GATE EC 2013: Electronics and Communication Engineering
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SESSION - 1
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2013 Question Booklet Code
A
EC : ELECTRONICS AND COMMUNICATION ENGINEERING
Duration: Three Hours Maximum Marks: 100
Read the following instructions carefully.
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal
and read the instructions printed on the ORS carefully. If you find that either:
a. The Question Booklet Code printed at the right hand top corner of this page does not match with
the Question Booklet Code at the right hand top corner of the ORS or
b. The Question Paper Code preceding the Registration number on the ORS is not EC,
then exchange the booklet immediately with a new sealed Question Booklet.
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate
bubble under each digit of your registration number and (ii) write your registration number, your
name and name of the examination centre and put your signature at the specified location.
4. This Question Booklet contains 24 pages including blank pages for rough work. After you are
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each
question has only one correct answer. Questions must be answered on the left hand side of the ORS
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen
against the question number. For each question darken the bubble of the correct answer. More
than one answer bubbled against a question will be treated as an incorrect response.
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the
bubbles in the ORS very carefully.
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted,
then the answer to the second question in the pair will not be evaluated.
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE
marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ mark will be deducted for each wrong answer. However, in the case of the linked
answer question pair, there will be negative marks only for wrong answer to the first question and no
negative marks for wrong answer to the second question.
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the
Question Booklet for rough work.
12. Before the start of the examination, write your name and registration number in the space provided
below using a black ink ballpoint pen.
Name
Registration Number EC
EC-A 1/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.1 to Q.25 carry one mark each.
Q.1 A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the
first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches
irrespective of the state of the other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
r r r r
Q.2 Consider a vector field A( r ) . The closed loop line integral ∫ • dl can be expressed as
A
r r
(A) ∫∫ (∇× A ) • ds over the closed surface bounded by the loop
r
(B) ∫∫∫ (∇ • A)dv over the closed volume bounded by the loop
r
(C) ∫∫∫ (∇ • A)dv over the open volume bounded by the loop
r r
(D) ∫∫ (∇ × A) • ds over the open surface bounded by the loop
Q.3 Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall
impulse response of the cascaded system is given by
(A) product of h1 (t ) and h2 (t )
(B) sum of h1 (t ) and h2 (t )
(C) convolution of h1 (t ) and h2 (t )
(D) subtraction of h2 (t ) from h1 (t )
Q.4 In a forward biased pn junction diode, the sequence of events that best describes the mechanism of
current flow is
(A) injection, and subsequent diffusion and recombination of minority carriers
(B) injection, and subsequent drift and generation of minority carriers
(C) extraction, and subsequent diffusion and generation of minority carriers
(D) extraction, and subsequent drift and recombination of minority carriers
Q.5 In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or
water vapor) produces
(A) superior quality oxide with a higher growth rate
(B) inferior quality oxide with a higher growth rate
(C) inferior quality oxide with a lower growth rate
(D) superior quality oxide with a lower growth rate
Q.6 The maximum value of θ until which the approximation sin θ ≈ θ holds to within 10% error is
(A) 10° (B) 18° (C) 50° (D) 90°
EC-A 2/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
r
Q.7 The divergence of the vector field A = xaˆ x + yaˆ y + zaˆ z is
(A) 0 (B) 1/3 (C) 1 (D) 3
Q.8 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
t2 t (t −1) (t −1) 2 t 2 −1
(A) u (t ) (B) u (t −1) (C) u (t −1) (D) u (t −1)
2 2 2 2
Q.9 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
The gain (20 log G ( s) ) is 32 dB and −8 dB at 1 rad/s and 10 rad/s respectively. The phase is
negative for all ω. Then G (s) is
39.8 39.8 32 32
(A) (B) (C) (D)
s s 2 s s2
Q.10 In the circuit shown below what is the output voltage (Vout) if a silicon transistor Q and an ideal
op-amp are used?
+15 V Q
1 kΩ
–
+ Vout
5V
– 15 V
(A) 15 V (B) 0.7 V (C) 0.7 V (D) 15 V
EC-A 3/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.11 Consider a delta connection of resistors and its equivalent star connection as shown below. If all
elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding
star equivalent will be scaled by a factor of
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
Q.12 For 8085 microprocessor, the following program is executed.
MVI A, 05H;
MVI B, 05H;
PTR: ADD B;
DCR B;
JNZ PTR;
ADI 03H;
HLT;
At the end of program, accumulator contains
(A) 17H (B) 20H (C) 23H (D) 05H
Q.13 The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The
minimum bandwidth required for ISI free transmission is
(A) R/10 Hz (B) R/10 kHz (C) R/5 Hz (D) R/5 kHz
Q.14 For a periodic signal v (t ) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental frequency in
rad/s is
(A) 100 (B) 300 (C) 500 (D) 1500
EC-A 4/24
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Q.15 In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if
the gain k is increased?
(A) The input impedance increases and output impedance decreases.
(B) The input impedance increases and output impedance also increases.
(C) The input impedance decreases and output impedance also decreases.
(D) The input impedance decreases and output impedance increases.
Q.16 A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the
sampling theorem, the sampling frequency which is not valid is
(A) 5 kHz (B) 12 kHz (C) 15 kHz (D) 20 kHz
Q.17 In a MOSFET operating in the saturation region, the channel length modulation effect causes
(A) an increase in the gate-source capacitance
(B) a decrease in the transconductance
(C) a decrease in the unity-gain cutoff frequency
(D) a decrease in the output resistance
Q.18 Which one of the following statements is NOT TRUE for a continuous time causal and stable
LTI system?
(A) All the poles of the system must lie on the left side of the jω axis.
(B) Zeros of the system can lie anywhere in the s-plane.
(C) All the poles must lie within s = 1 .
(D) All the roots of the characteristic equation must be located on the left side of the jω axis.
Q.19 The minimum eigenvalue of the following matrix is
3 5 2
5 12 7
2 7 5
(A) 0 (B) 1 (C) 2 (D) 3
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A polynomial f ( x) = a4 x + a3 x + a2 x + a1 x − a0 with all coefficients positive has
4 3 2
Q.20
(A) no real roots (B) no negative real root
(C) odd number of real roots (D) at least one positive and one negative real root
Q.21 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
2
(A) u (t ) (B) t u (t ) (C) t u (t )
2
(D) e − t u (t )
V2 ( s )
Q.22 The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6
(A) (B)
s +1 s+2
s+2 s +1
(C) (D)
s +1 s+2
Q.23 A source vs (t ) = V cos100 π t has an internal impedance of (4 + j3) Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should be
(A) 3 (B) 4 (C) 5 (D) 7
Q.24 The return loss of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and
magnitude of reflection coefficient are respectively
(A) 1.22 and 0.1 (B) 0.81 and 0.1 (C) − 1.22 and 0.1 (D) 2.44 and 0.2
− π t2
Q.25 Let g (t ) = e , and h (t ) is a filter matched to g (t ) . If g (t ) is applied as input to h (t ) , then
the Fourier transform of the output is
(C) e −π | f |
2 2
(A) e −π f (B) e−π f /2 (D) e−2π f
2
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Q.26 to Q.55 carry two marks each.
1 1
Q.26 Let U and V be two independent zero mean Gaussian random variables of variances and
4 9
respectively. The probability P (3V ≥ 2U ) is
(A) 4/9 (B) 1/2 (C) 2/3 (D) 5/9
Q.27 Let A be an m × n matrix and B an n × m matrix. It is given that determinant ( I m + AB ) =
determinant ( I n +BA) , where I k is the k × k identity matrix. Using the above property, the
determinant of the matrix given below is
2 1 1 1
1 2 1 1
1 1 2 1
1 1 1 2
(A) 2 (B) 5 (C) 8 (D) 16
Q.28 In the circuit shown below, if the source voltage VS = 100∠53.13° V then the Thevenin’s equivalent
voltage in Volts as seen by the load resistance RL is
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
ω (s)10
Q.29 The open-loop transfer function of a dc motor is given as = . When connected in
V a ( s ) 1 + 10 s
feedback as shown below, the approximate value of K a that will reduce the time constant of the
closed loop system by one hundred times as compared to that of the open-loop system is
(A) 1 (B) 5 (C) 10 (D) 100
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Q.30 In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V
across RL, the minimum value of RL in Ω and the minimum power rating of the Zener diode in mW,
respectively, are
(A) 125 and 125
(B) 125 and 250
(C) 250 and 125
(D) 250 and 250
Q.31 The following arrangement consists of an ideal transformer and an attenuator which attenuates
by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage
VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit
voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively,
W
1:1.25
Y
X Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
Q.32 Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating
frequency. Their respective resistances are R1 and R2. When connected in series, their effective
Q factor at the same operating frequency is
(A) q1 + q2 (B) (1 / q1 ) + (1 / q2 )
(C) ( q1 R1 + q2 R2 ) / ( R1 + R2 ) (D) ( q1 R2 + q2 R1 ) / ( R1 + R2 )
Q.33 The impulse response of a continuous time system is given by h (t ) = δ (t − 1) + δ (t − 3) . The value
of the step response at t = 2 is
(A) 0 (B) 1 (C) 2 (D) 3
EC-A 8/24
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Q.34 The small-signal resistance (i.e., dVB/dID) in kΩ offered by the n-channel MOSFET M shown in the
figure below, at a bias point of VB = 2 V is (device data for M: device transconductance parameter
kN = µn C ′ox (W L ) = 40 µA/V2, threshold voltage VTN = 1 V, and neglect body effect and channel
length modulation effects)
VB
ID
M
(A) 12.5 (B) 25 (C) 50 (D) 100
Q.35 The ac schematic of an NMOS common-source stage is shown in the figure below, where part of
the biasing circuits has been omitted for simplicity. For the n -channel MOSFET M, the
transconductance gm = 1 mA/V, and body effect and channel length modulation effect are to be
neglected. The lower cutoff frequency in Hz of the circuit is approximately at
RD C
10 kΩ 1 µF
v0
vi
M
RL
10 kΩ
(A) 8 (B) 32 (C) 50 (D) 200
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d2y dy
Q.36 A system is described by the differential equation 2
+ 5 + 6 y (t ) = x(t ) .
