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GATE 2017-2018 :: GATE CSE

  1. Using public key cryptography, X adds a digital signature σ to message M, encrypts , and sends it to Y, where it is decrypted. Which one of the following sequences of keys is used for the operations?
  2. A.
    Encryption: X's private key followed by Y's private key; Decryption: X's public key followed by Y's public key
    B.
    Encryption: X's private key followed by Y's public key; Decryption: X's public key followed by Y's private key
    C.
    Encryption: X's public key followed by Y's private key; Decryption: Y's public key followed by X's private key
    D.
    Encryption: X's private key followed by Y's public key; Decryption: Y's private key followed by X's public key

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  3. An index is clustered, if
  4. A.
    it is on a set of fields that form a candidate key.
    B.
    it is on a set of fields that include the primary key.
    C.
    the data records of the file are organized in the same order as the data entries of the index.
    D.
    the data records of the file are organized not in the same order as the data entries of the index.

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  5. Three concurrent processes X, Y, and Z execute three different code segments that access and update certain shared variables. Process X executes the P operation (i.e., wait) on semaphores a, b and c; process Y executes the P operation on semaphores b, c and d; process Z executes the P operation on semaphores c, d, and a before entering the respective code segments. After completing the execution of its code segment, each process invokes the V operation (i.e., signal) on its three semaphores. All semaphores are binary semaphores initialized to one. Which one of the following represents a deadlock-free order of invoking the P operations by the processes?
  6. A.
    X: P(a)P(b)P(c) Y: P(b)P(c)P(d) Z: P(c)P(d)P(a)
    B.
    X: P(b)P(a)P(c) Y: P(b)P(c)P(d) Z: P(a)P(c)P(d)
    C.
    X: P(b)P(a)P(c) Y: P(c)P(b)P(d) Z: P(a)P(c)P(d)
    D.
    X: P(a)P(b)P(c) Y: P(c)P(b)P(d) Z: P(c)P(d)P(a)

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  7. Which of the following statements is/are FALSE
    1. For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine. 
    2. Turing recognizable languages are closed under union and complementation. 
    3. Turing decidable languages are closed under intersection and complementation. 
    4. Turing recognizable languages are closed under union and intersection.
  8. A.
    1 and 4 only
    B.
    1 and 3 only
    C.
    2 only
    D.
    3 only

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  9. Which of the following statements are TRUE
    1. The problem of determining whether there exists a cycle in an undirected graph is in P. 
    2. The problem of determining whether there exists a cycle in an undirected graph is in NP. 
    3. If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.
  10. A.
    1, 2 and 3
    B.
    1 and 2 only
    C.
    2 and 3 only
    D.
    1 and 3 only

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  11. What is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of n vertices?
  12. A.
    Θ(n2)
    B.
    Θ(n2log n)
    C.
    Θ(n3)
    D.
    Θ(n3log n)

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  13. In a k-way set associative cache, the cache is divided into v sets, each of which consists of k lines. The lines of a set are placed in sequence one after another. The lines in set s are sequenced before the lines in set (s+1). The main memory blocks are numbered 0 onwards. The main memory block numbered j must be mapped to any one of the cache lines from
  14. A.
    (j mod v) * k to (j mod v) * k + (k-1)
    B.
    (j mod v) to (j mod v) + (k-1)
    C.
    (j mod k) to (j mod k) + (v-1)
    D.
    (j mod k) * v to (j mod k) * v + (v-1)

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  15. Which one of the following expressions does NOT represent exclusive NOR of x and y?
  16. A.
    xy + x' y'
    B.
    x ⊕ y'
    C.
    x' ⊕ y
    D.
    x' ⊕ y'

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  17. Which one of the following functions is continuous at x = 3?
  18. A.
    .

    B.
    .

    C.
    .

    D.
    .

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  19. Function f is known at the following points:

    The value of  computed using the trapezoidal rule is
  20. A.
    8.983
    B.
    9.003
    C.
    9.017
    D.
    9.045

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