GATE Last Ten Years EC Question Papers

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GATE 2004 ECE Question Paper With Solutions

GATE 2003 ECE Question Paper With Solutions

GATE 2002 ECE Question Paper With Solutions

GATE 2001 ECE Question Paper With Solutions

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GATE 2001 Question Paper With Solutions

SECTION - A
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each. For each of these sub-questions, four possible alternatives (A,B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.

1.5. The region of convergence of the z-transform of a unit step function is
(a) z > 1 (b) z < 1
(c) (Real part of z) > 0 (d) (Real part of z) < 0

1.7. MOSFET can be used as a
(a) current controlled capacitor (b) voltage controlled capacitor
(c) current controlled inductor (d) voltage controlled inductor

1.8. The effective channel length of a MOSFET in saturation decreases with increase in
(a) gate voltage (b) drain voltage
(c) source voltage (d) body voltage

1.10. The 2’s complement representation of –17 is
(a) 01110 (b) 01111 (c) 11110 (d) 10001

1.11. Consider the following two statements:
Statement 1: A stable multi-vibrator can be used for generating square wave.
Statement 2: B stable multi-vibrator can be used for storing binary information.
(a) Only statement 1 is correct
(b) Only statement 2 is correct
(c) Both the statements 1 and 2 are correct
(d) Both the statements 1 and 2 are incorrect

1.13. An 8085 microprocessor based system uses a 4K × 8-bit RAM whose starting
address is AA00. The address of the last byte in this RAM is
(a) 0FFFH (b) 1000 H (c) B9FF H (d) BA00 H

15. If the characteristic equation of a closed-loop system is
s2+2S+2= 0 , then the system is
(a) over damped (b) critically damped
(c) underdamped (d) undamped

1.19. A band limited signal is sampled at the Nyquist rate. The signal can be recovered
by passing the samples through
(a) an RC filter (b) an envelope detector
(c) a PLL
(d) an ideal low-pass filter with appropriate bandwidth

1.21. If a signal f(t) has energy E, the energy of the signal f(2t) is equal to
(a) E (b)E/2 (c) 2E (d) 4E

1.22. A transmission line is distortion-less if
(a)RL=1/GC (b) RL = GC (c) LG = RC (d) RG = LC

1.24. The phase velocity of waves propagating in a hollow metal waveguide is
(a) greater than the velocity of light in free space.
(b) less than the velocity of light in free space.
(c) equal to the velocity of light in free space.
(d) equal to the group velocity.

1.25. The dominant mode in a rectangular waveguide is TE10, because this mode has
(a) no attenuation (b) no cut-off
(c) no magnetic field component (d) the highest cut-off wavelength

2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks
each. For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.

2.18 A video transmission system transmits 625 picture frames per second. Each
frame consists of a 400 × 400 pixel grid with 64 intensity levels per pixel. The
data rate of the system is
(a) 16 Mbps (b) 100 Mbps (c) 600 Mbps (d) 6.4 Gbps

2.22 A material has conductivity of 10-2 mho/m and a relative permittivity of 4. The
frequency at which the conduction current in the medium is equal to the
displacement current is
(a) 45 MHz (b) 90 MHz (c) 450 MHz (d) 900 MHz

2.23 A uniform plane electromagnetic wave incident normally on a plane surface of a
dielectric material is reflected with a VSWR of 3. What is the percentage of
incident power that is reflected?
(a) 10% (b) 25% (c) 50% (d) 75%

2.24 A medium wave radio transmitter operating at a wavelength of 492 m has a
tower antenna of height 124m. What is the radiation resistance of the antenna?
(a) 25Ω (b) 36.5Ω (c) 50Ω (d) 73Ω

SECTION – B
This section consists of TWENTY questions of FIVE marks each. Attempt ANY FIFTEEN
questions. Answers must be given in the answer book provided.