dt dt
Let x(t) be a rectangular pulse given by
1 0 < t < 2
x (t ) =
0 otherwise
dy
Assuming that y(0) = 0 and = 0 at t = 0 , the Laplace transform of y ( t ) is
dt
e−2 s 1 − e−2 s
(A) (B)
s ( s + 2)( s + 3) s ( s + 2)( s + 3)
e−2s 1 − e−2 s
(C) (D)
(s + 2)(s + 3) (s + 2)(s + 3)
Q.37 A system described by a linear, constant coefficient, ordinary, first order differential equation has
an exact solution given by y (t ) for t > 0 , when the forcing function is x(t ) and the initial
condition is y (0) . If one wishes to modify the system so that the solution becomes
−2 y(t ) for t > 0 , we need to
(A) change the initial condition to − y(0) and the forcing function to 2 x(t )
(B) change the initial condition to 2 y (0) and the forcing function to − x(t )
(C) change the initial condition to j 2 y (0) and the forcing function to j 2 x ( t )
(D) change the initial condition to −2 y (0) and the forcing function to −2 x(t )
Q.38 Consider two identically distributed zero-mean random variables U and V . Let the cumulative
distribution functions of U and 2V be F ( x ) and G ( x ) respectively. Then, for all values of x
(A) F ( x ) − G ( x ) ≤ 0 (B) F ( x ) − G ( x ) ≥ 0
(C) ( F ( x ) − G ( x )) ⋅ x ≤ 0 (D) ( F ( x ) − G ( x )) ⋅ x ≥ 0
Q.39 The DFT of a vector [ a b c d ] is the vector [α β γ δ ] . Consider the product
a b c d
d a b c
[p q r s] = [a b c d ]
c
.
d a b
b c d a
The DFT of the vector [ p q r s ] is a scaled version of
(A) α 2 β 2 γ 2 δ 2 (B) α β γ δ
(C) [α + β β + δ δ + γ γ + α ] (D) [α β γ δ]
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Y (s)
Q.40 The signal flow graph for a system is given below. The transfer function for this system is
U ( s)
s +1 s +1
(A) (B)
5s + 6s + 2
2
s + 6s + 2
2
s +1 1
(C) (D)
s2 + 4 s + 2 5s2 + 6s + 2
Q.41 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
Q.42 In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode
drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals
with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is
(A) X Y (B) X Y (C) X Y (D) XY
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.43 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts, is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
Q.44 Three capacitors C1, C2 and C3 whose values are 10µF, 5µF, and 2µF respectively, have breakdown
voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe
voltage in Volts that can be applied across the combination, and the corresponding total charge
in µC stored in the effective capacitance across the terminals are respectively,
C2 C3
C1
(A) 2.8 and 36 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.45 There are four chips each of 1024 bytes connected to a 16 bit address bus as shown in the figure
below. RAMs 1, 2, 3 and 4 respectively are mapped to addresses
(A) 0C00H-0FFFH, 1C00H-1FFFH, 2C00H-2FFFH, 3C00H-3FFFH
(B) 1800H-1FFFH, 2800H-2FFFH, 3800H-3FFFH, 4800H-4FFFH
(C) 0500H-08FFH, 1500H-18FFH, 3500H-38FFH, 5500H-58FFH
(D) 0800H-0BFFH, 1800H-1BFFH, 2800H-2BFFH, 3800H-3BFFH
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Q.46 In the circuit shown below, the silicon npn transistor Q has a very high value of β . The required
value of R2 in kΩ to produce IC = 1 mA is
VCC
3V
IC
R1
60 kΩ
Q
R2
RE
500 Ω
(A) 20 (B) 30 (C) 40 (D) 50
Q.47 Let U and V be two independent and identically distributed random variables such that
1
P(U = +1) = P(U = −1) = . The entropy H (U + V ) in bits is
2
(A) 3/4 (B) 1 (C) 3/2 (D) log23
Common Data Questions
Common Data for Questions 48 and 49:
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received
signals for both bits are as shown below.
pdf of received
1
signal for bit 0
0.5 pdf of received
signal for bit 1
-1 0 1 2 4
Q.48 If the detection threshold is 1, the BER will be
1 1 1 1
(A) (B) (C) (D)
2 4 8 16
Q.49 The optimum threshold to achieve minimum bit error rate (BER) is
1 4 3
(A) (B) (C) 1 (D)
2 5 2
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Common Data for Questions 50 and 51:
Consider the following figure
IS
1Ω
+ 5Ω
VS
10V 2Ω
- 2A
Q.50 The current IS in Amps in the voltage source, and voltage VS in Volts across the current source
respectively, are
(A) 13, − 20 (B) 8, − 10 (C) − 8, 20 (D) − 13, 20
Q.51 The current in the 1Ω resistor in Amps is
(A) 2 (B) 3.33 (C) 10 (D) 12
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
A monochromatic plane wave of wavelength λ = 600 µ m is propagating in the direction as shown in the
r r r
figure below. Ei , Er , and Et denote incident, reflected, and transmitted electric field vectors associated
with the wave.
E
i E
r kr
Hi
Hr
ki θi θ r
ε r = 1.0
0 ε r = 4.5 x
Ht E
0 t
19.2
kt
z
r
Q.52 The angle of incidence θ i and the expression for Ei are
π ×104 ( x + z )
E −j
(A) 60 and 0 ( aˆ x − aˆ z ) e
0 3 2
V/m
2
π ×10 z 4
E0 −j
(B) 450 and ( aˆ x + aˆ z ) e 3 V/m
2
π ×104 ( x + z )
E −j
(C) 45 and 0 ( aˆ x − aˆ z ) e
0 3 2
V/m
2
π ×10 z4
E −j
(D) 60 0 and 0 ( aˆ x − aˆ z ) e 3
V/m
2
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r
Q.53 The expression for Er is
π ×104 ( x − z )
E −j
(A) 0.23 0 ( aˆ x + aˆ z ) e 3 2
V/m
2
π ×10 z 4
E
(B) − 0 ( aˆ x + aˆ z ) e 3 V/m
j
2
π ×104 ( x − z )
E −j
(C) 0.44 0 ( aˆ x + aˆ z ) e 3 2
V/m
2
π ×10 ( x + z )
4
E −j
(D) 0 ( aˆ x + aˆ z ) e 3
V/m
2
Statement for Linked Answer Questions 54 and 55:
The state diagram of a system is shown below. A system is described by the state-variable equations
•
X =AX+B u ; y = CX + D u
1 -1 1 -1 1
u y
1 1
s s
Q.54 The state-variable equations of the system shown in the figure above are
• −1 0 −1 • −1 0 −1
X= X+ u X= X+ u
(A) 1 −1 1 (B) −1 −1 1
y = [1 −1] X + u y = [ −1 −1] X + u
• −1 0 −1 • −1 −1 −1
X= X+ u X= X+ u
(C) −1 −1 1 (D) 0 −1 1
y = [ −1 −1] X − u y = [1 −1] X − u
At
Q.55 The state transition matrix e of the system shown in the figure above is
e −t 0 e−t 0 e−t 0 e −t −te − t
(A) − t (B) (C) − t (D)
te e −t −te
−t
e−t e e −t 0 e−t
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General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 Choose the grammatically CORRECT sentence:
(A) Two and two add four.
(B) Two and two become four.
(C) Two and two are four.
(D) Two and two make four.
Q.57 Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
(A) Because I have a nice caller tune.
(B) Because I have a better telephone facility.
(C) Because a friend in need is a friend indeed.
(D) Because you need not pay towards the telephone bills when you give me a ring.
Q.58 In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C
and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of
Monday, then the temperature in °C on Thursday was
(A) 40 (B) 43 (C) 46 (D) 49
Q.59 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.60 They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
(A) make out (B) call out (C) dig out (D) fall out
Q.61 to Q.65 carry two marks each.
Q.61 A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third
quarter. The average speed of the car in km per hour over the entire journey is
(A) 30 (B) 36 (C) 40 (D) 24
Q.62 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
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Q.63 Statement: There were different streams of freedom movements in colonial India carried out by the
moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?
(A) The emergence of nationalism in colonial India led to our Independence.
(B) Nationalism in India emerged in the context of colonialism.
(C) Nationalism in India is homogeneous.
(D) Nationalism in India is heterogeneous.
Q.64 The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is
(A) (–∞, 0) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
Q.65 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
END OF THE QUESTION PAPER
EC-A 18/24
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SESSION - 2
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2013 Question Booklet Code
B
`EC : ELECTRONICS AND COMMUNICATION ENGINEERING
Duration: Three Hours Maximum Marks: 100
Read the following instructions carefully.
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal
and read the instructions printed on the ORS carefully. If you find that either:
a. The Question Booklet Code printed at the right hand top corner of this page does not match with
the Question Booklet Code at the right hand top corner of the ORS or
b. The Question Paper Code preceding the Registration number on the ORS is not EC,
then exchange the booklet immediately with a new sealed Question Booklet.
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate
bubble under each digit of your registration number and (ii) write your registration number, your
name and name of the examination centre and put your signature at the specified location.
