GATE 2017 Electronics and Communication Engineering Session 1
Q. 1 Consider the 5×5 matrix.
It is given that A has only one real eigenvalue. Then the real eigenvalue of A is
A. -2.5
B. 0
C. 15
D. 25
Q. 2 The rank of the given matrix is
A. 0
B. 1
C. 2
D. 3
Q. 3 Consider the following statements about the linear dependence of the real-valued
functions y1=1, y2=x and y3=x^3, over the field of real numbers.
I. y1, y2 and y3 are linearly independent on -1<=x<=0
II. y1, y2 and y3 are linearly dependent on 0<=x<=1
III. y1, y2 and y3 are linearly independent on 0<=x<=1
IV. y1, y2 and y3 are linearly dependent on -1<=x<=0
Which one among the following is correct?
A. Both I and II are true
B. Both I and III are true
C. Both II and IV are true
D. Both III and IV are true
Q. 4 Three fair dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up (up to third decimal place) is
Q. 5 Consider the following statements for continuous-time linear time invariant (LTI) systems.
I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.
Which among the following is correct?
A. Both I and II are true.
B. Both I and II are not true.
C. Only I is true.
D. Only II is true.
Q. 6 Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as
y[n] = n[x[n]], for 0<=n<=10
y[n] = x[n] – x[n-1], otherwise
Which one of the following statements is true about the system?
A. It is causal and stable
B. It is causal but not stable
C. It is not causal but stable
D. It is neither causal nor stable
Q. 7 In the circuit shown, the positive angular frequency w (in radians per second) at which the magnitude of the phase difference between the voltages V1 and V2 equals pi/4 radians, is
Q. 8 A periodic signal x(t) has a trigonometric Fourier series expansion as given.
If x(t) = – x(-t) = – x(t – pi/w0), we can conclude that
A. an are zero for all n and bn are zero for all n even
B. an are zero for all n and bn are zero for all n odd
C. an are zero for n even and bn are zero for all n odd
D. an are zero for n odd and bn are zero for all n even
Q. 9 A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium abs Arsenic sites in the GaAs crystal. Which one of the following statements is true?
A. Silicon atoms act as p-type dopants in Arsenic sites and n-type dopants in Gallium sites
B. Silicon atoms act as n-type dopants in Arsenic sites and p-type dopants in Gallium sites
C. Silicon atoms act as p-type dopants in Arsenic as well as Gallium sites
D. Silicon atoms act as n-type dopants in Arsenic as well as Gallium sites
Q. 10 A n^+ -n Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of ND1 = 1 x 10^18 cm^-3 and ND2 = 1 x 10^15 cm^-3 corresponding to the n^+ and n regions respectively, At the operational temperature T, assume complete impurity ionization, kT/q = 25 mV, and intrinsic carrier concentration to be ni = 1 x 10^10 cm^-3. What is the magnitude of the built-in potential of this device?
A. 0.748 V
B. 0.460 V
C. 0.288 V
D. 0.173 V
Q. 11 For a narrow base PNP BJT, the excess minority carrier concentrations (nE for emitter, pB for base, nC for collector) normalized to equilibrium minority carrier concentrations (nE0 for emitter, pB0 for base, nC0 for collector) in the quasi-neutral emitter, base and collector regions are shown. Which one of the following biasing modes is the transistor operating in?
