**GATE-2023**

**EC: Electronics and Communications Engineering**

**General Aptitude**

**Q.1 – Q.5 Carry ONE mark each.**

1. “I cannot support this proposal. My ________ will not permit it.”

(A) conscious

(B) consensus

(C) conscience

(D) consent

2. Courts : _______ : : Parliament : Legislature

(By word meaning)

(A) Judiciary

(B) Executive

(C) Governmental

(D) Legal

3. What is the smallest number with distinct digits whose digits add up to 45?

(A) 123555789

(B) 123457869

(C) 123456789

(D) 99999

4. In a class of 100 students,

(i) there are 30 students who neither like romantic movies nor comedy movies,

(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and

(iii) the number of students who like both romantic movies and comedy movies is 20.

How many students in the class like romantic movies?

(A) 40

(B) 20

(C) 60

(D) 30

5. How many rectangles are present in the given figure?

(A) 8

(B) 9

(C) 10

(D) 12

**Q.6 – Q.10 Carry TWO marks Each**

6. Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious.

Based only on the information provided above, which one of the following options can be logically inferred with certainty?

(A) All creatures with claws are animals.

(B) Some creatures with claws are non-ferocious.

(C) Some non-ferocious creatures have claws.

(D) Some ferocious creatures are creatures with claws.

7. Which one of the following options represents the given graph?

(A) f(x) = x^{2} 2^{−}^{|x|}

(B) f(x) = x 2^{−}^{|x|}

(C) f(x) = |x|2^{−}^{x}

(D) f(x) = x 2^{−}^{x}

8. Which one of the following options can be inferred from the given passage alone?

When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet.

[Excerpt from The Truth about Stories by T. King]

(A) It is a child’s description of what he or she likes.

(B) It is an adult’s memory of what he or she liked as a child.

(C) The child in the passage read stories about interplanetary travel only in parts.

(D) It teaches us that stories are good for children.

9. Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:

(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.

(ii) Mix the samples within each set and test the mixed sample for covid.

(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.

(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.

Given this strategy, no more than _______ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.

(A) 700

(B) 600

(C) 800

(D) 1000

10. A 100 cm × 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm × 1 cm.

The total number of creases visible when the sheet is unfolded is _______.

(A) 32

(B) 5

(C) 31

(D) 63

**EC: Electronics and Communications Engineering**

**Q.11 – Q.35 Carry ONE mark Each**

11. Let be two vectors. The value of the coefficient α in the expression v_{1} = αv_{2} + e, which minimizes the length of the error vector e, is

(A) 7/2

(B) −2/7

(C) 2/7

(D) −7/2

12. The rate of increase, of a scalar field f(x, y, z) = xyz, in the direction v = (2, 1, 2) at a point (0,2,1) is

(A) 2/3

(B) 4/3

(C) 2

(D) 4

13. Let w^{4} = 16j. Which of the following cannot be a value of w?

(A) 2e^{j2}^{π}^{/8}

(B) 2e^{ j}^{π}^{/8}

(C) 2e^{ j5}^{π}^{/8}

(D) 2e^{ j9}^{π}^{/8}

14. The value of the contour integral, where the contour C is taken in the counter clockwise direction, is

(A) –π(1 + j)

(B) π(1 + j)

(C) π(1 – j)

(D) –π(1 – j)

15. Let the sets of eigenvalues and eigenvectors of a matrix B be {λ_{k} |1 ≤ k ≤ n} and {v_{k} | 1 ≤ k ≤ n}, respectively. For any invertible matrix P, the sets of eigenvalues and eigenvectors of the matrix A, where B = P^{−}^{1} AP, respectively, are

(A) {λ_{k} det(A) | 1 ≤ k ≤ n} and {Pv_{k} | 1 ≤ k ≤ n}

(B) {λ_{k} | 1 ≤ k ≤ n} and {v_{k} | 1 ≤ k ≤ n}

(C) {λ_{k} | 1 ≤ k ≤ n} and {Pv_{k} | 1 ≤ k ≤ n}

(D) {λ_{k} | 1 ≤ k ≤ n} and {P^{−}^{1}v_{k} | 1 ≤ k ≤ n}

16. In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as

(A) degenerate n-type.