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GATE 2002 ECE Question Paper

SECTION – A (75 marks)
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each. For each of these sub-questions, four possible alternatives (A,B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed

1.3 Convolution of x(t + 5) with impulse function δ(t – 7) is equal to
(a) x(t - 12) (b) x(t + 12) (c) x(t - 2) (d) x(t + 2)

1.4 Which of the following cannot be the Fourier series expansion of a periodic
signal?
(a) x(t) = 2cos t + 3 cos 3t (b) x(t) = 2cos πt + 7 cos t
(c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5πt + sin 3.5 πt

1.6 In a negative feedback amplifier using voltage-series (i.e. voltage-sampling
series mixing) feedback. (Ri and Ro denote the input and output resistance
respectively)
(a) Ri decreases and Ro decreases (b) Ri decreases and Ro increases
(c) Ri increases and Ro decreases (d) Ri increases and Ro increases

1.7 A 741-type op-amp has a gain-bandwidth product of 1 MHz. A non-inverting
amplifier using this op-amp and having a voltage gain of 20 dB will exhibit a 3-dB
bandwidth of
(a) 50 KHz (b) 100 KHz (c)1000/17 KHz (d) 1000/7.07

1.9 4-bit 2’s complement representation of a decimal number is 1000. The number is
(a) +8 (b) 0 (c) -7 (d) -8

1.11 The number of comparators required in a 3-bit comparator type ADC is
(a) 2 (b) 3 (c) 7 (d) 8

1.18 A linear phase channel with phase delay TP and group delay Tg must have
(a) TP= Tg=constant (b) TP ∝f and Tg∝f
(c) TP = constant and Tg∝f (d) TP ∝f and Tg =constant

1.19. A 1 MHz sinusoidal carrier is amplitude modulated by a symmetrical square wave
of period 100µsec. Which of the following frequencies will NOT be present in the
modulated signal?
(a) 990 KHz (b) 1010 KHz (c) 1020 KHz (d) 1030 KHz

1.21. For a bit-rate of 8 Kbps, the best possible values of the transmitted frequencies
in a coherent binary FSK system are
(a) 16 KHz and 20 KHz (b) 20 KHz and 32 KHz
(c) 20 KHz and 40 KHz (d) 32 KHz and 40 KHz

1.22. The line-of-sight communication requires the transmit and receive antenna to
face each other. If the transmit antenna is vertically polarized, for best reception
the receive antenna should be
(a) horizontally polarized (b) vertically polarized
(c) at 45° with respect to horizontal polarization
(d) at 45° with respect to vertical polarization

1.23. The VSWR can have any value between
(a) 0 and 1 (b) -1 and +1 (c) 0 and ∞ (d) 1 and ∞
1.24. In an impedance Smith chart, a clockwise movement along a constant resistance
circle gives rise to
(a) a decrease in the value of reactance
(b) an increase in the value of reactance
(c) no change in the reactance value
(d) no change in the impedance value

1.25 The phase velocity for the TE10-mode in an air-filled rectangular waveguide is (c is the velocity of plane waves in free space)
(a) less than c (b) equal to c
(c) greater than c (d) none of the above

2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks
each. For each of these sub-questions, four possible alternatives (A,B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.

2.5. An amplifier using an opamp with a slew-rate SR = 1V/µsec has a gain of 40 dB.
If this amplifier has to faithfully amplify sinusoidal signals from dc to 20 KHz
without introducing any slew-rate induced distortion, then the input signal level
must not exceed.
(a) 795 mV (b) 395 mV (c) 79.5 mV (d) 39.5 mV

2.20. A signal x(t) = 100 cos(24π×103)t is ideally sampled with a sampling period of 50 µsec and then passed through an ideal low-pass filter with cutoff frequency of 15
KHz. Which of the following frequencies is/are present at the filter output?
(a) 12 KHz only (b) 8 KHz only
(c) 12 KHz and 9 KHz (d) 12 KHz and 8 KHz

2.25. A person with a receiver is 5 Km away from the transmitter. What is the distance that this person must move further to detect a 3-dB decrease in signal strength?
(a) 942 m (b) 2070 m (c) 4978 m (d) 5320 m

SECTION – B (75 Marks)
This section consists of TWENTY questions (EC3-EC22) of FIVE marks each. Attempt ANY
FIFTEEN questions. Answers must be given in the answer book provided. Answer for
each question must start on a fresh page and must appear at one place only. (Answers
to all parts of a question must appear together).

