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GATE EC – 2004 Electronics and Communication Engineering Question Paper

Q.1 – Q.30 Carry One Mark Each
1.  Consider the network  graph shown in figure. Which one of the following is NOT a ”tree‘ of this graph?

2.  The  equivalent  inductance  measured  between  the  terminals  1  and  2  for  the circuit shown in figure, is

3.  The  circuit  shown  in  Fig.Q.3,  with  R  =1 1       U ; ; has  input  voltage  , , 3 L H C F

4.  For the circuit shown in  Fig.Q.4, the time constant RC  = 1ms. The input voltage

5.  For  the  R-L  circuit  shown  in  Fig.Q.5,  the  input  voltage     v t u t ; The  current  .

6.  The  impurity  commonly  used  for  realizing  the  base  region  of  a  silicon  n-p-n
transistor is
(a)  Gallium  (b)  Indium  (c)  Boron  (d) Phosphorus

7.  If for  a silicon n-p-n  transistor, the base-to-emitter voltage (V ) is 0.7V and the
collector-to-base voltage (V  ) is 0.2V, then the transistor is operating in the
(a)  normal active mode    (b)  saturation mode
(c)  inverse active mode    (d)  cutoff mode

8.  Consider the following statements S  and S .
The  ß  of a bipolar transistor reduces if the base width is increased.
The  ß  of a bipolar transistor increases if the doping concentration in the base in increased
Which one of the following is correct?
(a)  S         is FALSE and S  is TRUE  (b)  both S             and S  are TRUE
(c)  both S       and S  are FALSE  (d)  S                is TRUE and S  is FALSE

9.  An ideal op-amp is an ideal
(a)  voltage controlled current source  (b)  voltage controlled voltage source
(c)  current controlled current source  (d)  current controlled voltage source

10.  Voltage series feedback (also called series shunt feedback) results in
(a)  increase in both input and output impedances
(b)  decrease in both input and output impedances
(c)  increase in input impedance and decrease in output impedance
(d)  decrease in input impedance and increase in output impedance

11.  The circuit in Figure is a
(a)  low-pass filter      (b)  high-pass filter
(c)  band-pass filter      (d)  band-reject filter

12.   Assuming  V      =0.2V  and   ß   =  50,  the  minimum  base  current  (I  )  required  to
drive the transistor in Fig.Q.12 to saturation is
(a)  56  A
(b)  140 mA
(c)  60  A
(d)  3 mA

13.  A master slave flip-flop has the characteristic that
(a)  change in the input immediately reflected in the output
(b)  change in the output occurs when the state of the master is affected
(c)  change in the output occurs when the state of the slave is affected
(d)  both the master and the slave states are affected at the same time

14.  The  range  of  signed  decimal  numbers  that  can  be  represented  by  6-bite  1‘s
complement number is
(a)  -31 to +31  (b)  -63 to +64  (c)  -64 to +63  (d) -32 to +31

15.  A  digital  system is  required  to  amplify  a  binary-encoded  audio  signal.  The user
should be able to control the gain of the amplifier from a minimum to a maximum
in  100  increments.  The minimum  number  of  bits  required to  encode, in straight
binary is
(a)  8  (b)  6  (c)  5  (d) 7

16.  Choose  the  correct  one  from  among  the  alternatives  A,B,C,D  after  matching  an
item from Group 1 with the most appropriate item in Group 2.

Group 1  Group 2
P. Shift register  1. Frequency division
Q. Counter  2. Addressing in memory chips
R. Decoder  3. Serial to parallel data conversion

17.  Figure  shows  the internal schematic  of  a TTL AND-OR-Invert (AOI)  gate.  For the
inputs shown in Figure, the output Y is
(a)  0
(b)  1

