Gate 2017 Electronics and Communication Engineering Question Paper 5th Feb 2017 Session 1 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electronics and Communication Engineering 5th Feb 2017 Session 1

Subject Name: Electronics and Communication Engineering

Duration : 180

Total Marks: 100

1. The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 μs, then the number of T-states needed for executing the instruction is

(A)  1

(B)  6

(C)  7

(D)  8

Ans: (C)

2. 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

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

Ans: (A)

3. Consider the following statement about the linear dependence of the real valued functions y1 = 1, y2 = x and y3 = x2, 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

Ans: (B)

4. Consider the 5 × 5 matrix

It is given that A has only one real eigen value. Then the real eigen value of A is

(A)  −2.5

(B)  0

(C)  15

(D)  25

Ans: (C)

5. The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is V(ℓ) = e−−γℓ +jωt volts, Where ℓ is the distance along the length of the cable in meters. γ = (0.1 + j40)m−1 is the complex propagation constant, and ω = 2π × 109 rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/meter is __________.

Ans: (0.85 to 0.88)

6. A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statement 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

Ans: (A)

7. The rank of the matrix  is

(A)  0

(B)  1

(C)  2

(D)  3

Ans: (C)

8. For a narrow base PNP BJT, the excess minority carrier concentration (∆nE for emitter, ∆pB for base. ∆nC for collector) normalized to equilibrium minority carrier concentration (nE0 for emitter, pB0 for base, nC0 for collector) in the quasi-neutral emitter, base and collector regions are shown below. Which one of the following biasing modes is the transistor operating in?

(A) Forward active

(B) Saturation

(C) Inverse active

(D) Cutoff

Ans: (C)

9. 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

Ans: (D)

10. 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 latch in percentage is ___________.

Ans: (2.9 to 30.1)

11. Which of the following can be pole-zero configuration of a phase-lag controller (lag compensator)?

(A) 

(B) 

(C) 

(D) 

Ans: (A)

12. 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”

Ans: (B)

13. Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) __________.

Ans: (0.027 to 0.028)

14. A periodic signal x(t) has a trigonometric Fourier series expansion

If x(t) = −x – (t) = −x(t – π/ω0), we can conclude that

(A)  an are zero for all and bn are zero for n even

(B)  an are zero for all n and bn are zero for n odd

(C)  an are zero for n even and bn zero for n odd

(D)  an are zero for n odd and bn are zero for n even

Ans: (A)

15. The open loop transfer function  

Where p is an integer, is connected in unity feedback configuration as shown in 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 _________.

Ans: (0.99 to 1.01)

16. An n+ − n Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of ND1 = 1 × 1018 cm3 and ND2 = 1 × 1015 cm3 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 × 1010 cm3. What is the magnitude of the built-in potential of this device?

(A)  0.748V

(B)  0.460V

(C)  0.288V

(D)  0.173V

Ans: (D)

17. For the operational amplifier circuit shown, the output saturation voltages are ±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

Ans: (B)

18. In the circuit shown, the positive angular frequency ω (in radians per second) at which magnitude of the phase difference between the voltages V­1 and V2 equals  is________.

Ans: (0.9 to 1.1)

19. 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 inter symbol interference zero?

(A) 

(B) 

(C) 

(D) 

Ans: (B)

20. Consider a stable system with transfer function

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 ω→∞. A possible pair of values for p and q is

(A) p = 0 and q = 3

(B) p =1and q = 7

(C) p = 2 and q = 3

(D) p = 3 and q = 5

Ans: (A)

21. 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 resistance

Ans: (C)

22. Let (X1 ,X2) be independent random variables. X1 has been 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 _______.

Ans: (0)

23. 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 non causal and BIBO stable system with a pole in the right half of the complex plane.

Which one 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

Ans: (D)

24. 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 quantized, and its 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 predictions is quantized

Ans: (D)

25. Consider a wireless communication link between a transmitter and a receiver located 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) decrease by a factor 2

(C) remains unchanged

(D) decreases by a factor of √2

Ans: (C)

26. Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of Newton-Rapson’s method (up to two decimal places) is ________.