(B) degenerate p-type.

(C) non-degenerate n-type.

(D) non-degenerate p-type.

17. For an intrinsic semiconductor at temperature T = 0 K, which of the following statement is true?

(A) All energy states in the valence band are filled with electrons and all energy states in the conduction band are empty of electrons.

(B) All energy states in the valence band are empty of electrons and all energy states in the conduction band are filled with electrons.

(C) All energy states in the valence and conduction band are filled with holes.

(D) All energy states in the valence and conduction band are filled with electrons.

18. A series RLC circuit has a quality factor Q of 1000 at a center frequency of 10^{6} rad/s. The possible values of R, L and C are

(A) R = 1 Ω, L = 1 μH and C = 1 μF

(B) R = 0.1 Ω, L = 1 μH and C = 1 μF

(C) R = 0.01 Ω, L = 1 μH and C = 1 μF

(D) R = 0.001 Ω, L = 1 μH and C = 1 μF

19. For a MOS capacitor, V_{fb} and V_{t} are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width (W_{dep}) for varying gate voltage (V_{g}) is best represented by

20. Consider a narrow band signal, propagating in a lossless dielectric medium (ε_{r} = 4, μ_{r} = 1), with phase velocity v_{p} and group velocity v_{g}. Which of the following statement is true? (c is the velocity of light in vacuum.)

(A) v_{p} > c, v_{g} > c

(B) v_{p} < c, v_{g} > c

(C) v_{p} > c, v_{g} < c

(D) v_{p} < c, v_{g} < c

21. In the circuit shown below, V_{1} and V_{2} are bias voltages. Based on input and output impedances, the circuit behaves as a

(A) voltage controlled voltage source.

(B) voltage controlled current source.

(C) current controlled voltage source.

(D) current controlled current source.

22. A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when

(A) the closed loop gain is less than 1 and the phase shift is less than 180°.

(B) the closed loop gain is greater than 1 and the phase shift is less than 180°.

(C) the closed loop gain is less than 1 and the phase shift is greater than 180°.

(D) the closed loop gain is greater than 1 and the phase shift is greater than 180°.

23. In the circuit shown below, P and Q are the inputs. The logical function realized by the circuit shown below is

(A) Y = PQ

(B) Y = P + Q

(C)

(D)

24. The synchronous sequential circuit shown below works at a clock frequency of 1 GHz. The throughput, in Mbits/s, and the latency, in ns, respectively, are

(A) 1000, 3

(B) 333.33, 1

(C) 2000, 3

(D) 333.33, 3

25. The open loop transfer function of a unity negative feedback system is where k_{1}, T_{1} and T_{2} are positive constants. The phase cross-over frequency, in rad/s, is

26. Consider a system with input x(t) and output y(t) = x(e^{t}). The system is

(A) Causal and time invariant.

(B) Non-causal and time varying.

(C) Causal and time varying.

(D) Non-causal and time invariant.

27. Let m(t) be a strictly band-limited signal with bandwidth B and energy E. Assuming ω_{0} = 10B, the energy in the signal m(t) cos ω_{0}t is

(A) E/4

(B) E/2

(C) E

(D) 2E

28. The Fourier transform X(ω) of is

29. In the table shown below, match the signal type with its spectral characteristics.

(A) (i) → (a), (ii) → (b), (iii) → (c), (iv) → (d)

(B) (i) → (a), (ii) → (c), (iii) → (b), (iv) → (d)

(C) (i) → (d), (ii) → (b), (iii) → (c), (iv) → (a)

(D) (i) → (a), (ii) → (c), (iii) → (d), (iv) → (b)

30. For a real signal, which of the following is/are valid power spectral density/densities?

(A)

(B)

(C)

(D)

31. The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be 61.96 dB. The resolution of the ADC is ________ bits (rounded off to the nearest integer).

32. In the circuit shown below, the current i flowing through 200 Ω resistor is ______ mA (rounded off to two decimal places).

