GATE-CS-2017 (Set 2)

Question 41

In a two-level cache system, the access times of L₁ and L₂ 1 and 8 clock cycles, respectively. The miss penalty from the L₂ cache to main memory is 18 clock cycles. The miss rate of L₁ cache is twice that of L₂. The average memory access time(AMAT) of this cache system is 2 cycles. The miss rates of L₁ and L₂ respectively are:

• 0.111 and 0.056
• 0.056 and 0.111
• 0.0892 and 0.1784
• 0.1784 and 0.0892

Question 42

Consider the following C program:

#include 
int main()
{
    int m = 10;
    int n, n1;
    n = ++m;
    n1 = m++;
    n--;
    --n1;
    n -= n1;
    printf("%d",n);
    return 0;
}

The output of the program is ______. Note: This questions appeared as Numerical Answer Type.

• 0
• 1
• 2
• 3

Question 43

Consider two hosts X and Y, connected by a single direct link of rate 10⁶ bits/sec. The distance between the two hosts is 10,000 km and the propagation speed along the link is 2 x 10⁸ m/s. Hosts X send a file of 50,000 bytes as one large message to hosts Y continuously. Let the transmission and propagation delays be p milliseconds and q milliseconds, respectively. Then the vales of p and q are:

• p = 50 and q = 100

• p = 50 and q = 400

• p = 100 and q = 50

• p = 400 and q = 50

Question 44

If w, x, y, z are boolean variables, then which of the following in INCORRECT?

• wx + w(x+y) + x(x+y) = x + wy
• (wx\'(y + z\'))\' + w\'x = w\' + x + y\'z
• (wx\'(y + xz\') + w\'x\')y = xy\'
• (w + y)(wxy + wyz) = wxy + wyz

Question 45

The pre-order traversal of a binary search tree is given by 12, 8, 6, 2, 7, 9, 10, 16, 15, 19, 17, 20. Then the post-order traversal of this tree is:

• 2, 6, 7, 8, 9, 10, 12, 15, 16, 17, 19, 20
• 2, 7, 6, 10, 9, 8, 15, 17, 20, 19, 16, 12
• 7, 2, 6, 8, 9, 10, 20, 17, 19, 15, 16, 12
• 7, 6, 2, 10, 9, 8, 15, 16, 17, 20, 19, 12

Question 46

Consider the set of processes with arrival time(in milliseconds), CPU burst time (in milliseconds), and priority(0 is the highest priority) shown below. None of the processes have I/O burst time. The average waiting time (in milliseconds) of all the processes using preemptive priority scheduling algorithm is ____.
Note: This question appeared as Numerical Answer Type.

• 29
• 30
• 31
• 32

Question 47

Consider the following snippet of a C program. Assume that swap(&x, &y) exchanges the contents of x and y.

int main()
{
    int array[] = {3, 5, 1, 4, 6, 2};
    int done = 0;
    int i;

    while (done == 0)
    {
        done  = 1;
        for (i = 0; i <= 4; i++)
        {
            if (array[i] < array[i+1])
            {
                swap(&array[i], &array[i+1]);
                done = 0;
            }
        }
        for (i = 5; i >= 1; i--)
        {
            if (array[i] > array[i-1])
            {
                swap(&array[i], &array[i-1]);
                done = 0;
            }
        }
    }

    printf("%d", array[3]);
}

The output of the program is _____. Note: This question appeared as Numerical Answer Type.

• 1
• 2
• 3
• 4

Question 48

Consider the following languages. L₁ = {a^p | p is a prime number} L₂ = {aⁿb^mc^2m | n >= 0, m >= 0} L₃ = {aⁿbⁿc²ⁿ | n >= 0} L₄ = {aⁿbⁿ | n >= 1} Which of the following are CORRECT ? I. L₁ is context free but not regular. II. L₂ is not context free. III. L₃ is not context free but recursive. IV. L₄ is deterministic context free.

• I, II and IV only
• II and III only
• I and IV only
• III and IV only

Question 49

Consider the following C function.

int fun(int n)
{
    int i, j;
    for (i = 1; i <= n ; i++)
    {
        for (j = 1;  j < n; j += i)
        {
            printf("%d %d", i, j);
        }
    }
}

Time complexity of fun in terms of θ notation is:

• θ(n √n)
• θ(n²)
• θ(n log n)
• θ(n ² log n)

Question 50

Let L(R) be the language represented by regular expression R. Let L(G) be the language generated by a context free grammar G. Let L(M) be the language accepted by a Turing machine M. Which of the following decision problems are undecidable? I. Given a regular expression R and a string w, is w∈L(R)? II. Given a context-free grammar G, is L(G)=∅ III. Given a context-free grammar G, is L(G)=Σ^∗ for some alphabet Σ? IV. Given a Turing machine M and a string w, is w ∈ L(M)?

• I and IV only

• II and III only

• II, III and IV only

• III and IV only