4. This Question Booklet contains 24 pages including blank pages for rough work. After you are
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each
question has only one correct answer. Questions must be answered on the left hand side of the ORS
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen
against the question number. For each question darken the bubble of the correct answer. More
than one answer bubbled against a question will be treated as an incorrect response.
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the
bubbles in the ORS very carefully.
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted,
then the answer to the second question in the pair will not be evaluated.
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE
marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ mark will be deducted for each wrong answer. However, in the case of the linked
answer question pair, there will be negative marks only for wrong answer to the first question and no
negative marks for wrong answer to the second question.
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the
Question Booklet for rough work.
12. Before the start of the examination, write your name and registration number in the space provided
below using a black ink ballpoint pen.
Name
Registration Number EC
EC-B 1/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.1 to Q.25 carry one mark each.
Q.1 For a periodic signal v (t ) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental frequency in
rad/s is
(A) 100 (B) 300 (C) 500 (D) 1500
Q.2 In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if
the gain k is increased?
(A) The input impedance increases and output impedance decreases.
(B) The input impedance increases and output impedance also increases.
(C) The input impedance decreases and output impedance also decreases.
(D) The input impedance decreases and output impedance increases.
Q.3 A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the
sampling theorem, the sampling frequency which is not valid is
(A) 5 kHz (B) 12 kHz (C) 15 kHz (D) 20 kHz
Q.4 In a MOSFET operating in the saturation region, the channel length modulation effect causes
(A) an increase in the gate-source capacitance
(B) a decrease in the transconductance
(C) a decrease in the unity-gain cutoff frequency
(D) a decrease in the output resistance
Q.5 Which one of the following statements is NOT TRUE for a continuous time causal and stable
LTI system?
(A) All the poles of the system must lie on the left side of the jω axis.
(B) Zeros of the system can lie anywhere in the s-plane.
(C) All the poles must lie within s = 1 .
(D) All the roots of the characteristic equation must be located on the left side of the jω axis.
EC-B 2/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.6 The minimum eigenvalue of the following matrix is
3 5 2
5 12 7
2 7 5
(A) 0 (B) 1 (C) 2 (D) 3
A polynomial f ( x) = a4 x + a3 x + a2 x + a1 x − a0 with all coefficients positive has
4 3 2
Q.7
(A) no real roots (B) no negative real root
(C) odd number of real roots (D) at least one positive and one negative real root
Q.8 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
2
(A) u (t ) (B) t u (t ) (C) t u (t )
2
(D) e − t u (t )
V2 ( s )
Q.9 The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6
(A) (B)
s +1 s+2
s+2 s +1
(C) (D)
s +1 s+2
Q.10 A source vs (t ) = V cos100 π t has an internal impedance of (4 + j3) Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should be
(A) 3 (B) 4 (C) 5 (D) 7
Q.11 The return loss of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and
magnitude of reflection coefficient are respectively
(A) 1.22 and 0.1 (B) 0.81 and 0.1 (C) − 1.22 and 0.1 (D) 2.44 and 0.2
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2013 ELECTRONICS & COMMN. ENGG. - EC
− π t2
Q.12 Let g (t ) = e , and h ( t ) is a filter matched to g ( t ) . If g ( t ) is applied as input to h ( t ) , then
the Fourier transform of the output is
2 2
(A) e −π f (B) e−π f /2 (C) e −π | f | (D) e−2π f
2
r r r r
Q.13 Consider a vector field A( r ) . The closed loop line integral ∫ A • dl can be expressed as
r r
(A) ∫∫ (∇× A)r• ds over the closed surface bounded by the loop
(B) ∫∫∫ (∇ • A)dv over the closed volume bounded by the loop
r
(C) ∫∫∫ (∇ • A)dv over the open volume bounded by the loop
r r
(D) ∫∫ (∇ × A) • ds over the open surface bounded by the loop
Q.14 A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the
first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches
irrespective of the state of the other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
Q.15 Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall
impulse response of the cascaded system is given by
(A) product of h1 (t ) and h2 (t )
(B) sum of h1 (t ) and h2 (t )
(C) convolution of h1 (t ) and h2 (t )
(D) subtraction of h2 (t ) from h1 (t )
Q.16 In a forward biased pn junction diode, the sequence of events that best describes the mechanism of
current flow is
(A) injection, and subsequent diffusion and recombination of minority carriers
(B) injection, and subsequent drift and generation of minority carriers
(C) extraction, and subsequent diffusion and generation of minority carriers
(D) extraction, and subsequent drift and recombination of minority carriers
Q.17 In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or
water vapor) produces
(A) superior quality oxide with a higher growth rate
(B) inferior quality oxide with a higher growth rate
(C) inferior quality oxide with a lower growth rate
(D) superior quality oxide with a lower growth rate
Q.18 The maximum value of θ until which the approximation sin θ ≈ θ holds to within 10% error is
(A) 10° (B) 18° (C) 50° (D) 90°
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2013 ELECTRONICS & COMMN. ENGG. - EC
r
Q.19 The divergence of the vector field A = xaˆ x + yaˆ y + zaˆ z is
(A) 0 (B) 1/3 (C) 1 (D) 3
Q.20 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
t2 t (t −1) (t −1) 2 t 2 −1
(A) u (t ) (B) u (t −1) (C) u (t −1) (D) u (t −1)
2 2 2 2
Q.21 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
The gain (20 log G ( s) ) is 32 dB and −8 dB at 1 rad/s and 10 rad/s respectively. The phase is
negative for all ω. Then G (s) is
39.8 39.8 32 32
(A) (B) (C) (D)
s s2 s s2
Q.22 In the circuit shown below what is the output voltage (Vout) if a silicon transistor Q and an ideal
op-amp are used?
+15 V Q
1 kΩ
–
+ Vout
5V
– 15 V
(A) 15 V (B) 0.7 V (C) 0.7 V (D) 15 V
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.23 Consider a delta connection of resistors and its equivalent star connection as shown below. If all
elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding
star equivalent will be scaled by a factor of
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
Q.24 The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The
minimum bandwidth required for ISI free transmission is
(A) R/10 Hz (B) R/10 kHz (C) R/5 Hz (D) R/5 kHz
Q.25 For 8085 microprocessor, the following program is executed.
MVI A, 05H;
MVI B, 05H;
PTR: ADD B;
DCR B;
JNZ PTR;
ADI 03H;
HLT;
At the end of program, accumulator contains
(A) 17H (B) 20H (C) 23H (D) 05H
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.26 to Q.55 carry two marks each.
Q.26 Consider two identically distributed zero-mean random variables U and V . Let the cumulative
distribution functions of U and 2V be F ( x ) and G ( x ) respectively. Then, for all values of x
(A) F ( x ) − G ( x ) ≤ 0 (B) F ( x ) − G ( x ) ≥ 0
(C) ( F ( x ) − G ( x )) ⋅ x ≤ 0 (D) ( F ( x ) − G ( x )) ⋅ x ≥ 0
Q.27 A system described by a linear, constant coefficient, ordinary, first order differential equation has
an exact solution given by y (t ) for t > 0 , when the forcing function is x(t ) and the initial
condition is y (0) . If one wishes to modify the system so that the solution becomes
−2 y(t ) for t > 0 , we need to
(A) change the initial condition to − y(0) and the forcing function to 2 x(t )
(B) change the initial condition to 2 y (0) and the forcing function to − x(t )
(C) change the initial condition to j 2 y (0) and the forcing function to j 2 x (t )
(D) change the initial condition to −2 y (0) and the forcing function to −2 x (t )
Q.28 The DFT of a vector [ a b c d ] is the vector [α β γ δ ] . Consider the product
a b c d
d a b c
[p q r s] = [a b c d ]
c
.
