Download GATE (Graduate Aptitude Test in Engineering) GATE ECE 2019 Question Paper With Solution And Answer Key
2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
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2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
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2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
4
3. Consider the two-port resistive network
shown in the figure. When an excitation of
5 V is applied across Port 1, and Port 2 is
shorted, the current through the short
circuit at Port 2 is measured to be 1 A (see
(a) in the figure).
Now, if an excitation of 5 V is applied
across Port 2, and Port 1 is shorted (see
(b) in the figure), what is the current
through the short circuit at Port 1?
A. 0.5 A B. 1 A
C. 2 A D. 2.5 A
4. In the circuit shown, what are the values of
F for EN = 0 and EN = 1, respectively?
A. Hi-Z and D B. Hi-Z and D
C. 0 and 1 D. 0 and D
5. The number of distinct eigenvalues of the
matrix
2 2 3 3
0 1 1 1
0 0 3 3
0 0 0 2
A
??
??
??
=
??
??
??
is equal to __________.
6. The families of curves represented by the
solution of the equation
n
dy x
dx y
??
=?
??
??
for n = - 1 and n = + 1, respectively, are
A. Hyperbolas and Circles
B. Circles and Hyperbolas
C. Parabolas and Circles
D. Hyperbolas and Parabolas
7. Let H(z) be the z-transform of a real-
valued discrete-time signal h[n]. If P(z) =
H(z)
1
H
z
??
??
??
has a zero at
11
,
22
zj =+ and
P(z) has a total of four zeros, which one of
the following plots represents all the zeros
correctly?
A.
B.
C.
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2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
4
3. Consider the two-port resistive network
shown in the figure. When an excitation of
5 V is applied across Port 1, and Port 2 is
shorted, the current through the short
circuit at Port 2 is measured to be 1 A (see
(a) in the figure).
Now, if an excitation of 5 V is applied
across Port 2, and Port 1 is shorted (see
(b) in the figure), what is the current
through the short circuit at Port 1?
A. 0.5 A B. 1 A
C. 2 A D. 2.5 A
4. In the circuit shown, what are the values of
F for EN = 0 and EN = 1, respectively?
A. Hi-Z and D B. Hi-Z and D
C. 0 and 1 D. 0 and D
5. The number of distinct eigenvalues of the
matrix
2 2 3 3
0 1 1 1
0 0 3 3
0 0 0 2
A
??
??
??
=
??
??
??
is equal to __________.
6. The families of curves represented by the
solution of the equation
n
dy x
dx y
??
=?
??
??
for n = - 1 and n = + 1, respectively, are
A. Hyperbolas and Circles
B. Circles and Hyperbolas
C. Parabolas and Circles
D. Hyperbolas and Parabolas
7. Let H(z) be the z-transform of a real-
valued discrete-time signal h[n]. If P(z) =
H(z)
1
H
z
??
??
??
has a zero at
11
,
22
zj =+ and
P(z) has a total of four zeros, which one of
the following plots represents all the zeros
correctly?
A.
B.
C.
5
D.
8. The value of the integral
0
sin
,
y
x
dx dy
x
??
??
is equal to __________.
9. Radiation resistance of a small dipole
current element of length l at a frequency
of 3 GHz is 3 ohms. If the length is
changed by 1%, then the percentage
change in the radiation resistance, rounded
off to two decimal places, is _________%.
10. Let Y(s) be the unit-step response of a
causal system having a transfer function
( )
( ) ( )
3
13
s
Gs
ss
?
=
++
that is, ( )
( )
.
Gs
Ys
s
= The forced response
of the system is
A. u(t) ? 2e
-t
u(t) + e
-3t
u(t)
B. u(t)
C. 2u(t) ? 2e
-t
u(t) + e
-3t
u(t)
D. 2u(t)
11. The correct circuit representation of the
structure shown in the figure is
A.
B.
C.
D.
12. What is the electric flux
( )
? E da ?
?
through a
quarter-cylinder of height H (as shown in
the figure) due to an infinitely long line
charge along the axis of the cylinder with a
charge density of Q?
A.
0
4
H
Q
?
B.
0
HQ
?
C.
0
4
HQ
?
D.
0
4H
Q ?
13. In the circuit shown, A and B are the inputs
and F is the output. What is the
functionality of the circuit?
FirstRanker.com - FirstRanker's Choice
2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
4
3. Consider the two-port resistive network
shown in the figure. When an excitation of
5 V is applied across Port 1, and Port 2 is
shorted, the current through the short
circuit at Port 2 is measured to be 1 A (see
(a) in the figure).
Now, if an excitation of 5 V is applied
across Port 2, and Port 1 is shorted (see
(b) in the figure), what is the current
through the short circuit at Port 1?
A. 0.5 A B. 1 A
C. 2 A D. 2.5 A
4. In the circuit shown, what are the values of
F for EN = 0 and EN = 1, respectively?
A. Hi-Z and D B. Hi-Z and D
C. 0 and 1 D. 0 and D
5. The number of distinct eigenvalues of the
matrix
2 2 3 3
0 1 1 1
0 0 3 3
0 0 0 2
A
??
??
??
=
??
??
??
is equal to __________.
6. The families of curves represented by the
solution of the equation
n
dy x
dx y
??
=?
??
??
for n = - 1 and n = + 1, respectively, are
A. Hyperbolas and Circles
B. Circles and Hyperbolas
C. Parabolas and Circles
D. Hyperbolas and Parabolas
7. Let H(z) be the z-transform of a real-
valued discrete-time signal h[n]. If P(z) =
H(z)
1
H
z
??
??
??
has a zero at
11
,
22
zj =+ and
P(z) has a total of four zeros, which one of
the following plots represents all the zeros
correctly?
A.
B.
C.
5
D.
8. The value of the integral
0
sin
,
y
x
dx dy
x
??
??
is equal to __________.
9. Radiation resistance of a small dipole
current element of length l at a frequency
of 3 GHz is 3 ohms. If the length is
changed by 1%, then the percentage
change in the radiation resistance, rounded
off to two decimal places, is _________%.
10. Let Y(s) be the unit-step response of a
causal system having a transfer function
( )
( ) ( )
3
13
s
Gs
ss
?
=
++
that is, ( )
( )
.
Gs
Ys
s
= The forced response
of the system is
A. u(t) ? 2e
-t
u(t) + e
-3t
u(t)
B. u(t)
C. 2u(t) ? 2e
-t
u(t) + e
-3t
u(t)
D. 2u(t)
11. The correct circuit representation of the
structure shown in the figure is
A.
B.
C.
D.
12. What is the electric flux
( )
? E da ?
?
through a
quarter-cylinder of height H (as shown in
the figure) due to an infinitely long line
charge along the axis of the cylinder with a
charge density of Q?
A.
0
4
H
Q
?
B.
0
HQ
?
C.
0
4
HQ
?
D.
0
4H
Q ?
13. In the circuit shown, A and B are the inputs
and F is the output. What is the
functionality of the circuit?
6
A. XOR B. SRAM Cell
C. Latch D. XNOR
14. In the circuit shown, Vs is a square wave of
period T with maximum and minimum
values of 8 V and -10 V, respectively.
Assume that the diode is ideal and R1 = R2
= 50 ?.
The average value of VL is _________ volts
(rounded off to 1 decimal place).
15. If X and Y are random variables such that
E[2X + Y] = 0 and E[X + 2Y] = 33, then
E[X] + E[Y] = _________.
16. A standard CMOS inverter is designed with
equal rise and fall times (?n = ?p). If the
width of the pMOS transistor in the inverter
is increased, what would be the effect on
the LOW noise margin (NML) and the HIGH
noise margin NMH?
A. N ML increases and N MH decreases.
B. Both N ML and N MH increase.
C. N ML decreases and N MH increase.
D. No change in the noise margins.
17. In the table shown, List I and List II,
respectively, contain terms appearing on
the left-hand side and the right-hand side
of Maxwell?s equations (in their standard
form). Match the left-hand side with the
corresponding right-hand side.
List I List II
1 ? . D P 0
2 ? ? E Q ?
3 ? . B R
t
?
?
?
B
4 ? ? H S
D
J
t
?
+
?
A. 1 ? Q, 2 ? R, 3 ? P, 4 ? S
B. 1 ? Q, 2 ? S, 3 ? P, 4 ? R
C. 1 ? R, 2 ? Q, 3 ? S, 4 ? P
D. 1 ? P, 2 ? R, 3 ? Q, 4 ? S
18. For an LTI system, the Bode plot for its
gain is as illustrated in the figure shown.
The number of system poles Np and the
number of system zeros Nz in the
frequency range 1 Hz ? f ? 10
7
Hz is
A. Np = 6, Nz = 3
B. Np = 5, Nz = 2
C. Np = 4, Nz = 2
D. Np = 7, Nz = 4
19. The baseband signal m(t) shown in the
figure is phase-modulated to generate the
PM signal ?(t) = cos (2?fct + k m(t)). The
time t on the x-axis in the figure is in
milliseconds. If the carrier frequency is
fc = 50 kHz and k = 10?, then the ratio of
the minimum instantaneous frequency (in
kHz) to the maximum instantaneous
frequency (in kHz) is _________ (rounded
off to 2 decimal places).
20. In the circuit shown, the clock frequency,
i.e., the frequency of the Clk signal, is 12
kHz. The frequency of the signal at Q2 is
__________ kHz.
FirstRanker.com - FirstRanker's Choice
2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
4
3. Consider the two-port resistive network
shown in the figure. When an excitation of
5 V is applied across Port 1, and Port 2 is
shorted, the current through the short
circuit at Port 2 is measured to be 1 A (see
(a) in the figure).
Now, if an excitation of 5 V is applied
across Port 2, and Port 1 is shorted (see
(b) in the figure), what is the current
through the short circuit at Port 1?
A. 0.5 A B. 1 A
C. 2 A D. 2.5 A
4. In the circuit shown, what are the values of
F for EN = 0 and EN = 1, respectively?
A. Hi-Z and D B. Hi-Z and D
C. 0 and 1 D. 0 and D
5. The number of distinct eigenvalues of the
matrix
2 2 3 3
0 1 1 1
0 0 3 3
0 0 0 2
A
??
??
??
=
??
??
??
is equal to __________.
6. The families of curves represented by the
solution of the equation
n
dy x
dx y
??
=?
??
??
for n = - 1 and n = + 1, respectively, are
A. Hyperbolas and Circles
B. Circles and Hyperbolas
C. Parabolas and Circles
D. Hyperbolas and Parabolas
7. Let H(z) be the z-transform of a real-
valued discrete-time signal h[n]. If P(z) =
H(z)
1
H
z
??
??
??
has a zero at
11
,
22
zj =+ and
P(z) has a total of four zeros, which one of
the following plots represents all the zeros
correctly?
A.
B.
C.
5
D.
8. The value of the integral
0
sin
,
y
x
dx dy
x
??
??
is equal to __________.
9. Radiation resistance of a small dipole
current element of length l at a frequency
of 3 GHz is 3 ohms. If the length is
changed by 1%, then the percentage
change in the radiation resistance, rounded
off to two decimal places, is _________%.
10. Let Y(s) be the unit-step response of a
causal system having a transfer function
( )
( ) ( )
3
13
s
Gs
ss
?
=
++
that is, ( )
( )
.
Gs
Ys
s
= The forced response
of the system is
A. u(t) ? 2e
-t
u(t) + e
-3t
u(t)
B. u(t)
C. 2u(t) ? 2e
-t
u(t) + e
-3t
u(t)
D. 2u(t)
11. The correct circuit representation of the
structure shown in the figure is
A.
B.
C.
D.
