GATE EC - 2003 Electronics and Communication Engineering Question PaperQ.1 - Q.30 Carry One Mark Each
1. The minimum number of equations required to analyze the circuit shown in Fig.Q.1 is
(a) 3 (b) 4 (c) 6 (d) 7
2. A source of angular frequency 1 rad/sec has a source impedance consisting of resistance in series with 1 H inductance. The load that will obtain the maximum power transfer is
(a) 1 resistance
(b) 1 resistance in parallel with 1 H inductance
(c) 1 resistance in series with 1 F capacitor
(d) 1 resistance in parallel with 1 F capacitor
3. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q = 100. If each R, L and C is doubled from its original value, the new Q of the circuit is
(a) 25 (b) 50 (c) 100 (d) 200
4. The Laplace transform of i(t) is given by I s s s = +
As t � 8 , the value of i(t) tends to
(a) 0 (b) 1 (c) 2 (d)
5. The differential equation for the current i(t) in the circuit of Figure Q.5 is
6. n-type silicon is obtained by doping silicon with
(a) Germanium (b) Aluminum (c) Boron (d) Phosphorus
7. The band gap of silicon at 300 K is
(a) 1.36 eV (b) 1.10 eV (c) 0.80 eV (d) 0.67 eV
8. The intrinsic carrier concentration of silicon sample of 300 K is 1.5 � 10 /m . If after doping, the number of majority carriers is 5 � 10 /m , the minority carrier density is
(a) 4.50 � 10 /m (b) 3.33 � 10 /m
(c) 5.00 � 10 /m (d) 3.00 � 10 /m
9. Choose proper substitutes for X and Y to make the following statement correct Tunnel diode and Avalanche photodiode are operated in X bias and Y bias respectively.
(a) X: reverse, Y: reverse (b) X: reverse, Y: forward
(c) X: forward, Y: reverse (d) X: forward, Y: forward
10. For an n-channel enhancement type MOSFET, if the source is connected at a higher potential than that of the bulk (i.e. V > 0), the threshold voltage V of
the MOSFET will
(a) remain unchanged (b) decrease
(c) change polarity (d) increase
11. Choose the correct match for input resistance of various amplifier configurations shown below.
Configuration Input resistance
CB: Common Base LO: Low
CC: Common Collector MO: Moderate
CE: Common Emitter HI: High
(a) CB-LO, CC-MO, CE-HI (b) CB-LO, CC-HI, CE-MO
(c) CB-MO, CC-HI, CE-LO (d) CB-HI, CC-LO, CE-MO
12. The circuit shown in figure is best described as a
(a) bridge rectifier
(b) ring modulator
(c) frequency discriminatory
(d) voltage doubler
13. If the input to the ideal comparator shown in figure is a sinusoidal signal of 8V (peak to peak) without any DC component, then the output of the comparator has a duty cycle of
(a) 1
2 (b) 1 3 (c) 1 6 (d) 12
14. If the differential voltage gain and the common mode voltage gain of a differential amplifier are 48 dB and 2 dB respectively, then its common mode rejection ratio is
(a) 23 dB (b) 25 dB (c) 46 dB (d) 50 dB
15. Generally, the gain of a transistor amplifier falls at high frequencies due to the
(a) internal capacitances of the device
(b) coupling capacitor at the input
(c) skin effect
(d) coupling capacitor at the output
16. The number of distinct Boolean expression of 4 variables is
(a) 16 (b) 256 (c) 1024 (d) 65536
17. The minimum number of comparators required to build an 8 it flash ADC is
(a) 8 (b) 63 (c) 255 (d) 256
18. The output of the 74 series of TTL gates is taken from a BJT in
(a) totem pole and common collector configuration
(b) either totem pole or open collector configuration
(c) common base configuration
(d) common collector configuration
19. Without any additional circuitry, an 8:1 MUX can be used to obtain
(a) some but not all Boolean functions of 3 variables
(b) all function of 3 variables but none of 4 variables
(c) all functions of 3 variables and some but not all of 4 variables
(d) all functions of 4 variables
20. A 0 to 6 counter consists of 3 flip flops and a combination circuit of 2 input gate(s). The combination circuit consists of
