GATE CSE 2015 Set 1

## GATE CSE

Match the following:
List 1
(P) Prim’s algorithm for minimum spanning tree
(Q) Floyd-Warshall algorithm for all pairs sh

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Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for

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Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4.
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An algorithm performs $${\left( {\log N} \right)^{1/2}}$$ find operations, N insert operations, $${\left( {\log N} \righ

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The graph shown below has 8 edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight 36 an

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Consider the following C function.
int fun1 (int n) {
int i, j, k, p, q = 0;
for (i = 1; i < n; ++i)

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Which one of the following is TRUE at any valid state in shift-reduce parsing?

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A variable x is said to be live at a statement $${S_i}$$ in a programif the following three conditions hold simultaneous

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The least number of temporary variables required to create a three-address code in static single assignment form for the

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Consider a LAN with four nodes S1, S2, S3 and S4. Time is divided into fixed-size slots, and a node can begin its transm

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Suppose that the stop-and-wait protocol is used on a link with a bit rate of 64 kilobits per second and 20 milliseconds

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Which one of the following fields of an IP header is NOT modified by a typical IP router?

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Suppose two hosts use a TCP connection to transfer a large file. Which of the following statements is/are FALSE with res

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In one of the pairs of protocols given below, both the protocols can use multiple TCP connections between the same clien

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Suppose that everyone in a group of N people wants to communicate secretly with the N - 1 others using symmetric key cry

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For computers based on three-address instruction formats, each address field can be used to specify which of the followi

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Consider a disk pack with a seek time of 4 milliseconds and rotational speed of 10000 rotations per minute (RPM). It has

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Consider a non-pipelined processor with a clock rate of 2.5 gigahertz and average cycles per instruction of four. The sa

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The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a

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Which of the following is/are correct inorder traversal sequence(s) of binary search tree(s)?
I. 3, 5, 7, 8, 15, 19, 25

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What are the worst-case complexities of insertion and deletion of a key in a binary search tree?

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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

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A file is organized so that the ordering of data records is the same as or close to the ordering of data entries in some

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SELECT operation in SQL is equivalent to

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Consider an Entity-Relationship (ER) model in which entity sets E1 and E2 are connected by an m : n relationship R12. E1

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Consider the following relation:
Student
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Consider a 4-bit Johnson counter with an initial value of 0000. The counting sequence of this counter is

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The binary operator $$ \ne $$ is defined by the following truth table.
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Consider the operations
$$f\left( {x,y,z} \right) = X'YZ + XY' + Y'Z'$$ and $$g\left( {x,y,z} \right) = X'YZ + X'YZ' +

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A positive edge-triggered D flip-flop is connected to a positive edge-triggered JK flip-flop as follows. The Q output of

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Consider the following $$2 \times 2$$ matrix $$A$$ where two elements are unknown and are marked by $$a$$ and $$b.$$ The

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$$\,\,\mathop {\lim }\limits_{x \to \infty } \,{x^{1/x}}\,\,$$ is

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$$\,\int\limits_{1/\pi }^{2/\pi } {{{\cos \left( {1/x} \right)} \over {{x^2}}}dx = } $$ __________.

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If $$g(x)=1-x$$ & $$h\left( x \right) = {x \over {x - 1}}\,\,$$ then $$\,\,{{g\left( {h\left( x \right)} \right)} \

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Given Set $$\,\,\,A = \left\{ {2,3,4,5} \right\}\,\,\,$$ and Set $$\,\,\,B = \left\{ {11,12,13,14,15} \right\},\,\,\,$$

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The probabilities that a student passes in Mathematics, Physics and Chemistry are $$m, p$$ and $$c$$ respectively. Of th

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For a set A, the power set of A is denoted by 2A. If A = {5, {6}, {7}}, which of the following options are TRUE?
I. $$\p

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In the LU decomposition of the matrix $$\left[ {\matrix{
2 & 2 \cr
4 & 9 \cr
} } \right]$$, if the d

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Suppose L = { p, q, r, s, t } is a lattice represented by the following Hasse diagram:
For any $$x, y ∈ L$$, not necess

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$$\sum\limits_{x = 1}^{99} {{1 \over {x\left( {x + 1} \right)}}} $$ = _____________.

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

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Let $${a_n}$$ represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence rela

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A file is organized so that the ordering of data records is the same as or close to the ordering of data entries in some

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Consider a system with byte-addressable memory, 32-bit logical addresses, 4 kilobyte page size and page table entries of

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The following two functions P1 and P2 that share a variable B with an initial value of 2 execute concurrently.
P1( ) {

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Consider a uniprocessor system executing three tasks T1, T2 and T3, each of which is composed of an infinite sequence of

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Suppose the following disk request sequence (track numbers) for a disk with 100 tracks is given: 45, 20, 90, 10, 50, 60,

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Consider a main memory with five page frames and the following sequence of page references: 3, 8, 2, 3, 9, 1, 6, 3, 8, 9

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The output of the following C program is__________.
void f1(int a, int b) {
int c;
c=a; a=b; b=c;
}
void f2(int *a,

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What is the output of the following C code? Assume that the address of x is 2000 (in decimal) and an integer requires fo

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Consider the following pseudo code, where x and y are positive integers.
begin
q := 0
r := x
while r ≥ y d

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Match the following:
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Consider the following C program segment. while(first <= last)
{
if (array[middle] < search)
first

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For any two languages L1 and L2 such that L1 is context-free and L2 is recursively enumerable but not recursive, which o

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Consider the NPDA $$\left\langle {Q = \left\{ {{q_0},{q_1},{q_2}} \right\}} \right.,$$ $$\Sigma = \left \{ 0, 1 \right \

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Consider the DFAs M and N given above. The number of states in a minimal DFA that accepts the language L(M) ∩ L(N) is__

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Which of the following statements is/are FALSE?
I. XML overcomes the limitations in HTML to support a structured way of

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## General Aptitude

Didn't you buy _________ when you went shopping?

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Which of the following combinations is incorrect?

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Given set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one
from each set. What

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The pie chart below has the breakup of the number of students from different departments in an
engineering college for t

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The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p, and c
respectively. Of these sub

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Which of the following options is the closest in meaning to the sentence below?
She enjoyed herself immensely at the par

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Select the alternative meaning of the underlined part of the sentence.
The chain snatchers took to their heels when the

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Based on the given statements, select the most appropriate option to solve the given question.
If two floors in a certai

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The number of students in a class who have answered correctly, wrongly, or not attempted each
question in an exam, are l

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The given statement is followed by some courses of action. Assuming the statement to be true,
decide the correct option.

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