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GATE 2003 ECE Question Paper

2. A source of angular frequency 1 rad/sec has a source impedance consisting of 1Ω
resistance in series with 1 H inductance. The load that will obtain the maximum
power transfer is
(a) 1 Ω resistance
(b) 1 Ω resistance in parallel with 1 H inductance
(c) 1 Ω resistance in series with 1 F capacitor
(d) 1 Ω 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

6. n-type silicon is obtained by doping silicon with
(a) Germanium (b) Aluminum (c) Boron (d) Phosphorus

7. The bandgap of silicon at 300 K is
(a) 1.36 eV (b) 1.10 eV (c) 0.80 eV (d) 0.67 eV

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. VSB > 0), the threshold voltage VT 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

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

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/meter2
(d) Ampere-meter

30. The depth of penetration of electromagnetic wave in a medium having
conductivity σ 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

31. Twelve 1Ω resistances are used as edges to form a cube. The resistance between
two diagonally opposite corners of the cube is
(a)5/6Ω (b)1/6Ω (c) 6/5Ω (d)3/2Ω

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
(a) P – 1 Q – 2 R – 4 S - 3 (b) P – 2 Q – 3 R – 1 S - 4
(c) P – 3 Q – 4 R – 1 S - 2 (d) P – 2 Q – 1 R – 4 S - 3

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 × 10000 (d) 8 × 10000

43. When the gate-to-source voltage (VGS) of a MOSFET with threshold voltage of
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 VGS 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 KΩ
and output resistance of 2.5 KΩ. The input resistance of the current-shunt
negative feedback amplifier using the above amplifier with a feedback factor of
0.2, is
(a) 1/11KΩ (b)1/5KΩ (c) 5 KΩ (d) 11 KΩ

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

51. Three identical amplifiers with each one having a voltage gain of 50, input
resistance of 1 KΩ and output resistance of 250Ω, 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 µF 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

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

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)1/6 (c)1/3 (d)1/12

81. The input to a linear delta modulator having a step-size = 0.628 is a sine wave with frequency fm and peak amplitude Em. If the sampling frequency fs = 40 kHz,
the combination of the sine-wave frequency and the peak amplitude, where slope
overload will take place is
Em fm
(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 ρ represents the bandwidth efficiency, then the correct statement for the coherent binary PSK is
(a) ρ = 0.5, S is required (b) ρ = 1.0, S is required
(c) ρ = 0.5, S is not required (d) ρ = 1.0, S is not required

83. A signal is sampled at 8 kHz and is quantized using 8-bit uniform quantizer.
Assuming SNRq for a sinusoidal signal, the correct statement for PCM signal with
a bit rate of R is
(a) R = 32 kbps, SNRq = 25.8 dB (b) R = 64 kbps, SNRq = 49.8 dB
(c) R = 64 kbps, SNRq = 55.8 dB (d) R = 32 kbps, SNRq = 49.8 dB

89. A rectangular metal wave-guide filled with a dielectric material of relative
permitivity εr = 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

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GATE 2004 Electronics and Communication Engg Question Papers

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 (VBE) is 0.7V and the collector-to-base voltage (VCB) 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 S1 and S2.
S1: The β of a bipolar transistor reduces if the base width is increased.
S2: The β of a bipolar transistor increases if the doping concentration in the base
in increased
Which one of the following is correct?
(a) S1 is FALSE and S2 is TRUE (b) both S1 and S2 are TRUE
(c) both S1 and S2 are FALSE (d) S1 is TRUE and S2 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

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
(a) P – 3 Q – 2 R - 1 (b) P – 3 Q – 1 R - 2
(c) P – 2 Q – 1 R – 3 (d) P – 1 Q – 2 R - 2

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

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)8/6 (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 µsec (b) 20 µsec (c) 0.2 µsec (d) 1 µsec

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 t1≤t≤t2. 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 TE10 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)1/4 mW

37. Consider the following statements S1and S2
S1: At the resonant frequency the impedance of a series R-L-C circuit is zero.
S2: 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) S1 is FALSE and S2 is TRUE (b) both S1 and S2 are TRUE
(c) S1 is TRUE and S2 is FALSE (d) both S1 and S2 are FALSE

41. Consider the following statements S1 and S2.
S1: The threshold voltage (VT) of a MOS capacitor decreases with increase in gate
oxide thickness
S2: The threshold voltage (VT) of a MOS capacitor decreases with increase in
substrate doping concentration.
Which one of the following is correct?
(a) S1 is FALSE and S2 is TRUE (b) both S1 and S2 are TRUE
(c) S1 is TRUE and S2 is FALSE (d) both S1 and S2 are FALSE

