List of top Questions asked in GATE CS

What is the output of the following C code?

  void foo(int *p, int x) {
      *p = x;
  }

  void main() {
      int *z;
      int a = 20, b = 25;
      z = a;  // Incorrect: Should be z = a;
      foo(z, b);
      printf("%d", a);
  }
  

Issue: The statement z = a; is invalid because a is an integer, and z is a pointer.

Consider the following C code:

int main() {
    sum = 0;
    for (n = 1; n < 3; n++) {
        n++;
        sum += g(f(n));
    }
    printf("%d", sum);
}

int g(n) {
    return 10 + n;
}

int f(n) {
    return g(2 * n);
}
  

What is the output?

Consider the following code:

int a;
int arr[] = {30, 50, 10};
int *ptr = arr[10] + 1;
a = *ptr;
(*ptr)++;
ptr = ptr + 1;
printf("%d", a + arr[1] + *ptr);
  

Find the signed binary expansion of the number -6.

Match the following layers with their corresponding functionalities:

\[ \begin{array}{|c|c|} \hline \textbf{Layer} & \textbf{Functionality} \\ \hline \text{Networking Layer} & \text{Data packet transfer} \\ \text{Transport Layer} & \text{Host-to-host communication} \\ \text{Data Link Layer} & \text{Error detection and correction} \\ \hline \end{array} \]

Let \( A \) be a \( 3 \times 3 \) matrix defined as:

\[ A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & -1 \end{bmatrix} \]

Find the eigenvalues of \( A^{13} \).

Given an array \( A[n] \) such that:

\[ A[0] \to A[i] \text{ is in non-decreasing order}, \quad A[i+1] \to A[n] \text{ is in non-increasing order}. \]

Find the time complexity to find \( A[i] \).

Given the matrix \( A = \begin{bmatrix} 1 & 2 \\ 2 & -1 \end{bmatrix} \), find \( A^8 \).

Consider the following process information for Shortest Remaining Time First (SRTF) scheduling:

\[ \begin{array}{|c|c|c|} \hline \textbf{Process} & \textbf{Arrival Time (AT)} & \textbf{Burst Time (BT)} \\ \hline P1 & 0 & 10 \\ P2 & 1 & 13 \\ P3 & 2 & 6 \\ P4 & 8 & 9 \\ \hline \end{array} \]

Find the turnaround time for each process.

Given the following cache parameters:

\[ \begin{array}{|c|c|} \hline \textbf{Tag} & 4 \, \text{bits} \\ \textbf{Index} & 12 \, \text{bits} \\ \textbf{Block Size} & 1 \, \text{byte} \\ \hline \end{array} \]

Find the size of the main memory and the size of the cache memory.

Given a pipeline with 5 stages, the delay for each stage is as follows:

\[ \begin{array}{|c|c|} \hline \textbf{Stage} & \textbf{Delay (ns)} \\ \hline 1 & 250 \\ 2 & 150 \\ 3 & 100 \\ 4 & 200 \\ 5 & 50 \\ \hline \end{array} \]

The buffer delay is 10 ns. Find the time for \( n = 1000 \) instructions.

Consider the following hierarchical cache system with the following access times:

\[ \begin{array}{|c|c|c|} \hline \textbf{Cache Level} & \textbf{Hit Rate} & \textbf{Access Time} \\ \hline L1 & 90\% & 1 \text{ ns} \\ L2 & 80\% & 10 \text{ ns} \\ L3 & 100\% & 100 \text{ ns} \\ \hline \end{array} \]

Find \( T_{avg} \) for hierarchical or simultaneous access.

Consider the following code:

main() {
  int x = 126, y = 105;
  { 
    if (x > y) 
      x = x - y;
    else 
      y = y - x;
  }
  while (x != y) 
    printf("%d", x);
}