33. For the two port network shown below, the [Y]-parameters is given as

The value of load impedance Z_{L}, in Ω, for maximum power transfer will be _______ (rounded off to the nearest integer).

34. For the circuit shown below, the propagation delay of each NAND gate is 1 ns. The critical path delay, in ns, is __________ (rounded off to the nearest integer).

35. In the circuit shown below, switch S was closed for a long time. If the switch is opened at 𝑡 = 0, the maximum magnitude of the voltage VR, in volts, is _________ (rounded off to the nearest integer).

**Q.36 – Q.65 Carry TWO marks Each**

36. A random variable X, distributed normally as N(0, 1), undergoes the transformation Y = h(X), given in the figure. The form of the probability density function of Y is

(In the options given below, a, b, c are non-zero constants and g(y) is piece-wise continuous function)

(A) aδ(y – 1) + bδ(y + 1) + g(y)

(B) aδ(y + 1) + bδ(y) + cδ(y – 1) + g(y)

(C) aδ(y + 2) + bδ(y) + cδ(y – 2) + g(y)

(D) aδ(y + 2) + bδ(y – 2) + g(y)

37. The value of the line integral along the straight line joining the points P(1, 1, 2) and Q(2, 3, 1) is

(A) 20

(B) 24

(C) 29

(D) -5

38. Let **x** be an n × 1 real column vector with length The trace of the matrix P = xx^{T} is

(A) l^{2}

(B) l^{2}/4

(C) l

(D) l^{2}/2

39. The v_{OUT}/v_{IN} of the circuit shown below is

(A) –R_{4}/R_{3}

(B) R_{4}/R_{3}

(C) 1 + R_{4}/R_{3}

(D) 1 – R_{4}/R_{3}

40. In the circuit shown below, D_{1} and D_{2} are silicon diodes with cut-in voltage of 0.7 V. V_{IN} and V_{OUT} are input and output voltages in volts. The transfer characteristic is

41. A closed loop system is shown in the figure where k > 0 and α > 0. The steady state error due to a ramp input (R(s) = α/s^{2}) is given by

(A) 2α/k

(B) α/k

(C) α/2k

(D) α/4k

42. In the following block diagram, R(s) and D(s) are two inputs. The output Y(s) is expressed as Y(s) = G_{1}(s)R(s) + G_{2}(s)D(s).

G_{1}(s) and G_{2}(s) are given by

43. The state equation of a second order system is

is the initial condition.

Suppose λ_{1} and λ_{2} are two distinct eigenvalues of A and v_{1} and v_{2} are the corresponding eigenvectors. For constants α_{1} and α_{2}, the solution, x(t) of the state equation is

44. The switch S_{1} was closed and S_{2} was open for a long time. At t = 0, switch S_{1} is opened and S_{2} is closed, simultaneously. The value of i_{c}(0^{+}), in amperes, is

(A) 1

(B) −1

(C) 0.2

(D) 0.8

45. Let a frequency modulated (FM) signal where m(t) is a message signal of bandwidth W. It is passed through a non-linear system with output y(t) = 2x(t) + 5(x(t))^{2}. Let BT denote the FM bandwidth. The minimum value of ω_{c} required to recover x(t) from y(t) is

(A) B_{T} + W

(B)

(C) 2B_{T} + W

(D)

46. The h-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain V_{out}/V_{s} is

(A) h_{11} = 0, h_{12} = 0, h_{21} = very high and h_{22} = 0

(B) h_{11} = very high, h_{12} = 0, h_{21} = very high and h_{22} = 0

(C) h_{11} = 0, h_{12} = very high, h_{21} = very high and h_{22} = 0

(D) h_{11} = 0, h_{12} = 0, h_{21} = very high and h_{22} = very high

47. Consider a discrete-time periodic signal with period N = 5. Let the discrete-time Fourier series (DTFS) representation be where a_{0} = 1, a_{1} = 3j, a_{2} = 2j, a_{3} = −2j and a_{4} = − The value of the sum is