Ans: (0.65 to 0.72)

27. In binary frequency shift keying (FSK), the given signal waveform are

u0(t) = 5 cos(20000πt); 0≤t ≤ T, and

u1(t) = 5 cos(22000πt); 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

Ans: (B)

28. For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector current are equal. Given that VT = 25 mV, VBE = 0.7V, and  the BJT output resistance r0 is practically infinite. Under these conditions, the midband voltage gain magnitude. Ac = |Vo/Vi|V/V, is ____________.

Ans: (127.0 to 129.0)

29. The figure shows an RLC circuit exited by the sinusoidal voltage 100cos (3t) volts, where t is in seconds. The ratio  is _________.

Ans: (2.55 to 2.65)

30. Which one of the following is the general solution of the first order differential equation  where x, y are real?

(A)  y = 1 + x + tan1 (x + c), where c is a constant

(B)  y = 1 + x + tan(x + c), where c is a constant

(C)  y = 1 – x + tan1(x + c), where c is a constant

(D)  y = 1 – x + tan(x + c), where c is a constant

Ans: (D)

31. A linear time invariant (LTI) system with the transfer function is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K < ∞ 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

Ans: (A)

32. Let  where x, y, z are real, and let C be th straight line segment from point A : (0, 2, 1) to point B : (4, 1, −1). The value of I is _______.

Ans: (−11.1 to −10.9)

33. As shown, two Silicon (Si) abrupt p-n junction diodes are fabricated with uniform donor doping concentration of ND1 = 1014 cm−3 and ND2 = 1016 cm−3 in the n-regions of the diodes, and uniform acceptor doping concentration of NAl = 1014 cm−3 and NA2 = 1016 cm−3 in the p-regions of the diodes, respectively. Assuming that the reverse bias voltage is >> built-in potentials of the diodes, the ratio C2/C1 of their reverse bias capacitances for the same applied reverse bias, is __________.

Ans: (10.0 to 10.0)

34. An optical fiber is kept along the The refractive indices for the electric fields along  directions in the fiber are nx = 1.5000 and ny = 1.5001, respectively (nx ≠ ny due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5μm. If the light wave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeter, is ___________.

Ans: (0.36 to 0.38)

35. Two discrete-time signals x[n] and h[n] are both non-zero 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 _______.

Ans: (31)

36. Which one of the following options correctly describes the locations of the roots of the equations s4 + s2 + 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

Ans: (C)

37. The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of n = 1 × 1016 cm−3 and electronic charge q = 1.6 × 10−19 C. If a bias of 5V is applied across a 1 μm region of this semiconductor, the resulting current density in this region, in kA/cm2, is ________.

Ans: (1.5 to 1.7)

38. For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage Vtn = 1V and its transconductance parameter  Neglect channel length modulation and body bias effects. Under these conditions, the drain current ID in mA is _________.

Ans: (1.9 to 2.1)

39. 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 low pass filter with frequency response

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(X2(t)) = E(Y2(t))

III. E(Y2(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

Ans: (A)

40. As shown a uniformly doped Silicon (Si) bar of length L = 0.1 μm with a donor concentration ND = 1016 cm−3 is illuminated at x = 0 such that electron and hole pairs are generated at the rate of   where GL0 = 1017 cm−3 s−1. Hole lifetime is 10−4 s, electronic charge q = 1.6 × 10−19 C, hole diffusion coefficient Dp = 100 cm2/s and low level injection condition prevails. Assuming 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/cm2, is _______.

Ans: (15.9 to 16.1)

41. The Nyquist plot of the transfer function  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

Ans: (B)

42. 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 saturation VCE(sat) = 0.2 V and base-to-emitter voltage VBE = 0.7V. The minimum value of the common-base current gain (α) of the transistor for the switching should be _______.

Ans: (0.89 to 0.91)

43. A three dimensional region R of finite volume is described by x2 + y2 ≤ z3; 0 ≤ z ≤ 1, Where x, y, z are real. The volume of R(up to two decimal places) is _________.