d a b
b c d a
The DFT of the vector [ p q r s ] is a scaled version of
(A) α β 2 γ 2 δ 2 (B) α β γ δ
2
(C) [α + β β + δ δ + γ γ + α ] (D) [α β γ δ]
Y (s)
Q.29 The signal flow graph for a system is given below. The transfer function for this system is
U ( s)
1
U(s) 1 s-1 s-1 1 Y(s)
–4
–2
s +1 s +1
(A) (B)
5s2 + 6s + 2 s2 + 6 s + 2
s +1 1
(C) (D)
s2 + 4 s + 2 5s2 + 6s + 2
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.30 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
Q.31 In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode
drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals
with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is
(A) X Y (B) X Y (C) X Y (D) XY
Q.32 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts, is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.33 Three capacitors C1, C2 and C3 whose values are 10µF, 5µF, and 2µF respectively, have breakdown
voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe
voltage in Volts that can be applied across the combination, and the corresponding total charge
in µC stored in the effective capacitance across the terminals are respectively,
C2 C3
C1
(A) 2.8 and 36 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
Q.34 There are four chips each of 1024 bytes connected to a 16 bit address bus as shown in the figure
below. RAMs 1, 2, 3 and 4 respectively are mapped to addresses
(A) 0C00H-0FFFH, 1C00H-1FFFH, 2C00H-2FFFH, 3C00H-3FFFH
(B) 1800H-1FFFH, 2800H-2FFFH, 3800H-3FFFH, 4800H-4FFFH
(C) 0500H-08FFH, 1500H-18FFH, 3500H-38FFH, 5500H-58FFH
(D) 0800H-0BFFH, 1800H-1BFFH, 2800H-2BFFH, 3800H-3BFFH
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.35 In the circuit shown below, the silicon npn transistor Q has a very high value of β . The required
value of R2 in kΩ to produce IC = 1 mA is
VCC
3V
IC
R1
60 kΩ
Q
R2
RE
500 Ω
(A) 20 (B) 30 (C) 40 (D) 50
Q.36 Let U and V be two independent and identically distributed random variables such that
1
P(U = +1) = P(U = −1) = . The entropy H (U + V ) in bits is
2
(A) 3/4 (B) 1 (C) 3/2 (D) log23
1 1
Q.37 Let U and V be two independent zero mean Gaussian random variables of variances and
4 9
respectively. The probability P (3V ≥ 2U ) is
(A) 4/9 (B) 1/2 (C) 2/3 (D) 5/9
Q.38 Let A be an m × n matrix and B an n × m matrix. It is given that determinant ( I m + AB ) =
determinant ( I n +BA) , where I k is the k × k identity matrix. Using the above property, the
determinant of the matrix given below is
2 1 1 1
1 2 1 1
1 1 2 1
1 1 1 2
(A) 2 (B) 5 (C) 8 (D) 16
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Q.39 In the circuit shown below, if the source voltage VS = 100∠53.13° V then the Thevenin’s equivalent
voltage in Volts as seen by the load resistance RL is
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
ω (s) 10
Q.40 The open-loop transfer function of a dc motor is given as = . When connected in
Va ( s) 1 + 10 s
feedback as shown below, the approximate value of K a that will reduce the time constant of the
closed loop system by one hundred times as compared to that of the open-loop system is
(A) 1 (B) 5 (C) 10 (D) 100
Q.41 In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V
across RL, the minimum value of RL in Ω and the minimum power rating of the Zener diode in mW,
respectively, are
(A) 125 and 125
(B) 125 and 250
(C) 250 and 125
(D) 250 and 250
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.42 The following arrangement consists of an ideal transformer and an attenuator which attenuates
by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage
VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit
voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively,
W
1:1.25
Y
X Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
Q.43 Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating
frequency. Their respective resistances are R1 and R2. When connected in series, their effective
Q factor at the same operating frequency is
(A) q1 + q2 (B) (1/ q1 ) + (1/ q2 )
(C) ( q1 R1 + q2 R2 ) / ( R1 + R2 ) (D) ( q1 R2 + q2 R1 ) / ( R1 + R2 )
Q.44 The impulse response of a continuous time system is given by h (t ) = δ (t − 1) + δ (t − 3) . The value
of the step response at t = 2 is
(A) 0 (B) 1 (C) 2 (D) 3
Q.45 The small-signal resistance (i.e., dVB/dID) in kΩ offered by the n-channel MOSFET M shown in the
figure below, at a bias point of VB = 2 V is (device data for M: device transconductance parameter
′ (W L ) = 40 µA/V2, threshold voltage VTN = 1 V, and neglect body effect and channel
kN = µn Cox
length modulation effects)
VB
ID
M
(A) 12.5 (B) 25 (C) 50 (D) 100
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2013 ELECTRONICS & COMMN. ENGG. - EC
d2y dy
Q.46 A system is described by the differential equation 2
+ 5 + 6 y (t ) = x(t ) .
dt dt
Let x(t) be a rectangular pulse given by
1 0 < t < 2
x (t ) =
0 otherwise
dy
Assuming that y(0) = 0 and = 0 at t = 0 , the Laplace transform of y ( t ) is
dt
e−2 s 1 − e−2 s
(A) (B)
s ( s + 2)( s + 3) s ( s + 2)( s + 3)
e−2s 1 − e−2 s
(C) (D)
(s + 2)(s + 3) (s + 2)(s + 3)
Q.47 The ac schematic of an NMOS common-source stage is shown in the figure below, where part of
the biasing circuits has been omitted for simplicity. For the n -channel MOSFET M, the
transconductance gm = 1 mA/V, and body effect and channel length modulation effect are to be
neglected. The lower cutoff frequency in Hz of the circuit is approximately at
RD C
10 kΩ 1 µF
v0
vi
M
RL
10 kΩ
(A) 8 (B) 32 (C) 50 (D) 200
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2013 ELECTRONICS & COMMN. ENGG. - EC
Common Data Questions
Common Data for Questions 48 and 49:
Consider the following figure
IS
1Ω
+ 5Ω
VS
10V 2Ω
- 2A
Q.48 The current IS in Amps in the voltage source, and voltage VS in Volts across the current source
respectively, are
(A) 13, − 20 (B) 8, − 10 (C) − 8, 20 (D) − 13, 20
Q.49 The current in the 1Ω resistor in Amps is
(A) 2 (B) 3.33 (C) 10 (D) 12
Common Data for Questions 50 and 51:
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received
signals for both bits are as shown below.
pdf of received
1
signal for bit 0
0.5 pdf of received
signal for bit 1
-1 0 1 2 4
Q.50 If the detection threshold is 1, the BER will be
1 1 1 1
(A) (B) (C) (D)
2 4 8 16
Q.51 The optimum threshold to achieve minimum bit error rate (BER) is
1 4 3
(A) (B) (C) 1 (D)
2 5 2
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2013 ELECTRONICS & COMMN. ENGG. - EC
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
The state diagram of a system is shown below. A system is described by the state-variable equations
•
X =AX+B u ; y = CX + D u
1 -1 1 -1 1
u y
1 1
s s
Q.52 The state-variable equations of the system shown in the figure above are
• −1 0 −1 • −1 0 −1
X= X+ u X= X+ u
(A) 1 −1 1 (B) −1 −1 1
y = [1 −1] X + u y = [ −1 −1] X + u
• −1 0 −1 • −1 −1 −1
X= X + 1 u X= X + 1 u
(C) −1 −1 (D) 0 −1
y = [ −1 −1] X − u y = [1 −1] X − u
At
Q.53 The state transition matrix e of the system shown in the figure above is
e −t 0 e−t 0 e−t 0 e −t −te − t
(A) − t (B) (C) − t (D)
te e −t −te
−t
e−t e e −t 0 e−t
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2013 ELECTRONICS & COMMN. ENGG. - EC
Statement for Linked Answer Questions 54 and 55:
A monochromatic plane wave of wavelength λ = 600 µ m is propagating in the direction as shown in the
r r r
figure below. Ei , Er , and Et denote incident, reflected, and transmitted electric field vectors associated
with the wave.
E
i E
r kr
Hi
Hr
ki θi θ r
ε r = 1.0
0 ε r = 4.5 x
Ht E
0 t
19.2
kt
z
r
Q.54 The angle of incidence θ i and the expression for Ei are
π ×104 ( x + z )
E −j
(A) 60 0 and 0 ( aˆ x − aˆ z ) e 3 2
V/m
2
π ×10 z 4
E0 −j
(B) 450 and ( aˆ x + aˆ z ) e 3 V/m
2
π ×104 ( x + z )
E −j
(C) 450 and 0 ( aˆ x − aˆ z ) e 3 2
V/m
2
π ×10 z 4
E −j
(D) 60 0 and 0 ( aˆ x − aˆ z ) e 3
V/m
2
r
Q.55 The expression for Er is
π ×104 ( x − z )
E −j
(A) 0.23 0 ( aˆ x + aˆ z ) e 3 2
V/m
2
π ×10 z 4
E
(B) − 0 ( aˆ x + aˆ z ) e 3 V/m
j
2
π ×104 ( x − z )
E −j
(C) 0.44 0 ( aˆ x + aˆ z ) e 3 2
V/m
2
π ×10 ( x + z )
4
E −j
(D) 0 ( aˆ x + aˆ z ) e 3
V/m
2
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2013 ELECTRONICS & COMMN. ENGG. - EC
General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
(A) Because I have a nice caller tune.
(B) Because I have a better telephone facility.
(C) Because a friend in need is a friend indeed.
(D) Because you need not pay towards the telephone bills when you give me a ring.
Q.57 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.58 Choose the grammatically CORRECT sentence:
(A) Two and two add four.
(B) Two and two become four.
(C) Two and two are four.
(D) Two and two make four.
Q.59 They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
(A) make out (B) call out (C) dig out (D) fall out
Q.60 In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C
and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of
Monday, then the temperature in °C on Thursday was
(A) 40 (B) 43 (C) 46 (D) 49
Q.61 to Q.65 carry two marks each.
Q.61 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
Q.62 The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is
(A) (–∞, 0) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
Q.63 A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third
quarter. The average speed of the car in km per hour over the entire journey is
(A) 30 (B) 36 (C) 40 (D) 24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.64 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
Q.65 Statement: There were different streams of freedom movements in colonial India carried out by the
moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?
(A) The emergence of nationalism in colonial India led to our Independence.
(B) Nationalism in India emerged in the context of colonialism.
(C) Nationalism in India is homogeneous.
(D) Nationalism in India is heterogeneous.
END OF THE QUESTION PAPER
EC-B 18/24
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SESSION - 3
Text of page 40
2013 Question Booklet Code
C
EC : ELECTRONICS AND COMMUNICATION ENGINEERING
Duration: Three Hours Maximum Marks: 100
Read the following instructions carefully.
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal
and read the instructions printed on the ORS carefully. If you find that either:
a. The Question Booklet Code printed at the right hand top corner of this page does not match with
the Question Booklet Code at the right hand top corner of the ORS or
b. The Question Paper Code preceding the Registration number on the ORS is not EC,
then exchange the booklet immediately with a new sealed Question Booklet.
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate
bubble under each digit of your registration number and (ii) write your registration number, your
name and name of the examination centre and put your signature at the specified location.
4. This Question Booklet contains 24 pages including blank pages for rough work. After you are
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each
question has only one correct answer. Questions must be answered on the left hand side of the ORS
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen
against the question number. For each question darken the bubble of the correct answer. More
than one answer bubbled against a question will be treated as an incorrect response.