12. What is the electric flux
( )
? E da ?
?
through a
quarter-cylinder of height H (as shown in
the figure) due to an infinitely long line
charge along the axis of the cylinder with a
charge density of Q?
A.
0
4
H
Q
?
B.
0
HQ
?
C.
0
4
HQ
?
D.
0
4H
Q ?
13. In the circuit shown, A and B are the inputs
and F is the output. What is the
functionality of the circuit?
6
A. XOR B. SRAM Cell
C. Latch D. XNOR
14. In the circuit shown, Vs is a square wave of
period T with maximum and minimum
values of 8 V and -10 V, respectively.
Assume that the diode is ideal and R1 = R2
= 50 ?.
The average value of VL is _________ volts
(rounded off to 1 decimal place).
15. If X and Y are random variables such that
E[2X + Y] = 0 and E[X + 2Y] = 33, then
E[X] + E[Y] = _________.
16. A standard CMOS inverter is designed with
equal rise and fall times (?n = ?p). If the
width of the pMOS transistor in the inverter
is increased, what would be the effect on
the LOW noise margin (NML) and the HIGH
noise margin NMH?
A. N ML increases and N MH decreases.
B. Both N ML and N MH increase.
C. N ML decreases and N MH increase.
D. No change in the noise margins.
17. In the table shown, List I and List II,
respectively, contain terms appearing on
the left-hand side and the right-hand side
of Maxwell?s equations (in their standard
form). Match the left-hand side with the
corresponding right-hand side.
List I List II
1 ? . D P 0
2 ? ? E Q ?
3 ? . B R
t
?
?
?
B
4 ? ? H S
D
J
t
?
+
?
A. 1 ? Q, 2 ? R, 3 ? P, 4 ? S
B. 1 ? Q, 2 ? S, 3 ? P, 4 ? R
C. 1 ? R, 2 ? Q, 3 ? S, 4 ? P
D. 1 ? P, 2 ? R, 3 ? Q, 4 ? S
18. For an LTI system, the Bode plot for its
gain is as illustrated in the figure shown.
The number of system poles Np and the
number of system zeros Nz in the
frequency range 1 Hz ? f ? 10
7
Hz is
A. Np = 6, Nz = 3
B. Np = 5, Nz = 2
C. Np = 4, Nz = 2
D. Np = 7, Nz = 4
19. The baseband signal m(t) shown in the
figure is phase-modulated to generate the
PM signal ?(t) = cos (2?fct + k m(t)). The
time t on the x-axis in the figure is in
milliseconds. If the carrier frequency is
fc = 50 kHz and k = 10?, then the ratio of
the minimum instantaneous frequency (in
kHz) to the maximum instantaneous
frequency (in kHz) is _________ (rounded
off to 2 decimal places).
20. In the circuit shown, the clock frequency,
i.e., the frequency of the Clk signal, is 12
kHz. The frequency of the signal at Q2 is
__________ kHz.
7
21. A linear Hamming code is used to map 4-
bit messages to 7-bit codewords. The
encoder mapping is linear. If the message
0001 is mapped to the codeword 0000111,
and the message 0011 is mapped to the
codeword 100110, then the message 0010
is mapped to
A. 1111000 B. 0010011
C. 1111111 D. 1100001
22. Let Z be an exponential random variable
with mean 1. That is, the cumulative
distribution function of Z is given by
( )
1 if 0
0 if 0
?
??? ?
=
?
? ?
?
x
Z
ex
Fx
x
Then Pr(Z > 2 |Z > 1), rounded off to two
decimal places, is equal to __________.
23. Consider the signal f(t) = 1 + 2cos ( ?t) + 3
2
sin 4cos ,
3 2 4
? ? ? ? ? ? ?
++
? ? ? ?
? ? ? ?
tt where t is in
seconds. Its fundamental time period, in
seconds, is ____________.
24. The figure shows the high-frequency C-V
curve of a MOS capacitor (at T = 300 K)
with ?ms = 0 V and no oxide charges. The
flat-band, inversion, and accumulation
conditions are represented, respectively,
by the points
A. Q, R, P B. Q, P, R
C. R, P, Q D. P, Q, R
25. The value of the contour integral
2
11
2 ?
??
+
??
??
?
z dz
jz
evaluated over the unit circle |z| = 1 is
_____________.
26. The state transition diagram for the circuit
shown is
A.
B.
C.
D.
27. In the circuits shown, the threshold voltage
of each nMOS transistor is 0.6 V. Ignoring
the effect of channel length modulation and
body bias, the values of Vout 1 and Vout 2,
respectively, in volts, are
FirstRanker.com - FirstRanker's Choice
2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
4
3. Consider the two-port resistive network
shown in the figure. When an excitation of
5 V is applied across Port 1, and Port 2 is
shorted, the current through the short
circuit at Port 2 is measured to be 1 A (see
(a) in the figure).
Now, if an excitation of 5 V is applied
across Port 2, and Port 1 is shorted (see
(b) in the figure), what is the current
through the short circuit at Port 1?
A. 0.5 A B. 1 A
C. 2 A D. 2.5 A
4. In the circuit shown, what are the values of
F for EN = 0 and EN = 1, respectively?
A. Hi-Z and D B. Hi-Z and D
C. 0 and 1 D. 0 and D
5. The number of distinct eigenvalues of the
matrix
2 2 3 3
0 1 1 1
0 0 3 3
0 0 0 2
A
??
??
??
=
??
??
??
is equal to __________.
6. The families of curves represented by the
solution of the equation
n
dy x
dx y
??
=?
??
??
for n = - 1 and n = + 1, respectively, are
A. Hyperbolas and Circles
B. Circles and Hyperbolas
C. Parabolas and Circles
D. Hyperbolas and Parabolas
7. Let H(z) be the z-transform of a real-
valued discrete-time signal h[n]. If P(z) =
H(z)
1
H
z
??
??
??
has a zero at
11
,
22
zj =+ and
P(z) has a total of four zeros, which one of
the following plots represents all the zeros
correctly?
A.
B.
C.
5
D.
8. The value of the integral
0
sin
,
y
x
dx dy
x
??
??
is equal to __________.
9. Radiation resistance of a small dipole
current element of length l at a frequency
of 3 GHz is 3 ohms. If the length is
changed by 1%, then the percentage
change in the radiation resistance, rounded
off to two decimal places, is _________%.
10. Let Y(s) be the unit-step response of a
causal system having a transfer function
( )
( ) ( )
3
13
s
Gs
ss
?
=
++
that is, ( )
( )
.
Gs
Ys
s
= The forced response
of the system is
A. u(t) ? 2e
-t
u(t) + e
-3t
u(t)
B. u(t)
C. 2u(t) ? 2e
-t
u(t) + e
-3t
u(t)
D. 2u(t)
11. The correct circuit representation of the
structure shown in the figure is
A.
B.
C.
D.
12. What is the electric flux
( )
? E da ?
?
through a
quarter-cylinder of height H (as shown in
the figure) due to an infinitely long line
charge along the axis of the cylinder with a
charge density of Q?
A.
0
4
H
Q
?
B.
0
HQ
?
C.
0
4
HQ
?
D.
0
4H
Q ?
13. In the circuit shown, A and B are the inputs
and F is the output. What is the
functionality of the circuit?
6
A. XOR B. SRAM Cell
C. Latch D. XNOR
14. In the circuit shown, Vs is a square wave of
period T with maximum and minimum
values of 8 V and -10 V, respectively.
Assume that the diode is ideal and R1 = R2
= 50 ?.
The average value of VL is _________ volts
(rounded off to 1 decimal place).
15. If X and Y are random variables such that
E[2X + Y] = 0 and E[X + 2Y] = 33, then
E[X] + E[Y] = _________.
16. A standard CMOS inverter is designed with
equal rise and fall times (?n = ?p). If the
width of the pMOS transistor in the inverter
is increased, what would be the effect on
the LOW noise margin (NML) and the HIGH
noise margin NMH?
A. N ML increases and N MH decreases.
B. Both N ML and N MH increase.
C. N ML decreases and N MH increase.
D. No change in the noise margins.
17. In the table shown, List I and List II,
respectively, contain terms appearing on
the left-hand side and the right-hand side
of Maxwell?s equations (in their standard
form). Match the left-hand side with the
corresponding right-hand side.
List I List II
1 ? . D P 0
2 ? ? E Q ?
3 ? . B R
t
?
?
?
B
4 ? ? H S
D
J
t
?
+
?
A. 1 ? Q, 2 ? R, 3 ? P, 4 ? S
B. 1 ? Q, 2 ? S, 3 ? P, 4 ? R
C. 1 ? R, 2 ? Q, 3 ? S, 4 ? P
D. 1 ? P, 2 ? R, 3 ? Q, 4 ? S
18. For an LTI system, the Bode plot for its
gain is as illustrated in the figure shown.
The number of system poles Np and the
number of system zeros Nz in the
frequency range 1 Hz ? f ? 10
7
Hz is
A. Np = 6, Nz = 3
B. Np = 5, Nz = 2
C. Np = 4, Nz = 2
D. Np = 7, Nz = 4
19. The baseband signal m(t) shown in the
figure is phase-modulated to generate the
PM signal ?(t) = cos (2?fct + k m(t)). The
time t on the x-axis in the figure is in
milliseconds. If the carrier frequency is
fc = 50 kHz and k = 10?, then the ratio of
the minimum instantaneous frequency (in
kHz) to the maximum instantaneous
frequency (in kHz) is _________ (rounded
off to 2 decimal places).
20. In the circuit shown, the clock frequency,
i.e., the frequency of the Clk signal, is 12
kHz. The frequency of the signal at Q2 is
__________ kHz.
7
21. A linear Hamming code is used to map 4-
bit messages to 7-bit codewords. The
encoder mapping is linear. If the message
0001 is mapped to the codeword 0000111,
and the message 0011 is mapped to the
codeword 100110, then the message 0010
is mapped to
A. 1111000 B. 0010011
C. 1111111 D. 1100001
22. Let Z be an exponential random variable
with mean 1. That is, the cumulative
distribution function of Z is given by
( )
1 if 0
0 if 0
?
??? ?
=
?
? ?
?
x
Z
ex
Fx
x
Then Pr(Z > 2 |Z > 1), rounded off to two
decimal places, is equal to __________.
23. Consider the signal f(t) = 1 + 2cos ( ?t) + 3
2
sin 4cos ,
3 2 4
? ? ? ? ? ? ?
++
? ? ? ?
? ? ? ?
tt where t is in
seconds. Its fundamental time period, in
seconds, is ____________.
24. The figure shows the high-frequency C-V
curve of a MOS capacitor (at T = 300 K)
with ?ms = 0 V and no oxide charges. The
flat-band, inversion, and accumulation
conditions are represented, respectively,
by the points
A. Q, R, P B. Q, P, R
C. R, P, Q D. P, Q, R
25. The value of the contour integral
2
11
2 ?
??
+
??
??
?
z dz
jz
evaluated over the unit circle |z| = 1 is
_____________.
26. The state transition diagram for the circuit
shown is
A.
B.
C.
D.
27. In the circuits shown, the threshold voltage
of each nMOS transistor is 0.6 V. Ignoring
the effect of channel length modulation and
body bias, the values of Vout 1 and Vout 2,
respectively, in volts, are
8
A. 2.4 and 2.4 B. 1.8 and 1.2
C. 1.8 and 2.4 D. 2.4 and 1.2
28. The block diagram of a system is illustrated
in the figure shown, where X(s) is the input
and Y(s) is the output. The transfer
function ( )
( )
( )
=
Ys
Hs
Xs
is
A. ( )
2
2
1
21
+
=
+
s
Hs
s
B. ( )
2
32
1
21
+
=
+ + +
s
Hs
s s s
C. ( )
2
1
1
+
=
++
s
Hs
ss
D. ( )
2
32
1
1
+
=
+ + +
s
Hs
s s s
29. A random variable X takes -1 and +1 with
probabilities 0.2 and 0.8, respectively. It is
transmitted across a channel which adds
noise N, so that the random variable at the
channel output is Y = X + N. The noise n is
independent of X, and is uniformly
distributed over the interval [-2, 2]. The
receiver makes a decision
1, if
?