Ans: (0.70 to 0.85)

44. The expression for an electric field in free space is

where x, y, z represent the spatial coordinates, t represents time, and ω, k are constants. This electric field

(A) does not represent a plane wave

(B) represents a circular polarized plane wave propagating normal to the z-axis

(C) represents an elliptically polarized plane wave propagating along x-y plane.

(D) represents a linearly polarized plane wave

Ans: (C)

45. A finite state machine (FSM) is implemented using the D flip-flops A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are QAQB = 00, 01, 10 and 11.

Assume that XIN = 1is 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 = 1

(C)  only two of the four possible states if XIN = 1

(D)  only two of the four possible states is XIN = 0

Ans: (D)

46. 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 6π 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

Ans: (B)

47. 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 _______.

Ans: (10.0 to 10.0)

48. Let  for real x. From among the following choose the Taylor series approximation of f(x) around x = 0, which included all powers of x less than or equal to 3.

(A)    1 + x + x2 + x3

(B) 

(C) 

(D) 

Ans: (C)

49. The following FIVE instructions were executed on an 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

Ans: (B)

50. In the circuit shown, the voltage VIN(t) is described by:

Where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is ___________.

Ans: (0.30 to 0.40)

51. A half wavelength dipole is kept in the x-y plane and oriented along 45° from the x-axis. Determine the direction of null in the radiation pattern for 0 ≤ ϕ ≤ π. Here the angle θ(0 ≤ θ < π) is measured from the z-axis, and the angle ϕ(0 ≤ ϕ ≤ 2π) is measured from the x-axis in the x-y plane.

(A)  θ = 90°, ϕ = 45°

(B)  θ = 45°, ϕ = 90°

(C)  θ = 90°, ϕ = 135°

(D)  θ = 45°, ϕ = 135°

Ans: (A)

52. The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, Ao = 105V/V and an open-loop cut-off frequency fc = 8Hz. The voltage gain of the amplifier at 15 kHz, in V/V is _______.

Ans: (43.3 to 45.3)

53. Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by and h[n] = 0 for n < 0 and n > 2.

Let H(ω) be the discrete-time Fourier system transform (DTFT) of h[n], where ω is the normalized angular frequency in radians. Given that H(ω0) = 0 and 0 < ω0 < π, the value of ω0 (in radians) is equal to ________.

Ans: (2.05 to 2.15)

54. 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 and m5 are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?

(A) 

(B) 

(C) 

(D) 

Ans: (B)

55. A continuous time signal x(t) = 4 cos (200 πt) + 8 cos (400 πt), where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response

Let y(t) be the output of this filter. The maximum value of |y(t)| is _______.

Ans: (7.90 to 8.10)

56. She has a sharp tongue and it can occasionally turn _______.

(A)   hurtful

(B)   left

(C)   methodical

(D)   vital

Ans: (A)

57. Some table are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding 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)

Ans: (B)

58. 40% of deaths on city roads may be attributed to drunken driving. The number of degree needed to represent this as a slice of a pie chart is

(A)  120

(B)  144

(C)  160

(D)  212

Ans: (B)

59. In the summer, water consumption is known to decrease overall by 25%. A water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.

Which of the following statement 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

Ans: (D)

60. I ________ made arrangements had I _________informed earlier.

(A) could have, been

(B) would have, being

(C) had, have

(D) had been, been

Ans: (A)

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 effects this mutilation will have in the respective section, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the 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

Ans: (D)

62. 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

Ans: (A)

63. A contour line joints 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 25 m 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

Ans: (C)

64. Trucks (10m long) and cars (5 m long) go on a single lane bridge. There must be a gap of atleast 20 m after each truck and a gap of atleast 15m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternatively, what is the maximum number of vehicles that can use the bridge in one hour?

(A)  1440

(B)  1200

(C)  720

(D)  600

Ans: (A)

65. 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 third 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

Ans: (A)

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