GATE CS question library

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)?

Let $G = (V, E)$ be a simple undirected graph, and $s$ be a particular vertex in it called the source. For $x \in V$, let $d(x)$ denote the shortest distance in $G$ from $s$ to $x$. A breadth first search (BFS) is performed starting at $s$. Let $T$ be the resultant BFS tree. If $(u, v)$ is an edge of $G$ that is not in $T$, then which …

Consider a uniprocessor system executing three tasks $T_{1}, T_{2}$ and $T_{3}$ each of which is composed of an infinite sequence of jobs (or instances) which arrive periodically at intervals of $3, 7$ and $20$ milliseconds, respectively. The priority of each task is the inverse of its period, and the available tasks are scheduled in order of …

Compute the value of: $$\large \int \limits_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$$

Consider an Entity-Relationship $(\text{ER})$ model in which entity sets $E_{1}$ and $E_{2}$ are connected by an $m:n$ relationship $R_{12}$. $E_{1}$ and $E_{3}$ are connected by a $1 : n$ ($1$ on the side of $E_{1}$ and $n$ on the side of $E_{3}$) relationship $R_{13}$. $E_{1}$ has two-singled attributes $a_{11}$ and $a_{12}$ …

The graph shown below has $8$ edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight $36$ and contains the edges: $\{(A, C), (B, C), (B, E), (E, F), (D, F)\}$. The edge weights of only those edges which are in the MST are given in the figure shown below. The minimum possible sum of weights of all $8$ edges of this …

Consider the following C program segment. while (first <= last) { if (array[middle] < search) first = middle + 1; else if (array[middle] == search) found = TRUE; else last = middle - 1; middle = (first + last)/2; } if (first > last) notpresent = TRUE; The cyclomatic complexity of the program segment is_______________.

An algorithm performs $(\log N)^{\frac{1}{2}}$ find operations , $N$ insert operations, $(\log N)^{\frac{1}{2}}$ delete operations, and $(\log N)^{\frac{1}{2}}$ decrease-key operations on a set of data items with keys drawn from a linearly ordered set . For a delete operation, a pointer is provided to the record that must be deleted . For the …

Consider the operations $\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'}$ and $\textit{g (X, Y, Z) = X'YZ + X'YZ' + XY}$ Which one of the following is correct?

Consider a non-pipelined processor with a clock rate of $2.5$ gigahertz and average cycles per instruction of four. The same processor is upgraded to a pipelined processor with five stages; but due to the internal pipeline delay, the clock speed is reduced to $2$ gigahertz. Assume that there are no stalls in the pipeline. The speedup achieved in this …

A positive edge-triggered $D$ flip-flop is connected to a positive edge-triggered $JK$ flip-flop as follows. The $Q$ output of the $D$ flip-flop is connected to both the $J$ and $K$ inputs of the $JK$ flip-flop, while the $Q$ output of the $JK$ flip-flop is connected to the input of the $D$ flip-flop. Initially, the output of the $D$ …

Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are $-1$ and $7.$ What are the values of $a$ and $b$? $\qquad A = \begin{pmatrix}1 & 4\\ b&a \end{pmatrix}$