1, if
?
?
?? ?
=
?
+?
?
Y
X
Y
Where the threshold ? ? [-1, 1] is chosen
so as to minimize the probability of error
?
Pr .
??
?
??
XX The minimum probability of
error, rounded off to 1 decimal place, is
______________.
30. A germanium sample of dimensions 1 cm ?
1 cm is illuminated with a 20 mW, 600 nm
laser light source as shown in the figure.
The illuminated sample surface has a 100
nm of loss-less Silicon dioxide layer that
reflects one-fourth of the incident light.
From the remaining light, one-third of the
power is reflected from the Silicon dixodie-
Germanium interface, one-third is
absorbed in the Germanium layer, and
one-third is transmitted through the other
side of the sample. If the absorption
coefficient of Germanium at 600 nm is 3 ?
10
4
cm
-1
and the bandgap is 0.66 eV, the
thickness of the Germanium layer, rounded
off to 3 decimal places, is _________ ?m.
31. In the circuit shown, the threshold voltages
of the pMOS (|Vtp|) and nMOS (Vtn)
transistors are both equal to 1 V. All the
transistors have the same output
resistance rds of 6 M?. The other
parameters are listed below.
2
nMOS
2
ox
pMOS
60 A/V ; 5
30 A/V ; 10
??
??
??
==
??
??
??
==
??
??
n ox
p
W
C
L
W
C
L
?n and ?p are the carrier mobilites, and Cox
is the oxide capacitance per unit area.
Ignoring the effect of channel length
modulation and body bias, the gain of the
circuit is ____________(rounded off to 1
decimal place).
FirstRanker.com - FirstRanker's Choice
2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
4
3. Consider the two-port resistive network
shown in the figure. When an excitation of
5 V is applied across Port 1, and Port 2 is
shorted, the current through the short
circuit at Port 2 is measured to be 1 A (see
(a) in the figure).
Now, if an excitation of 5 V is applied
across Port 2, and Port 1 is shorted (see
(b) in the figure), what is the current
through the short circuit at Port 1?
A. 0.5 A B. 1 A
C. 2 A D. 2.5 A
4. In the circuit shown, what are the values of
F for EN = 0 and EN = 1, respectively?
A. Hi-Z and D B. Hi-Z and D
C. 0 and 1 D. 0 and D
5. The number of distinct eigenvalues of the
matrix
2 2 3 3
0 1 1 1
0 0 3 3
0 0 0 2
A
??
??
??
=
??
??
??
is equal to __________.
6. The families of curves represented by the
solution of the equation
n
dy x
dx y
??
=?
??
??
for n = - 1 and n = + 1, respectively, are
A. Hyperbolas and Circles
B. Circles and Hyperbolas
C. Parabolas and Circles
D. Hyperbolas and Parabolas
7. Let H(z) be the z-transform of a real-
valued discrete-time signal h[n]. If P(z) =
H(z)
1
H
z
??
??
??
has a zero at
11
,
22
zj =+ and
P(z) has a total of four zeros, which one of
the following plots represents all the zeros
correctly?
A.
B.
C.
5
D.
8. The value of the integral
0
sin
,
y
x
dx dy
x
??
??
is equal to __________.
9. Radiation resistance of a small dipole
current element of length l at a frequency
of 3 GHz is 3 ohms. If the length is
changed by 1%, then the percentage
change in the radiation resistance, rounded
off to two decimal places, is _________%.
10. Let Y(s) be the unit-step response of a
causal system having a transfer function
( )
( ) ( )
3
13
s
Gs
ss
?
=
++
that is, ( )
( )
.
Gs
Ys
s
= The forced response
of the system is
A. u(t) ? 2e
-t
u(t) + e
-3t
u(t)
B. u(t)
C. 2u(t) ? 2e
-t
u(t) + e
-3t
u(t)
D. 2u(t)
11. The correct circuit representation of the
structure shown in the figure is
A.
B.
C.
D.
12. What is the electric flux
( )
? E da ?
?
through a
quarter-cylinder of height H (as shown in
the figure) due to an infinitely long line
charge along the axis of the cylinder with a
charge density of Q?
A.
0
4
H
Q
?
B.
0
HQ
?
C.
0
4
HQ
?
D.
0
4H
Q ?
13. In the circuit shown, A and B are the inputs
and F is the output. What is the
functionality of the circuit?
6
A. XOR B. SRAM Cell
C. Latch D. XNOR
14. In the circuit shown, Vs is a square wave of
period T with maximum and minimum
values of 8 V and -10 V, respectively.
Assume that the diode is ideal and R1 = R2
= 50 ?.
The average value of VL is _________ volts
(rounded off to 1 decimal place).
15. If X and Y are random variables such that
E[2X + Y] = 0 and E[X + 2Y] = 33, then
E[X] + E[Y] = _________.
16. A standard CMOS inverter is designed with
equal rise and fall times (?n = ?p). If the
width of the pMOS transistor in the inverter
is increased, what would be the effect on
the LOW noise margin (NML) and the HIGH
noise margin NMH?
A. N ML increases and N MH decreases.
B. Both N ML and N MH increase.
C. N ML decreases and N MH increase.
D. No change in the noise margins.
17. In the table shown, List I and List II,
respectively, contain terms appearing on
the left-hand side and the right-hand side
of Maxwell?s equations (in their standard
form). Match the left-hand side with the
corresponding right-hand side.
List I List II
1 ? . D P 0
2 ? ? E Q ?
3 ? . B R
t
?
?
?
B
4 ? ? H S
D
J
t
?
+
?
A. 1 ? Q, 2 ? R, 3 ? P, 4 ? S
B. 1 ? Q, 2 ? S, 3 ? P, 4 ? R
C. 1 ? R, 2 ? Q, 3 ? S, 4 ? P
D. 1 ? P, 2 ? R, 3 ? Q, 4 ? S
18. For an LTI system, the Bode plot for its
gain is as illustrated in the figure shown.
The number of system poles Np and the
number of system zeros Nz in the
frequency range 1 Hz ? f ? 10
7
Hz is
A. Np = 6, Nz = 3
B. Np = 5, Nz = 2
C. Np = 4, Nz = 2
D. Np = 7, Nz = 4
19. The baseband signal m(t) shown in the
figure is phase-modulated to generate the
PM signal ?(t) = cos (2?fct + k m(t)). The
time t on the x-axis in the figure is in
milliseconds. If the carrier frequency is
fc = 50 kHz and k = 10?, then the ratio of
the minimum instantaneous frequency (in
kHz) to the maximum instantaneous
frequency (in kHz) is _________ (rounded
off to 2 decimal places).
20. In the circuit shown, the clock frequency,
i.e., the frequency of the Clk signal, is 12
kHz. The frequency of the signal at Q2 is
__________ kHz.
7
21. A linear Hamming code is used to map 4-
bit messages to 7-bit codewords. The
encoder mapping is linear. If the message
0001 is mapped to the codeword 0000111,
and the message 0011 is mapped to the
codeword 100110, then the message 0010
is mapped to
A. 1111000 B. 0010011
C. 1111111 D. 1100001
22. Let Z be an exponential random variable
with mean 1. That is, the cumulative
distribution function of Z is given by
( )
1 if 0
0 if 0
?
??? ?
=
?
? ?
?
x
Z
ex
Fx
x
Then Pr(Z > 2 |Z > 1), rounded off to two
decimal places, is equal to __________.
23. Consider the signal f(t) = 1 + 2cos ( ?t) + 3
2
sin 4cos ,
3 2 4
? ? ? ? ? ? ?
++
? ? ? ?
? ? ? ?
tt where t is in
seconds. Its fundamental time period, in
seconds, is ____________.
24. The figure shows the high-frequency C-V
curve of a MOS capacitor (at T = 300 K)
with ?ms = 0 V and no oxide charges. The
flat-band, inversion, and accumulation
conditions are represented, respectively,
by the points
A. Q, R, P B. Q, P, R
C. R, P, Q D. P, Q, R
25. The value of the contour integral
2
11
2 ?
??
+
??
??
?
z dz
jz
evaluated over the unit circle |z| = 1 is
_____________.
26. The state transition diagram for the circuit
shown is
A.
B.
C.
D.
27. In the circuits shown, the threshold voltage
of each nMOS transistor is 0.6 V. Ignoring
the effect of channel length modulation and
body bias, the values of Vout 1 and Vout 2,
respectively, in volts, are
8
A. 2.4 and 2.4 B. 1.8 and 1.2
C. 1.8 and 2.4 D. 2.4 and 1.2
28. The block diagram of a system is illustrated
in the figure shown, where X(s) is the input
and Y(s) is the output. The transfer
function ( )
( )
( )
=
Ys
Hs
Xs
is
A. ( )
2
2
1
21
+
=
+
s
Hs
s
B. ( )
2
32
1
21
+
=
+ + +
s
Hs
s s s
C. ( )
2
1
1
+
=
++
s
Hs
ss
D. ( )
2
32
1
1
+
=
+ + +
s
Hs
s s s
29. A random variable X takes -1 and +1 with
probabilities 0.2 and 0.8, respectively. It is
transmitted across a channel which adds
noise N, so that the random variable at the
channel output is Y = X + N. The noise n is
independent of X, and is uniformly
distributed over the interval [-2, 2]. The
receiver makes a decision
1, if
?
1, if
?
?
?? ?
=
?
+?
?
Y
X
Y
Where the threshold ? ? [-1, 1] is chosen
so as to minimize the probability of error
?
Pr .
??
?
??
XX The minimum probability of
error, rounded off to 1 decimal place, is
______________.
30. A germanium sample of dimensions 1 cm ?
1 cm is illuminated with a 20 mW, 600 nm
laser light source as shown in the figure.
The illuminated sample surface has a 100
nm of loss-less Silicon dioxide layer that
reflects one-fourth of the incident light.
From the remaining light, one-third of the
power is reflected from the Silicon dixodie-
Germanium interface, one-third is
absorbed in the Germanium layer, and
one-third is transmitted through the other
side of the sample. If the absorption
coefficient of Germanium at 600 nm is 3 ?
10
4
cm
-1
and the bandgap is 0.66 eV, the
thickness of the Germanium layer, rounded
off to 3 decimal places, is _________ ?m.
31. In the circuit shown, the threshold voltages
of the pMOS (|Vtp|) and nMOS (Vtn)
transistors are both equal to 1 V. All the
transistors have the same output
resistance rds of 6 M?. The other
parameters are listed below.
2
nMOS
2
ox
pMOS
60 A/V ; 5
30 A/V ; 10
??
??
??
==
??
??
??
==
??
??
n ox
p
W
C
L
W
C
L
?n and ?p are the carrier mobilites, and Cox
is the oxide capacitance per unit area.
Ignoring the effect of channel length
modulation and body bias, the gain of the
circuit is ____________(rounded off to 1
decimal place).
9
32. It is desired to find a three-tap causal filter
which gives zero signal as an output to an
input of the form
12
exp exp ,
22
?? ? ? ? ?
= ? + ??
? ? ? ? ??
? ? ? ?
j n j n
x n c c
where c1 and c2 are arbitrary real numbers.