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the
bubbles in the ORS very carefully.
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted,
then the answer to the second question in the pair will not be evaluated.
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE
marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ mark will be deducted for each wrong answer. However, in the case of the linked
answer question pair, there will be negative marks only for wrong answer to the first question and no
negative marks for wrong answer to the second question.
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the
Question Booklet for rough work.
12. Before the start of the examination, write your name and registration number in the space provided
below using a black ink ballpoint pen.
Name
Registration Number EC
EC-C 1/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.1 to Q.25 carry one mark each.
Q.1 The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The
minimum bandwidth required for ISI free transmission is
(A) R/10 Hz (B) R/10 kHz (C) R/5 Hz (D) R/5 kHz
Q.2 For 8085 microprocessor, the following program is executed.
MVI A, 05H;
MVI B, 05H;
PTR: ADD B;
DCR B;
JNZ PTR;
ADI 03H;
HLT;
At the end of program, accumulator contains
(A) 17H (B) 20H (C) 23H (D) 05H
Q.3 Consider a delta connection of resistors and its equivalent star connection as shown below. If all
elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding
star equivalent will be scaled by a factor of
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
Q.4 In the circuit shown below what is the output voltage (Vout) if a silicon transistor Q and an ideal
op-amp are used?
+15 V Q
1 kΩ
–
+ Vout
5V
– 15 V
(A) 15 V (B) 0.7 V (C) 0.7 V (D) 15 V
EC-C 2/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.5 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
The gain (20 log G ( s) ) is 32 dB and −8 dB at 1 rad/s and 10 rad/s respectively. The phase is
negative for all ω. Then G (s) is
39.8 39.8 32 32
(A) (B) (C) (D)
s s 2 s s2
Q.6 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
t2 t (t −1) (t −1) 2 t 2 −1
(A) u (t ) (B) u (t −1) (C) u (t −1) (D) u (t −1)
2 2 2 2
r
Q.7 The divergence of the vector field A = xaˆ x + yaˆ y + zaˆ z is
(A) 0 (B) 1/3 (C) 1 (D) 3
Q.8 The maximum value of θ until which the approximation sin θ ≈ θ holds to within 10% error is
(A) 10° (B) 18° (C) 50° (D) 90°
Q.9 In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or
water vapor) produces
(A) superior quality oxide with a higher growth rate
(B) inferior quality oxide with a higher growth rate
(C) inferior quality oxide with a lower growth rate
(D) superior quality oxide with a lower growth rate
Q.10 In a forward biased pn junction diode, the sequence of events that best describes the mechanism of
current flow is
(A) injection, and subsequent diffusion and recombination of minority carriers
(B) injection, and subsequent drift and generation of minority carriers
(C) extraction, and subsequent diffusion and generation of minority carriers
(D) extraction, and subsequent drift and recombination of minority carriers
EC-C 3/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.11 Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall
impulse response of the cascaded system is given by
(A) product of h1 (t ) and h2 (t )
(B) sum of h1 (t ) and h2 (t )
(C) convolution of h1 (t ) and h2 (t )
(D) subtraction of h2 (t ) from h1 (t )
r r r r
Q.12 Consider a vector field A( r ) . The closed loop line integral ∫ A • dl can be expressed as
r r
(A) ∫∫ (∇× A)r• ds over the closed surface bounded by the loop
(B) ∫∫∫ (∇ • A)dv over the closed volume bounded by the loop
r
(C) ∫∫∫ (∇ • A)dv over the open volume bounded by the loop
r r
(D) ∫∫ (∇ × A) • ds over the open surface bounded by the loop
Q.13 A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the
first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches
irrespective of the state of the other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
− π t2
Q.14 Let g (t ) = e , and h (t ) is a filter matched to g (t ) . If g (t ) is applied as input to h (t ) , then
the Fourier transform of the output is
(C) e −π | f |
2 2
(A) e −π f (B) e−π f /2 (D) e−2π f
2
Q.15 The return loss of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and
magnitude of reflection coefficient are respectively
(A) 1.22 and 0.1 (B) 0.81 and 0.1 (C) − 1.22 and 0.1 (D) 2.44 and 0.2
Q.16 A source vs (t ) = V cos100 π t has an internal impedance of (4 + j3) Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should be
(A) 3 (B) 4 (C) 5 (D) 7
EC-C 4/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
V2 ( s )
Q.17 The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6
(A) (B)
s +1 s+2
s+2 s +1
(C) (D)
s +1 s+2
Q.18 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
2
(A) u (t ) (B) t u (t ) (C) t u (t )
2
(D) e − t u (t )
A polynomial f ( x) = a4 x + a3 x + a2 x + a1 x − a0 with all coefficients positive has
4 3 2
Q.19
(A) no real roots (B) no negative real root
(C) odd number of real roots (D) at least one positive and one negative real root
Q.20 The minimum eigenvalue of the following matrix is
3 5 2
5 12 7
2 7 5
(A) 0 (B) 1 (C) 2 (D) 3
Q.21 Which one of the following statements is NOT TRUE for a continuous time causal and stable
LTI system?
(A) All the poles of the system must lie on the left side of the jω axis.
(B) Zeros of the system can lie anywhere in the s-plane.
(C) All the poles must lie within s = 1 .
(D) All the roots of the characteristic equation must be located on the left side of the jω axis.
EC-C 5/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.22 In a MOSFET operating in the saturation region, the channel length modulation effect causes
(A) an increase in the gate-source capacitance
(B) a decrease in the transconductance
(C) a decrease in the unity-gain cutoff frequency
(D) a decrease in the output resistance
Q.23 A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the
sampling theorem, the sampling frequency which is not valid is
(A) 5 kHz (B) 12 kHz (C) 15 kHz (D) 20 kHz
Q.24 In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if
the gain k is increased?
(A) The input impedance increases and output impedance decreases.
(B) The input impedance increases and output impedance also increases.
(C) The input impedance decreases and output impedance also decreases.
(D) The input impedance decreases and output impedance increases.
Q.25 For a periodic signal v (t ) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental frequency in
rad/s is
(A) 100 (B) 300 (C) 500 (D) 1500
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.26 to Q.55 carry two marks each.
d2y dy
Q.26 A system is described by the differential equation 2
+ 5 + 6 y (t ) = x(t ) .
dt dt
Let x(t) be a rectangular pulse given by
1 0 < t < 2
x (t ) =
0 otherwise
dy
Assuming that y(0) = 0 and = 0 at t = 0 , the Laplace transform of y ( t ) is
dt
e−2 s 1 − e−2 s
(A) (B)
s ( s + 2)( s + 3) s ( s + 2)( s + 3)
e−2s 1 − e−2 s
(C) (D)
(s + 2)(s + 3) (s + 2)(s + 3)
Q.27 The ac schematic of an NMOS common-source stage is shown in the figure below, where part of
the biasing circuits has been omitted for simplicity. For the n -channel MOSFET M, the
transconductance gm = 1 mA/V, and body effect and channel length modulation effect are to be
neglected. The lower cutoff frequency in Hz of the circuit is approximately at
RD C
10 kΩ 1 µF
v0
vi
M
RL
10 kΩ
(A) 8 (B) 32 (C) 50 (D) 200
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.28 The small-signal resistance (i.e., dVB/dID) in kΩ offered by the n-channel MOSFET M shown in the
figure below, at a bias point of VB = 2 V is (device data for M: device transconductance parameter
kN = µn C ′ox (W L ) = 40 µA/V2, threshold voltage VTN = 1 V, and neglect body effect and channel
length modulation effects)
VB
ID
M
(A) 12.5 (B) 25 (C) 50 (D) 100
Q.29 The impulse response of a continuous time system is given by h (t ) = δ (t − 1) + δ (t − 3) . The value
of the step response at t = 2 is
(A) 0 (B) 1 (C) 2 (D) 3
Q.30 Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating
frequency. Their respective resistances are R1 and R2. When connected in series, their effective
Q factor at the same operating frequency is
(A) q1 + q2 (B) (1/ q1 ) + (1/ q2 )
(C) ( q1 R1 + q2 R2 ) / ( R1 + R2 ) (D) ( q1 R2 + q2 R1 ) / ( R1 + R2 )
Q.31 The following arrangement consists of an ideal transformer and an attenuator which attenuates
by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage
VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit
voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively,
W
1:1.25
Y
X Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
EC-C 8/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.32 In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V
across RL, the minimum value of RL in Ω and the minimum power rating of the Zener diode in mW,
respectively, are
(A) 125 and 125
(B) 125 and 250
(C) 250 and 125
(D) 250 and 250
ω (s) 10
Q.33 The open-loop transfer function of a dc motor is given as = . When connected in
V a ( s ) 1 + 10 s
feedback as shown below, the approximate value of K a that will reduce the time constant of the
closed loop system by one hundred times as compared to that of the open-loop system is
(A) 1 (B) 5 (C) 10 (D) 100
Q.34 In the circuit shown below, if the source voltage VS = 100∠53.13° V then the Thevenin’s equivalent
voltage in Volts as seen by the load resistance RL is
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
EC-C 9/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.35 Let A be an m × n matrix and B an n × m matrix. It is given that determinant ( I m + AB ) =
determinant ( I n +BA) , where I k is the k × k identity matrix. Using the above property, the
determinant of the matrix given below is
2 1 1 1
1 2 1 1
1 1 2 1
1 1 1 2
(A) 2 (B) 5 (C) 8 (D) 16
1 1
Q.36 Let U and V be two independent zero mean Gaussian random variables of variances and
4 9
respectively. The probability P (3V ≥ 2U ) is
(A) 4/9 (B) 1/2 (C) 2/3 (D) 5/9
Q.37 Let U and V be two independent and identically distributed random variables such that
1
P(U = +1) = P(U = −1) = . The entropy H (U + V ) in bits is
2
(A) 3/4 (B) 1 (C) 3/2 (D) log23
Q.38 In the circuit shown below, the silicon npn transistor Q has a very high value of β . The required
value of R2 in kΩ to produce IC = 1 mA is
VCC
3V
IC
R1
60 kΩ
Q
R2
RE
500 Ω
(A) 20 (B) 30 (C) 40 (D) 50
EC-C 10/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.39 There are four chips each of 1024 bytes connected to a 16 bit address bus as shown in the figure
below. RAMs 1, 2, 3 and 4 respectively are mapped to addresses
(A) 0C00H-0FFFH, 1C00H-1FFFH, 2C00H-2FFFH, 3C00H-3FFFH
(B) 1800H-1FFFH, 2800H-2FFFH, 3800H-3FFFH, 4800H-4FFFH
(C) 0500H-08FFH, 1500H-18FFH, 3500H-38FFH, 5500H-58FFH
(D) 0800H-0BFFH, 1800H-1BFFH, 2800H-2BFFH, 3800H-3BFFH
Q.40 Three capacitors C1, C2 and C3 whose values are 10µF, 5µF, and 2µF respectively, have breakdown
voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe
voltage in Volts that can be applied across the combination, and the corresponding total charge
in µC stored in the effective capacitance across the terminals are respectively,
C2 C3
C1
(A) 2.8 and 36 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
EC-C 11/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Q.41 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts, is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
Q.42 In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode
drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals
with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is
(A) X Y (B) X Y (C) X Y (D) XY
Q.43 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
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2013 ELECTRONICS & COMMN. ENGG. - EC
Y (s)
Q.44 The signal flow graph for a system is given below. The transfer function for this system is
U ( s)
1
U(s) 1 s-1 s-1 1 Y(s)
–4
–2
s +1 s +1
(A) (B)
5s + 6s + 2
2
s + 6s + 2
2
s +1 1
(C) (D)
s2 + 4 s + 2 5s2 + 6s + 2
Q.45 The DFT of a vector [ a b c d ] is the vector [α β γ δ ] . Consider the product
a b c d
d a b c
[p q r s] = [a b c d ]
c
.