(c)  AB
(d)  AB

18.  Figure is the voltage transfer characteristic of
(a)  an  NMOS  inverter  with  enhancement  mode
transistor as load
(b)  an NMOS inverter with depletion mode transistor
as load
(c)  A CMOS inverter
(d)  A BJT inverter
19.  The  impulse  response  h[n]  of  a  linear  time-invariant  system  is  given  by
Y [ Y [ Y [ Y [ hn un u n un ; ) ) + + +   3 2 2 7
where u[n] is the unit step sequence. The above system is
(a)  stable but not causal    (b)  stable and causal
(c)  causal but unstable    (d)  unstable and not causal

20.  The  distribution  function  f x of  a random  variable  X  is  shown  in  Fig.Q.20.  the probability that X = 1 is

21.  The z-transfrom of a system is  H z z ; +
If the ROC is  0.2, z : then the impulse response of the system is

22.  The Fourier transform of a conjugate symmetric function is always
(a)  imaginary      (b)  conjugate anti-symmetric
(c)  real      (d)  conjugate symmetric

23.  The  gain  margin  for  the  system  with  open-loop  transfer  function

25.  In a PCM system, if the code word length is increased from 6 to 8 bits, the signal to quantization noise ratio improves by the factor

(a)  8    (b)  12  (c)  16  (d) 8

26.  An  AM  signal is  detected  using  an  envelope detector.  The  carrier frequency and modulating  signal  frequency  are  1  MHz  and  2  KHz  respectively.  An  appropriate value for the time constant of the envelope detector is
(a)  500  sec  (b)  20  sec  (c)  0.2  sec  (d) 1  sec

27.  An  AM  signal  and  a  narrow-band  FM  signal  with  identical  carriers,  modulating signals  and  modulation  indices  of  0.1  are  added  together.  The  resultant  signal can be closely approximated by
(a)  broadband FM      (b)  SSB with carrier
(c)  DSB-SC      (d)  SSB without carrier

28.  In  the  output  of  a  DM  speech  encoder,  the  consecutive  pulses  are  of  opposite polarity during time interval t = t = t . This indicates that during this interval
(a)  the input to the modulator is essentially constant
(b)  the modulator is going through slope overload
(c)  the accumulator is in saturation
(d)  the speech signal is being sampled at the Nyquist rate

29.  The  phase  velocity  of  an electromagnetic wave  propagating  in  a  hallow  metallic rectangular waveguide in the TE  mode is
(a)  equal to its group velocity
(b)  less than the velocity of light in free space
(c)  equal to the velocity of light in free space
(d)  greater than the velocity of light in free space

30.  Consider a lossless antenna with a directive gain of +6db. If 1mW of power is fed to it the total power radiated by the antenna will be

(a)  4mW  (b)  1mW  (c)  7mW  (d)  1

Q.31 – Q.90 Carry Two Marks Each

31.  For  the  lattice  circuit  shown  in  Fig.  Q.31,  2  and Z 2 Z j ; U ; U.  The  values  of

32.  The  circuit shown  in  Fig.Q.32  has  initial current  i A 0 1  ; through the  inductor  and an initial voltage  V V 0 1  ; + across the capacitor. For input v(t) = u(t), the  Laplace transform of the current i(t) for t  = 0 is

33.  Consider the Bode magnitude plot shown in Fig.33. The transfer function H(s) is

34.  The transfer function  H s V s ; of an R-L-C circuit is given by  0
the Quality factor (Q-factor) of this circuit is
(a)  25  (b)  50  (c)  100  (d) 5000

35.  For  the  circuit  shown  in  Fig.Q.35,  the  initial  conditions  are  zero.  Its  transfer function  H s V s ; is  c

36.  A  system  described  by  the  following  differential  equation
dy dy y x t 2              & ‘  3 2
dt ) ) ; is initially at rest. For input x(t) = 2u(t), the output y(t) is  dt

37.  Consider the following statements S and S
S     : At the resonant frequency the impedance of a series R-L-C circuit is zero.
S : In a parallel G-L-C circuit, increasing the conductance G results in increase in its Q factor.
Which one of the following is correct?
(a)  S        is FALSE and S  is TRUE  (b)  both S           and S  are TRUE