The desired three-tap filter is given by
h[0] = 1, h[1] = a, h[2] = b
and
h[n] = 0 for n < 0 or n > 2.
What are the values of the filter taps a and
b if the output is y[n] = 0 for all n, when
x[n] is as given above?
A. a = 0, b = -1 B. a = 1, b = 1
C. a = -1, b = 1 D. a = 0, b = 1
33. Consider a long-channel MOSFET with a
channel length 1 ?m and width 10 ?m. The
device parameters are acceptor
concentration NA = 5 ? 10
16
cm
-3
, electron
mobility ?n = 800 cm
2
/V-s, oxide
capacitance/area Cox = 3.45 ? 10
-7
F/cm
2
,
threshold voltage VT = 0.7 V. The drain
saturation current (IDsat) for a gate voltage
of 5 V is ____________ mA (rouonded off
to two decimal places).
[ ?0 = 8.854 ? 10
-14
F/cm, ?si = 11.9]
34. In the circuit shown, V1 = 0 and V2 = Vdd.
The other relevant parameters are
mentioned in the figure. Ignoring the effect
of channel length modulation and the body
effect, the value of Iout is ___________ mA
(rounded off to 1 decimal place).
35. The quantum efficiency ( ?) and
responsivity (R) at wavelength ? (in ?m)
in a p-i-n photodetector are related by
A.
1.24
R
?
?
?
= B. R
1.24
?? ?
=
C.
1.24
R
??
=
?
D. R
1.24
?
?
=
?
36. In the circuit shown, if v(t) = 2 sin (1000 t)
volts, R = 1 k? and C = 1 ?F, then the
steady-state current i(t), in milliamperes
(mA), is
A. sin(1000 t) + cos(1000 t)
B. 2 sin(1000 t) + 2 cos(1000 t)
C. 3 sin(1000 t) + cos(1000 t)
D. sin(1000 t) + 3 cos(1000 t)
37. In the circuit shown, the breakdown
voltage and the maximum current of the
Zener diode are 20 V and 60 mA,
respectively. The values of R1 and RL are
200 ? and 1 k?, respectively. What is the
range of Vi that will maintain the Zener
diode in the ?on? state?
FirstRanker.com - FirstRanker's Choice
2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
4
3. Consider the two-port resistive network
shown in the figure. When an excitation of
5 V is applied across Port 1, and Port 2 is
shorted, the current through the short
circuit at Port 2 is measured to be 1 A (see
(a) in the figure).
Now, if an excitation of 5 V is applied
across Port 2, and Port 1 is shorted (see
(b) in the figure), what is the current
through the short circuit at Port 1?
A. 0.5 A B. 1 A
C. 2 A D. 2.5 A
4. In the circuit shown, what are the values of
F for EN = 0 and EN = 1, respectively?
A. Hi-Z and D B. Hi-Z and D
C. 0 and 1 D. 0 and D
5. The number of distinct eigenvalues of the
matrix
2 2 3 3
0 1 1 1
0 0 3 3
0 0 0 2
A
??
??
??
=
??
??
??
is equal to __________.
6. The families of curves represented by the
solution of the equation
n
dy x
dx y
??
=?
??
??
for n = - 1 and n = + 1, respectively, are
A. Hyperbolas and Circles
B. Circles and Hyperbolas
C. Parabolas and Circles
D. Hyperbolas and Parabolas
7. Let H(z) be the z-transform of a real-
valued discrete-time signal h[n]. If P(z) =
H(z)
1
H
z
??
??
??
has a zero at
11
,
22
zj =+ and
P(z) has a total of four zeros, which one of
the following plots represents all the zeros
correctly?
A.
B.
C.
5
D.
8. The value of the integral
0
sin
,
y
x
dx dy
x
??
??
is equal to __________.
9. Radiation resistance of a small dipole
current element of length l at a frequency
of 3 GHz is 3 ohms. If the length is
changed by 1%, then the percentage
change in the radiation resistance, rounded
off to two decimal places, is _________%.
10. Let Y(s) be the unit-step response of a
causal system having a transfer function
( )
( ) ( )
3
13
s
Gs
ss
?
=
++
that is, ( )
( )
.
Gs
Ys
s
= The forced response
of the system is
A. u(t) ? 2e
-t
u(t) + e
-3t
u(t)
B. u(t)
C. 2u(t) ? 2e
-t
u(t) + e
-3t
u(t)
D. 2u(t)
11. The correct circuit representation of the
structure shown in the figure is
A.
B.
C.
D.
12. What is the electric flux
( )
? E da ?
?
through a
quarter-cylinder of height H (as shown in
the figure) due to an infinitely long line
charge along the axis of the cylinder with a
charge density of Q?
A.
0
4
H
Q
?
B.
0
HQ
?
C.
0
4
HQ
?
D.
0
4H
Q ?
13. In the circuit shown, A and B are the inputs
and F is the output. What is the
functionality of the circuit?
6
A. XOR B. SRAM Cell
C. Latch D. XNOR
14. In the circuit shown, Vs is a square wave of
period T with maximum and minimum
values of 8 V and -10 V, respectively.
Assume that the diode is ideal and R1 = R2
= 50 ?.
The average value of VL is _________ volts
(rounded off to 1 decimal place).
15. If X and Y are random variables such that
E[2X + Y] = 0 and E[X + 2Y] = 33, then
E[X] + E[Y] = _________.
16. A standard CMOS inverter is designed with
equal rise and fall times (?n = ?p). If the
width of the pMOS transistor in the inverter
is increased, what would be the effect on
the LOW noise margin (NML) and the HIGH
noise margin NMH?
A. N ML increases and N MH decreases.
B. Both N ML and N MH increase.
C. N ML decreases and N MH increase.
D. No change in the noise margins.
17. In the table shown, List I and List II,
respectively, contain terms appearing on
the left-hand side and the right-hand side
of Maxwell?s equations (in their standard
form). Match the left-hand side with the
corresponding right-hand side.
List I List II
1 ? . D P 0
2 ? ? E Q ?
3 ? . B R
t
?
?
?
B
4 ? ? H S
D
J
t
?
+
?
A. 1 ? Q, 2 ? R, 3 ? P, 4 ? S
B. 1 ? Q, 2 ? S, 3 ? P, 4 ? R
C. 1 ? R, 2 ? Q, 3 ? S, 4 ? P
D. 1 ? P, 2 ? R, 3 ? Q, 4 ? S
18. For an LTI system, the Bode plot for its
gain is as illustrated in the figure shown.
The number of system poles Np and the
number of system zeros Nz in the
frequency range 1 Hz ? f ? 10
7
Hz is
A. Np = 6, Nz = 3
B. Np = 5, Nz = 2
C. Np = 4, Nz = 2
D. Np = 7, Nz = 4
19. The baseband signal m(t) shown in the
figure is phase-modulated to generate the
PM signal ?(t) = cos (2?fct + k m(t)). The
time t on the x-axis in the figure is in
milliseconds. If the carrier frequency is
fc = 50 kHz and k = 10?, then the ratio of
the minimum instantaneous frequency (in
kHz) to the maximum instantaneous
frequency (in kHz) is _________ (rounded
off to 2 decimal places).
20. In the circuit shown, the clock frequency,
i.e., the frequency of the Clk signal, is 12
kHz. The frequency of the signal at Q2 is
__________ kHz.
7
21. A linear Hamming code is used to map 4-
bit messages to 7-bit codewords. The
encoder mapping is linear. If the message
0001 is mapped to the codeword 0000111,
and the message 0011 is mapped to the
codeword 100110, then the message 0010
is mapped to
A. 1111000 B. 0010011
C. 1111111 D. 1100001
22. Let Z be an exponential random variable
with mean 1. That is, the cumulative
distribution function of Z is given by
( )
1 if 0
0 if 0
?
??? ?
=
?
? ?
?
x
Z
ex
Fx
x
Then Pr(Z > 2 |Z > 1), rounded off to two
decimal places, is equal to __________.
23. Consider the signal f(t) = 1 + 2cos ( ?t) + 3
2
sin 4cos ,
3 2 4
? ? ? ? ? ? ?
++
? ? ? ?
? ? ? ?
tt where t is in
seconds. Its fundamental time period, in
seconds, is ____________.
24. The figure shows the high-frequency C-V
curve of a MOS capacitor (at T = 300 K)
with ?ms = 0 V and no oxide charges. The
flat-band, inversion, and accumulation
conditions are represented, respectively,
by the points
A. Q, R, P B. Q, P, R
C. R, P, Q D. P, Q, R
25. The value of the contour integral
2
11
2 ?
??
+
??
??
?
z dz
jz
evaluated over the unit circle |z| = 1 is
_____________.
26. The state transition diagram for the circuit
shown is
A.
B.
C.
D.
27. In the circuits shown, the threshold voltage
of each nMOS transistor is 0.6 V. Ignoring
the effect of channel length modulation and
body bias, the values of Vout 1 and Vout 2,
respectively, in volts, are
8
A. 2.4 and 2.4 B. 1.8 and 1.2
C. 1.8 and 2.4 D. 2.4 and 1.2
28. The block diagram of a system is illustrated
in the figure shown, where X(s) is the input
and Y(s) is the output. The transfer
function ( )
( )
( )
=
Ys
Hs
Xs
is
A. ( )
2
2
1
21
+
=
+
s
Hs
s
B. ( )
2
32
1
21
+
=
+ + +
s
Hs
s s s
C. ( )
2
1
1
+
=
++
s
Hs
ss
D. ( )
2
32
1
1
+
=
+ + +
s
Hs
s s s
29. A random variable X takes -1 and +1 with
probabilities 0.2 and 0.8, respectively. It is
transmitted across a channel which adds
noise N, so that the random variable at the
channel output is Y = X + N. The noise n is
independent of X, and is uniformly
distributed over the interval [-2, 2]. The
receiver makes a decision
1, if
?
1, if
?
?
?? ?
=
?
+?
?
Y
X
Y
Where the threshold ? ? [-1, 1] is chosen
so as to minimize the probability of error
?
Pr .
??
?
??
XX The minimum probability of
error, rounded off to 1 decimal place, is
______________.
30. A germanium sample of dimensions 1 cm ?
1 cm is illuminated with a 20 mW, 600 nm
laser light source as shown in the figure.
The illuminated sample surface has a 100
nm of loss-less Silicon dioxide layer that
reflects one-fourth of the incident light.
From the remaining light, one-third of the
power is reflected from the Silicon dixodie-
Germanium interface, one-third is
absorbed in the Germanium layer, and
one-third is transmitted through the other
side of the sample. If the absorption
coefficient of Germanium at 600 nm is 3 ?
10
4
cm
-1
and the bandgap is 0.66 eV, the
thickness of the Germanium layer, rounded
off to 3 decimal places, is _________ ?m.
31. In the circuit shown, the threshold voltages
of the pMOS (|Vtp|) and nMOS (Vtn)
transistors are both equal to 1 V. All the
transistors have the same output
resistance rds of 6 M?. The other
parameters are listed below.
2
nMOS
2
ox
pMOS
60 A/V ; 5
30 A/V ; 10
??
??
??
==
??
??
??
==
??
??
n ox
p
W
C
L
W
C
L
?n and ?p are the carrier mobilites, and Cox
is the oxide capacitance per unit area.
Ignoring the effect of channel length
modulation and body bias, the gain of the
circuit is ____________(rounded off to 1
decimal place).
9
32. It is desired to find a three-tap causal filter
which gives zero signal as an output to an
input of the form
12
exp exp ,
22
?? ? ? ? ?
= ? + ??
? ? ? ? ??
