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Recent questions tagged gatecse-2005
21
votes
2
answers
61
GATE CSE 2005 | Question: 18
The switching expression corresponding to $f(A,B,C,D)=\Sigma(1, 4, 5, 9, 11, 12)$ is: $BC’D’ + A’C’D + AB’D$ $ABC’ + ACD + B’C’D$ $ACD’ + A’BC’ + AC’D’$ $A’BD + ACD’ + BCD’$
Kathleen
asked
in
Digital Logic
Sep 22, 2014
by
Kathleen
5.6k
views
gatecse-2005
digital-logic
normal
min-sum-of-products-form
20
votes
2
answers
62
GATE CSE 2005 | Question: 17
The hexadecimal representation of (657)8 is: $\text{1AF}$ $\text{D78}$ $\text{D71}$ $\text{32F}$
Kathleen
asked
in
Digital Logic
Sep 22, 2014
by
Kathleen
7.3k
views
gatecse-2005
digital-logic
number-representation
easy
24
votes
5
answers
63
GATE CSE 2005 | Question: 16, ISRO2009-18, ISRO2015-2
The range of integers that can be represented by an $n$ bit $2’s$ complement number system is: $-2^{n-1} \text{ to } (2^{n-1} -1)$ $-(2^{n-1} -1) \text{ to } (2^{n-1} -1)$ $-2^{n-1} \text{ to } 2^{n-1}$ $-(2^{n-1} +1) \text{ to } (2^{n-1} -1)$
Kathleen
asked
in
Digital Logic
Sep 22, 2014
by
Kathleen
9.7k
views
gatecse-2005
digital-logic
number-representation
easy
isro2009
isro2015
21
votes
4
answers
64
GATE CSE 2005 | Question: 15
Consider the following circuit. Which one of the following is TRUE? $f$ is independent of $x$ $f$ is independent of $y$ $f$ is independent of $z$ None of $x, y, z$ is redundant
Kathleen
asked
in
Digital Logic
Sep 22, 2014
by
Kathleen
8.5k
views
gatecse-2005
digital-logic
circuit-output
normal
37
votes
4
answers
65
GATE CSE 2005 | Question: 14
The grammar $A \rightarrow AA \mid (A) \mid \epsilon$ is not suitable for predictive-parsing because the grammar is: ambiguous left-recursive right-recursive an operator-grammar
Kathleen
asked
in
Compiler Design
Sep 22, 2014
by
Kathleen
23.3k
views
gatecse-2005
compiler-design
parsing
grammar
easy
36
votes
6
answers
66
GATE CSE 2005 | Question: 7
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
Kathleen
asked
in
Set Theory & Algebra
Sep 22, 2014
by
Kathleen
24.5k
views
gatecse-2005
set-theory&algebra
normal
relations
36
votes
2
answers
67
GATE CSE 2005 | Question: 6
An undirected graph $G$ has $n$ nodes. its adjacency matrix is given by an $n \times n$ square matrix whose (i) diagonal elements are 0's and (ii) non-diagonal elements are 1's. Which one of the following is TRUE? Graph $G$ has no minimum ... cost $n-1$ Graph $G$ has multiple distinct MSTs, each of cost $n-1$ Graph $G$ has multiple spanning trees of different costs
Kathleen
asked
in
Algorithms
Sep 22, 2014
by
Kathleen
13.9k
views
gatecse-2005
algorithms
spanning-tree
normal
46
votes
4
answers
68
GATE CSE 2005 | Question: 5
A program $P$ reads in $500$ integers in the range $[0, 100]$ representing the scores of $500$ students. It then prints the frequency of each score above $50$. What would be the best way for $P$ to store the frequencies? An array of $50$ numbers An array of $100$ numbers An array of $500$ numbers A dynamically allocated array of $550$ numbers
Kathleen
asked
in
DS
Sep 22, 2014
by
Kathleen
20.7k
views
gatecse-2005
data-structures
array
easy
11
votes
4
answers
69
GATE CSE 2005 | Question: 4
Which one of the following are essential features of an object-oriented programming language? Abstraction and encapsulation Strictly-typedness Type-safe property coupled with sub-type rule Polymorphism in the presence of inheritance I and II only I and IV only I, II and IV only I, III and IV only
Kathleen
asked
in
Object Oriented Programming
Sep 22, 2014
by
Kathleen
5.8k
views
gatecse-2005
programming
normal
object-oriented-programming
non-gate
13
votes
3
answers