(A) −10

(B) 10

(C) −2

(D) 2

48. Let an input x[n] having discrete time Fourier transform X(e^{j}^{Ω}) = 1 – e^{−}^{j}^{Ω} + 2e^{−}^{3j}^{Ω} be passed through an LTI system. The frequency response of the LTI system is The output y[n] of the system is

49. Let x(t) = 10 cos(10.5 Wt) be passed through an LTI system having impulse response The output of the system is

50. Let x_{1}(t) and x_{2}(t) be two band-limited signals having bandwidth B = 4π × 10^{3} rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is

(A) 20π × 10^{3}

(B) 40π × 10^{3}

(C) 8π × 10^{3}

(D) 32π × 10^{3}

51. The S-parameters of a two port network is given as with reference to Z_{0}. Two lossless transmission line sections of electrical lengths θ_{1} = βl_{1} and θ_{2} = βl_{2} are added to the input and output ports for measurement purposes, respectively. The S-parameters [Sꞌ] of the resultant two port network is

52. The standing wave ratio on a 50 Ω lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load. Z_{L} can be replaced by an equivalent length l_{m} and terminating resistance R_{m} of the same line. The value of R_{m} and l_{m}, respectively, are

(A) R_{m} = 100 Ω, l_{m} = 20 cm

(B) R_{m} = 25 Ω, l_{m} = 20 cm

(C) R_{m} = 100 Ω, l_{m} = 5 cm

(D) R_{m} = 25 Ω, l_{m} = 5 cm

53. The electric field of a plane electromagnetic wave is

E = a_{x}C_{1x}cos(ωt – βz) + a_{y}C_{1y}cos(ωt – βz + θ) V/m.

Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

(A) C_{1x} = 1, C_{1y} = 1, θ = π/4

(B) C_{1x} = 2, C_{1y} = 1, θ = π/2

(C) C_{1x} = 1, C_{1y} = 2, θ = 3π/2

(D) C_{1x} = 2, C_{1y} = 1, θ = 3π/4

54. The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are

55. The value of the integral over the region R, given in the figure, is ________ (rounded off to the nearest integer).

56. In an extrinsic semiconductor, the hole concentration is given to be 1.5n_{i} where n_{i} is the intrinsic carrier concentration of 1 × 10^{10} cm^{−3}. The ratio of electron to hole mobility for equal hole and electron drift current is given as __________ (rounded off to two decimal places).

57. The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is where k, z, p, a, b and c are positive constants. The value (a + b + c) is _______ (rounded off to the nearest integer).

58. Let x_{1}(t) = u(t + 1.5) − u(t − 1.5) and x_{2}(t) is shown in the figure below. For y(t) = x_{1}(t) ∗ x_{2}(t), the is __________ (rounded off to the nearest integer).

59. Let X(t) be a white Gaussian noise with power spectral density If X(t) is input to an LTI system with impulse response e^{−}^{t}u(t). The average power of the system output is _________ W (rounded off to two decimal places).

60. A transparent dielectric coating is applied to glass (ε_{r} = 4, μ_{r} = 1) to eliminate the reflection of red light (λ_{0} = 0.75 μm). The minimum thickness of the dielectric coating, in μm, that can be used is ________ (rounded off to two decimal places).

61. In a semiconductor device, the Fermi-energy level is 0.35 eV above the valence band energy. The effective density of states in the valence band at T = 300 K is 1 × 10^{19}cm^{−3}. The thermal equilibrium hole concentration in silicon at 400 K is ____________ × 10^{13}cm^{−3} (rounded off to two decimal places).

Given kT at 300 K is 0.026 eV.

62. A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 μs. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is _______ μs (rounded off to two decimal places).

63. In a given sequential circuit, initial states are Q_{1} = 1 and Q_{2} = 0. For a clock frequency of 1 MHz, the frequency of signal Q_{2} in kHz, is ___________ (rounded off to the nearest integer).

64. In the circuit below, the voltage V_{L} is ____________ V (rounded off to two decimal places).

65. The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of “yes/no” questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _______ (rounded off to two decimal places).

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