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2
answers
1
GATE198810ia
Consider the following grammar: $S \rightarrow S$ $S \rightarrow SS \mid a \mid \epsilon$ Construct the collection of sets of LR (0) items for this grammar and draw its goto graph.
answered
Jul 7, 2019
in
Compiler Design

438
views
gate1988
descriptive
grammar
parsing
3
answers
2
GATE201148
Consider the following recursive C function that takes two arguments. unsigned int foo(unsigned int n, unsigned int r) { if (n>0) return ((n%r) + foo(n/r, r)); else return 0; } What is the return value of the function $\text{foo}$ when it is called as $\text{foo(345, 10)}$? $345$ $12$ $5$ $3$
answer edited
Jul 6, 2019
in
Algorithms

1.8k
views
gate2011
algorithms
recursion
identifyfunction
normal
6
answers
3
GATE20067
Consider the following grammar $S \rightarrow S * E$ $S \rightarrow E$ $E \rightarrow F + E$ $E \rightarrow F$ $F \rightarrow id$ Consider the following LR(0) items corresponding to the grammar above $S \rightarrow S *.E$ $E \rightarrow F. + E$ ... them will appear in the same set in the canonical setsofitems for the grammar? i and ii ii and iii i and iii None of the above
answer edited
Jul 6, 2019
in
Compiler Design

3k
views
gate2006
compilerdesign
parsing
normal
2
answers
4
TIFR2017A10
For a set $A$ define $P(A)$ to be the set of all subsets of $A$. For example, if $A = \{1, 2\}$ then $P(A) = \{ \emptyset, \{1, 2\}, \{1\}, \{ 2 \} \}$. Let $A \rightarrow P(A)$ be a function and $A$ is not empty. Which of the ... $f$ is both onetoone and onto (bijective) there is no such $f$ possible if such a function $f$ exists, then $A$ is infinite
answer edited
Jun 16, 2019
in
Set Theory & Algebra

592
views
tifr2017
settheory&algebra
sets
functions
easy
3
answers
5
GATE2017 ME1: GA10
The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of $0.8$ (in suitable units) is needed to form curd. In the graph below, the population density of lactobacillus in $1$ litre of milk is plotted as a ... $37^{\circ}$C Which one of the following options is correct? Only i Only ii Both i and ii Neither i nor ii
edited
Jun 16, 2019
in
Numerical Ability

215
views
gate2017me1
generalaptitude
numericalability
datainterpretation
graphicaldata
1
answer
6
GATE2017 CE2: GA10
The points in the graph below represent the halts of a lift for a durations of $1$ minute, over a period of $1$ hour. Which of the following statements are correct? The elevator moves directly from any nonground floor to another nonground floor over the ... on the fourth floor for the longest duration over the one hour period. Only i Only ii Both i and ii Neither i nor ii
edited
Jun 13, 2019
in
Numerical Ability

220
views
gate2017ce2
datainterpretation
graphicaldata
1
answer
7
GATE19879d
Specify an adjacencylists representation of the undirected graph given above.
edited
Jun 5, 2019
in
Graph Theory

400
views
gate1987
graphtheory
easy
graphconnectivity
descriptive
1
answer
8
GATE199525a
Find the minimum value of $34x+2x^2$.
answer edited
Jun 4, 2019
in
Calculus

876
views
gate1995
calculus
maximaminima
easy
1
answer
9
GATE2018 ME1: GA9
Which of the following functions describe the graph shown in the below figure? $y=\mid \mid x \mid + 1 \mid 2$ $y=\mid \mid x \mid  1 \mid 1$ $y=\mid \mid x \mid + 1 \mid 1$ $y=\mid \mid x  1 \mid 1 \mid$
edited
Jun 4, 2019
in
Numerical Ability

258
views
gate2018me1
generalaptitude
numericalability
functions
absolutevalue
4
answers
10
GATE20002.4
A polynomial $p(x)$ satisfies the following: $p(1) = p(3) = p(5) = 1$ $p(2) = p(4) = 1$ The minimum degree of such a polynomial is $1$ $2$ $3$ $4$
answer edited
Jun 3, 2019
in
Set Theory & Algebra

2.4k
views
gate2000
settheory&algebra
normal
polynomials
5
answers
11
TIFR2015A11
Suppose that $f(x)$ is a continuous function such that $0.4 \leq f(x) \leq 0.6$ for $0 \leq x \leq 1$. Which of the following is always true? $f(0.5) = 0.5$. There exists $x$ between $0$ and $1$ such that $f(x) = 0.8x$. There exists $x$ between $0$ and $0.5$ such that $f(x) = x$. $f(0.5) > 0.5$. None of the above statements are always true.
answer edited
Jun 3, 2019
in
Calculus

681
views
tifr2015
maximaminima
calculus
2
answers
12
GATE199810b
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m < n$ and $R^m = R^n$.
edited
Jun 3, 2019
in
Set Theory & Algebra