? ? ? ?
j n j n
x n c c
where c1 and c2 are arbitrary real numbers.
The desired three-tap filter is given by
h[0] = 1, h[1] = a, h[2] = b
and
h[n] = 0 for n < 0 or n > 2.
What are the values of the filter taps a and
b if the output is y[n] = 0 for all n, when
x[n] is as given above?
A. a = 0, b = -1 B. a = 1, b = 1
C. a = -1, b = 1 D. a = 0, b = 1
33. Consider a long-channel MOSFET with a
channel length 1 ?m and width 10 ?m. The
device parameters are acceptor
concentration NA = 5 ? 10
16
cm
-3
, electron
mobility ?n = 800 cm
2
/V-s, oxide
capacitance/area Cox = 3.45 ? 10
-7
F/cm
2
,
threshold voltage VT = 0.7 V. The drain
saturation current (IDsat) for a gate voltage
of 5 V is ____________ mA (rouonded off
to two decimal places).
[ ?0 = 8.854 ? 10
-14
F/cm, ?si = 11.9]
34. In the circuit shown, V1 = 0 and V2 = Vdd.
The other relevant parameters are
mentioned in the figure. Ignoring the effect
of channel length modulation and the body
effect, the value of Iout is ___________ mA
(rounded off to 1 decimal place).
35. The quantum efficiency ( ?) and
responsivity (R) at wavelength ? (in ?m)
in a p-i-n photodetector are related by
A.
1.24
R
?
?
?
= B. R
1.24
?? ?
=
C.
1.24
R
??
=
?
D. R
1.24
?
?
=
?
36. In the circuit shown, if v(t) = 2 sin (1000 t)
volts, R = 1 k? and C = 1 ?F, then the
steady-state current i(t), in milliamperes
(mA), is
A. sin(1000 t) + cos(1000 t)
B. 2 sin(1000 t) + 2 cos(1000 t)
C. 3 sin(1000 t) + cos(1000 t)
D. sin(1000 t) + 3 cos(1000 t)
37. In the circuit shown, the breakdown
voltage and the maximum current of the
Zener diode are 20 V and 60 mA,
respectively. The values of R1 and RL are
200 ? and 1 k?, respectively. What is the
range of Vi that will maintain the Zener
diode in the ?on? state?
10
A. 18 V to 24 V B. 20 V to 28 V
C. 24 V to 36 V D. 22 V to 34 V
38. Consider a differentiable function f(x) on
the set of real numbers such that f(-1) = 0
and |f?(x)| ? 2. Given these conditions,
which one of the following inequalities is
necessarily true for all x ? [-2, 2]?
A. ( )
1
f x x
2
? B.
( ) f x 2 x 1 ?+
C. ( )
1
f x x 1
2
?+ D.
( ) f x 2 x ?
39. Two identical copper wires W1 and W2,
placed in parallel as shown in the figure,
carry currents I and 2I, respectively, in
opposite directions. If the two wires are
separated by a distance of 4r, then the
magnitude of the magnetic field B between
the wires at a distance r from W1 is
A.
0
6
?
?
I
r
B.
22
0
2
2
?
?
I
r
C.
0
5
6
?
?
I
r
D.
0
6
5
?
?
I
r
40. The dispersion equation of a waveguide,
which relates the wavenumber k to the
frequency ?, is
( ) ( )
22
1/ ? ? ? =?
o
kc
where the speed of light c = 3 ? 10
8
m/s,
and ?o is a constant. If the group velocity
is 2 ? 10
8
m/s, then the phase velocity is
A. 1.5 ? 10
8
m/s B. 2 ? 10
8
m/s
C. 4.5 ? 10
8
m/s D. 3 ? 10
8
m/s
41. Consider a causal second-order system
with the transfer function
( )
2
1
12
=
++
Gs
ss
with a unit-step ( )
1
= Rs
s
as an input. Let
C(s) be the corresponding output. The time
taken by the system output c(t) to reach
94% of its steady-state value
( ) lim
?? t
ct
rounded off to two decimal places, is
A. 4.50 B. 2.81
C. 5.25 D. 3.89
42. Consider a six-point decimation-in-time
Fast Fourier Transform (FFT) algorithm, for
which the signal-flow graph corresponding
to X[1] is shown in the figure. Let
6
2
exp .
6
? ??
=?
??
??
j
W In the figure, what
should be the values of the coefficients a1,
a2, a3 in terms of W6 so that X[1] is
obtained correctly?
A.
2
1 2 6 3 6
1, , = = = a a W a W
B.
2
1 2 6 3 6
1, , = ? = = a a W a W
C.
2
1 2 6 3 6
1, , = = = a a W a W
D.
2
1 2 6 3 6
1, , = ? = = a a W a W
43. Let the state-space representation of an
LTI system be ( ) ( ) ( ), =+ x t Ax t Bu t y(t)
= C x(t) + d u(t) where A, B, C are
matrics, d is a scalar, u(t) is the input to
the system, and y(t) is its output. Let B =
[0 0 1]
T
and d = 0. Which one of the
following options for A and C will ensure
that the transfer function of this LTI
system is
( )
32
1
?
3 2 1
=
+ + +
Hs
s s s
FirstRanker.com - FirstRanker's Choice
2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
4
3. Consider the two-port resistive network
shown in the figure. When an excitation of
5 V is applied across Port 1, and Port 2 is
shorted, the current through the short
circuit at Port 2 is measured to be 1 A (see
(a) in the figure).
Now, if an excitation of 5 V is applied
across Port 2, and Port 1 is shorted (see
(b) in the figure), what is the current
through the short circuit at Port 1?
A. 0.5 A B. 1 A
C. 2 A D. 2.5 A
4. In the circuit shown, what are the values of
F for EN = 0 and EN = 1, respectively?
A. Hi-Z and D B. Hi-Z and D
C. 0 and 1 D. 0 and D
5. The number of distinct eigenvalues of the
matrix
2 2 3 3
0 1 1 1
0 0 3 3
0 0 0 2
A
??
??
??
=
??
??
??
is equal to __________.
6. The families of curves represented by the
solution of the equation
n
dy x
dx y
??
=?
??
??
for n = - 1 and n = + 1, respectively, are
A. Hyperbolas and Circles
B. Circles and Hyperbolas
C. Parabolas and Circles
D. Hyperbolas and Parabolas
7. Let H(z) be the z-transform of a real-
valued discrete-time signal h[n]. If P(z) =
H(z)
1
H
z
??
??
??
has a zero at
11
,
22
zj =+ and
P(z) has a total of four zeros, which one of
the following plots represents all the zeros
correctly?
A.
B.
C.
5
D.
8. The value of the integral
0
sin
,
y
x
dx dy
x
??
??
is equal to __________.
9. Radiation resistance of a small dipole
current element of length l at a frequency
of 3 GHz is 3 ohms. If the length is
changed by 1%, then the percentage
change in the radiation resistance, rounded
off to two decimal places, is _________%.
10. Let Y(s) be the unit-step response of a
causal system having a transfer function
( )
( ) ( )
3
13
s
Gs
ss
?
=
++
that is, ( )
( )
.
Gs
Ys
s
= The forced response
of the system is
A. u(t) ? 2e
-t
u(t) + e
-3t
u(t)
B. u(t)
C. 2u(t) ? 2e
-t
u(t) + e
-3t
u(t)
D. 2u(t)
11. The correct circuit representation of the
structure shown in the figure is
A.
B.
C.
D.
12. What is the electric flux
( )
? E da ?
?
through a
quarter-cylinder of height H (as shown in
the figure) due to an infinitely long line
charge along the axis of the cylinder with a
charge density of Q?
A.
0
4
H
Q
?
B.
0
HQ
?
C.
0
4
HQ
?
D.
0
4H
Q ?
13. In the circuit shown, A and B are the inputs
and F is the output. What is the
functionality of the circuit?
6
A. XOR B. SRAM Cell
C. Latch D. XNOR
14. In the circuit shown, Vs is a square wave of
period T with maximum and minimum
values of 8 V and -10 V, respectively.
Assume that the diode is ideal and R1 = R2
= 50 ?.
The average value of VL is _________ volts
(rounded off to 1 decimal place).
15. If X and Y are random variables such that
E[2X + Y] = 0 and E[X + 2Y] = 33, then
E[X] + E[Y] = _________.
16. A standard CMOS inverter is designed with
equal rise and fall times (?n = ?p). If the
width of the pMOS transistor in the inverter
is increased, what would be the effect on
the LOW noise margin (NML) and the HIGH
noise margin NMH?
A. N ML increases and N MH decreases.
B. Both N ML and N MH increase.
C. N ML decreases and N MH increase.
D. No change in the noise margins.
17. In the table shown, List I and List II,
respectively, contain terms appearing on
the left-hand side and the right-hand side
of Maxwell?s equations (in their standard
form). Match the left-hand side with the
corresponding right-hand side.
List I List II
1 ? . D P 0
2 ? ? E Q ?
3 ? . B R
t
?
?
?
B
4 ? ? H S
D
J
t
?
+
?
A. 1 ? Q, 2 ? R, 3 ? P, 4 ? S
B. 1 ? Q, 2 ? S, 3 ? P, 4 ? R
C. 1 ? R, 2 ? Q, 3 ? S, 4 ? P
D. 1 ? P, 2 ? R, 3 ? Q, 4 ? S
18. For an LTI system, the Bode plot for its
gain is as illustrated in the figure shown.
The number of system poles Np and the
number of system zeros Nz in the
frequency range 1 Hz ? f ? 10
7
Hz is
A. Np = 6, Nz = 3
B. Np = 5, Nz = 2
C. Np = 4, Nz = 2
D. Np = 7, Nz = 4
19. The baseband signal m(t) shown in the
figure is phase-modulated to generate the
PM signal ?(t) = cos (2?fct + k m(t)). The
time t on the x-axis in the figure is in
milliseconds. If the carrier frequency is
fc = 50 kHz and k = 10?, then the ratio of
the minimum instantaneous frequency (in
kHz) to the maximum instantaneous
frequency (in kHz) is _________ (rounded
off to 2 decimal places).
20. In the circuit shown, the clock frequency,
i.e., the frequency of the Clk signal, is 12
kHz. The frequency of the signal at Q2 is
__________ kHz.
7
21. A linear Hamming code is used to map 4-
bit messages to 7-bit codewords. The
encoder mapping is linear. If the message
0001 is mapped to the codeword 0000111,
and the message 0011 is mapped to the
codeword 100110, then the message 0010
is mapped to
A. 1111000 B. 0010011
C. 1111111 D. 1100001
22. Let Z be an exponential random variable
with mean 1. That is, the cumulative
distribution function of Z is given by
( )
1 if 0
0 if 0
?
??? ?
=
?
? ?
?
x
Z
ex
Fx
x
Then Pr(Z > 2 |Z > 1), rounded off to two
decimal places, is equal to __________.
23. Consider the signal f(t) = 1 + 2cos ( ?t) + 3
2
sin 4cos ,
3 2 4
? ? ? ? ? ? ?
++
? ? ? ?
? ? ? ?
tt where t is in
seconds. Its fundamental time period, in
seconds, is ____________.
24. The figure shows the high-frequency C-V
curve of a MOS capacitor (at T = 300 K)
with ?ms = 0 V and no oxide charges. The
flat-band, inversion, and accumulation
conditions are represented, respectively,
by the points
A. Q, R, P B. Q, P, R
C. R, P, Q D. P, Q, R
25. The value of the contour integral
2
11
2 ?
??
+
??
??
?
z dz
jz
evaluated over the unit circle |z| = 1 is
_____________.
26. The state transition diagram for the circuit
shown is
A.
B.
C.
D.