A. Forward active
B. Saturation
C. Inverse active
D. Cutoff
Q. 12 For the operational amplifier circuit shown, the output saturation voltages are +15V or -15V. The upper and lower threshold voltages for the circuit are, respectively
A. +5V and -5V
B. +7V and -3V
C. +3V and -7V
D. +3V and -3V
Q. 13 A good transconductance amplifier should have
A. high input resistance and low output resistance
B. low input resistance and high output resistance
C. high input and output resistances
D. low input and output resistances
Q. 14 The Miller Effect in the context of a Common Emitter amplifier explains
A. an increase in the low-frequency cutoff frequency
B. an increase in the high-frequency cutoff frequency
C. a decrease in the low-frequency cutoff frequency
D. a decrease in the high-frequency cutoff frequency
Q. 15 In the latch circuit shown, the NAND gates have non-zero, but unequal propagation delays. The present input condition is: P = Q = ‘0’. If the input condition is changed simultaneously to P = Q = ‘1’, the outputs X and Y are
A. X = ‘1’, Y = ‘1’
B. either X = ‘1’, Y = ‘0’ or X = ‘0’, Y = ‘1’
C. either X = ‘1’, Y = ‘1’ or X = ‘0’, Y = ‘0’
D. X = ‘0’, Y = ‘0’
Q. 16 The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 us, then the number of T-states needed for executing the instruction is
A. 1
B. 6
C. 7
D. 8
Q. 17 Consider the D-Latch shown in the figure, which is transparent when its clock input CK is high and has zero propagation delay. In the figure, the clock signal CLK1 has a 50% duty cycle and CLK2 is a one-fifth period delayed version of CLK1. The duty cycle at the output of the latch in percentage is
Q. 18 The open loop transfer function
G(s) = (s+1) / s^P(s+2)(s+3)
where p is an integer, is connected in unity feedback configuration as shown in the figure. Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is
Q. 19 Consider a stable system with transfer function
G(s) = (s^p + b1s^p-1 + … + bp) / (s^q + a1s^q-1 + … + aq)
where b1, …, bp and a1, … , aq are real valued constants. The slope of the Bode log magnitude curve of G(s) converges to -60 dB/decade as x —> infinity. A possible pair of
value for p and q is
A. p = 0 and q = 3
B. p = 1 and q = 7
C. p = 2 and q = 3
D. p = 3 and q = 5
Q. 20 Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?
A. (A)
B. (B)
C. (C)
D. (D)
Q. 21 Let (X1, X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I(X1; X2) between X1 and X2 in bits is
Q. 22 Which one of the following statements about differential pulse code modulation (DPCM) is true?
A. The sum of message signal sample with its prediction is quantized
B. The message signal sample is directly quantization, and it’s prediction is not used
C. The difference of message signal sample and a random signal is quantized
D. The difference of message signal sample with its prediction is quantized
Q. 23 In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is the inter symbol interference zero?
A. (A)
B. (B)
C. (C)
D. (D)
Q. 24 The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is V(l) = e^(-yl+jwt) Volts, where l is the distance of the cable in metres, y = (0.1 + j40)m^-1 is the complex propagation constant, and w = 2pi x 10^9 rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/metre is
Q. 25 Consider a wireless communication link between a transmitter and a receiver in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link
A. increases by a factor of 2
B. decreases by a factor of 2
C. remains unchanged
D. decreases by a factor of root of 2
Q. 26 Let f(x) = e^x+x^2 for real x. From among the following, choose the Taylor series
approximation of f(x) around x = 0, which includes all powers of x less than or equal to 3.
A. 1 + x + x^2 + x^3
B. 1 + x + 3/2 x^2 + x^3
C. 1 + x + 3/2 x^2 + 7/6 x^3
D. 1 + x + 3x^2 + 7x^3
Q. 27 A three dimensional region R of finite volume is described by
x^2 + y^2 <= z^3; 0 <= z <= 1,
where x, y, z are real. The volume of R (up to two decimal places) is
Q. 28 Let C be the straight line segment from point A: (0, 2, 1) to point B: (4, 1, -1). The value of I is
Q. 29 Which one of the following is the general solution of the first order differential equation dy/dx = (x + y + 1)^2, where x, y are real?
A. y = 1 + x + tan^-1(x + c), where c is a constant.
B. y = 1 + x + tan(x + c), where c is a constant.
C. y = 1 – x + tan^-1(x + c), where c is a constant.
D. y = 1 – x + tan(x + c), where c is a constant.
Q. 30 Starting with x = 1, the solution of the equation x^3 + x = 1, after two iterations of Newton- Raphson’s method (up to two decimal places)0 is
Q. 31 Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
I. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued
II. The complex Fourier series coefficients of x(3t) are {3ak} where k is integer valued
III. The fundamental angular frequency of x(3t) is 6pi rad/s
For the three statements above, which one of the following is correct?