433
views
gate1998
descriptive
settheory&algebra
relations
2
answers
13
GATE19976.1
A partial order $≤$ is defined on the set $S=\left \{ x, a_1, a_2, \ldots, a_n, y \right \}$ as $x$ $\leq _{i}$ $a_{i}$ for all $i$ and $a_{i}\leq y$ for all $i$, where $n ≥ 1$. The number of total orders on the set S which contain the partial order $≤$ is $n!$ $n+2$ $n$ $1$
answer edited
Jun 2, 2019
in
Set Theory & Algebra

2.7k
views
gate1997
settheory&algebra
partialorder
normal
1
answer
14
GATE200726
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:
edited
Jun 1, 2019
in
Set Theory & Algebra

4.2k
views
gate2007
settheory&algebra
normal
partialorder
descriptive
2
answers
15
GATE20024
$S=\{(1,2), (2,1)\}$ is binary relation on set $A = \{1,2,3\}$. Is it irreflexive? Add the minimum number of ordered pairs to S to make it an equivalence relation. Give the modified $S$. Let $S=\{a,b\}$ and let $\square(S)$ be the ... . Consider the binary relation '$\subseteq$ (set inclusion)' on $\square(S)$. Draw the Hasse diagram corresponding to the lattice ($\square(S), \subseteq$)
answer edited
Jun 1, 2019
in
Set Theory & Algebra

1k
views
gate2002
settheory&algebra
normal
lattice
descriptive
3
answers
16
GATE20059
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
edited
Jun 1, 2019
in
Set Theory & Algebra

2.1k
views
gate2005
settheory&algebra
lattice
normal
6
answers
17
GATE2015134
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 $x \wedge y$ are join and meet of $x, y$ ... $p_r = 0$ $p_r = 1$ $0 < p_r ≤ \frac{1}{5}$ $\frac{1}{5} < p_r < 1$
edited
Jun 1, 2019
in
Set Theory & Algebra

6.1k
views
gate20151
settheory&algebra
normal
lattice
2
answers
18
GATE19881vii
The complement(s) of the element 'a' in the lattice shown in below figure is (are) ____
edited
Jun 1, 2019
in
Set Theory & Algebra

1.1k
views
gate1988
descriptive
lattice
settheory&algebra
2
answers
19
GATE199214b
Consider the set of integers $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent? group ring field lattice
answer edited
May 29, 2019
in
Set Theory & Algebra

1.2k
views
gate1992
settheory&algebra
grouptheory
normal
2
answers
20
TIFR2012A3
Long ago,in a planet far far away, there lived three races of intelligent inhabitants: the blues (who always tell the truth), the whites (who always lie), and the pinks (who, when asked a series of questions, start with a lie and then tell the truth and lie alternately). To ... $C$ is Pink. $A$ is White, $B$ is Pink, $C$ is Blue. Cannot be determined from the above data.
edited
May 29, 2019
in
Mathematical Logic

939
views
tifr2012
mathematicallogic
logicalreasoning
4
answers
21
ISI2017MMA29
Suppose the rank of the matrix $\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$
commented
May 27, 2019
in
Linear Algebra

563
views
isi2017mma
engineeringmathematics
linearalgebra
rankofmatrix
3
answers
22
GATE200321
Consider the following graph: Among the following sequences: abeghf abfehg abfhge afghbe Which are the depthfirst traversals of the above graph? I, II and IV only I and IV only II, III and IV only I, III and IV only
edited
May 27, 2019
in
Algorithms

2k
views
gate2003
algorithms
graphalgorithms
normal
2
answers
23
TIFR2015B11
Let $K_{n}$ be the complete graph on $n$ vertices labeled $\left\{1, 2,\dots ,n\right\}$ with $m=\frac{n (n  1)}{2}$ edges. What is the number of spanning trees of $K_{n}$? $\frac{m}{n  1}$ $m^{n  1}$ $n^{n  2}$ $n^{n  1}$ None of the above.
answer edited
May 27, 2019
in
Graph Theory

710
views
tifr2015
graphtheory
spanningtree
4
answers
24
GATE20171GA7
Six people are seated around a circular table. There are at least two men and two women. There are at least three righthanded persons. Every woman has a lefthanded person to her immediate right. None of the women are righthanded. The number of women at the table is $2$ $3$ $4$ Cannot be determined
answer edited
May 26, 2019
in
Numerical Ability

3.4k
views
gate20171
numericalability
roundtablearrangement
6
answers
25
GATE2014251
A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.
answer edited
May 24, 2019
in
Graph Theory

4.4k
views
gate20142
graphtheory
numericalanswers
normal
graphisomorphism
nongate
3
answers
26
GATE2004IT25
A sender is employing public key cryptography to send a secret message to a receiver. Which one of the following statements is TRUE? Sender encrypts using receiver's public key Sender encrypts using his own public key Receiver decrypts using sender's public key Receiver decrypts using his own public key
answer edited
May 24, 2019
in
Computer Networks

5.9k
views
gate2004it
computernetworks
networksecurity
normal
4
answers
27
GATE201226
Which of the following graphs is isomorphic to
edited
May 11, 2019
in
Graph Theory