d a b
b c d a
The DFT of the vector [ p q r s ] is a scaled version of
(A) α 2 β 2 γ 2 δ 2 (B) α β γ δ
(C) [α + β β + δ δ + γ γ + α ] (D) [α β γ δ]
Q.46 Consider two identically distributed zero-mean random variables U and V . Let the cumulative
distribution functions of U and 2V be F ( x ) and G ( x ) respectively. Then, for all values of x
(A) F ( x ) − G ( x ) ≤ 0 (B) F ( x ) − G ( x ) ≥ 0
(C) ( F ( x ) − G ( x )) ⋅ x ≤ 0 (D) ( F ( x ) − G ( x )) ⋅ x ≥ 0
Q.47 A system described by a linear, constant coefficient, ordinary, first order differential equation has
an exact solution given by y (t ) for t > 0 , when the forcing function is x(t ) and the initial
condition is y (0) . If one wishes to modify the system so that the solution becomes
−2 y(t ) for t > 0 , we need to
(A) change the initial condition to − y(0) and the forcing function to 2 x(t )
(B) change the initial condition to 2 y (0) and the forcing function to − x(t )
(C) change the initial condition to j 2 y (0) and the forcing function to j 2 x ( t )
(D) change the initial condition to −2 y (0) and the forcing function to −2 x(t )
EC-C 13/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Common Data Questions
Common Data for Questions 48 and 49:
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received
signals for both bits are as shown below.
pdf of received
1
signal for bit 0
0.5 pdf of received
signal for bit 1
-1 0 1 2 4
Q.48 The optimum threshold to achieve minimum bit error rate (BER) is
1 4 3
(A) (B) (C) 1 (D)
2 5 2
Q.49 If the detection threshold is 1, the BER will be
1 1 1 1
(A) (B) (C) (D)
2 4 8 16
Common Data for Questions 50 and 51:
Consider the following figure
IS
1Ω
+ 5Ω
VS
10V 2Ω
- 2A
Q.50 The current in the 1Ω resistor in Amps is
(A) 2 (B) 3.33 (C) 10 (D) 12
Q.51 The current IS in Amps in the voltage source, and voltage VS in Volts across the current source
respectively, are
(A) 13, − 20 (B) 8, − 10 (C) − 8, 20 (D) − 13, 20
EC-C 14/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
The state diagram of a system is shown below. A system is described by the state-variable equations
•
X =AX+B u ; y = CX + D u
1 -1 1 -1 1
u y
1 1
s s
Q.52 The state-variable equations of the system shown in the figure above are
• −1 0 −1 • −1 0 −1
X= X+ u X= X+ u
(A) 1 −1 1 (B) −1 −1 1
y = [1 −1] X + u y = [ −1 −1] X + u
• −1 0 −1 • −1 −1 −1
X= X + 1 u X= X + 1 u
(C) −1 −1 (D) 0 −1
y = [ −1 −1] X − u y = [1 −1] X − u
At
Q.53 The state transition matrix e of the system shown in the figure above is
e −t 0 e−t 0 e−t 0 e −t −te − t
(A) − t (B) (C) − t (D)
te e −t −te
−t
e−t e e −t 0 e−t
EC-C 15/24
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2013 ELECTRONICS & COMMN. ENGG. - EC
Statement for Linked Answer Questions 54 and 55:
A monochromatic plane wave of wavelength λ = 600 µ m is propagating in the direction as shown in the
r r r
figure below. Ei , Er , and Et denote incident, reflected, and transmitted electric field vectors associated
with the wave.
E
i E
r kr
Hi
Hr
ki θi θr
ε r = 1.0
0 ε r = 4.5 x
Ht E
0 t
19.2
kt
z
r
Q.54 The angle of incidence θ i and the expression for Ei are
π ×104 ( x + z )
E −j
(A) 60 0 and 0 ( aˆ x − aˆ z ) e 3 2
V/m
2
π ×10 z 4
E0 −j
(B) 450 and ( aˆ x + aˆ z ) e 3 V/m
2
π ×104 ( x + z )
E −j
(C) 450 and 0 ( aˆ x − aˆ z ) e 3 2
V/m
2
π ×10 z 4
E −j
(D) 60 0 and 0 ( aˆ x − aˆ z ) e 3
V/m
2
r
Q.55 The expression for Er is
π ×104 ( x − z )
E −j
(A) 0.23 0 ( aˆ x + aˆ z ) e 3 2
V/m
2
π ×10 z 4
E
(B) − 0 ( aˆ x + aˆ z ) e 3 V/m
j
2
π ×104 ( x − z )
E −j
(C) 0.44 0 ( aˆ x + aˆ z ) e 3 2
V/m
2
π ×10 ( x + z )
4
E −j
(D) 0 ( aˆ x + aˆ z ) e 3
V/m
2
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General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.57 They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
(A) make out (B) call out (C) dig out (D) fall out
Q.58 Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
(A) Because I have a nice caller tune.
(B) Because I have a better telephone facility.
(C) Because a friend in need is a friend indeed.
(D) Because you need not pay towards the telephone bills when you give me a ring.
Q.59 In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C
and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of
Monday, then the temperature in °C on Thursday was
(A) 40 (B) 43 (C) 46 (D) 49
Q.60 Choose the grammatically CORRECT sentence:
(A) Two and two add four.
(B) Two and two become four.
(C) Two and two are four.
(D) Two and two make four.
Q.61 to Q.65 carry two marks each.
Q.61 The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is
(A) (–∞, 0) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
Q.62 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
Q.63 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
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Q.64 Statement: There were different streams of freedom movements in colonial India carried out by the
moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?
(A) The emergence of nationalism in colonial India led to our Independence.
(B) Nationalism in India emerged in the context of colonialism.
(C) Nationalism in India is homogeneous.
(D) Nationalism in India is heterogeneous.
Q.65 A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third
quarter. The average speed of the car in km per hour over the entire journey is
(A) 30 (B) 36 (C) 40 (D) 24
END OF THE QUESTION PAPER
EC-C 18/24
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SESSION - 4
Text of page 59
2013 Question Booklet Code
D
EC : ELECTRONICS AND COMMUNICATION ENGINEERING
Duration: Three Hours Maximum Marks: 100
Read the following instructions carefully.
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal
and read the instructions printed on the ORS carefully. If you find that either:
a. The Question Booklet Code printed at the right hand top corner of this page does not match with
the Question Booklet Code at the right hand top corner of the ORS or
b. The Question Paper Code preceding the Registration number on the ORS is not EC,
then exchange the booklet immediately with a new sealed Question Booklet.
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate
bubble under each digit of your registration number and (ii) write your registration number, your
name and name of the examination centre and put your signature at the specified location.
4. This Question Booklet contains 24 pages including blank pages for rough work. After you are
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator.
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each
question has only one correct answer. Questions must be answered on the left hand side of the ORS
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen
against the question number. For each question darken the bubble of the correct answer. More
than one answer bubbled against a question will be treated as an incorrect response.
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the
bubbles in the ORS very carefully.
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted,
then the answer to the second question in the pair will not be evaluated.
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE
marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks
questions, ⅔ mark will be deducted for each wrong answer. However, in the case of the linked
answer question pair, there will be negative marks only for wrong answer to the first question and no
negative marks for wrong answer to the second question.
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the
Question Booklet for rough work.