A. only II and III are true
B. only I and III are true
C. only III is true
D. only I is true
Q. 32 Two discrete-time signals x[n] and h[n] are both non-zero only for n = 0, 1, 2, and are zero otherwise. It is given that
x[0] = 1, x[1] = 2, x[2] = 1, h[0] = 1.
Let y(n) be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is
Q. 33 Let h[n] be the impulse response of a discrete-time linear time invariant (LTII) filter. The impulse response is given by
h[0] = 1/3; h[1] = 1/3; and h[n] = 0 for n < 0 and n > 2.
Let H(w) be the discrete-time Fourier transform (DTFT) of h[n] where w is the normalized angular frequency in radians. Given that H(w0) = 0 and 0 < w0 < pi, the value of w0 (in radians) is equal to
Q. 34 The figure shows an RLC circuit excited by the sinusoidal voltage 100cos(3t) Volts, where t is in seconds. The ratio amplitude of V2/amplitude of V1 is
Q. 35 In the circuit shown, the voltage Vin(t) is described by:
Vin(t) = 0, for t < 0
Vin(t) = 15 Volts, for t >= 0
where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is
Q. 36 The dependence of drift velocity of electrons on electric field in a semiconductor is shown. The semiconductor has a uniform electron concentration of n = 1 x 10^16 cm^-3 and electronic charge q = 1.6 x 10^-19 C. If a bias of 5 V is applied across a 1 um region of this semiconductor, the resulting current density in this region, in kA/cm^2, is
Q. 37 As shown, a uniformly doped silicon (Si) bar of length L = 0.1 um with a donor concentration ND = 10^16 cm^-3 is illuminated at x = 0 such that electron and hole pairs are generated at the rate of GL = GL0 (1 – x/L0, 0 <=x<=L, where GL0 = 10^17 cm^-3 s^-1. Hole lifetime is 10^-4 s, electronic charge q = 1.6 x 10^-19 C, hole diffusion coefficient DP = 100 cm^2/s and low level injection condition prevails. Assuming a linearly decaying steady state excess hole concentration that goes to 0 at x = L, the magnitude of the diffusion current density at x = L/2, in A/cm^2, is
Q. 38 As shown, two Silicon (Si) abrupt p-n junction diodes are fabricated with uniform donor doping concentrations of ND1 = 10^14 cm6-3 and ND2 = 10^16 cm^-3 in the n-regions, and uniform acceptor doping concentrations of NA1 = 10^14 cm^-3 and NA2 = 10^16 cm^-3 in the p-regions of the diodes, respectively. Assuming that the reverse bias voltage is >> builtin potentials of the diodes, te ratio C2/C1 of their reverse bias capacitances for the same applied reverse bias, is
Q. 39 In the figure shown, the npn transistor acts as a switch. For the input Vin(t) as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when T is large. Assume collector-to-emitter voltage at saturation VCE(sat) = 0.2 V and base-to-emitter voltage VBE = 0.7 V. The minimum value of the common-base current gain of the transistor for the switching should be
Q. 40 For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage Vtn = 1 V and its transconductance parameter is 1 mA/V^2. Neglect channel length modulation and body bias effects. Under these conditions, the drain current ID in mA is
Q. 41 For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector currents are equal. Given that VT = 25 mV, VBE = 0.7 V, and the BJT output resistance ro is practically infinite. Under these conditions, the midband voltage gain magnitude, Av = |vo/vi| V/V, is
Q. 42 The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, A0 = 10^5 V/V and an open-loop cutoff frequency, fc = 8 Hz. The voltage gain of the amplifier at 15 kHz, in V/V, is
Q. 43 Which one of the following gives the simplified sum of products expression for the Boolean function F = m0 + m2 + m3 + m5, where m0, m2, m3 , m5 are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?