42. The drain of an n-channel MOSFET is shorted to the gate so that VGS = VDS. The
threshold voltage (VT) of MOSFET is 1V. If the drain current (ID) is 1 mA for VGS =
2V, then for VGS = 3V, ID is
(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 1.1µm. If the longest wavelength that can be absorbed by another
material is 0.87 µm, then the bandgap of this material is
(a) 1.416 eV (b) 0.886 eV (c) 0.854 eV (d) 0.706 eV

50. In a full-wave rectifier using two ideal diodes, Vdc and Vm are the dc and peak
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

(a)Vdc=Vm/p PIV=2Vm (b)Vdc=2Vm/p PIV=2Vm
(c)Vdc=2Vm/p PIV=Vm (d)Vdc=Vm/p PIV=Vm

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

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 –6 respectively
(c) -7, -7 and –7 respectively (d) -25, -9 and –57 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 bidirectional 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
II. LXI D, FOF 1H
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

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

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

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 10-20 Watt/Hz, then the signal to noise ratio at the
receiver is
(a) 50 db (b) 30 db (c) 40 db (d) 60 db

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

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

89. A plane electromagnetic wave propagating in free space in incident normally on a
large slab of loss-less, non-magnetic, dielectric material with ε >ε0. 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 πΩ (b) 60 πΩ (c) 600 πΩ (d) 24 πΩ

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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GATE 2005 EC Solved Paper

3.A fair dice is rolled twice. The probability that anodd number will follow an even
number is
a)1/2
(b)1/6
(c)1/3
(d)1/4

11. The band gap of Silicon at room temperature is:
(a) 1.3 eV (b) 0.7 eV (c) 1.1 eV (d) 1.4 eV

12. A Silicon PN junction at a temperature of 20°C has a reverse saturation current of 10 pico-Amperes (pA). The reverse saturation current at 40°C for the same bias
is approximately
(a) 30 pA (b) 40 pA (c) 50 pA (d) 60 pA

13. The primary reason for the widespread use of Silicon in semiconductor device
technology is
(a) abundance of Silicon on the surface of the Earth.
(b) larger bandgap of Silicon in comparison to Germanium.
(c) favorable properties of Silicon-dioxide (SiO2)
(d) lower melting point

14. The effect of current shunt feedback in an amplifier is to
(a) increase the input resistance and decrease the output resistance.
(b) increase both input and output resistances.
(c) decreases both input and output resistances.
(d) decrease the input resistance and increase the output resistance

16. The first and the last critical frequency of an RC-driving point impedance function
must respectively be
(a) a zero and a pole (b) a zero and a zero
(c) a pole and a pole (d) a pole and a zero

17. The cascode amplifier is a multistage configuration of
(a) CC-CB (b) CE-CB (c) CB-CC (d) CE-CC

18. Decimal 43 in Hexadecimal and BCD number system is respectively
(a) B2, 0100 0011 (b) 2B, 0100 0011
(c) 2B, 0011 0100 (d) B2, 0100 0100

24. Which of the following analog modulation scheme requires the minimum
transmitted power and minimum channel bandwidth?
(a) VSB (b) DSB-SC (c) SSB (d) AM

27. Despite the presence of negative feedback, control systems still have problems of
instability because the
(a) components used have nonlinearities.
(b) dynamic equations of the subsystems are not known exactly.
(c) mathematical analysis involves approximations.
(d) system has large negative phase angle at high frequencies.

30. Refractive index of glass is 1.5. Find the wavelength of a beam of light with a
frequency of 1014 Hz in glass. Assume velocity of light is 3×108 m/s in vacuum.
(a) 3 µm (b) 3 mm (c) 2 µm (d) 1 µm

36. Match the following and choose the correct combination:

Group 1 Group 2
E. Newton –Raphson method 1. Solving nonlinear equations
F. Runge-Kutta method 2. Solving linear simultaneous equations
G. Simpson’s Rule 3. Solving ordinary differential equations
H. Gauss elimination 4. Numerical integration
5. Interpolation
6. Calculation of Eigen values
(a) E – 6 F – 1 G – 5 H - 3 (b) E – 1 F – 6 G – 4 H - 3
(c) E – 1 F – 3 G – 4 H - 2 (d) E – 5 F – 3 G – 4 H - 1