12. Before the start of the examination, write your name and registration number in the space provided
below using a black ink ballpoint pen.
Name
Registration Number EC
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Q.1 to Q.25 carry one mark each.
− π t2
Q.1 Let g (t ) = e , and h (t ) is a filter matched to g (t ) . If g (t ) is applied as input to h (t ) , then
the Fourier transform of the output is
(C) e −π | f |
2 2
(A) e −π f (B) e−π f /2 (D) e−2π f
2
Q.2 The return loss of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and
magnitude of reflection coefficient are respectively
(A) 1.22 and 0.1 (B) 0.81 and 0.1 (C) − 1.22 and 0.1 (D) 2.44 and 0.2
Q.3 A source vs (t ) = V cos100 π t has an internal impedance of (4 + j3) Ω. If a purely resistive load
connected to this source has to extract the maximum power out of the source, its value in Ω should be
(A) 3 (B) 4 (C) 5 (D) 7
V2 ( s )
Q.4 The transfer function of the circuit shown below is
V1 ( s )
0.5 s + 1 3s + 6
(A) (B)
s +1 s+2
s+2 s +1
(C) (D)
s +1 s+2
Q.5 Assuming zero initial condition, the response y (t ) of the system given below to a unit step input
u (t ) is
2
(A) u (t ) (B) t u (t ) (C) t u (t )
2
(D) e − t u (t )
A polynomial f ( x) = a4 x + a3 x + a2 x + a1 x − a0 with all coefficients positive has
4 3 2
Q.6
(A) no real roots (B) no negative real root
(C) odd number of real roots (D) at least one positive and one negative real root
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Q.7 The minimum eigenvalue of the following matrix is
3 5 2
5 12 7
2 7 5
(A) 0 (B) 1 (C) 2 (D) 3
Q.8 Which one of the following statements is NOT TRUE for a continuous time causal and stable
LTI system?
(A) All the poles of the system must lie on the left side of the jω axis.
(B) Zeros of the system can lie anywhere in the s-plane.
(C) All the poles must lie within s = 1 .
(D) All the roots of the characteristic equation must be located on the left side of the jω axis.
Q.9 In a MOSFET operating in the saturation region, the channel length modulation effect causes
(A) an increase in the gate-source capacitance
(B) a decrease in the transconductance
(C) a decrease in the unity-gain cutoff frequency
(D) a decrease in the output resistance
Q.10 A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the
sampling theorem, the sampling frequency which is not valid is
(A) 5 kHz (B) 12 kHz (C) 15 kHz (D) 20 kHz
Q.11 In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if
the gain k is increased?
(A) The input impedance increases and output impedance decreases.
(B) The input impedance increases and output impedance also increases.
(C) The input impedance decreases and output impedance also decreases.
(D) The input impedance decreases and output impedance increases.
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Q.12 For a periodic signal v (t ) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental frequency in
rad/s is
(A) 100 (B) 300 (C) 500 (D) 1500
Q.13 For 8085 microprocessor, the following program is executed.
MVI A, 05H;
MVI B, 05H;
PTR: ADD B;
DCR B;
JNZ PTR;
ADI 03H;
HLT;
At the end of program, accumulator contains
(A) 17H (B) 20H (C) 23H (D) 05H
Q.14 The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The
minimum bandwidth required for ISI free transmission is
(A) R/10 Hz (B) R/10 kHz (C) R/5 Hz (D) R/5 kHz
Q.15 Consider a delta connection of resistors and its equivalent star connection as shown below. If all
elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding
star equivalent will be scaled by a factor of
Ra RC RB
Rb Rc
RA
(A) k2 (B) k (C) 1/k (D) k
Q.16 In the circuit shown below what is the output voltage (Vout) if a silicon transistor Q and an ideal
op-amp are used?
+15 V Q
1 kΩ
–
+ Vout
5V
– 15 V
(A) 15 V (B) 0.7 V (C) 0.7 V (D) 15 V
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Q.17 The Bode plot of a transfer function G (s ) is shown in the figure below.
Gain (dB)
The gain (20 log G ( s) ) is 32 dB and −8 dB at 1 rad/s and 10 rad/s respectively. The phase is
negative for all ω. Then G (s) is
39.8 39.8 32 32
(A) (B) (C) (D)
s s 2 s s2
Q.18 The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is
t2 t (t −1) (t −1) 2 t 2 −1
(A) u (t ) (B) u (t −1) (C) u (t −1) (D) u (t −1)
2 2 2 2
r
Q.19 The divergence of the vector field A = xaˆ x + yaˆ y + zaˆ z is
(A) 0 (B) 1/3 (C) 1 (D) 3
Q.20 The maximum value of θ until which the approximation sin θ ≈ θ holds to within 10% error is
(A) 10° (B) 18° (C) 50° (D) 90°
Q.21 In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or
water vapor) produces
(A) superior quality oxide with a higher growth rate
(B) inferior quality oxide with a higher growth rate
(C) inferior quality oxide with a lower growth rate
(D) superior quality oxide with a lower growth rate
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Q.22 In a forward biased pn junction diode, the sequence of events that best describes the mechanism of
current flow is
(A) injection, and subsequent diffusion and recombination of minority carriers
(B) injection, and subsequent drift and generation of minority carriers
(C) extraction, and subsequent diffusion and generation of minority carriers
(D) extraction, and subsequent drift and recombination of minority carriers
Q.23 Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall
impulse response of the cascaded system is given by
(A) product of h1 (t ) and h2 (t )
(B) sum of h1 (t ) and h2 (t )
(C) convolution of h1 (t ) and h2 (t )
(D) subtraction of h2 (t ) from h1 (t )
Q.24 A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the
first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches
irrespective of the state of the other switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate
r r r r
Q.25 Consider a vector field A( r ) . The closed loop line integral ∫ • dl can be expressed as
A
r r
(A) ∫∫ (∇× A ) • ds over the closed surface bounded by the loop
r
(B) ∫∫∫ (∇ • A)dv over the closed volume bounded by the loop
r
(C) ∫∫∫ (∇ • A)dv over the open volume bounded by the loop
r r
(D) ∫∫ (∇× A) • ds over the open surface bounded by the loop
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Q.26 to Q.55 carry two marks each.
Q.26 Let U and V be two independent and identically distributed random variables such that
1
P(U = +1) = P(U = −1) = . The entropy H (U + V ) in bits is
2
(A) 3/4 (B) 1 (C) 3/2 (D) log23
Q.27 In the circuit shown below, the silicon npn transistor Q has a very high value of β . The required
value of R2 in kΩ to produce IC = 1 mA is
VCC
3V
IC
R1
60 kΩ
Q
R2
RE
500 Ω
(A) 20 (B) 30 (C) 40 (D) 50
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Q.28 There are four chips each of 1024 bytes connected to a 16 bit address bus as shown in the figure
below. RAMs 1, 2, 3 and 4 respectively are mapped to addresses
(A) 0C00H-0FFFH, 1C00H-1FFFH, 2C00H-2FFFH, 3C00H-3FFFH
(B) 1800H-1FFFH, 2800H-2FFFH, 3800H-3FFFH, 4800H-4FFFH
(C) 0500H-08FFH, 1500H-18FFH, 3500H-38FFH, 5500H-58FFH
(D) 0800H-0BFFH, 1800H-1BFFH, 2800H-2BFFH, 3800H-3BFFH
Q.29 Three capacitors C1, C2 and C3 whose values are 10µF, 5µF, and 2µF respectively, have breakdown
voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe
voltage in Volts that can be applied across the combination, and the corresponding total charge
in µC stored in the effective capacitance across the terminals are respectively,
C2 C3
C1
(A) 2.8 and 36 (B) 7 and 119
(C) 2.8 and 32 (D) 7 and 80
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Q.30 A voltage 1000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured
across WX in Volts, is
1kΩ
W Y X
Z
+ 1kΩ _
(A) sin ω t (B) (sin ω t + sin ω t ) / 2
(C) (sin ω t − sin ω t ) / 2 (D) 0 for all t
Q.31 In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode
drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals
with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is
(A) X Y (B) X Y (C) X Y (D) XY
Q.32 In the circuit shown below the op-amps are ideal. Then Vout in Volts is
(A) 4 (B) 6 (C) 8 (D) 10
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Y (s)
Q.33 The signal flow graph for a system is given below. The transfer function for this system is
U ( s)
1
U(s) 1 s-1 s-1 1 Y(s)
–4
–2
s +1 s +1
(A) (B)
5s + 6s + 2
2
s + 6s + 2
2
s +1 1
(C) (D)
s2 + 4 s + 2 5s2 + 6s + 2
Q.34 The DFT of a vector [ a b c d ] is the vector [α β γ δ ] . Consider the product
a b c d
d a b c
[p q r s] = [a b c d ]
c
.
d a b
b c d a
The DFT of the vector [ p q r s ] is a scaled version of
(A) α β 2 γ 2 δ 2 (B) α β γ δ
2
(C) [α + β β + δ δ + γ γ + α ] (D) [α β γ δ]
Q.35 Consider two identically distributed zero-mean random variables U and V . Let the cumulative
distribution functions of U and 2V be F ( x ) and G ( x ) respectively. Then, for all values of x
(A) F ( x ) − G ( x ) ≤ 0 (B) F ( x ) − G ( x ) ≥ 0
(C) ( F ( x ) − G ( x )) ⋅ x ≤ 0 (D) ( F ( x ) − G ( x )) ⋅ x ≥ 0
Q.36 A system described by a linear, constant coefficient, ordinary, first order differential equation has
an exact solution given by y (t ) for t > 0 , when the forcing function is x(t ) and the initial
condition is y (0) . If one wishes to modify the system so that the solution becomes
−2 y(t ) for t > 0 , we need to
(A) change the initial condition to − y(0) and the forcing function to 2 x(t )
(B) change the initial condition to 2 y (0) and the forcing function to − x(t )
(C) change the initial condition to j 2 y (0) and the forcing function to j 2 x ( t )
(D) change the initial condition to −2 y (0) and the forcing function to −2 x(t )
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d2y dy
Q.37 A system is described by the differential equation 2
+ 5 + 6 y (t ) = x(t ) .
