
10. In the circuit shown below what is the output voltage
( )
out
V if a silicon transistor
Q and an ideal opamp are used?
(A) –15V (B) –0.7V (C) +0.7V (D) +15V
+

1 kO
5V
15V +
15V 
Q
out
V +

( ) 20log G j?
40
32
20
8 
w
10
( ) w rad
1
ECGATE2013 PAPER
5
Answer: (B)
Exp:
11. Consider a delta connection of resistors and its equivalent star connection as
shown below. If all elements of the delta connection are scaled by a factor k, k> 0,
the elements of the corresponding star equivalent will be scaled by a factor of
(A)
2
k (B) k (C) 1/k (D) k
Answer: (B)
Exp:
a b
C
a b c
R R
R
R R R
=
+ +
=
+ +
=
+ +
a c
B
a b c
b c
A
a b c
R R
R
R R R
R R
R
R R R
Above expression shown that if
a b c
R , R & R is scaled by k, R
A
, R
B
& R
C
is scaled
by k only.
12. For 8085 microprocessor, the following program is executed
MVI A, 05H;
MVIB, 05H;
PTR: ADD B;
DCR B;
JNZ PTR;
ADI 03H;
HLT;
At the end of program, accumulator contains
(A) 17 H (B) 20 H (C) 23 H (D) 05 H
b
R
a
R
c
R
C
R
B
R
A
R
a
R
b
R
c
R
C
R
A
R
B
R
out
V
1 kO
+

Q
+

5V
15V +
15V 
0.7v
+

out
V 0.7v = 
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