(c)  S        is TRUE and S  is FALSE  (d)  both S            and S  are FALSE

38.  In an abrupt p-n junction, the doping concentrations on the p-side and n-side are N cm N cm ; è ; è respectively. The p-n junction is reverse  9 10 /  and  1 10
biased and the total depletion width is 3  m. The depletion width on the p-side is
(a)  2.7  m  (b)  0.3  m  (c)  2.25  m  (d) 0.75  m

39.   The  resistivity  of  a  uniformly  doped  n-type  silicon  sample  is  0.5 -cm.  If  the
electron  mobility  ( )  is  1250  cm  /V-sec  and  the  charge  of  an  electron  is
1.6 10  Coulomb, the donor impurity concentration (N  ) in the sample is  – 19 ×D
(a)       2 10 /cm è   (b)               1 10 /cm è   (c)                2.5 10 /cm è  (d)          2 10 /cm è

40.  Consider an abrupt p-junction. Let V   be the built-in potential of this junction and V  be the applied reverse bias. If the junction capacitance (C ) is 1 pF for V  + V
= 1V, then for V + V  = 4V, C will be
(a)  4 pF  (b)  2 pF  (c)  0.25 pF  (d) 0.5 pF

41.  Consider the following statements S and S .
S : The threshold voltage (V  ) of a MOS capacitor decreases with increase in gate oxide thickness
S :  The  threshold  voltage  (V  )  of  a  MOS  capacitor  decreases  with  increase  in substrate doping concentration.
Which one of the following is correct?
(a)  S         is FALSE and S  is TRUE  (b)  both S             and S  are TRUE
(c)  S         is TRUE and S  is FALSE  (d)  both S              and S  are FALSE

42.  The drain of an n-channel MOSFET is shorted to the gate so that V  = V . The threshold voltage (V  ) of MOSFET is 1V. If the drain current (I  ) is 1 mA for V   =
2V, then for V   = 3V, I   is
GS         D
(a)  2 mA  (b)  3 mA  (c)  9 mA  (d) 4 mA

43.  The  longest  wavelength  that can be absorbed by silicon, which has the  bandgap of  1.12eV, is  1.1 m. If the  longest  wavelength  that can be  absorbed  by another material is 0.87  m, then the bandgap of this material is
(a)  1.416 eV  (b)  0.886 eV  (c)  0.854 eV  (d) 0.706 eV

44.  The  neutral  base width of a bipolar transistor, biased  in the  active region, is  0.5 m. the  maximum  electron  concentration  and  the diffusion  constant in the  base are  10 /cm   and  D   =  25  cm    /sec  respectively.  Assuming  negligible  recombination I  the base,  the collector  current density is  (the  electron  charge is – 19 1.6 × 10  coulomb)
(a)  800 A/cm          (b)  8 A/cm        (c)  200 A/cm            (d) 2 A/cm

45.  Assuming  that  the   ß   of the transistor  is  extremely  large  and  V   =  0.7V, I   and V  in the circuit shown in Figure, are

(a)  1 , 4.7 I mA V V ; ;     (b)  0.5 , 3.75                           I mA V V ; ;
(c)  1 , 2.5 I mA V V ; ;     (d)  0.5 , 3.9                            I mA V V ; ;

46.  A  bipolar  transistor  is  operating  in  the  active  region  with  a  collector  current  of 1mA. Assuming that the  ß  of the transistor is 100 and the thermal voltage (V  ) is 25 mV,  the  transconductance (g ) and the input resistance (r  )  of the transistor in the common emitter configuration, are
(a)  25 /  and  15.625 g mA V r k ; ; U   (b)  40 /  and  4.0                     g mA V r k ; ; U
(c)  25 /  and  2.5 g mA V r k ; ; U   (d)  40 /  and  2.5                     g mA V r k ; ; U

47.  The value of C required for sinusoidal oscillations of frequency 1kHz in the circuit of Fig.Q.47 is

48.  In the op-amp circuit given in Fig.Q.48, the load current I   is

49.  In  the  voltage  regulator  shown  in  Fig.Q.49,  the  load  current  can  vary  from 100mA to  500mA.  Assuming  that  the  Zener  diode  is  ideal (i.e.,  the  Zener  knee
current is negligibly small and Zener resistance is zero in the breakdown region), the value of R is

