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GATE 2017-2018 :: GATE CSE

  1. Consider the following logical inferences. 
    I1: If it rains then the cricket match will not be played. 
    The cricket match was played. 
    Inference: There was no rain. 
    I2: If it rains then the cricket match will not be played. 
    It did not rain. 
    Inference: The cricket match was played. 
    Which of the following is TRUE?
  2. A.
    Both I1 and I2 are correct inferences
    B.
    I1 is correct but I2 is not a correct inference
    C.
    I1 is not correct but I2 is a correct inference
    D.
    Both I1 and I1 are not correct inferences

  3. Which of the following is TRUE?
  4. A.
    Every relation in 3NF is also in BCNF
    B.
    A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R
    C.
    Every relation in BCNF is also in 3NF
    D.
    No relation can be in both BCNF and 3NF

  5. Assuming P ≠ NP, which of the following is TRUE?
  6. A.
    NP-complete = NP
    B.
    NP-complete ∩ P = φ
    C.
    NP-hard = NP
    D.
    P = NP-complete

  7. The worst case running time to search for an element in a balanced binary search tree with n2n elements is
  8. A.
    Θ (n log n)
    B.
    Θ (n2n)
    C.
    Θ (n)
    D.
    Θ (log n)

  9. The truth table 

    represents the Boolean function
  10. A.
    X
    B.
    X + Y
    C.
    X  Y
    D.
    Y

  11. A process executes the code 
    fork(); 
    fork(); 
    fork(); 
    The total number of child processes created is
  12. A.
    3
    B.
    4
    C.
    7
    D.
    8

  13. Consider the function f(x) = sin(x) in the interval x ϵ [π/4, 7π/4]. The number and location(s) of the local minima of this function are
  14. A.
    One, at π/2
    B.
    One, at 3Ï€/2
    C.
    Two, at π/2 and 3π/2
    D.
    Two, at π/4 and 3π/2

  15. The protocol data unit (PDU) for the application layer in the Internet stack is
  16. A.
    Segment
    B.
    Datagram
    C.
    Message
    D.
    Frame

  17. Let A be the 2 * 2 matrix with elements a11 = a12 = a21 = +1 and a22 = -1. Then the eigenvalues of the matrix A19 are
  18. A.
    1024 and −1024
    B.
    1024√2 and −1024√2
    C.
    4√2 and −4√2
    D.
    512√2 and −512√2

  19. What is the complement of the language accepted by the NFA shown below? 
    Assume Σ = {a} and ε is the empty string.

  20. A.
    φ
    B.
    {ε}
    C.
    a*
    D.
    {a, ε}