70
GATE CSE 2005 | Question: 3, UGCNET-June2012-III: 15
A common property of logic programming languages and functional languages is: both are procedural languages both are based on $\lambda$-calculus both are declarative both use Horn-clauses
Kathleen
asked
in
Programming in C
Sep 22, 2014
by
Kathleen
12.4k
views
gatecse-2005
programming
normal
ugcnetcse-june2012-paper3
programming-paradigms
non-gate
43
votes
8
answers
71
GATE CSE 2005 | Question: 2
An Abstract Data Type (ADT) is: same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used, but none else all of the above
Kathleen
asked
in
DS
Sep 22, 2014
by
Kathleen
19.4k
views
gatecse-2005
data-structures
normal
abstract-data-type
37
votes
5
answers
72
GATE CSE 2005 | Question: 1, ISRO2017-55
What does the following C-statement declare? int (*f) (int * ); A function that takes an integer pointer as argument and returns an integer A function that takes an integer as argument and returns an integer pointer A pointer ... pointer as argument and returns an integer A function that takes an integer pointer as argument and returns a function pointer
Kathleen
asked
in
Programming in C
Sep 22, 2014
by
Kathleen
20.6k
views
gatecse-2005
programming
programming-in-c
pointers
easy
isro2017
27
votes
11
answers
73
GATE CSE 2005 | Question: 52
A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is: $\frac{1}{2^n}$ $1 - \frac{1}{n}$ $\frac{1}{n!}$ $1 - \frac{1}{2^n}$
gatecse
asked
in
Probability
Sep 21, 2014
by
gatecse
8.5k
views
gatecse-2005
probability
binomial-distribution
easy
21
votes
9
answers
74
GATE CSE 2005 | Question: 51
Box $P$ has $2$ red balls and $3$ blue balls and box $Q$ has $3$ red balls and $1$ blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities ... that it came from the box $P$ is: $\dfrac{4}{19}$ $\dfrac{5}{19}$ $\dfrac{2}{9}$ $\dfrac{19}{30}$
gatecse
asked
in
Probability
Sep 21, 2014
by
gatecse
5.9k
views
gatecse-2005
probability
conditional-probability
normal
27
votes
8
answers
75
GATE CSE 2005 | Question: 50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
gatecse
asked
in
Combinatory
Sep 21, 2014
by
gatecse
8.2k
views
gatecse-2005
normal
generating-functions
21
votes
3
answers
76
GATE CSE 2005 | Question: 49
What are the eigenvalues of the following $2\times 2$ matrix? $\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$ $-1$ and $1$ $1$ and $6$ $2$ and $5$ $4$ and $-1$
gatecse
asked
in
Linear Algebra
Sep 21, 2014
by
gatecse
6.0k
views
gatecse-2005
linear-algebra
eigen-value
easy
19
votes
4
answers
77
GATE CSE 2005 | Question: 48
Consider the following system of linear equations : $2x_1 - x_2 + 3x_3 = 1$ $3x_1 + 2x_2 + 5x_3 = 2$ $-x_1+4x_2+x_3 = 3$ The system of equations has no solution a unique solution more than one but a finite number of solutions an infinite number of solutions
gatecse
asked
in
Linear Algebra
Sep 21, 2014
by
gatecse
7.2k
views
gatecse-2005
linear-algebra
system-of-equations
normal
15
votes
2
answers
78
GATE CSE 2005 | Question: 47
Which one of the following graphs is NOT planar? G1 G2 G3 G4
gatecse
asked
in
Graph Theory
Sep 21, 2014
by
gatecse
8.3k
views
gatecse-2005
graph-theory
graph-planarity
normal
31
votes
4
answers
79
GATE CSE 2005 | Question: 46
Consider the set $H$ of all $3 * 3$ matrices of the type $\left( \begin{array}{ccc} a & f & e \\ 0 & b & d \\ 0 & 0 & c \end{array} \right)$ where $a,b,c,d,e$ and $f$ ... the matrix multiplication operation, the set $H$ is: a group a monoid but not a group a semi group but not a monoid neither a group nor a semi group
gatecse
asked
in
Set Theory & Algebra
Sep 21, 2014
by
gatecse
7.5k
views
gatecse-2005
set-theory&algebra