50.  In  a  full-wave  rectifier  using  two  ideal  diodes,  V  and  V    are  the  dc  and  peak dc         m
values  of  the  voltage  respectively  across  a  resistive  load.  If  PIV  is  the  peak inverse  voltage  of  the diode,  then the appropriate  relationships  for this rectifier are

51.  The  minimum  number  of  2  to  1  multiplexers  required  to  realize  a  4  to  1 mutliplexer is
(a)  1  (b)  2  (c)  3  (d) 4

52.  The Boolean expression AC +  BC is equivalent to
(a)  AC BC AC ) )       (b)  BC AC BC AC B
(c)  AC BC BC ABC ) ) )    (d)  ABC ABC ABC ABC

53.  11001,  1001  and  111001  correspond  to  the  2‘s  complement  representation of which one of the following sets of number?
(a)  25, 9 and 57 respectively  (b)  -6, -6 and œ6 respectively
(c)  -7, -7 and œ7 respectively  (d)  -25, -9 and œ57 respectively

54.  The 8255 Programmable Peripheral Interface is used as described below.
I.  An  A/D  converter  is  interfaced  to  a  microprocessor  through  an  8255.  the conversion is initiated by a signal from the 8255 on Port C. A signal on Port C causes data to be strobed into Port A.
II.  Two  computers  exchange  data  using  a pair of 8255s. Port A  works  as  a bi-directional data port supported by appropriate handshaking signals.
The appropriate modes of operation of the 8255 for I and II would be
(a)  Mode 0 for I and Mode 1 for II  (b)  Mode 1 for I and Mode 0 for II
(c)  Mode 2 for I and Mode 0 for II  (d)  Mode 2 for I and Mode 1 for II

55.  The number of memory cycles required to execute the following 8085 instructions
I.  LDA 3000H
Would be
(a)  2 for I and 2 for II    (b)  4 for I and 3 for II
(c)  3 for I and 3 for II    (d)  3 for I and 4 for II

56.  In the modulo-6 ripple counter shown in Figure, the output of the 2-input gate is used to clear the J-K flip-flops.
The 2-input gate is:
(a)  a NAND gate  (b)  a NOR gate  (c)  an OR gate  (d) an AND gate

57.  Consider the sequence of 8085 instructions given below.
LXI H, 9258  MOV A, M,   CMA,   MOV M, A
Which one of the following is performed by this sequence?
(a)  contents of location 9258 are moved to the accumulator
(b)  contents of location 9258 are compared with the contents of the accumulator
(c)  contents of location 8529 are complemented and stored in location 8529
(d)  contents of location 5892 are complemented and stored in location 5892

58.  A Boolean function f of two variables x and y is defined as follows:
f(0,0) = f(0,1) = f(1,1)=1; f(1,0) = 0
Assuming complements of x and y are not available, a minimum cost solution for realizing f  using only 2-input NOR gates and 2-input OR gates (each  having unit cost) would have a total cost of
(a)  1 unit  (b)  4 unit  (c)  3 unit  (d) 2 unit

59.  It  is  desired  to  multiply  the  numbers  0AH  by  0BH  and  store  the  result  in  the accumulator.  The numbers are  available in registers B and C respectively. A part of the 8085 program for this purpose is given below:
MVI A, 00H
Loop; – – – – – – – – –  –

The sequence of instruction to the complete the program would be

60.  A 1 kHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal  is  passed  through  an  ideal  low-pass  filter  with  cut-off  frequency  800  Hz.
The output signal has the frequency
(a)  zero Hz  (b)  0.75 kHz  (c)  0.5 kHz  (d) 0.25 kHz

61.  A  rectangular  pulse  train  s(t)  as  shown  in  Fig.Q.61  is  convolved  with  the signal cos 4 10 . p t è the convolved signal will be a