(a) one AND gate (b) one OR gate
(c) one AND gate and one OR gate (d) two AND gates
21. The Fourier series expansion of a real periodic signal with fundamental frequency
� 8 ( ) p j nf t 2 f is given by g t c e = it is given that C = 3 + j5. Then C is
(a) 5+j3 (b) -3-j5 (c) -5+j3 (d) 3-j5
22. Let x(t) be the input to a linear, time-invariant system. The required output is
4x(t-2). The transfer function of the system should be
23. A sequence x(n) with the z-transform X(z) = z z z z + - + - 2 2 3 is applied as an input to a linear, time-invariant system with the impulse response h(n) =
2 d (n-3) where
24. Figure shows the Nyquist plot of the open-loop transfer function G(s)H(s) of a system. If G(s)H(s) has one right hand pole, the closed loop system is
(a) always stable
(b) unstable with one closed loop right hand pole
(c) unstable with two closed loop right hand poles
(d) unstable with three closed loop right hand poles
25. A PD controller is used to compensate a system. Compared to the
uncompensated system, the compensated system has
(a) a higher type number (b) reduced damping
(c) higher noise amplification (d) larger transient overshoot
26. The input to a coherent detector is DSB-SC signal plus noise. The noise at the detector output is
(a) the in-phase component (b) the quadrature-component
(c) zero (d) the envelope
27. The noise at the input to an ideal frequency detector is white. The detector is operating above threshold. The power spectral density of the noise at the output is
(a) raised cosine (b) flat (c) parabolic (d) Gaussian
28. At a given probability of error, binary coherent FSK is inferior to binary coherent PSK by
(a) 6 dB (b) 3 dB (c) 2 dB (d) 0 dB
29. The unit of � H is
(a) Ampere (b) Ampere/meter
(c) Ampere/meter (d) Ampere-meter 2
30. The depth of penetration of electromagnetic wave in a medium having conductivity s at a frequency of 1 MHz is 25 cm. The depth of penetration at a frequency of 4 MHz will be
(a) 6.25 cm (b) 12.50 cm (c) 50.00 cm (d) 100.00 cm
Q.31 - Q.90 Carry Two Marks Each
31. Twelve 1 resistances are used as edges to form a cube. The resistance between two diagonally opposite corners of the cube is
(a) 5 (b) 1 (c) 6 (d) 3
32. The current flowing through the resistance R in the circuit in figure has the form P cos 4t, where P is M=0.75H
1/10.24F
(a) (0.18+j0.72)
(b) (0.46+j1.90)
(c) -(0.18+j1.90)
(d) -(0.192+j0.144)
The circuit for Q.33-34 is given in figure. For both the questions, assume that the switch S is in position 1 for a long time and thrown to position 2 at t = 0.
Q.33-34, after the switch is brought from position 1 to position 2 at t = 0, are
35. An input voltage v(t) = 10 2 cos 10 10 3 cos 2 10 t t V + � + + � is applied to a series combination of resistance R = 1 and an inductance L = 1H. The resulting steady state current i(t) in ampere is
36. The driving point impedance Z(s) of a network has the pole-zero locations as shown in figure. If Z(0) =3, then Z(s) is
37. The impedance parameters Z and Z of the two-port network in figure are
38. An n-type silicon bar 0.1 cm long and m in cross-sectional area has a majority carrier concentration of 5 � 10 /m and the carrier mobility is 0.13m /V-s at 300K. if the charge of an electron is 1.6 � 10 coulomb, then the resistance of the bar is
(a) 10 ohm (b) 10 ohm (c) 10 ohm (d) 10 ohm
39. The electron concentration in a sample of uniformly doped n-type silicon at 300 K varies linearly from 10 /cm at x = 0 to 6 � 10 /cm at x = 2 m. Assume situation that electrons are supplied to keep this concentration gradient constant with time. If electronic charge is 1.6 � 10 coulomb and the diffusion constant
D = 35 cm /s, the current density in the silicon, if no electric field is present, is