45. A Silicon PN junction diode under reverse bias has depletion region of width 10
µm. The relative permittivity of Silicon,εr= 11.7 and the permittivity of free space
εd=8.85X10-12 f/m The depletion capacitance of the diode per square meter is
(a) 100 µF (b) 10 µF (c) 1 µF (d) 20 µF

56. The present output Qn of an edge triggered JK flip-flop is logic 0. If J=1, then Qn+1
(a) cannot be determined (b) will be logic 0
(c) will be logic 1 (d) will race around

69. A MOS capacitor made using p type substrate is in the accumulation mode. The
dominant charge in the channel is due to the presence of
(a) holes (b) electrons
(c) positively charged ions (d) negatively charged ions

73. A carrier is phase modulated (PM) with frequency deviation of 10 kHz by a single
tone frequency of 1 kHz. If the single tone frequency is increased to 2 kHz,
assuming that phase deviation remains unchanged, the bandwidth of the PM
signal is
(a) 21 kHz (b) 22 kHz (c) 42 kHz (d) 44 kHz


76. Characteristic impedance of a transmission line is 50 Ω.Input impedance of the
open circuited line is Zoc=100+j150Ω.When the transmission line is shortcircuited the value of the input impedance will be
(a) 50 Ω (b) 100 + j150Ω
(c) 7.69 + j11.54 Ω (d) 7.69 – j11.54

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GATE 2006 ECE Question Papes With Solutions

7. The values of voltage (VD ) across a tunnel-diode corresponding to peak and valley currents are and Vp and Vd respectively.The range of tunnel-diode voltage VD for which the slope of its I−Vd characteristics is negative would be
(A) VD< 0
(B) 0≤VD (C)Vp≤vD (D) VD≥Vv

8.The concentration of minority carriers in an extrinsic semiconductor under
equilibrium is:
(A) directly proportional to the doping concentration
(B) inversely proportional to the doping concentration
(C) directly proportional to the intrinsic concentration
(D) inversely proportional to the intrinsic concentration
9. Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the
(A) diffusion current
(B) drift current
(C) recombination current
(D) induced current

10. The phenomenon known as “Early Effect” in a bipolar transistor refers to a
reduction of the effective base-width caused by
(A) electron-hole recombination at the base
(B) the reverse biasing of the base-collector junction
(C) the forward biasing of emitter-base junction
(D) the early removal of stored base charge during saturation-to-cutoff
switching.

20. A transmission line is feeding 1 Watt of power to a horn antenna having a gain of 10 dB. The antenna is matched to the transmission line. The total power radiated
by the horn antenna into the free-space is:
(A) 10 Watts
(B) 1 Watt
(C) 0.1 Watt
(D) 0.01 Watt

22. For the function of a complex Variable W=lnZ
where, W=u+jv Z= x+jy ), the u = constant lines get mapped in Z-plane
as
(A) set of radial straight lines
(B) set of concentric circles
(C) set of confocal hyperbolas
(D) set of confocal ellipses

32. The first and the last critical frequencies (singularities) of a driving point
impedance function of a passive network having two kinds of elements, are a
pole and a zero respectively. The above property will be satisfied by
(A) RL network only
(B) RC network only
(C) LC network only
(D) RC as well as RL networks

38. The majority carriers in an n-type semiconductor have an average drift velocity v
in a direction perpendicular to a uniform magnetic field B. the electric field E
induced due to Hall effect acts in the direction
(A) v × B
(B) B × v
(C) along v
(D) opposite to v

43. A new Binary Coded Pentary (BCP) number system is proposed in which every
digit of a base-5 number is represented by its corresponding 3-bit binary code.
For example, the base-5 number 24 will be represented by its BCP code 010100.
In this numbering system, the BCP code 100010011001 corresponds to the
following number in base-5 system
(A) 423
(B) 1324
(C) 2201
(D) 4231

61. A zero-mean white Gaussian noise is passed through an ideal lowpass filter of
bandwidth 10 kHz. The output is then uniformly sampled with sampling period
ts= 0.03 msec. The samples so obtained would be
(A) correlated
(B) statistically independent
(C) uncorrelated
(D) orthogonal

62. A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming independent generation of symbols, the
most efficient source encoder would have average bit rate as
(A) 6000 bits/sec
(B) 4500 bits/sec
(C) 3000 bits/sec
(D) 1500 bits/sec