(a)  DC
(b)  12 kHz sinusoid
(c)  8 kHz sinusoid
(d)  14 kHz sinusoid

62.  Consider the sequence

The conjugate anti-symmetric part of the sequence is

63.  A casual LTI system is described by the difference equation
the system is stable only if

64.  A causal system having the  transfer function  H s s ; ) is excited  with 10u(t). The time at which the output reaches 99%  of its steady state value is
(a)  2.7 sec  (b)  2.5 sec  (c)  2.4 sec  (d) 2.1 sec

65.  The impulse response h[n] of a linear time invariant system is given as
If the input to the above system is the sequence       e  ,  then the output is
(a)       4 2 e    (b)          4 2 e    (c)         4 e    (d)          +   4 e

66.  Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in Figure.  x(t)

67.  A system has poles at 0.01 Hz, 1  Hz  and 80  Hz; zeros at 5 Hz,  100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is
(a)  -90°  (b)  0°  (c)  90°  (d) -180°

68.  Consider the signal flow graph shown in Figure. The gain

70.  The  open  loop  transfer  function  of  a  unity  feedback  system  is. The range of K for which the system is stable is   .

71.  For the polynomial  P s s s s s s ; ) ) ) ) ) the number of roots which  2 2 3 15,  5 4 3 2
lie in the right half of the s-plane is
(a)  4  (b)  2  (c)  3  (d) 1

72.  The state variable equations of a system are:   the system is
(a)  controllable but not observable  (b)  observable but not controllable
(c)  neither controllable nor observable  (d)  controllable and observable

73.  Given  1 0 , A æ Õ ; ø Œ the state transition matrix  e is given by   A t

74.  Consider the signal x(t) shown in Fig.Q.74. Let h(t) denote the impulse response of  the filter matched  to x(t),  with h(t) being non-zero only in the  interval 0 to  4 sec. The slop of h(t) in the interval 3 < t < sec is

75.  A 1mW  video signal  having  a bandwidth  of  100 MHz is  transmitted to  a receiver through  a  cable  that  has  40  dB  loss.  If  the  effective  one-sided  noise  spectral density  at  the  receiver  is  10   Watt/Hz,  then  the  signal  to  noise  ratio  at  the  – 20 receiver is
(a)  50 db  (b)  30 db  (c)  40 db  (d) 60 db

76.  A  100  MHz  carrier  of  1  V  amplitude  and  a  1  MHz  modulating  signal  of  1  V amplitude  are  fed  to  a  balanced  modulator.  The  output  of  the  modulator  is passed through  an  ideal  high-pass  filter  with  cut-off frequency  of  100 MHz.  The output of the filter is added with 100 MHz signals of 1 V amplitude and 90° phase shift as shown in Fig.Q.76. The envelope of the resultant signal is

77.  Two  sinusoidal  signals  of  same  amplitude and  frequencies  10  kHz  and 10.1 kHz are added together. The  combined signal is given to an ideal frequency detector. The output of the detector is
(a)  0.1 kHz sinusoid      (b)  20.1 kHz sinusoid
(c)  a linear function of time  (d)  a constant

78.  Consider  a  binary  digital  communication  system  with  equally  likely  0‘s  and  1‘s. When  binary  0  is  transmitted  the voltage  at  the  detector  input  can  lie  between the  level  s-0.25V  and  +0.25V  with  equal  probability:  when  binary  1  is
transmitted,  the voltage  at  the detector can have  any  value between 0 and 1 V with equal probability. If the detector has a threshold of 2.0V (i.e., if the received signal  is  greater  than  0.2  V,  the  bit  is  taken  as  1),  the  average  bit  error probability is
(a)  0.15  (b)  0.2  (c)  0.05  (d) 0.5

79.  A  random  variable  X with uniform  density  in  the  interval  0  to 1 is  quantized as  follows:
If  0          X   0.3,  x       = 0  = =
If  0.3 < X         1,   x     = 0.7  =
Where x    is the quantized value of X
The root-mean square value of the quantization noise is
(a)  0.573  (b)  0.198  (c)  2.205  (d) 0.266