27. In the circuits shown, the threshold voltage
of each nMOS transistor is 0.6 V. Ignoring
the effect of channel length modulation and
body bias, the values of Vout 1 and Vout 2,
respectively, in volts, are
8
A. 2.4 and 2.4 B. 1.8 and 1.2
C. 1.8 and 2.4 D. 2.4 and 1.2
28. The block diagram of a system is illustrated
in the figure shown, where X(s) is the input
and Y(s) is the output. The transfer
function ( )
( )
( )
=
Ys
Hs
Xs
is
A. ( )
2
2
1
21
+
=
+
s
Hs
s
B. ( )
2
32
1
21
+
=
+ + +
s
Hs
s s s
C. ( )
2
1
1
+
=
++
s
Hs
ss
D. ( )
2
32
1
1
+
=
+ + +
s
Hs
s s s
29. A random variable X takes -1 and +1 with
probabilities 0.2 and 0.8, respectively. It is
transmitted across a channel which adds
noise N, so that the random variable at the
channel output is Y = X + N. The noise n is
independent of X, and is uniformly
distributed over the interval [-2, 2]. The
receiver makes a decision
1, if
?
1, if
?
?
?? ?
=
?
+?
?
Y
X
Y
Where the threshold ? ? [-1, 1] is chosen
so as to minimize the probability of error
?
Pr .
??
?
??
XX The minimum probability of
error, rounded off to 1 decimal place, is
______________.
30. A germanium sample of dimensions 1 cm ?
1 cm is illuminated with a 20 mW, 600 nm
laser light source as shown in the figure.
The illuminated sample surface has a 100
nm of loss-less Silicon dioxide layer that
reflects one-fourth of the incident light.
From the remaining light, one-third of the
power is reflected from the Silicon dixodie-
Germanium interface, one-third is
absorbed in the Germanium layer, and
one-third is transmitted through the other
side of the sample. If the absorption
coefficient of Germanium at 600 nm is 3 ?
10
4
cm
-1
and the bandgap is 0.66 eV, the
thickness of the Germanium layer, rounded
off to 3 decimal places, is _________ ?m.
31. In the circuit shown, the threshold voltages
of the pMOS (|Vtp|) and nMOS (Vtn)
transistors are both equal to 1 V. All the
transistors have the same output
resistance rds of 6 M?. The other
parameters are listed below.
2
nMOS
2
ox
pMOS
60 A/V ; 5
30 A/V ; 10
??
??
??
==
??
??
??
==
??
??
n ox
p
W
C
L
W
C
L
?n and ?p are the carrier mobilites, and Cox
is the oxide capacitance per unit area.
Ignoring the effect of channel length
modulation and body bias, the gain of the
circuit is ____________(rounded off to 1
decimal place).
9
32. It is desired to find a three-tap causal filter
which gives zero signal as an output to an
input of the form
12
exp exp ,
22
?? ? ? ? ?
= ? + ??
? ? ? ? ??
? ? ? ?
j n j n
x n c c
where c1 and c2 are arbitrary real numbers.
The desired three-tap filter is given by
h[0] = 1, h[1] = a, h[2] = b
and
h[n] = 0 for n < 0 or n > 2.
What are the values of the filter taps a and
b if the output is y[n] = 0 for all n, when
x[n] is as given above?
A. a = 0, b = -1 B. a = 1, b = 1
C. a = -1, b = 1 D. a = 0, b = 1
33. Consider a long-channel MOSFET with a
channel length 1 ?m and width 10 ?m. The
device parameters are acceptor
concentration NA = 5 ? 10
16
cm
-3
, electron
mobility ?n = 800 cm
2
/V-s, oxide
capacitance/area Cox = 3.45 ? 10
-7
F/cm
2
,
threshold voltage VT = 0.7 V. The drain
saturation current (IDsat) for a gate voltage
of 5 V is ____________ mA (rouonded off
to two decimal places).
[ ?0 = 8.854 ? 10
-14
F/cm, ?si = 11.9]
34. In the circuit shown, V1 = 0 and V2 = Vdd.
The other relevant parameters are
mentioned in the figure. Ignoring the effect
of channel length modulation and the body
effect, the value of Iout is ___________ mA
(rounded off to 1 decimal place).
35. The quantum efficiency ( ?) and
responsivity (R) at wavelength ? (in ?m)
in a p-i-n photodetector are related by
A.
1.24
R
?
?
?
= B. R
1.24
?? ?
=
C.
1.24
R
??
=
?
D. R
1.24
?
?
=
?
36. In the circuit shown, if v(t) = 2 sin (1000 t)
volts, R = 1 k? and C = 1 ?F, then the
steady-state current i(t), in milliamperes
(mA), is
A. sin(1000 t) + cos(1000 t)
B. 2 sin(1000 t) + 2 cos(1000 t)
C. 3 sin(1000 t) + cos(1000 t)
D. sin(1000 t) + 3 cos(1000 t)
37. In the circuit shown, the breakdown
voltage and the maximum current of the
Zener diode are 20 V and 60 mA,
respectively. The values of R1 and RL are
200 ? and 1 k?, respectively. What is the
range of Vi that will maintain the Zener
diode in the ?on? state?
10
A. 18 V to 24 V B. 20 V to 28 V
C. 24 V to 36 V D. 22 V to 34 V
38. Consider a differentiable function f(x) on
the set of real numbers such that f(-1) = 0
and |f?(x)| ? 2. Given these conditions,
which one of the following inequalities is
necessarily true for all x ? [-2, 2]?
A. ( )
1
f x x
2
? B.
( ) f x 2 x 1 ?+
C. ( )
1
f x x 1
2
?+ D.
( ) f x 2 x ?
39. Two identical copper wires W1 and W2,
placed in parallel as shown in the figure,
carry currents I and 2I, respectively, in
opposite directions. If the two wires are
separated by a distance of 4r, then the
magnitude of the magnetic field B between
the wires at a distance r from W1 is
A.
0
6
?
?
I
r
B.
22
0
2
2
?
?
I
r
C.
0
5
6
?
?
I
r
D.
0
6
5
?
?
I
r
40. The dispersion equation of a waveguide,
which relates the wavenumber k to the
frequency ?, is
( ) ( )
22
1/ ? ? ? =?
o
kc
where the speed of light c = 3 ? 10
8
m/s,
and ?o is a constant. If the group velocity
is 2 ? 10
8
m/s, then the phase velocity is
A. 1.5 ? 10
8
m/s B. 2 ? 10
8
m/s
C. 4.5 ? 10
8
m/s D. 3 ? 10
8
m/s
41. Consider a causal second-order system
with the transfer function
( )
2
1
12
=
++
Gs
ss
with a unit-step ( )
1
= Rs
s
as an input. Let
C(s) be the corresponding output. The time
taken by the system output c(t) to reach
94% of its steady-state value
( ) lim
?? t
ct
rounded off to two decimal places, is
A. 4.50 B. 2.81
C. 5.25 D. 3.89
42. Consider a six-point decimation-in-time
Fast Fourier Transform (FFT) algorithm, for
which the signal-flow graph corresponding
to X[1] is shown in the figure. Let
6
2
exp .
6
? ??
=?
??
??
j
W In the figure, what
should be the values of the coefficients a1,
a2, a3 in terms of W6 so that X[1] is
obtained correctly?
A.
2
1 2 6 3 6
1, , = = = a a W a W
B.
2
1 2 6 3 6
1, , = ? = = a a W a W
C.
2
1 2 6 3 6
1, , = = = a a W a W
D.
2
1 2 6 3 6
1, , = ? = = a a W a W
43. Let the state-space representation of an
LTI system be ( ) ( ) ( ), =+ x t Ax t Bu t y(t)
= C x(t) + d u(t) where A, B, C are
matrics, d is a scalar, u(t) is the input to
the system, and y(t) is its output. Let B =
[0 0 1]
T
and d = 0. Which one of the
following options for A and C will ensure
that the transfer function of this LTI
system is
( )
32
1
?
3 2 1
=
+ + +
Hs
s s s
11
A.
0 1 0
0 0 1
1 2 3
=
? ? ?
A and C = [1 0 0]
B.
0 1 0
0 0 1
1 2 3
=
? ? ?
A and C = [0 0 1]
C.
010
0 0 1
3 2 1
=
? ? ?
A and C = [0 0 1]
D.
010
0 0 1
3 2 1
=
? ? ?
A and C = [1 0 0]
44. A CMOS inverter, designed to have a mid-
point voltage VI equal to half of Vdd, as
shown in the figure, has the following
parameters :
Vdd = 3 V
?nCox = 100 ?A/V
2
; Vtn = 0.7 V for nMOS
?nCox = 40 ?A/V
2
; |Vtp| = 0.9 V for pMOS
The ratio of
??
??
??
n
W
L
to
??
??
??
p
W
L
is equal to
__________ (rounded off to 3 decimal
places).
45. A rectangular waveguide of width w and
height h has cut-off frequencies for TE10
and TE11 modes in the ratio 1 : 2. The
aspect ratio w/h, rounded off to two
decimal places, is ____________.
46. Let a random process Y(t) be described as
Y(t) = h(t) * X(t) + Z(t), where X(t) is a
white noise process with power spectral
density SX(f) = 5 W/Hz. The filter h(t) has
a magnitude response given by |H(f)| =
0.5 for -5 ? f ? 5, and zero elsewhere. Z(t)
is a stationary random process,
uncorrelated with X(t), with power spectral
density as shown in the figure. The power
in Y(t), in watts, is equal to _________ W
(rounded off to two decimal places).
47. Let h[n] be a length-7 discrete-time finite
impulse response filter, given by
h[0] = 4, h[1] = 3, h[2] = 2, h[3] = 1,
h[-1] = - 3, h[-2] = -2, h[-3] = -1,
and h[n] is zero for [n] ? 4. A length-3
finite impulse response approximation g[n]
of h[n] has to be obtained such that
( ) ( ) ( )
2
,
?
??
?
?
?
=?
?
jj
E h g H e G e d
is minimized, where H(e
j?
) and (e
j?
) are
the discrete-time Fourier transforms of
h[n] and g[n], respectively. For the filter
that minimizes E(h, g), the value of
10 g[-1] + g[1], rounded off to 2 decimal
places, is ____________.
48. In an ideal pn junction with an ideality
factor of 1 at T = 300 Km the magnitude of
the reverse-bias voltage required to reach
75% of its reverse saturation current,
rounded off to 2 decimal places, is
__________ mV.
[k = 1.38 ? 10
-23
JK
-1
, h = 6.625 ? 10
-34
J-
s, q = 1.602 ? 10
-19
C]
49. Consider the homogeneous ordinary
differential equation
2
2
2
3 3 0, 0 ? + = ?
d y dy
x x y x
dx dx
with y(x) as a general solution. Given that
y(1) = 1 and y(2) = 14 the value of y(1.5),
rounded off to two decimal places, is
_______________.
50. The RC circuit shown below has a variable
resistance R(t) given by the following
expression :
( )
0
1
??
=?
??
??
t
R t R
T
for 0 ? t < T
where R0 = 1 ?, and C = 1 F. We are also
given that T = 3 R0C and the source
voltage is Vs = 1 V. If the current at time
t = 0 is 1 A, then the current I(t), in
FirstRanker.com - FirstRanker's Choice
2
1. The strategies that the company ________
to sell its products _________ house-to-
house marketing.
A. uses, include B. used, includes
C. uses, including D. use, includes
2. The boat arrived _______ dawn.
A. under B. in
C. on D. at
3. Five different books (P, Q, S, R, T) are to
be arranged on a shelf. The books R and S
are to be arranged first and second,
respectively from the right side of the
shelf. The number of different orders in
which P, Q and T may be arranged is
___________.
A. 12 B. 120
C. 6 D. 2
4. When he did not come home, she _______
him lying dead on the roadside
somewhere.