(a) zero (b) -112 A/cm
(c) +1120 A/cm (d) -1112 A/cm
40. Match items in Group 1 with items in Group 2, most suitably.
Group 1 Group 2
P LED 1 Heavy doping
Q Avalanche photodiode 2 Coherent radiation
R Tunnel diode 3 Spontaneous emission
S LASER 4 Current gain
41. At 300 K, for a diode current of 1 mA, a certain germanium diode requires a forward bias of 0.1435V, whereas a certain silicon diode requires a forward bias of 0.718V. Under the conditions stated above, the closest approximation of the ratio of reverse saturation current in germanium diode to that in silicon diode is
(a) 1 (b) 5 (c) 4 � 10 (d) 8 � 10
42. A particular green LED emits light of wavelength 5490�A. The energy bandgap of the semiconductor material used there is (Planck's constant = 6.626 � 10 J-s) - 34
(a) 2.26 eV (b) 1.98 eV (c) 1.17 eV (d) 0.74 eV
43. When the gate-to-source voltage (V ) of a MOSFET with threshold voltage of GS
400mV, working in saturation is 900 mV, the drain current in observed to be 1 mA. Neglecting the channel width modulation effect and assuming that the MOSFET is operating at saturation, the drain current for an applied V of 1400 mV is
(a) 0.5 mA (b) 2.0 mA (c) 3.5 mA (d) 4.0 mA
44. If P is Passivation, Q is n-well implant, R is metallization and S is soruce/drain diffusion, then the order in which they are carried out in a standard n-well CMOS fabrication process, is
(a) P-Q-R-S (b) Q-S-R-P (c) R-P-S-Q (d) S-R-Q-P
45. An amplifier without feedback has a voltage gain of 50, input resistance of 1 K and output resistance of 2.5 K . The input resistance of the current-shunt negative feedback amplifier using the above amplifier with a feedback factor of 0.2, is
(a) 1 (b) 1 (c) 5 K (d) 11 K K
46. In the amplifier circuit shown in figure, the values of R and R are such that the transistor is operating at V = 3V and I = 1.5mA when its � is 150. For a transistor with � of 200, the operating point (V I ) is
(a) (2V, 2 mA)
(b) (3V, 2 mA)
(c) (4V, 2 mA)
(d) (4V, 1 mA)
47. The oscillator circuit shown in figure has an ideal inverting amplifier. Its frequency of oscillation (in Hz) is
48. The output voltage of the regulated power supply shown in figure is
(a) 3V (b) 6V (c) 9V (d) 12V
49. The action of a JFET in its equivalent circuit can best be represented as a
(a) Current Controlled Current Source
(b) Current Controlled Voltage Source
(c) Voltage Controlled Voltage Source
(d) Voltage Controlled Current Source
50. If the op-amp in figure is ideal, the output voltage V will (a) 1V
(b) 6V
(c) 14V
(d) 17V
51. Three identical amplifiers with each one having a voltage gain of 50, input resistance of 1 K and output resistance of 250 , are cascaded. The open circuit voltage gain of the combined amplifier is
(a) 49 dB (b) 51 dB (c) 98 dB (d) 102 dB
52. An ideal sawtooth voltage waveform of frequency 500 Hz and amplitude 3V is generated by charging a capacitor of 2 F in every cycle. The charging requires
(a) constant voltage source of 3 V for 1 ms
(b) constant voltage source of 3 V for 2 ms
(c) constant current source of 3 mA for 1 ms
(d) constant current source of 3 mA for 2 ms
53. The circuit shown in figure has 4 boxes each described by inputs P, Q, R and outputs Y, Z with
= Y P Q R
The circuit acts as a
(a) 4 bit adder giving P + Q (b) 4 bit subtractor-giving P - Q
(c) 4 bit subtractor-giving Q - P (d) 4 bit adder giving P + Q + R
54. If the functions W, X, Y and Z are as follows
Then
(a) W = Z, X = Z (b) W = Z, X = Y (c) W = Y (d) W = Y = Z
55. A 4 bit ripple counter and a 4 bit synchronous counter are made using flip-flops having a propagation delay of 10 ns each. If the worst case delay in the ripple
counter and the synchronous counter be R and S respectively, then
(a) R = 10 ns, S = 40 ns (b) R = 40 ns, S = 10 ns
(c) R = 10 ns, S = 30 ns (d) R = 30 ns, S = 10 ns
56. The DTL, TTL, ECL and CMOS families of digital ICs are compared in the following 4 columns
(P) (Q) (R) (S)
Fanout is minimum DTL DTL TTL CMOS
Power consumption is minimum TTL CMOS ECL DTL
Propagation delay is minimum CMOS ECL TTL TTL
The correct column is
