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Recent questions tagged gatecse-2015-set1

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Gate 2015 set1
What is meaning of " L is recursively enumerable but not recursive " ?
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GATE CSE 2015 Set 1 | Question: 55
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_...
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GATE CSE 2015 Set 1 | Question: 54
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_______________.
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GATE CSE 2015 Set 1 | Question: 53
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 th...
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GATE CSE 2015 Set 1 | Question: 52
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_____________.
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GATE CSE 2015 Set 1 | Question: 51
Consider the NPDA $$ \left \langle Q= \left \{ q_{0}, q_{1}, q_{2} \right \},\Sigma = \left \{ 0, 1 \right \}, \Gamma = \left \{ 0, 1, \perp \right \}, \delta, q_{0}, \p...
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GATE CSE 2015 Set 1 | Question: 50
A variable $x$ is said to be live at a statement $s_{i}$ in a program if the following three conditions hold simultaneously:There exists a statement $S_{j}$ that uses $x$...
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GATE CSE 2015 Set 1 | Question: 49
Let a$_{n}$ represent the number of bit strings of length n containing two consecutive $1$s. What is the recurrence relation for $a_{n}$?$a_{n - 2} + a_{n - 1} + 2^{n - 2...
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GATE CSE 2015 Set 1 | Question: 48
Consider a disk pack with a seek time of $4$ milliseconds and rotational speed of $10000$ rotations per minute (RPM). It has $600$ sectors per track and each sector can s...
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GATE CSE 2015 Set 1 | Question: 47
Consider a main memory with five-page frames and the following sequence of page references: $\text{3, 8, 2, 3, 9, 1, 6, 3, 8, 9, 3, 6, 2, 1, 3}$. Which one of the followi...
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GATE CSE 2015 Set 1 | Question: 46
Consider a uniprocessor system executing three tasks $T_{1}, T_{2}$ and $T_{3}$ each of which is composed of an infinite sequence of jobs (or instances) which arrive peri...
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GATE CSE 2015 Set 1 | Question: 45
Let $G = (V, E)$ be a simple undirected graph, and $s$ be a particular vertex in it called the source. For $x \in V$, let $d(x)$ denote the shortest distance in $G$ from ...
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GATE CSE 2015 Set 1 | Question: 44
Compute the value of:$$ \large \int \limits_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$$
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GATE CSE 2015 Set 1 | Question: 43
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...
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GATE CSE 2015 Set 1 | Question: 42
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...
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GATE CSE 2015 Set 1 | Question: 41
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 conn...
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GATE CSE 2015 Set 1 | Question: 40
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-...
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GATE CSE 2015 Set 1 | Question: 39
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?Both $\left\{\textit...
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GATE CSE 2015 Set 1 | Question: 38
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 processo...
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GATE CSE 2015 Set 1 | Question: 37
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 ...
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GATE CSE 2015 Set 1 | Question: 36
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...
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GATE CSE 2015 Set 1 | Question: 35
What is the output of the following C code? Assume that the address of $x$ is $2000$ (in decimal) and an integer requires four bytes of memory.int main () { unsigned int ...
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GATE CSE 2015 Set 1 | Question: 34
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram:For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \we...
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GATE CSE 2015 Set 1 | Question: 33
Consider the following pseudo code, where $x$ and $y$ are positive integers.begin q := 0 r := x while r ≥ y do begin r := r - y q := q + 1 end endThe post condition tha...
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GATE CSE 2015 Set 1 | Question: 32
Consider a max heap, represented by the array: $40, 30, 20, 10, 15, 16, 17, 8, 4$.$$\begin{array}{|l|l|}\hline \text{Array index} & \text{1} & \text{2} & \text{3} & \...
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GATE CSE 2015 Set 1 | Question: 31
Consider the following C function.int fun1 (int n) { int i, j, k, p, q = 0; for (i = 1; i < n; ++i) { p = 0; for (j = n; j 1; j = j/2) ++p; for (k = 1; k < p; k = k * 2)...
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GATE CSE 2015 Set 1 | Question: 29
Consider a LAN with four nodes $S_1, S_2, S_3,$ and $S_4$. Time is divided into fixed-size slots, and a node can begin its transmission only at the beginning of a slot. A...
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GATE CSE 2015 Set 1 | Question: 26
$\sum\limits_{x=1}^{99}\frac{1}{x(x+1)}$ = ______.
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GATE CSE 2015 Set 1 | Question: 21
Suppose that everyone in a group on $N$ people wants to communicate secretly with the $(\text{N - 1})$ others using symmetric Key cryptographic system. The communication ...
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GATE CSE 2015 Set 1 | Question: 1‏8
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ o...
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