dt dt
Let x(t) be a rectangular pulse given by
1 0 < t < 2
x (t ) =
0 otherwise
dy
Assuming that y(0) = 0 and = 0 at t = 0 , the Laplace transform of y ( t ) is
dt
e−2 s 1 − e−2 s
(A) (B)
s ( s + 2)( s + 3) s ( s + 2)( s + 3)
e−2s 1 − e−2 s
(C) (D)
(s + 2)(s + 3) (s + 2)(s + 3)
Q.38 The ac schematic of an NMOS common-source stage is shown in the figure below, where part of
the biasing circuits has been omitted for simplicity. For the n -channel MOSFET M, the
transconductance gm = 1 mA/V, and body effect and channel length modulation effect are to be
neglected. The lower cutoff frequency in Hz of the circuit is approximately at
RD C
10 kΩ 1 µF
v0
vi
M
RL
10 kΩ
(A) 8 (B) 32 (C) 50 (D) 200
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Q.39 The small-signal resistance (i.e., dVB/dID) in kΩ offered by the n-channel MOSFET M shown in the
figure below, at a bias point of VB = 2 V is (device data for M: device transconductance parameter
kN = µn C ′ox (W L ) = 40 µA/V2, threshold voltage VTN = 1 V, and neglect body effect and channel
length modulation effects)
VB
ID
M
(A) 12.5 (B) 25 (C) 50 (D) 100
Q.40 The impulse response of a continuous time system is given by h (t ) = δ (t − 1) + δ (t − 3) . The value
of the step response at t = 2 is
(A) 0 (B) 1 (C) 2 (D) 3
Q.41 Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating
frequency. Their respective resistances are R1 and R2. When connected in series, their effective
Q factor at the same operating frequency is
(A) q1 + q2 (B) (1/ q1 ) + (1/ q2 )
(C) ( q1 R1 + q2 R2 ) / ( R1 + R2 ) (D) ( q1 R2 + q2 R1 ) / ( R1 + R2 )
Q.42 The following arrangement consists of an ideal transformer and an attenuator which attenuates
by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage
VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit
voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively,
W
1:1.25
Y
X Z
(A) 125/100 and 80/100 (B) 100/100 and 80/100
(C) 100/100 and 100/100 (D) 80/100 and 80/100
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Q.43 In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V
across RL, the minimum value of RL in Ω and the minimum power rating of the Zener diode in mW,
respectively, are
(A) 125 and 125
(B) 125 and 250
(C) 250 and 125
(D) 250 and 250
ω (s) 10
Q.44 The open-loop transfer function of a dc motor is given as = . When connected in
Va ( s) 1 + 10 s
feedback as shown below, the approximate value of K a that will reduce the time constant of the
closed loop system by one hundred times as compared to that of the open-loop system is
(A) 1 (B) 5 (C) 10 (D) 100
Q.45 In the circuit shown below, if the source voltage VS = 100∠53.13° V then the Thevenin’s equivalent
voltage in Volts as seen by the load resistance RL is
3Ω j4 Ω j6 Ω 5Ω
VL1
VS j40I2 10VL1 RL=10 Ω
I1 I2
(A) 100∠90° (B) 800∠0° (C) 800∠90° (D) 100∠60°
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Q.46 Let A be an m × n matrix and B an n × m matrix. It is given that determinant ( I m + AB ) =
determinant ( I n +BA) , where I k is the k × k identity matrix. Using the above property, the
determinant of the matrix given below is
2 1 1 1
1 2 1 1
1 1 2 1
1 1 1 2
(A) 2 (B) 5 (C) 8 (D) 16
1 1
Q.47 Let U and V be two independent zero mean Gaussian random variables of variances and
4 9
respectively. The probability P (3V ≥ 2U ) is
(A) 4/9 (B) 1/2 (C) 2/3 (D) 5/9
Common Data Questions
Common Data for Questions 48 and 49:
Consider the following figure
IS
1Ω
+ 5Ω
VS
10V 2Ω
- 2A
Q.48 The current in the 1Ω resistor in Amps is
(A) 2 (B) 3.33 (C) 10 (D) 12
Q.49 The current IS in Amps in the voltage source, and voltage VS in Volts across the current source
respectively, are
(A) 13, − 20 (B) 8, − 10 (C) − 8, 20 (D) − 13, 20
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Common Data for Questions 50 and 51:
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received
signals for both bits are as shown below.
pdf of received
1
signal for bit 0
0.5 pdf of received
signal for bit 1
-1 0 1 2 4
Q.50 The optimum threshold to achieve minimum bit error rate (BER) is
1 4 3
(A) (B) (C) 1 (D)
2 5 2
Q.51 If the detection threshold is 1, the BER will be
1 1 1 1
(A) (B) (C) (D)
2 4 8 16
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
A monochromatic plane wave of wavelength λ = 600 µ m is propagating in the direction as shown in the
r r r
figure below. Ei , Er , and Et denote incident, reflected, and transmitted electric field vectors associated
with the wave.
E E
i r kr
Hi
Hr
ki θi θ r
ε r = 1.0
0 ε r = 4.5 x
Ht E
0 t
19.2
kt
z
r
Q.52 The angle of incidence θ i and the expression for Ei are
π ×104 ( x + z )
E −j
(A) 60 and 0 ( aˆ x − aˆ z ) e
0 3 2
V/m
2
π ×10 z 4
E0 −j
(B) 450 and ( aˆ x + aˆ z ) e 3 V/m
2
π ×104 ( x + z )
E0 −j
(C) 45 and0
( aˆ x − aˆ z ) e V/m 3 2
2
π ×10 z 4
E −j
(D) 60 0 and 0 ( aˆ x − aˆ z ) e 3
V/m
2
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r
Q.53 The expression for Er is
π ×104 ( x − z )
E0 −j
(A) 0.23 ( aˆx + aˆz ) e 3 2
V/m
2
π ×10 z 4
E
(B) − 0 ( aˆ x + aˆ z ) e 3 V/m
j
2
π ×104 ( x − z )
E0 −j
(C) 0.44 ( aˆ x + aˆz ) e 3 2
V/m
2
π ×10 ( x + z )4
E −j
(D) 0 ( aˆ x + aˆ z ) e 3
V/m
2
Statement for Linked Answer Questions 54 and 55:
The state diagram of a system is shown below. A system is described by the state-variable equations
•
X =AX+B u ; y = CX + D u
1 -1 1 -1 1
u y
1 1
s s
Q.54 The state-variable equations of the system shown in the figure above are
• −1 0 −1 • −1 0 −1
X= X+ u X= X+ u
(A) 1 −1 1 (B) −1 −1 1
y = [1 −1] X + u y = [ −1 −1] X + u
• −1 0 −1 • −1 −1 −1
X= X+ u X= X+ u
(C) −1 −1 1 (D) 0 −1 1
y = [ −1 −1] X − u y = [1 −1] X − u
At
Q.55 The state transition matrix e of the system shown in the figure above is
e −t 0 e−t 0 e−t 0 e −t −te − t
(A) −t (B) (C) − t (D)
te e −t −te
−t
e−t e e −t 0 e−t
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General Aptitude (GA) Questions
Q.56 to Q.60 carry one mark each.
Q.56 They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
(A) make out (B) call out (C) dig out (D) fall out
Q.57 In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C
and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of
Monday, then the temperature in °C on Thursday was
(A) 40 (B) 43 (C) 46 (D) 49
Q.58 Complete the sentence:
Dare _______________ mistakes.
(A) commit (B) to commit (C) committed (D) committing
Q.59 Choose the grammatically CORRECT sentence:
(A) Two and two add four.
(B) Two and two become four.
(C) Two and two are four.
(D) Two and two make four.
Q.60 Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
(A) Because I have a nice caller tune.
(B) Because I have a better telephone facility.
(C) Because a friend in need is a friend indeed.
(D) Because you need not pay towards the telephone bills when you give me a ring.
Q.61 to Q.65 carry two marks each.
Q.61 What is the chance that a leap year, selected at random, will contain 53 Saturdays?
(A) 2/7 (B) 3/7 (C) 1/7 (D) 5/7
Q.62 Statement: There were different streams of freedom movements in colonial India carried out by the
moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?
(A) The emergence of nationalism in colonial India led to our Independence.
(B) Nationalism in India emerged in the context of colonialism.
(C) Nationalism in India is homogeneous.
(D) Nationalism in India is heterogeneous.
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Q.63 The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is
(A) (–∞, 0) (B) (0, 1) (C) (1, ∞) (D) (0, ∞)
Q.64 A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third
quarter. The average speed of the car in km per hour over the entire journey is
(A) 30 (B) 36 (C) 40 (D) 24
Q.65 Find the sum to n terms of the series 10+84+ 734 + .....
(A)
(
9 9n + 1 )
+1
10
(B)
(
9 9n − 1 )
+1
8
(C)
(
9 9n −1 )
+n
8
(D)
(
9 9n − 1 )
+ n2
8
END OF THE QUESTION PAPER
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Page 1 of 76
Source: GATE. Question paper published by GATE.