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GATE 2007 EC Question Paper

GATE 2007 ECE Question Paper

Q.1 – Q.20 Carry One Mark Each
Q.21 – Q.75 Carry Two Marks Each
Linked Answer Questions: Q.76 to Q.85 Carry Two Marks Each

10. In a P+ n junction diode under reverse bias, the magnitude of electric field is maximum at
(A) the edge of the depletion region on the p-side
(B) the edge of the depletion region on the n-side
(C) the p+ n junction
(D) the centre of the depletion region on the n-side

12. In a transconductance amplifier, it is desirable to have
(A) a large input resistance and a large output resistance
(B) a large input resistance and a small output resistance
(C) a small input resistance and a large output resistance
(D) a small input resistance and a small output resistance
13. X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s
complement format. The sum of X and Y represented in two’s complement format
using 6 bits is:
(A) 100111 (B) 001000 (C) 000111 (D) 101001
14. The Boolean function Y AB CD = + is to be realized using only 2-input NAND
gates. The minimum number of gates required is:
(A) 2 (B) 3 (C) 4 (D) 5

21. It is given that X1,X2,.... Xm are M non-zero, orthogonal vectors. The dimension of the vector space spanned by the 2M vectors X1, X2.... Xm,-X1,-X2,...-Xm is:
(A) 2M (B) M + 1 (C) M
(D) dependent on the choice of X1,X2,... Xm

22. Consider the function F(x)=X2-X-2 The maximum value of f x( ) in the closed
interval [−4, 4] is:
(A) 18 (B) 10
(C) -2.25 (D) indeterminate

23. An examination consists of two papers, Paper 1 and Paper 2. The probability of
failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is:
(A) 0.5 (B) 0.18 (C) 0.12 (D) 0.06

33. Group I lists four types of p-n junction diodes. Match each device in Group I with
one of the option in Group II to indicate the bias condition of that device in its
normal mode of operation.
Group I Group II
(P) Zener Diode (1) Forward bias
(Q) Solar cell (2) Reverse bias
(R) LASER diode
(S) Avalanche Photodiode
(A) P-1 Q-2 R-1 S-2 (B) P-2 Q-1 R-1 S-2
(C) P-2 Q-2 R-1 S-1 (D) P-2 Q-1 R-2 S-2

34. The DC current gain ( β ) of a BJT is 50. Assuming that the emitter injection
efficiency is 0.995, the base transport factor is:
(A) 0.980 (B) 0.985 (C) 0.990 (D) 0.995

35. Group I lists four different semiconductor devices. Match each device in Group I
with its characteristic property in Group II.
Group I Group II
(P) BJT (1) Population inversion
(Q) MOS capacitor (2) Pinch-off voltage
(R) LASER diode (3) Early effect
(S) JFET (4) Flat-band voltage
(A) P-3 Q-1 R-4 S-2 (B) P-1 Q-4 R-3 S-2
(C) P-3 Q-4 R-1 S-2 (D) P-3 Q-2 R-1 S-4

48. A Hilbert transformer is a
(A) non-linear system (B) non-causal system
(C) time-varying system (D) low-pass system

58. In delta modulation, the slope overload distortion can be reduced by
(A) decreasing the step size (B) decreasing the granular noise
(C) decreasing the sampling rate (D) increasing the step size

62. In a GSM system, 8 channels can co-exist in 200 KHz bandwidth using TDMA. A
GSM based cellular operator is allocated 5 MHz bandwidth. Assuming a frequency
reuse factor of 1/5 i.e. a five-cell repeat pattern, the maximum number of
simultaneous channels that can exist in one cell is:
(A) 200 (B) 40 (C) 25 (D) 5

64. An air-filled rectangular waveguide has inner dimensions of 3 cm × 2 cm. The
wave impedance of the TE20 mode of propagation in the waveguide at a frequency of 30 GHz is (free space impedance η0= Ω 377 )
(A) 308 Ω (B) 355 Ω (C) 400 Ω (D) 461 Ω

71. The gate oxide thickness in the MOS capacitor is:
(A) 50 nm (B) 143 nm (C) 350 nm (D) 1 µm

72. The maximum depletion layer width in silicon is
(A) 0.143 µm (B) 0.857 µm (C) 1 µm (D) 1.143 µm

73. Consider the following statements about the C-V characteristics plot:
S1: The MOS capacitor has an n-type substrate.
S2: If positive charges are introduced in the oxide, the C-V plot will shift to the
left. Then which of the following is true?
(A) Both S1 and S2 are true (B) S1 is true and S2 is false
(C) S1 is false and S2 is true (D) Both S1 and S2 are false