A. (A)
B. (B)
C. (C)
D. (D)
Q. 44 A 4-bit shift register circuit configured for right-shift operation, i.e. Din —-> A, A —-> B, B —- > C, C —-> D, is shown. If the present state of the shift register is ABCD = 1101, the number of clock cycles required to reach the state ABCD = 1111 is
Q. 45 The following FIVE instructions were executed on 8085 microprocessor.
MVI A 33H
MVI B 78H
ADD B
CMA
ANI 32H
The Accumulator value immediately after the execution of the fifth instruction is
A. 00H
B. 10H
C. 11H
D. 32H
Q. 46 A finite state machine (FSM) is implemented using the D flip-flops A and B, and logic gates, as shown in the figure. The four possible states of the FSM are QAQB = 00, 01, 10 and 11. Assume that Xin is held at a constant logic level throughout the operation of the FSM. When the FSM is initialized to the state QAQB = 00 and clocked, after a few clock cycles, it starts cycling through
A. all of the four possible states if Xin = 1
B. three of the four possible states if Xin = 0
C. only two of the four possible states if Xin = 1
D. only two of the four possible states if Xin = 0
Q. 47 A linear time invariant (LTI) system with the transfer function
G(s) = K(s62 + 2s + 2) / (s^2 – 3s + 2)
is connected in unity feedback configuration as shown in the figure. For the closed loop system shown, the root locus for 0 < K < infinity intersects the imaginary axis for K = 1.5. The closed loop system is stable for
A. K > 1.5
B. 1 < K < 1.5
C. 0 < K < 1
D. no positive value of K
Q. 48 Which one of the following options correctly describes the location of the roots of the equation
s^4 + s^2 +1 = 0
on the complex plane?
A. Four left half plane (LHP) roots
B. One right half plane (RHP) root, one LHP root, and two roots on the imaginary axis
C. Two RHP roots and two LHP roots
D. All four roots are on the imaginary axis
Q. 49 The Nyquist plot of the transfer function
G(s) = K / (s^2 + 2s + 2)(s + 2)
does not encircle the point (-1 + j0) for K=10 but does encircle the point (-1 + j0) for K=100. Then the closed loop system (having unity gain feedback) is
A. stable for K=10 and stable for K=100
B. stable for K=10 and unstable for K=100
C. unstable for K=10 and stable for K=100
D. unstable for K=10 and unstable for K=100
Q. 50 In binary frequency shift keying (FSK), the given signal waveforms are
u0(t) = 5cos(20000(pi)t); 0<=t<=T, and
u1(t) = 5cos(22000(pi)t); 0<=t<=T,
where T is the bit-duration interval and t is in seconds. Both u0(t) and u1(t) are zero outside the interval 0<=t<=T. With a matched filter (correlator) based receiver, the smallest positive value of T (in milliseconds) required to have u0(t) and u1(t) uncorrelated is
A. 0.25 ms
B. 0.5 ms
C. 0.75 ms
D. 1.0 ms
Q. 51 Let X(t) be a wide sense stationary random process with the power spectral density Sx(f) as shown in figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal lowpass filter with the frequency response
H(f)) = 1, |f| <= 1/2 Hz
H(f) = 0, |f| > 1/2 Hz
as shown in Figure (b). The output of the lowpass filter is Y(t).
