List of top Questions asked in GATE CS

Given the following information:
The logical address (L.A.) is 32 bits. The physical address (P.A.) is 20 bits. The page size (P.S.) is 2048 bytes (2 KB). What is the maximum number of entries in the page table?

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} $.

What is the time complexity of the following algorithm?
int func(int n) {
for (int i = 1; i < = n; i++) {
for (int j = 1; j < = n; j++) {
printf("Hello");
}
}
}

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 operations on an initially empty stack:
Push 10
Push 20
Pop
Push 30
Pop
Push 40

What is the final content of the stack?

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.

Which of the following is true about the binary search algorithm when applied to a sorted array?

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 code:

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

Given N distinct elements in an array, determine the number of comparisons required to find the element which is not the largest:

In the case of a 4-bit ripple counter, if the time period of the waveform at the last flip-flop is 64 microseconds, what is the input frequency?

In an IPv4 packet, if $ X $ is written in the protocol field, which of the following is not a valid protocol $ X $?

Let $ L $, $ M $, and $ N $ be non-singular matrices of size $ 3 \times 3 $, such that $ L^2 = L^{-1} $, $ M = L^8 $, and $ N = L^2 $. Find $ |M - N| $.

Given that the integral $ I = \int_{x}^{i} \log t \, dt = \frac{1}{4} $, find the value of $ x $.

Bird: Nest :: Bee: ............ ?

What is included in the Instruction Set Architecture (ISA)?

Consider a binary tree in which every node has either 0 or 2 children. Let $ N>0 $ be the number of nodes in the tree. The number of nodes that have exactly 2 children is:

In the $4 \times 4$ array shown below, each cell of the first three rows has either a cross (X) or a number. \[ \begin{array}{|c|c|c|c|} \hline 1 & X & 4 & 3
\hline X & 5 & 5 & 4
\hline 3 & X & 6 & X
\hline ? & ? & ? & ?
\hline \end{array} \] The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is:

Let $P$ be the partial order defined on the set $\{1, 2, 3, 4\}$ as follows: \[ P = \{(x, x) \mid x \in \{1, 2, 3, 4\}\} \cup \{(1, 2), (3, 2), (3, 4)\} \] The number of total orders on $\{1, 2, 3, 4\}$ that contain $P$ is ...........\_\_\_.

For positive non-zero real variables $p$ and $q$, if $\log (p^2 + q^2) = \log p + \log q + 2\log 3$, then, the value of $\frac{p^4 + q^4}{p^2 q^2}$ is:

Consider the following read-write schedule $ S $ over three transactions $ T_1, T_2, \text{and } T_3 $, where the subscripts in the schedule indicate transaction IDs:
$ S: r_1(z); w_1(z); r_2(x); r_3(y); w_3(y); r_2(y); w_2(x); w_2(y); $
Which of the following transaction schedules is/are conflict equivalent to $ S $?

A person sold two different items at the same price. He made 10% profit in one item and 10% loss in the other item. In, selling the person made a total of

The number of distinct minimum-weight spanning trees of the following graph is ............ \begin{center} \includegraphics[width=0.5\textwidth]{59.png} \end{center}