(a) P (b) Q (c) R (d) S
57. The circuit shown in figure is a 4-bit DAC
The input bits 0 and 1 are represented by 0 and 5 V respectively. The OP AMP is ideal, but all the resistances and the 5V inputs have a tolerance of � 10%. The specification (rounded to the nearest multiple of 5% ) for the
tolerance of the DAC is
(a) � 35% (b) � 20% (c) � 10% (d) � 5%
58. The circuit shown in figure converts
(a) BCD to binary code (b) Binary to excess � 3 code
(c) Excess � 3 to Gray code (d) Gray to Binary code
59. In the circuit shown in Figure, A is a parallel in, parallel-out 4-bit register, which loads at the rising edge of the clock C. The input lines are connected to a 4-bit bus, W. Its output acts as the input to a 16 � 4 ROM whose output is floating when the enable input E is 0. A partial table of the contents of the ROM is as follows Address 0 2 4 6 8 10 11 14
Data 0011 1111 0100 1010 1011 1000 0010 1000
The clock to the register is shown, and the data on the W bus at time t is 0110. The data on the bus at time t is
(a) 1111 (b) 1011 (c) 1000 (d) 0010
60. In an 8085 microprocessor, the instruction CMP B has been executed while the content of the accumulator is less than that of register B. As a result
(a) Carry flag will be set but Zero flag will be reset
(b) Carry flag will be reset but Zero flag will be set
(c) Both Carry flag and Zero flag will be reset
(d) Both Carry flag and Zero flag will be set
61. Let X and Y be two statistically independent random variables uniformly distributed in the ranges (-1,1) and (-2,1) respectively. Let Z = X + Y. then the probability that [Z = -2] is
(a) zero (b) 1
(c) 1 3 (d) 1 12
62. Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete time system has the input-output relationship,
where x(n) is the input and y(n) is the output. The above system has the properties
(a) P, S but not Q, R (b) P, Q, S but not R
(c) P, Q, R, S (d) Q, R, S but not P
Data for are given below. Solve the problems and choose the correct answers. Q.63-64
The system under consideration is an RC low-pass filter (RC-LPF) with R = 1.0 k and C = 1.0 F.
63. Let H(f) denote the frequency response of the RC-LPF. Let f be the highest
(a) 327.8 (b) 163.9 (c) 52.2 (d) 104.4
64. Let t (f) be the group delay function of the given RC-LPF and f = 100 Hz. Then
(a) 0.717 (b) 7.17 (c) 71.7 (d) 4.505
Data for are given below. Solve the problems and choose the correct Q.65 - 66 answers. X(t) is a random process with a constant mean value of 2 and the autocorrelation
65. Let X be the Gaussian random variable obtained by sampling the process at t = t
66. Let Y and Z be the random variables obtained by sampling X(t) at t =2 and t = 4 respectively. Let W = Y � Z. The variance of W is
(a) 13.36 (b) 9.36 (c) 2.64 (d) 8.00
67. Let x(t) = 2cos(800 p t) + cos(1400 p t). x(t) is sampled with the rectangular pulse train shown in figure. The only spectral components (in kHz) present in the sampled signal in the frequency range 2.5 kHz to 3.5 kHz are
68. The signal flow graph of a system is shown in figure. The transfer function
69. The root locus of the system G s H s s s s = has the break-away point located at
(a) (-0.5,0) (b) (-2.548,0) (c) (-4,0) (d) (-0.784,0)
70. The approximate Bode magnitude plot of a minimum-phase system is shown in figure. The transfer function of the system is
71. A second-order system has the transfer function =
with r(t) as the unit-step function, the response c(t) of the system is represented by
72. The gain margin and the phase margin of a feedback system with
73. The zero-input response of a system given by the state-space equation
74. A DSB-SC signal is to be generated with a carrier frequency f = 1MHz using a nonlinear device with the input-output characteristic
where a and a are constants. The output of the nonlinear device can be filtered by an appropriate band-pass filter.
The data for Q.75 � 76 are given below. Solve the problems and choose the correct answers.
75. c(t) and m(t) are used to generate an AM signal. The modulation index of the generated AM signal is 0.5. Then the quantity Total sideband power.