2.6k
views
gate2012
graphtheory
graphisomorphism
normal
nongate
3
answers
28
GATE2008IT3
What is the chromatic number of the following graph? $2$ $3$ $4$ $5$
answer edited
May 11, 2019
in
Graph Theory

2.2k
views
gate2008it
graphtheory
graphcoloring
normal
1
answer
29
CMI2012B01
Let $G=(V, E)$ be a graph where $\mid V \mid =n$ and the degree of each vertex is strictly greater than $\frac{n}{2}$. Prove that $G$ has a Hamiltonian path. (Hint: Consider a path of maximum length in $G$.)
answer edited
May 11, 2019
in
Graph Theory

351
views
cmi2012
descriptive
graphtheory
graphconnectivity
5
answers
30
GATE19995
Let $G$ be a connected, undirected graph. A cut in $G$ is a set of edges whose removal results in $G$ being broken into two or more components, which are not connected with each other. The size of a cut is called its cardinality. A mincut of $G$ is a cut in $G$ of ... $n$ vertices has a mincut of cardinality $k$, then $G$ has at least $\left(\frac{n\times k}{2}\right)$ edges.
edited
May 10, 2019
in
Graph Theory

1.5k
views
gate1999
graphtheory
graphconnectivity
normal
2
answers
31
GATE19991.15
The number of articulation points of the following graph is $0$ $1$ $2$ $3$
edited
May 10, 2019
in
Graph Theory

1.9k
views
gate1999
graphtheory
graphconnectivity
normal
6
answers
32
GATE200477
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
answer edited
May 8, 2019
in
Graph Theory

2.8k
views
gate2004
graphtheory
graphcoloring
easy
5
answers
33
GATE200723
Which of the following graphs has an Eulerian circuit? Any $k$regular graph where $k$ is an even number. A complete graph on $90$ vertices. The complement of a cycle on $25$ vertices. None of the above
answer edited
May 8, 2019
in
Graph Theory

6.3k
views
gate2007
graphtheory
normal
graphconnectivity
9
answers
34
GATE19941.6, ISRO200829
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
answer edited
May 6, 2019
in
Graph Theory

10.8k
views
gate1994
graphtheory
permutationandcombination
normal
isro2008
counting
6
answers
35
TIFR2017B12
An undirected graph is complete if there is an edge between every pair of vertices. Given a complete undirected graph on $n$ vertices, in how many ways can you choose a direction for the edges so that there are no directed cycles? $n$ $\frac{n(n1)}{2}$ $n!$ $2^n$ $2^m, \: \text{ where } m=\frac{n(n1)}{2}$
answer edited
May 5, 2019
in
Graph Theory

2k
views
tifr2017
graphtheory
counting
2
answers
36
GATE19991.8
Which of the following functions implements the Karnaugh map shown below? $\bar{A}B + CD$ $D(C+A)$ $AD+\bar{A}B$ $(C+D) (\bar{C}+D) + (A+B)$
edited
Apr 27, 2019
in
Digital Logic

1k
views
gate1999
digitallogic
kmap
easy
5
answers
37
GATE201114
The simplified SOP (Sum of Product) from the Boolean expression $(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$ is $(\bar{P}.Q+\bar{R})$ $(P+\bar{Q}.\bar{R})$ $(\bar{P}.Q+R)$ $(P.Q+R)$
answer edited
Apr 27, 2019
in
Digital Logic

1.8k
views
gate2011
digitallogic
normal
minsumofproductsform
5
answers
38
GATE201230
What is the minimal form of the Karnaugh map shown below? Assume that $X$ denotes a don’t care term $\bar{b} \bar{d}$ $ \bar { b } \bar { d } + \bar{b} \bar{c} $ $ \bar{b} \bar{d} + {a} \bar{b} \bar{c} {d}$ $ \bar{b} \bar{d} + \bar{b} \bar{c} + \bar{c} \bar{d} $
answer edited
Apr 25, 2019
in
Digital Logic

1.9k
views
gate2012
digitallogic
kmap
easy
4
answers
39
GATE20085
In the Karnaugh map shown below, $X$ denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map? $\bar{b}.\bar{d} + \bar{a}.\bar{d}$ $\bar{a}.\bar{b} + \bar{b}.\bar{d} + \bar{a}.b.\bar{d}$ $\bar{b}.\bar{d} + \bar{a}.b.\bar{d}$ $\bar{a}.\bar{b} + \bar{b}.\bar{d} + \bar{a}.\bar{d}$
answer edited
Apr 25, 2019
in
Digital Logic

1.8k
views
gate2008
digitallogic
kmap
easy
2
answers
40
GATE2006IT35
The boolean function for a combinational circuit with four inputs is represented by the following Karnaugh map. Which of the product terms given below is an essential prime implicant of the function? $\text{QRS}$ $\text{PQS}$ $\text{PQ'S'}$ $\text{Q'S'}$
edited
Apr 25, 2019
in
Digital Logic

1.5k
views
gate2006it
digitallogic
kmap
normal
50,834
questions
57,750
answers
199,479
comments
108,169
users