Let E be the expectation operator and consider the following statements:
I. E(X(t)) = E(Y(t))
II. E(X^2(t)) = E(Y^2(t))
III. E(Y^2(t)) = 2
Select the correct option:
A. only I is true
B. only II and III are true
C. only I and II are true
D. only I and III are true
Q. 52 A continuous time signal x(t) = 4cos(200(pi)t) + 8cos(400(pi)t), where t is in seconds, is the output to a linear time invariant (LTI) filter with the impulse response
h(t) = 2sin(300(pi)t)/pi(t), t is not = 0
h(t) = 600, t = 0
Let y(t) be the output of this filter. The maximum value of |y(t)| is
Q. 53 An optical fiber is kept along the z direction. The refractive indices for the electric fields along x and y directions in the fiber are nx = 1.5000 and ny = 1.5001, respectively (nx is not equal to ny due to the imperfection in the cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5um. If the light wave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeters, is
Q. 54 The expression for an electric field in free space is given, where x, y, z represent the spatial coordinates, t represents time, and w, k are constants. This electric field
A. does not represent a plane wave
B. represents a circularly polarized plane wave propagating normal to the z-axis
C. represents an elliptically polarized plane wave propagating along the x-y plane
D. represents a linearly polarized plane wave
Q. 55 A half wavelength dipole is kept in the x-y plane and oriented along 45 degrees from the xaxis. Determine the direction of null in the radiation pattern for 0 <= x <= pi. Here the angle y (0 <= y <= pi) is measured from the z-axis, and the angle x (0 <= x <= 2pi) is measured from the x-axis in the x-y plane.
A. y = 90 degrees, x = 45 degrees
B. y = 45 degrees, x = 90 degrees
C. y = 90 degrees, x = 135 degrees
D. y = 45 degrees, x = 135 degrees
Q. 56 She has a sharp tongue and it can occasionally turn ______
A. hurtful
B. left
C. methodical
D. vital
Q. 57 I _____ made arrangements had I _____ informed earlier.
A. could have, been
B. would have, being
C. had, have
D. had been, been
Q. 58 In the summer, water consumption is known to decrease overall by 25%. A Water Boars official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%
Which of the following statements is correct?
A. The ratio of household to other consumption is 8/17
B. The ratio of household to other consumption is 1/17
C. The ratio of household to other consumption is 17/8
D. There are errors in the official’s statement
Q. 59 40% of deaths on city roads may be attributed to drunk driving. The number of degrees needed to represent this as a slice of a pie chart is
A. 120
B. 144
C. 160
D. 212
Q. 60 Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be deduced from the previous sentences?
i. At least one bench is a table
ii. At least one shelf is a bench
iii. At least one chair is a table
iv. All benches are chairs
A. Only i
B. Only ii
C. Only ii and iii
D. Only iv
Q. 61 “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effect this mutilation will have on the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in this country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”. Here, the word ‘antagonistic’ is closest in meaning to
A. impartial
B. argumentative
C. separated
D. hostile
Q. 62 S, T, U, V, W, X, Y and Z are seated around a circular table. T’s neighbours are Y and V. Z is seated this to the left of T and second to the right of S. U’s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?
A. X
B. W
C. U
D. T
Q. 63 Trucks (10m long) and cars (5m long) go on a single lane bridge. There must be a gap of at least 20m after each truck and a gap of at least 15m after each car. Trucks and cars travel at a speed of 36km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?
A. 1440
B. 1200
C. 720
D. 600
Q. 64 There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?
A. 56
B. 52
C. 48
D. 44
Q. 65 A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot. The path from P to Q is best described by
A. Up-Down-Up-Down
B. Down-Up-Down-Up
C. Down-Up-Down
D. Up-Down-Up
| Answer Sheet |
||||||||||
| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | C | C | B | 0.027 To 0.028 | D | A | 0.9 to 1.1 | A | A | D |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | C | B | C | D | B | C | 29.9 to 30.1 | 0.991 to 0.88 | C | C |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | 0 | D | B | 0.85 to 0.88 | C | C | 0.7 to 0.88 | C | C | 0.7 To 0.85 |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | D | 31 | 2.05 to 2.15 | 2.55 to 2.65 | 0.3 to 0.4 | 1.5 to 1.7 | 15.9 to 16.1 | 10 | 0.89 to 0.91 | 1.9 to 2.1 |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | 127 To 129 | 43.3 to 45.3 | B | 10 | B | D | A | C | B | B |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | A | 7.9 to 8.1 | 0.36 to 0.38 | C | A | A | A | D | B | B |
| Question | 61 | 62 | 63 | 64 | 65 | |||||
| Answer | D | A | A | A | C |