Carrier power is
(a) 1
2 (b) 1 4 (c) 1 3 (d) 1 8
76. c(t) and m(t) are used to generate an FM signal. If the peak frequency deviation of the generated FM signal is three times the transmission bandwidth of the AM
77. Choose the correct one from among the alternatives A, B, C, D after matching an item in Group 1 with the most appropriate item in Group 2.
Group 1 Group 2
P Ring modulator 1 Clock recovery
Q VCO 2 Demodulation of FM
R Foster-Seely discriminator 3 Frequency conversion
S Mixer 4 Summing the two inputs
5 Generation of FM
6 Generation of DSB-Sc
78. A super heterodyne receiver is to operate in the frequency range 550 kHz � 1650 kHz, with the intermediate frequency of 450 kHz. Let R =
required capacitance ratio of the local oscillator and I denote the image frequency
(in kHz) of the incoming signal. If the receiver is tuned to 700 kHz, then
(a) R = 4.41, I = 1600 (b) R = 2.10, I = 1150
(c) R = 3.0, I = 1600 (d) R = 9.0, I = 1150
79. A sinusoidal signal with peak-to-peak amplitude of 1.536 V is quantized into 128 levels using a mid-rise uniform quantizer. The quantization noise power is
(a) 0.768 V (b) 48 � 10 V (c) 12 � 10 V (d) 3.072 V
80. If E , the energy per bit of a binary digital signal, is 10 watt-sec and the one-sided power spectral density of the white noise, N = 10 W/Hz, then the output SNR of the matched filter is
(a) 26 dB (b) 10 dB (c) 20 dB (d) 13 dB
81. The input to a linear delta modulator having a step-size � = 0.628 is a sine wave with frequency f and peak amplitude E . If the sampling frequency f = 40 kHz, the combination of the sine-wave frequency and the peak amplitude, where slope overload will take place is
(a) 0.3 V 8 kHz
(b) 1.5 V 4 kHz
(c) 1.5 V 2 kHz
(d) 3.0 V 1 kHz
82. If S represents the carrier synchronization at the receiver and represents the bandwidth efficiency, then the correct statement for the coherent binary PSK is
(a) = 0.5, S is required (b) = 1.0, S is required
(c) = 0.5, S is not required (d) = 1.0, S is not required
83. A signal is sampled at 8 kHz and is quantized using 8-bit uniform quantizer. Assuming SNR for a sinusoidal signal, the correct statement for PCM signal with a bit rate of R is
(a) R = 32 kbps, SNR = 25.8 dB (b) R = 64 kbps, SNR = 49.8 dB
(c) R = 64 kbps, SNR = 55.8 dB (d) R = 32 kbps, SNR = 49.8 dB
84. Medium 1 has the electrical permitivity e =1.5 e farad/m and occupies the region to the left of x = 0 plane. Medium 2 has the electrical permitivity e = 2.5 e farad/m and occupies the region to the right of x = 0 plane. If E in medium 1 is E u u u = - + 2 3 1 volt/m, then E in medium 2 is
85. If the electric field intensity is given by E xu yu zu = volt/m, the potential difference between X(20,0) and Y(1,2,3) is
(a) +1 volt (b) -1 volt (c) +5 volt (d) +6 volt
86. A uniform plane wave traveling in air is incident on the plane boundary between air and another dielectric medium with e = 4. The reflection coefficient for the normal incidence, is
(a) zero (b) 0.5 180� (c) 0.333 0� (d) 0.333 180�
87. If the electric field intensity associated with a uniform plane electromagnetic wave traveling in a perfect dielectric medium is give by
88. A short-circuited stub is shunt connected to a transmission line as shown in Figure. If Z = 50 ohm, the admittance Y seen at the junction of the stub and the transmission line is
89. A rectangular metal wave-guide filled with a dielectric material of relative permitivity e = 4 has the inside dimensions 3.0cm � 1.2cm. The cut-off frequency for the dominant mode is
(a) 2.5 GHz (b) 5.0 GHz (c) 10.0 GHz (d) 12.5 GHz
90. Two identical antennas are placed in the = 2 plane as shown in figure. The elements have equal amplitude excitation with 180� polarity difference, operating at wavelength . The correct value of the magnitude of the far-zone resultant electric field strength normalized with that of a single element, both computed for f = 0, is .
