GATE CSE 2000

## GATE CSE

Consider the following functions
$$f(n) = 3{n^{\sqrt n }}$$
$$g(n) = {2^{\sqrt n {{\log }_2}n}}$$
$$h(n) = n!$$
Which of

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Let s be a sorted array of n integers. Let t(n) denote the time taken for the most efficient algorithm to determined if

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Let G be an undirected connected graph with distinct edge weight. Let emax be the edge with maximum weight and emin the

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The number of tokens in the following C statement is:
printf("i = %d, &i = %x",i, &i);

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Comparing the time $$T1$$ taken for a single instruction on a pipelined $$CPU$$ with time $$T2$$ taken on a non-pipeline

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An instruction pipeline has five stages where each stage takes $$2$$ nanoseconds and all instructions use all five stage

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The most appropriate matching for the following pairs
$$X:$$ Indirect addressing
$$Y:$$ Immediate addressing
$$Z:$$ Au

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A graphics card has on board memory of $$1$$ $$MB.$$ Which of the following modes can the card not support?

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An n $$\times$$ n array v is defined as follows V [i, j] = i - j for all i, j, $$1 \le i \le n,\,1 \le j \le n$$ The sum

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Suppose you are given an array s[1..n] and a procedure reverse (s, i, j) which reverse the order of elements in s betwee

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Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stres

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Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal. Respecti

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Let G be an undirected graph. Consider a depth-first traversal of G, and let T be
the resulting depth-first search tree.

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Given the following relation instance
$$\eqalign{
& X\,\,\,\,\,Y\,\,\,\,\,Z \cr
& \,\,1\,\,\,\,\,\,4\,\,\,

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Given relations r( w, x ) and s( y, z ), the result of
select distinct w,x
from r, s;
is guaranteed to be same as r, pr

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In SQL, relations can contain null values, and comparisons with null values are treated as unknown. Suppose all comparis

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Given the relations
employee (name, salary, deptno), and department (deptno, deptname, address)
Which of the following

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B+-trees are preferred to binary trees in databases because

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The number $$43$$ in $$2's$$ complement representation is

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The simultaneous equations on the Boolean variables $$x, y, z$$ and $$w,$$
$$$x+y+z=1$$$
$$$xy=0$$$
$$$xz+w=1$$$
$$$xy

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Which function does NOT implement the Karnaugh map given below?

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The following arrangement of master-slave flip-flop
Has the initial state of $$P, Q$$ as $$0, 1$$ (respectively). After

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Let $$a, b, c, d$$ be propositions. Assume that the equivalences $$a \leftrightarrow \left( {b \vee \neg b} \right)$$ an

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Let P(S) denote the power set of a set S. Which of the following is always true?

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A relation R is defined on the set of integers as zRy if f (x + y) is even. Which of the following statements is true?

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$${{E_1}}$$ and $${{E_2}}$$ are events in a probability space satisfying the following constraints:
$$ \bullet $$ $$\Pr

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The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are

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The solution to the recurrence equation
$$T\left( {{2^k}} \right)$$ $$ = 3T\left( {{2^{k - 1}}} \right) + 1$$,
$$T\lef

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The determinant of the matrix
$$$\left[ {\matrix{
2 & 0 & 0 & 0 \cr
8 & 1 & 7 & 2 \cr

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An $$n\,\, \times \,\,n$$ array v is defined as follows v[i, j] = i - j for all i, j, $$1\,\, \le \,\,i\,\, \le \,\,n,\,

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A multiset is an unordered collection of elements where elements may repeat ay number of times. The size of a multiset i

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Let $$S = \left\{ {0,1,2,3,4,5,6,7} \right\}$$ and $$ \otimes $$ denote multiplication modulo $$8$$, that is, $$x \otime

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Let m[0] ..m[4] be mutexes (binary semaphores) and P[0] ...P[4] be processes. Suppose each process P[i] executes the fol

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Suppose the time to service a page fault is on the average $$10$$ milliseconds, while a memory access takes $$1$$ micros

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Which of the following is NOT a valid deadlock prevention scheme?

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The value of j at the end of the execution of the following C program
int incr (int i)
{
static int count = 0;

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The following C declarations
struct node{
int i:
float j;
};
struct node *s[10];
define s to be

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The most appropriate matching for the following pairs
X: m=malloc(5); m= NULL;
Y: free(n); n->value = 5;
Z: char *p

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Consider the following C declaration
struct {
short s[5];
union {
float y;
long z;
} u;
}t

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Let $$S$$ and $$T$$ be languages over $$\sum { = \left\{ {a,b} \right\}} $$ represented by the regular expressions $${\l

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Let $$L$$ denote the language generated by the grammar $$S \to 0S\left. 0 \right|00.$$ Which one of the following is tru

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What can be said about a regular language $$L$$ over $$\left\{ a \right\}$$ whose minimal finite state automation has t

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Consider the following decision problems:
$${P_1}$$ Does a given finite state machine accept a given string
$${P_2}$$ Do

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