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GATE 2008 EC Question Paper

1 to 20 Carry One Mark Each

2. The system of linear equations
4x+ 2y= 7
2x+ y= 6

has
(A) a unique solution (B) no solution
(C) an infinite number of solutions (D) exactly two distinct solutions
3. The equation sin(z)= 10has
(A) no real or complex solution
(B) exactly two distinct complex solutions
(C) a unique solution
(D) an infinite number of complex solutions
4. For real values of x, the minimum value of the function f(x)= exp(x)+ exp(-x) is
(A) 2 (B) 1 (C) 0.5 (D) 0

10. The impulse response h(t) of a linear time-invariant continuous time system is
described by h(t)= exp(αt)u(t)+ exp(βt)(-ut)where u(t) denotes the unit step
function, and α and β are real constants. This system is stable if
(A) α is positive and β is positive (B) α is negative and β is negative
(C) α is positive and β is negative (D) α is negative and β is positive

13. Which of the following is NOT associated with a p-n junction?
(A) Junction capacitance (B) Charge Storage Capacitance
(C) Depletion Capacitance (D) Channel Length Modulation
14. Which of the following is true?
(A) A silicon wafer heavily doped with boron is a p+ substrate
(B) A silicon wafer lightly doped with boron is a p+ substrate
(C) A silicon wafer heavily doped with arsenic is a p+ substrate
(D) A silicon wafer lightly doped with arsenic is a p+ substrate
15. For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is
(A) 360º (B) 180º (C) 90º (D) 45

18. A silicon wafer has 100nm of oxide on it and is inserted in a furnace at a
temperature above 1000ºC for further oxidation in dry oxygen. The oxidation
rate
(A) is independent of current oxide thickness and temperature
(B) is independent of current oxide thickness but depends on temperature
(C) slows down as the oxide grows
(D) is zero as the existing oxide prevents further oxidation

49. An 8085 executes the following instructions
2710 LXI H, 30A0H
2713 DAD H
2714 PCHL
All addresses and constants are in Hex. Let PC be the contents of the program
counter and HL be the contents of the HL register pair just after executing PCHL.
Which of the following statements is correct
(A) PC 2715H = (B) PC 30A0H = (C) PC 6140H = (D) PC 6140H =
HL 30A0H = HL 2715H = HL 6140H = HL 2715H

55. Consider the following assertions
S1: For Zener effect to occur, a very abrupt junction is required
S2: For quantum tunneling to occur, a very narrow energy barrier is required
Which of the following is correct?
(A) Only S2 is true
(B) S1 and S2 are both true but S2 is not a reason for S1
(C) S1 and S2 are both true and S2 is a reason for S1
(D) Both S1 and S2 are false

56. The two numbers represented in signed 2’s complement form are
P 11101101 and Q 11100110 = = . If Q is subtracted from P, the value obtained in
signed 2’s complement form is
(A) 100000111 (B) 00000111 (C) 11111001 (D) 11111100

61.A rectangular waveguide of internal dimensions (a 4cm and b 3 = = ) is to be
operated in TE11 mode. The minimum operating frequency is
(A) 6.25GHz (B) 6.0GHz (C) 5.0GHz (D) 3.75GHz
62. One of a loss-less transmission line having the characteristic impedance of 75Ω
and length of 1cm is short-circuited. At 3GHz, the input impedance at the other
end of the transmission line is
(A) 0 (B) Resistive (C) Capacitive (D) Inductive
63. A uniform plane wave in the free space is normally incident on an infinitely thick
dielectric slab (dielectric constant ε =
r 9 ). The magnitude of the reflection
coefficient is
(A) 0 (B) 0.3 (C) 0.5 (D) 0.8
64. In the design of a single mode step index optical fiber close to upper cut-off, the
single mode operations is NOT preserved if
(A) Radius as well as operating wavelength are halved
(B) Radius as well as operating wavelength are doubled
(C) Radius is halved and operating wavelength is doubled
(D) Radius is doubled and operating wavelength is halved
65. At 20GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70%
efficiency is
(A) 15dB (B) 25dB (C) 35dB (D) 45dB
66. Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3dB cut-off frequency of fc. The noise power at the filter output is
(A) K (B) Kfc (C) K fcπ (D) ∞
68. Four messages band limited to W, W, 2W and 3W respectively are to be
multiplexed using Time Division Multiplexing (TDM). The minimum bandwidth
required for transmission of this TDM signal is
(A) W (B) 3W (C) 6W (D) 7W