Group 1  Group 2
1. FM  P. Slope overload
2. DM  Q.  -law
3. PSK  R. Envelope detector
4. PCM  S. Capture effect
T. Hilbert transform
U. Matched filter

(a)  1 œ T  2 œ P  3 œ U  4  – S   (b)  1 œ S  2 œ U  3 œ P  4  – T
(c)  1 œ S  2 œ P  3 œ U  4  – Q  (d)  1 œ U  2 œ R  3 œ S  4  – Q

81.  Three  analog  signals,  having  bandwidths  1200  Hz,  600  Hz  and  600  Hz,  are sampled  at  their  respective  Nyquist rates,  encoded  with  12  bit  words,  and  time division multiplexed. The bit rate for the multiplexed signal is
(a)  115.2 kbps  (b)  28.8 kbps  (c)  57.6 kbps  (d) 38.4 kbps

82.  Consider  a  system  shown  in  Fig.Q.82.  Let  X(f)  and  Y(f)  denote  the  Fourier transforms  of x(t)  and y(t)  respectively.  The  ideal HPF has  the cutoff  frequency The positive frequencies where Y(f) has spectral peaks are
(a)  1 kHz and 24 kHz     (b)  2 kHz and 24 kHz
(c)  1 kHz and 14 kHz     (d)  2 kHz and 14 kHz

83.  A parallel plate air-filled capacitor has plate area of 10  m   and plate separation  of  10   m.  It  is  connected  to  a  0.5  V,  3.6  GHz  source.  The  magnitude  of  the    (a)  10 mA  (b)  100 mA  (c)  10 A  (d) 1.59 mA

84.  A  source  produces  binary  data  at  the  rate  of  10  kbps.  The  binary  symbols  are represented as shown in Figure.

The  source output  is  transmitted  using two modulation schemes,  namely  Binary PSK  (BPSK)  and  Quadrature  PSK  (QPSK).  Let  B   and  B   be  the  bandwidth
requirements  of  BPSK  and  QPSK  respectively.  Assuming  that  the  bandwidth  of the above rectangular pulses is 10 kHz, B  and B are
(a)  B        = 20 kHz, B = 20 kHz  (b)  B             = 10 kHz, B = 20 kHz
(c)  B        = 20 kHz, B = 10 kHz  (d)  B             = 10 kHz, B = 10 kHz

85.  Consider  a  300   quarter-wave  long  (at  1  GHz)  transmission  line  as  shown  in  Figure. It is connected to a 10V, 50  sources at one end and is left open circuited   at the other end. The magnitude of the voltage at the open circuit end of the line is

(a)  10 V  (b)  5 V  (c)  60 V  (d)  60

86.  In  a microwave test bench, why is the microwave signal amplitude modulated at 1 kHz
(a)  To increase the sensitivity of measurement
(b)  To transmit the signal to a far-off place
(c)  To study amplitude modulation
(d)  Because crystal detector fails at microwave frequencies.

88.  Consider an impedance  Z =  R +  jX marked  with  point  P in  an impedance Smith chart  as  shown  in  Fig.Q.88.  The  movement  from  point  P  along  a  constant resistance circle in the clockwise direction by an angle 45° is equivalent to

(a)  adding an inductance in series with Z
(b)  adding a capacitance in series with Z
(c)  adding an inductance in shunt across Z
(d)  adding a capacitance in shunt across Z

89.  A plane electromagnetic wave propagating in free space in incident normally on a large  slab  of  loss-less,  non-magnetic, dielectric  material  with   > . Maxima and  minima are observed when the electric field is measured in front of the slab. The maximum  electric  field  is  found  to  be  5  times  the  minimum  field.  The  intrinsic impedance of the medium should be
(a)  120           (b)  60               (c)  600                (d) 24

90.  A  lossless  transmission  line  is  terminated  in  a  load  which  reflects  a  part  of  the incident  power.  The  measured  VSWR  is  2.  the  percentage  of  the  power  that  is reflected back is
(a)  57.73  (b)  33.33  (c)  0.11  (d) 11.11

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