GATE CS question library

Let, $x_{1} ⊕ x_{2} ⊕ x_{3} ⊕ x_{4}= 0$ where $x_{1}, x_{2}, x_{3}, x_{4}$ are Boolean variables, and $⊕$ is the XOR operator. Which one of the following must always be TRUE?

In a $2 \times 4$ rectangle grid shown below, each cell is rectangle. How many rectangles can be observed in the grid? $$\begin{array}{|c|c|c|c|c|}\hline{\;\;\;}&{\;\;\;}&{\;\;\;}&{\;\;\;}\\ \hline{}&{}&{}&\\ \hline\end{array}$$

Among $150$ faculty members in an institute, $55$ are connected with each other through Facebook and $85$ are connected through Whatsapp. $30$ faculty members do not have Facebook or Whatsapp accounts. The numbers of faculty members connected only through Facebook accounts is _______.

Open the full question

All hill-stations have a lake. Ooty has two lakes. Which of the statement(s) below is/are logically valid and can be inferred from the above sentences? Ooty is not a hill-station. No hill-station can have more than one lake.

Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension …

In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is $4$. Find the value of $\dfrac{\alpha^{n}+\beta^{n}}{\alpha^{-n}+\beta^{-n}}$

Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia. Choose the option which is closest in meaning to the underlined phrase in the above sentence.

Find the odd one in the following group of words. mock, deride, praise, jeer

The man who is now Municipal Commissioner worked as ________________.

Pick the odd one from the following options.

The least number of temporary variables required to create a three-address code in static single assignment form for the expression $q + r / 3 + s - t * 5 + u * v/w$ is__________________.

Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.

Suppose that the stop-and-wait protocol is used on a link with a bit rate of $64$ $\text{kilobits}$ per second and $20$ $\text{milliseconds}$ propagation delay. Assume that the transmission time for the acknowledgment and the processing time at nodes are negligible. Then the minimum frame size in bytes to achieve a link utilization of at least $50$ …

Consider the DFAs $M$ and $N$ given above. The number of states in a minimal DFA that accept the language $L(M) \cap L(N)$ is_____________.

Consider the NPDA $$\left \langle Q= \left \{ q_{0}, q_{1}, q_{2} \right \},\Sigma = \left \{ 0, 1 \right \}, \Gamma = \left \{ 0, 1, \perp \right \}, \delta, q_{0}, \perp, F =\left \{ q_{2} \right \} \right \rangle$$, where (as per usual convention) $Q$ is the set of states, $\Sigma$ is the input alphabet, $\Gamma$ is the stack alphabet, $\delta$ is …

A variable $x$ is said to be live at a statement $s_{i}$ in a program if the following three conditions hold simultaneously: There exists a statement $S_{j}$ that uses $x$ There is a path from $S_{i}$ to $S_{j}$ in the flow graph corresponding to the program The path has no intervening assignment to $x$ including at $S_{i}$ and $S_{j}$ The …

Let a$_{n}$ represent the number of bit strings of length n containing two consecutive $1$s. What is the recurrence relation for $a_{n}$?

Consider a disk pack with a seek time of $4$ milliseconds and rotational speed of $10000$ rotations per minute (RPM). It has $600$ sectors per track and each sector can store $512$ bytes of data. Consider a file stored in the disk. The file contains $2000$ sectors. Assume that every sector access necessitates a seek, and the average rotational …

Consider a main memory with five-page frames and the following sequence of page references: $\text{3, 8, 2, 3, 9, 1, 6, 3, 8, 9, 3, 6, 2, 1, 3}$. Which one of the following is true with respect to page replacement policies First In First Out (FIFO) and Least Recently Used (LRU)?