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GATE 2017-2018 :: GATE ECE

  1. Two independent random variables X and Y are uniformly distributed in the interval [“1, 1]. The probability that max[X, Y] is less than 1 2 is
  2. A.
    3/4
    B.
    9/16
    C.
    1/4
    D.
    2/3

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  3. If x = √-1 , then the value of xx is
  4. A.
    e-Ï€/2
    B.
    eπ/2
    C.
    x
    D.
    1

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  5. A BPSK scheme operating over an AWGN channel with noise power spectral density of N0 / 2 , uses equiprobable signals s1(t) = √2E/T sin(wc t) and s2(t) = -√2E/T sin(wc t) over the symbol interval (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45o with respect to the received signal, the probability of error in the resulting system is
  6. A.
    Q(√2E/N0)
    B.
    Q(√E/N0)
    C.
    Q(√E/2N0)
    D.
    Q(√E/4N0)

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  7. A transmission line with a characteristic impedance of 100 Ω is used to match a 50 Ω section to a 200 Ω section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line can be approximately
  8. A.
    82.5 cm
    B.
    1.05 m
    C.
    1.58 m
    D.
    1.75 m

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  9. The input x(t) and output y(t) of a system are related as y(t) = . The system is
  10. A.
    time-invariant and stable
    B.
    stable and not time-invariant
    C.
    time-invariant and not stable
    D.
    not time-invariant and not stable

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  11. The feedback system shown below oscillates at 2 rad/s when

  12. A.
    K = 2 and a = 0.75
    B.
    K = 3 and a = 0.75
    C.
    K = 4 and a = 0.5
    D.
    K = 2 and a = 0.5

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  13. The Fourier transform of a signal h(t) is H(jw) = (2cosw)(sin2w) /w . The value of h(0) is
  14. A.
    1/4
    B.
    1/2
    C.
    1
    D.
    2

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  15. The state variable description of an LTI system is given by

    where y is the output and u is the input. The system is controllable for
  16. A.
    a1 ≠ 0, a2 = 0, a3 ≠ 0
    B.
    a1 = 0, a2 ≠ 0, a3 ≠ 0
    C.
    a1 = 0, a2 ≠ 0, a3 = 0
    D.
    a1 ≠ 0, a2 ≠ 0, a3 = 0

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  17. Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is


  18. A.
    0.8 Ω
    B.
    1.4 Ω
    C.
    2 Ω
    D.
    2.8 Ω

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  19. A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
  20. A.
    1/3
    B.
    1/2
    C.
    2/3
    D.
    3/4

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