A speech signal, band limited to 4kHz and peak voltage varying between +5V and
-5V is sampled at the Nyquist rate. Each sample is quantized and represented by
8 bits.
71. If the bits 0 and 1 are transmitted using bipolar pulses, the minimum bandwidth
required for distortion free transmission is
(A) 64kHz (B) 32kHz (C) 8kHz (D) 4kHz
72. Assuming the signal to be uniformly distributed between its peak values, the
signal to noise ratio at the quantizer output is
(A) 16dB (B) 32dB (C) 48dB (D) 64dB

73. The number of quantitization levels required to reduce the quantization noise by
a factor of 4 would be
(A) 1024 (B) 512 (C) 256 (D) 64

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GATE 2012 Online Application Process

Application Process:

Step 1:Decide Payment Option
Gateway Payment:
Payment can be made using netbanking. Bank service charge is extra (maximum of Rs.30/-)

Challan Payment:
Payment by cash at ICICI, Indian Bank or State Bank of India branches. Bank service charge is extra (maximum of Rs.25/-)

Step 2: Obtain SC / ST / PD Certificate (if applicable)

Authorities empowered to issue Certificates

Step 3: Apply Online

Candidates must follow the instructions provided while applying online.

At the end of this process, a PDF file will be generated with the following pages:
Page-1: Instructions
Page-2: GATE 2012 Application - GATE Copy
Page-3: GATE 2012 Application - Candidate's Copy
Page-4: Address Slip of respective zonal GATE office
Page-5: Bank Challan (for Challan Payment option only)
Take a print out of the entire file on A4 size white sheets using a laser/inkjet printer.

Step 4: Cash Payment: (only for Challan Payment option)

The bank challan (Page-5) will be printed in triplicate. Take it to any one of the branches of ICICI, Indian Bank or State Bank of India (as opted by the candidate) and pay the fees. Bank will retain a copy and will return two copies to you. In those two copies, retain the Candidate's copy with you and attach the GATE Copy with the application.

Step 5:
Paste your recent photograph (3.5 cm X 3.5 cm) in the designated place of Page-2. Before pasting, please write your name and application number on the backside of the photo with black ball point pen.
Sign at the designated place of Page-2.
Paste Page-4 on top of a 10 inch x 12 inch size laminated envelope.

Step 6: Post/Submission
Before posting your application form, make sure that, in addition to the other relevant attachments, you have attached either a copy of the degree certificate or a certificate from your college principal as indicated below:
Candidates should submit a copy of the degree certificate or provisional certificate if they have passed their qualifying degree in 2011 or before.

Candidates with the following eligibility conditions should submit a certificate signed by the Principal of the college, where the candidate is studying, clearly indicating the year of passing of the candidate in the qualifying degree.

Students in the final year of Bachelor's degree programme in Engineering/Technology/ Architecture (4 years after 10+2).

Students in the final year of Bachelor's degree programme in Engineering/Technology/Architecture (Post-B.Sc./Post-Diploma).

Students in the final year of Master's degree programmes in any branch of Science/Mathematics/ Statistics/Computer Applications or equivalent.

Students in the second or higher year of the Four-year Integrated Master's degree programme (Post-B.Sc.) in Engineering/Technology.

Students in the fourth or higher year of Five-year Integrated Master's degree programme or Dual Degree programme in Engineering/Technology.

To download the format of the certificate to be sent by the candidates, click here.

Candidates With Backlog: Candidates with a backlog of papers should submit a copy of the marks sheet of final semester / final year or copy of the course completion certificate or a letter from the principal indicating that the student has a backlog and will be completing the degree in 2012.

Duly filled-in Application with appropriate enclosures must be sent by Speed Post (preferably) or by Registered Post to The Chairman, GATE of the Zone corresponding to the 1st Choice of Examination City, so as to reach on or before Monday, 24th October, 2011

OR

It can be handed over personally to the respective Zonal GATE Office on or before Monday, 24th October, 2011.

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