A. concluded B. looked
C. notice D. pictured
5. It would take one machine 4 hours to
complete a production order and another
machine 2 hours to complete the same
order. If both machines work
simultaneously at their respective constant
rates, the time taken to complete the same
order is __________ hours.
A. 2/3 B. ?
C. 4/3 D. 7/3
6. The bar graph in Panel (a) shows the
proportion of male and female iliterates in
2001 and 2011. The proportions of males
and females in 2001 and 2011 are given in
Panel (b) and (c), respectively. The total
population did not change during this
period.
The percentage increase in the total
number of litertes from 2001 to 2011 is
___________.
A. 34.43 B. 35.43
C. 30.43 D. 33.43
7. Four people are standing in a line facing
you. They are Rahul, Mathew, Seema and
Lohit. One is an engineer, one is a doctor,
one a teacher and another a dancer. You
are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between
Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are
standing next to each other
5. Seema is turning to her right to speak
to the doctor standing next to her
Who among them is an engineer?
A. Seema B. Rahul
C. Lohit D. Mathew
8. ?Indian history was written by British
historians ? extremely well documented
and researched, but not always impartial.
History had to serve its purpose:
Everything was made subservient to the
glory of the Union Jack. Latter-day Indian
scholars presented a contrary picture.?
From the text above, we can infer that :
Indian history written by British historians
_________
A. was not well documented and
researched and was always biased
B. was not well documented and
researched and was sometimes biased
C. was well documented and researched
but was sometimes biased
D. was well documented and not
researched but was always biased
9. Two design consultants, P and Q started
working from 8 AM for a client. The client
budgeted a total of USD 3000 for the
consultants. P stopped working when the
hour hand moved by 210 degrees on the
clock. Q stopped working when the hour
hand moved by 240 degrees. P took two
tea breaks of 15 minutes each during her
shift, but took no lunch break. Q took only
3
one lunch break for 20 minutes, but no tea
breaks. The market rate for consultants is
USD 200 per hour and breaks are not paid.
After paying the consultants, the client
shall have USD ________ remaining in the
budget.
A. 000.00 B. 166.67
C. 300.00 D. 433.33
10. Five people P, Q, R, S and T work in a
bank. P and Q don?t like each other but
have to share an office till T gets a
promotion and moves to the big office next
to the garden. R, who is currently sharing
an office with T wants to move to the
adjacent office with S, the handsome new
intern. Given the floor plan, what is the
current location of Q, R and T?
(O = Office, WR = Washroom)
A.
B.
C.
D.
Section : EC ELECTRONICS AND COMMUNCIATION ENGINEERING
1. Which one of the following functions is
analystic over the entire complex plane?
A. e
1/z
B. In(z)
C.
1
1 z ?
D. cos (z)
2. Which one of the following options
describes correctly the equilibrium band
diagram at T = 300 K of a Silicon pnn
+
p
++
configuration shown in the figure?
A.
B.
C.
D.
4
3. Consider the two-port resistive network
shown in the figure. When an excitation of
5 V is applied across Port 1, and Port 2 is
shorted, the current through the short
circuit at Port 2 is measured to be 1 A (see
(a) in the figure).
Now, if an excitation of 5 V is applied
across Port 2, and Port 1 is shorted (see
(b) in the figure), what is the current
through the short circuit at Port 1?
A. 0.5 A B. 1 A
C. 2 A D. 2.5 A
4. In the circuit shown, what are the values of
F for EN = 0 and EN = 1, respectively?
A. Hi-Z and D B. Hi-Z and D
C. 0 and 1 D. 0 and D
5. The number of distinct eigenvalues of the
matrix
2 2 3 3
0 1 1 1
0 0 3 3
0 0 0 2
A
??
??
??
=
??
??
??
is equal to __________.
6. The families of curves represented by the
solution of the equation
n
dy x
dx y
??
=?
??
??
for n = - 1 and n = + 1, respectively, are
A. Hyperbolas and Circles
B. Circles and Hyperbolas
C. Parabolas and Circles
D. Hyperbolas and Parabolas
7. Let H(z) be the z-transform of a real-
valued discrete-time signal h[n]. If P(z) =
H(z)
1
H
z
??
??
??
has a zero at
11
,
22
zj =+ and
P(z) has a total of four zeros, which one of
the following plots represents all the zeros
correctly?
A.
B.
C.
5
D.
8. The value of the integral
0
sin
,
y
x
dx dy
x
??
??
is equal to __________.
9. Radiation resistance of a small dipole
current element of length l at a frequency
of 3 GHz is 3 ohms. If the length is
changed by 1%, then the percentage
change in the radiation resistance, rounded
off to two decimal places, is _________%.
10. Let Y(s) be the unit-step response of a
causal system having a transfer function
( )
( ) ( )
3
13
s
Gs
ss
?
=
++
that is, ( )
( )
.
Gs
Ys
s
= The forced response
of the system is
A. u(t) ? 2e
-t
u(t) + e
-3t
u(t)
B. u(t)
C. 2u(t) ? 2e
-t
u(t) + e
-3t
u(t)
D. 2u(t)
11. The correct circuit representation of the
structure shown in the figure is
A.
B.
C.
D.
12. What is the electric flux
( )
? E da ?
?
through a
quarter-cylinder of height H (as shown in
the figure) due to an infinitely long line
charge along the axis of the cylinder with a
charge density of Q?
A.
0
4
H
Q
?
B.
0
HQ
?
C.
0
4
HQ
?
D.
0
4H
Q ?
13. In the circuit shown, A and B are the inputs
and F is the output. What is the
functionality of the circuit?
6
A. XOR B. SRAM Cell
C. Latch D. XNOR
14. In the circuit shown, Vs is a square wave of
period T with maximum and minimum
values of 8 V and -10 V, respectively.
Assume that the diode is ideal and R1 = R2
= 50 ?.
The average value of VL is _________ volts
(rounded off to 1 decimal place).
15. If X and Y are random variables such that
E[2X + Y] = 0 and E[X + 2Y] = 33, then
E[X] + E[Y] = _________.
16. A standard CMOS inverter is designed with
equal rise and fall times (?n = ?p). If the
width of the pMOS transistor in the inverter
is increased, what would be the effect on
the LOW noise margin (NML) and the HIGH
noise margin NMH?
A. N ML increases and N MH decreases.
B. Both N ML and N MH increase.
C. N ML decreases and N MH increase.
D. No change in the noise margins.
17. In the table shown, List I and List II,
respectively, contain terms appearing on
the left-hand side and the right-hand side
of Maxwell?s equations (in their standard
form). Match the left-hand side with the
corresponding right-hand side.
List I List II
1 ? . D P 0
2 ? ? E Q ?
3 ? . B R
t
?
?
?
B
4 ? ? H S
D
J
t
?
+
?
A. 1 ? Q, 2 ? R, 3 ? P, 4 ? S
B. 1 ? Q, 2 ? S, 3 ? P, 4 ? R
C. 1 ? R, 2 ? Q, 3 ? S, 4 ? P
D. 1 ? P, 2 ? R, 3 ? Q, 4 ? S
18. For an LTI system, the Bode plot for its
gain is as illustrated in the figure shown.
The number of system poles Np and the
number of system zeros Nz in the
frequency range 1 Hz ? f ? 10
7
Hz is
A. Np = 6, Nz = 3
B. Np = 5, Nz = 2
C. Np = 4, Nz = 2
D. Np = 7, Nz = 4
19. The baseband signal m(t) shown in the
figure is phase-modulated to generate the
PM signal ?(t) = cos (2?fct + k m(t)). The
time t on the x-axis in the figure is in
milliseconds. If the carrier frequency is
fc = 50 kHz and k = 10?, then the ratio of
the minimum instantaneous frequency (in
kHz) to the maximum instantaneous
frequency (in kHz) is _________ (rounded
off to 2 decimal places).
20. In the circuit shown, the clock frequency,
i.e., the frequency of the Clk signal, is 12
kHz. The frequency of the signal at Q2 is
__________ kHz.
7
21. A linear Hamming code is used to map 4-
bit messages to 7-bit codewords. The
encoder mapping is linear. If the message
0001 is mapped to the codeword 0000111,
and the message 0011 is mapped to the
codeword 100110, then the message 0010
is mapped to
A. 1111000 B. 0010011
C. 1111111 D. 1100001
22. Let Z be an exponential random variable
with mean 1. That is, the cumulative
distribution function of Z is given by
( )
1 if 0
0 if 0
?
??? ?
=
?
? ?
?
x
Z
ex
Fx
x
Then Pr(Z > 2 |Z > 1), rounded off to two
decimal places, is equal to __________.
23. Consider the signal f(t) = 1 + 2cos ( ?t) + 3
2
sin 4cos ,
3 2 4
? ? ? ? ? ? ?
++
? ? ? ?
? ? ? ?
tt where t is in
seconds. Its fundamental time period, in
seconds, is ____________.
24. The figure shows the high-frequency C-V
curve of a MOS capacitor (at T = 300 K)
with ?ms = 0 V and no oxide charges. The
flat-band, inversion, and accumulation
conditions are represented, respectively,
by the points
A. Q, R, P B. Q, P, R
C. R, P, Q D. P, Q, R
25. The value of the contour integral
2
11
2 ?
??
+
??
??
?
z dz
jz
evaluated over the unit circle |z| = 1 is
_____________.
26. The state transition diagram for the circuit
shown is
A.
B.
C.
D.
27. In the circuits shown, the threshold voltage
of each nMOS transistor is 0.6 V. Ignoring
the effect of channel length modulation and
body bias, the values of Vout 1 and Vout 2,
respectively, in volts, are
8
A. 2.4 and 2.4 B. 1.8 and 1.2
C. 1.8 and 2.4 D. 2.4 and 1.2
28. The block diagram of a system is illustrated
in the figure shown, where X(s) is the input
and Y(s) is the output. The transfer
function ( )
( )
( )
=
Ys
Hs
Xs
is
A. ( )
2
2
1
21
+
=
+
s
Hs
s
B. ( )
2
32
1
21
+
=
+ + +
s
Hs
s s s
C. ( )
2
1
1
+
=
++
s
Hs
ss
D. ( )
2
32
1
1
+
=
+ + +
s
Hs
s s s
29. A random variable X takes -1 and +1 with
probabilities 0.2 and 0.8, respectively. It is
transmitted across a channel which adds
noise N, so that the random variable at the
channel output is Y = X + N. The noise n is
independent of X, and is uniformly
distributed over the interval [-2, 2]. The
receiver makes a decision
1, if
?
1, if
?
?
?? ?
=
?
+?
?
Y
X
Y
Where the threshold ? ? [-1, 1] is chosen
so as to minimize the probability of error
?
Pr .
??
?
??
XX The minimum probability of
error, rounded off to 1 decimal place, is
______________.
30. A germanium sample of dimensions 1 cm ?
1 cm is illuminated with a 20 mW, 600 nm
laser light source as shown in the figure.
The illuminated sample surface has a 100
nm of loss-less Silicon dioxide layer that
reflects one-fourth of the incident light.
From the remaining light, one-third of the
power is reflected from the Silicon dixodie-
Germanium interface, one-third is
absorbed in the Germanium layer, and
one-third is transmitted through the other
side of the sample. If the absorption
coefficient of Germanium at 600 nm is 3 ?
10
4
cm
-1
and the bandgap is 0.66 eV, the
thickness of the Germanium layer, rounded
off to 3 decimal places, is _________ ?m.