group-theory
normal
60
votes
9
answers
80
GATE CSE 2005 | Question: 44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
gatecse
asked
in
Combinatory
Sep 21, 2014
by
gatecse
13.4k
views
gatecse-2005
set-theory&algebra
normal
pigeonhole-principle
40
votes
7
answers
81
GATE CSE 2005 | Question: 43
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto
gatecse
asked
in
Set Theory & Algebra
Sep 21, 2014
by
gatecse
10.0k
views
gatecse-2005
set-theory&algebra
functions
normal
26
votes
4
answers
82
GATE CSE 2005 | Question: 42
Let $R$ and $S$ be any two equivalence relations on a non-empty set $A$. Which one of the following statements is TRUE? $R$ $∪$ $S$, $R$ $∩$ $S$ are both equivalence relations $R$ $∪$ $S$ is an equivalence relation $R$ $∩$ $S$ is an equivalence relation Neither $R$ $∪$ $S$ nor $R$ $∩$ $S$ are equivalence relations
gatecse
asked
in
Set Theory & Algebra
Sep 21, 2014
by
gatecse
9.1k
views
gatecse-2005
set-theory&algebra
normal
relations
50
votes
4
answers
83
GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
gatecse
asked
in
Mathematical Logic
Sep 21, 2014
by
gatecse
11.7k
views
gatecse-2005
mathematical-logic
easy
first-order-logic
34
votes
4
answers
84
GATE CSE 2005 | Question: 40
Let $P, Q,$ and $R$ be three atomic propositional assertions. Let $X$ denote $( P ∨ Q ) → R$ and $Y$ denote $(P → R) ∨ (Q → R).$ Which one of the following is a tautology? $X ≡ Y$ $X → Y$ $Y → X$ $¬Y → X$
gatecse
asked
in
Mathematical Logic
Sep 21, 2014
by
gatecse
6.5k
views
gatecse-2005
mathematical-logic
propositional-logic
normal
24
votes
3
answers
85
GATE CSE 2005 | Question: 13
The set \(\{1, 2, 4, 7, 8, 11, 13, 14\}\) is a group under multiplication modulo $15$. The inverses of $4$ and $7$ are respectively: $3$ and $13$ $2$ and $11$ $4$ and $13$ $8$ and $14$
gatecse
asked
in
Set Theory & Algebra
Sep 21, 2014
by
gatecse
7.1k
views
gatecse-2005
set-theory&algebra
normal
group-theory
24
votes
3
answers
86
GATE CSE 2005 | Question: 12, ISRO2009-64
Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is : $f(b-a)$ $f(b) - f(a)$ $\int\limits_a^b f(x) dx$ $\int\limits_a^b xf (x)dx$
gatecse
asked
in
Probability
Sep 21, 2014
by
gatecse
11.5k
views
gatecse-2005
probability
random-variable
easy
isro2009
38
votes
4
answers
87
GATE CSE 2005 | Question: 11
Let $G$ be a simple graph with $20$ vertices and $100$ edges. The size of the minimum vertex cover of G is $8$. Then, the size of the maximum independent set of $G$ is: $12$ $8$ less than $8$ more than $12$
gatecse
asked
in
Graph Theory
Sep 21, 2014
by
gatecse
11.6k
views
gatecse-2005
graph-theory
normal
graph-connectivity
19
votes
3
answers
88
GATE CSE 2005 | Question: 10
Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is: $6$ $8$ $9$ $13$
gatecse
asked
in
Graph Theory
Sep 21, 2014
by
gatecse
9.2k
views
gatecse-2005
graph-theory
graph-planarity
25
votes
4
answers
89
GATE CSE 2005 | Question: 9
The following is the Hasse diagram of the poset $\left[\{a,b,c,d,e\},≺\right]$ The poset is : not a lattice a lattice but not a distributive lattice a distributive lattice but not a Boolean algebra a Boolean algebra
gatecse
asked
in
Set Theory & Algebra
Sep 21, 2014
by
gatecse
9.1k
views
gatecse-2005
set-theory&algebra
lattice
normal
25
votes
5
answers
90
GATE CSE 2005 | Question: 8
Let $A, B$ and $C$ be non-empty sets and let $X = ( A - B ) - C$ and $Y = ( A - C ) - ( B - C ).$ Which one of the following is TRUE? $X = Y$ $X ⊂ Y$ $Y ⊂ X$ None of these
gatecse
asked
in
Set Theory & Algebra
Sep 21, 2014
by
gatecse
6.9k
views
gatecse-2005
set-theory&algebra
easy
set-theory
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