31. In the circuit shown, the threshold voltages
of the pMOS (|Vtp|) and nMOS (Vtn)
transistors are both equal to 1 V. All the
transistors have the same output
resistance rds of 6 M?. The other
parameters are listed below.
2
nMOS
2
ox
pMOS
60 A/V ; 5
30 A/V ; 10
??
??
??
==
??
??
??
==
??
??
n ox
p
W
C
L
W
C
L
?n and ?p are the carrier mobilites, and Cox
is the oxide capacitance per unit area.
Ignoring the effect of channel length
modulation and body bias, the gain of the
circuit is ____________(rounded off to 1
decimal place).
9
32. It is desired to find a three-tap causal filter
which gives zero signal as an output to an
input of the form
12
exp exp ,
22
?? ? ? ? ?
= ? + ??
? ? ? ? ??
? ? ? ?
j n j n
x n c c
where c1 and c2 are arbitrary real numbers.
The desired three-tap filter is given by
h[0] = 1, h[1] = a, h[2] = b
and
h[n] = 0 for n < 0 or n > 2.
What are the values of the filter taps a and
b if the output is y[n] = 0 for all n, when
x[n] is as given above?
A. a = 0, b = -1 B. a = 1, b = 1
C. a = -1, b = 1 D. a = 0, b = 1
33. Consider a long-channel MOSFET with a
channel length 1 ?m and width 10 ?m. The
device parameters are acceptor
concentration NA = 5 ? 10
16
cm
-3
, electron
mobility ?n = 800 cm
2
/V-s, oxide
capacitance/area Cox = 3.45 ? 10
-7
F/cm
2
,
threshold voltage VT = 0.7 V. The drain
saturation current (IDsat) for a gate voltage
of 5 V is ____________ mA (rouonded off
to two decimal places).
[ ?0 = 8.854 ? 10
-14
F/cm, ?si = 11.9]
34. In the circuit shown, V1 = 0 and V2 = Vdd.
The other relevant parameters are
mentioned in the figure. Ignoring the effect
of channel length modulation and the body
effect, the value of Iout is ___________ mA
(rounded off to 1 decimal place).
35. The quantum efficiency ( ?) and
responsivity (R) at wavelength ? (in ?m)
in a p-i-n photodetector are related by
A.
1.24
R
?
?
?
= B. R
1.24
?? ?
=
C.
1.24
R
??
=
?
D. R
1.24
?
?
=
?
36. In the circuit shown, if v(t) = 2 sin (1000 t)
volts, R = 1 k? and C = 1 ?F, then the
steady-state current i(t), in milliamperes
(mA), is
A. sin(1000 t) + cos(1000 t)
B. 2 sin(1000 t) + 2 cos(1000 t)
C. 3 sin(1000 t) + cos(1000 t)
D. sin(1000 t) + 3 cos(1000 t)
37. In the circuit shown, the breakdown
voltage and the maximum current of the
Zener diode are 20 V and 60 mA,
respectively. The values of R1 and RL are
200 ? and 1 k?, respectively. What is the
range of Vi that will maintain the Zener
diode in the ?on? state?
10
A. 18 V to 24 V B. 20 V to 28 V
C. 24 V to 36 V D. 22 V to 34 V
38. Consider a differentiable function f(x) on
the set of real numbers such that f(-1) = 0
and |f?(x)| ? 2. Given these conditions,
which one of the following inequalities is
necessarily true for all x ? [-2, 2]?
A. ( )
1
f x x
2
? B.
( ) f x 2 x 1 ?+
C. ( )
1
f x x 1
2
?+ D.
( ) f x 2 x ?
39. Two identical copper wires W1 and W2,
placed in parallel as shown in the figure,
carry currents I and 2I, respectively, in
opposite directions. If the two wires are
separated by a distance of 4r, then the
magnitude of the magnetic field B between
the wires at a distance r from W1 is
A.
0
6
?
?
I
r
B.
22
0
2
2
?
?
I
r
C.
0
5
6
?
?
I
r
D.
0
6
5
?
?
I
r
40. The dispersion equation of a waveguide,
which relates the wavenumber k to the
frequency ?, is
( ) ( )
22
1/ ? ? ? =?
o
kc
where the speed of light c = 3 ? 10
8
m/s,
and ?o is a constant. If the group velocity
is 2 ? 10
8
m/s, then the phase velocity is
A. 1.5 ? 10
8
m/s B. 2 ? 10
8
m/s
C. 4.5 ? 10
8
m/s D. 3 ? 10
8
m/s
41. Consider a causal second-order system
with the transfer function
( )
2
1
12
=
++
Gs
ss
with a unit-step ( )
1
= Rs
s
as an input. Let
C(s) be the corresponding output. The time
taken by the system output c(t) to reach
94% of its steady-state value
( ) lim
?? t
ct
rounded off to two decimal places, is
A. 4.50 B. 2.81
C. 5.25 D. 3.89
42. Consider a six-point decimation-in-time
Fast Fourier Transform (FFT) algorithm, for
which the signal-flow graph corresponding
to X[1] is shown in the figure. Let
6
2
exp .
6
? ??
=?
??
??
j
W In the figure, what
should be the values of the coefficients a1,
a2, a3 in terms of W6 so that X[1] is
obtained correctly?
A.
2
1 2 6 3 6
1, , = = = a a W a W
B.
2
1 2 6 3 6
1, , = ? = = a a W a W
C.
2
1 2 6 3 6
1, , = = = a a W a W
D.
2
1 2 6 3 6
1, , = ? = = a a W a W
43. Let the state-space representation of an
LTI system be ( ) ( ) ( ), =+ x t Ax t Bu t y(t)
= C x(t) + d u(t) where A, B, C are
matrics, d is a scalar, u(t) is the input to
the system, and y(t) is its output. Let B =
[0 0 1]
T
and d = 0. Which one of the
following options for A and C will ensure
that the transfer function of this LTI
system is
( )
32
1
?
3 2 1
=
+ + +
Hs
s s s
11
A.
0 1 0
0 0 1
1 2 3
=
? ? ?
A and C = [1 0 0]
B.
0 1 0
0 0 1
1 2 3
=
? ? ?
A and C = [0 0 1]
C.
010
0 0 1
3 2 1
=
? ? ?
A and C = [0 0 1]
D.
010
0 0 1
3 2 1
=
? ? ?
A and C = [1 0 0]
44. A CMOS inverter, designed to have a mid-
point voltage VI equal to half of Vdd, as
shown in the figure, has the following
parameters :
Vdd = 3 V
?nCox = 100 ?A/V
2
; Vtn = 0.7 V for nMOS
?nCox = 40 ?A/V
2
; |Vtp| = 0.9 V for pMOS
The ratio of
??
??
??
n
W
L
to
??
??
??
p
W
L
is equal to
__________ (rounded off to 3 decimal
places).
45. A rectangular waveguide of width w and
height h has cut-off frequencies for TE10
and TE11 modes in the ratio 1 : 2. The
aspect ratio w/h, rounded off to two
decimal places, is ____________.
46. Let a random process Y(t) be described as
Y(t) = h(t) * X(t) + Z(t), where X(t) is a
white noise process with power spectral
density SX(f) = 5 W/Hz. The filter h(t) has
a magnitude response given by |H(f)| =
0.5 for -5 ? f ? 5, and zero elsewhere. Z(t)
is a stationary random process,
uncorrelated with X(t), with power spectral
density as shown in the figure. The power
in Y(t), in watts, is equal to _________ W
(rounded off to two decimal places).
47. Let h[n] be a length-7 discrete-time finite
impulse response filter, given by
h[0] = 4, h[1] = 3, h[2] = 2, h[3] = 1,
h[-1] = - 3, h[-2] = -2, h[-3] = -1,
and h[n] is zero for [n] ? 4. A length-3
finite impulse response approximation g[n]
of h[n] has to be obtained such that
( ) ( ) ( )
2
,
?
??
?
?
?
=?
?
jj
E h g H e G e d
is minimized, where H(e
j?
) and (e
j?
) are
the discrete-time Fourier transforms of
h[n] and g[n], respectively. For the filter
that minimizes E(h, g), the value of
10 g[-1] + g[1], rounded off to 2 decimal
places, is ____________.
48. In an ideal pn junction with an ideality
factor of 1 at T = 300 Km the magnitude of
the reverse-bias voltage required to reach
75% of its reverse saturation current,
rounded off to 2 decimal places, is
__________ mV.
[k = 1.38 ? 10
-23
JK
-1
, h = 6.625 ? 10
-34
J-
s, q = 1.602 ? 10
-19
C]
49. Consider the homogeneous ordinary
differential equation
2
2
2
3 3 0, 0 ? + = ?
d y dy
x x y x
dx dx
with y(x) as a general solution. Given that
y(1) = 1 and y(2) = 14 the value of y(1.5),
rounded off to two decimal places, is
_______________.
50. The RC circuit shown below has a variable
resistance R(t) given by the following
expression :
( )
0
1
??
=?
??
??
t
R t R
T
for 0 ? t < T
where R0 = 1 ?, and C = 1 F. We are also
given that T = 3 R0C and the source
voltage is Vs = 1 V. If the current at time
t = 0 is 1 A, then the current I(t), in
12
amperes, at time t = T/2 is __________
(rounded off to 2 decimal places).
51. In the circuit shown, Vs is a 10 V square
wave of period, T = 4 ms with R = 500 ?
and C = 10 ?F. The capacitor is initially
uncharged at t = 0, and the diode is
assumed to be ideal. The voltage across
the capacitor (Vc) at 3 ms is equal to
________ volts (rounded off to one
decimal place).
52. Consider the line integral
( )
C
xdy ydx ?
?
the integral being taken in a counterclock-
wise direction over the closed curve C that
forms the boundary of the region R shown
in figure below. The region R is the area
enclosed by the union of a 2 ? 3 rectangle
and a semi-circle of radius 1. The line
integral evaluates to
A. 16 + 2 ? B. 8 + ?
C. 12 + 8 ? D. 6 + ?/2
53. Consider a unity feedback system, as in
the figure shown, with an integral
compensator and open-loop transfer
function
( )
2
1
32
Gs
ss
=
++
Where K > 0. The positive value of K for
which there are exactly two poles of the
unity feedback system on the j? axis is
equal to ___________ (rounded off to two
decimal places).
54. A voice signal m(t) is in the frequency
range 5 kHz to 15 kHz. The signal is
amplitude-modulated to generate an AM
signal f(t) = A(1 + m(t)) cos 2 ?fct, where fc
= 600 kHz. The AM signal f(t) is to be
digitized and archived. This is done by first
sampling f(t) at 1.2 times the Nyquist
frequency, and then quantizing each
sample using a 256-level quantizer. Finally,
each quantized sample is binary coded
using K bits, where K is the minimum
number of bits required for the encoding.
The rate, in Megabits per second (rounded
off to 2 decimal places), of the resulting
stream of coded bits is _________ Mbps.
55. A single bit, equally likely to be 0 and 1, is
to be sent across an additive white
Gaussian noise (AWGN) channel with
power spectral density N0/2. Binary
signaling, with 0 ? p(t) and 1 ? q(t), is
used for the transmission, along with an
optimal receiver that minimizes the bit-
error probability.
Let ?1(t), ?2(t) form an orthonormal signal
set.
If we choose p(t) = ?1(t) and q(t) = -
?1(t), we would obtain a certain bit-error
probability Pb.
If we keep p(t) = ?1(t), but take q(t) = ?E
?2(t), for what value of E would we obtain
the same bit-error probability Pb?
A. 3 B. 2
C. 0 D. 1
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This post was last modified on 18 December 2019