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Previous GATE
+29
votes
13
answers
1
GATE201846
The number of possible minheaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
asked
Feb 14, 2018
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

9.8k
views
gate2018
permutationandcombination
numericalanswers
+14
votes
12
answers
2
TIFR2012A1
Amar and Akbar both tell the truth with probability $\dfrac{3 } {4}$ and lie with probability $\dfrac{1}{4}$. Amar watches a test match and talks to Akbar about the outcome. Akbar, in turn, tells Anthony, "Amar told me that India won". What probability should Anthony ... $\left(\dfrac{7}{16}\right)$ $\left(\dfrac{10}{16}\right)$ None of the above
asked
Oct 25, 2015
in
Probability
by
makhdoom ghaya
Boss
(
30.8k
points)

1.8k
views
tifr2012
probability
conditionalprobability
+40
votes
11
answers
3
GATE2016126
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
asked
Feb 12, 2016
in
Combinatory
by
Sandeep Singh
Loyal
(
7.2k
points)

9.8k
views
gate20161
permutationandcombination
generatingfunctions
normal
numericalanswers
+46
votes
11
answers
4
GATE201535
The number of $4$ digit numbers having their digits in nondecreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
asked
Feb 14, 2015
in
Combinatory
by
jothee
Veteran
(
105k
points)

4.6k
views
gate20153
permutationandcombination
normal
numericalanswers
+40
votes
11
answers
5
GATE2014351
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $nk$ $nk+1$
asked
Sep 28, 2014
in
Graph Theory
by
jothee
Veteran
(
105k
points)

5k
views
gate20143
graphtheory
graphconnectivity
normal
+41
votes
11
answers
6
GATE2014149
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4$pennant. The set of all possible $1$pennants is ${(1)}$, the set of all possible $2$pennants is ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10$pennants is________
asked
Sep 28, 2014
in
Combinatory
by
jothee
Veteran
(
105k
points)

3.3k
views
gate20141
permutationandcombination
numericalanswers
normal
+8
votes
10
answers
7
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
asked
Feb 7, 2019
in
Combinatory
by
Arjun
Veteran
(
431k
points)

4.2k
views
gate2019
numericalanswers
permutationandcombination
modulararithmetic
+19
votes
10
answers
8
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
asked
Feb 14, 2018
in
Combinatory
by
gatecse
Boss
(
17.5k
points)

7k
views
gate2018
generatingfunctions
normal
permutationandcombination
+25
votes
10
answers
9
GATE2014 EC1: GA10
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is $\dfrac{1}{4}$ $\dfrac{1}{3}$ $\dfrac{1}{2}$ $\dfrac{2}{3}$
asked
Mar 18, 2016
in
Probability
by
makhdoom ghaya
Boss
(
30.8k
points)

1.9k
views
gate2014ec1
numericalability
probability
conditionalprobability
+58
votes
10
answers
10
GATE2015139
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 $\left\{\textit{f} \right\}$ and $\left\{ \textit{g}\right\}$ are ... Only $\left\{ \textit{g}\right\}$ is functionally complete Neither $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete
asked
Feb 13, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

8.3k
views
gate20151
settheory&algebra
functions
difficult
+34
votes
10
answers
11
GATE2015240
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
asked
Feb 13, 2015
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

8.2k
views
gate20152
settheory&algebra
functions
normal
numericalanswers
+22
votes
10
answers
12
GATE2014353
The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
asked
Sep 28, 2014
in
Mathematical Logic
by
jothee
Veteran
(
105k
points)

1.9k
views
gate20143
mathematicallogic
easy
firstorderlogic
+48
votes
10
answers
13
GATE201233
Suppose a fair sixsided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of values that turn up is at least $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$
asked
Sep 26, 2014
in
Probability
by
gatecse
Boss
(
17.5k
points)

7k
views
gate2012
probability
conditionalprobability
normal
+8
votes
9
answers
14
GATE201912
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n1)!$ $1$ $\frac{(n1)!}{2}$
asked
Feb 7, 2019
in
Graph Theory
by
Arjun
Veteran
(
431k
points)

4k
views
gate2019
engineeringmathematics
discretemathematics
graphtheory
graphconnectivity
+18
votes
9
answers
15
GATE201830
Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements. No edge of $G$ is a cross edge with respect to $T_D$. (A cross edge in $G$ is between ... then $\mid ij \mid =1$. Which of the statements above must necessarily be true? I only II only Both I and II Neither I nor II
asked
Feb 14, 2018
in
Graph Theory
by
gatecse
Boss
(
17.5k
points)

6.3k
views
gate2018
graphtheory
graphsearch
normal
+10
votes
9
answers
16
ISRO201722
Which one of the following Boolean expressions is NOT a tautology? $((a \rightarrow b) \wedge (b \rightarrow c)) \rightarrow (a \rightarrow c)$ $(a \leftrightarrow c) \rightarrow (\sim b\rightarrow (a\wedge c))$ $(a\wedge b \wedge c)\rightarrow (c \vee a)$ $a\rightarrow (b\rightarrow a)$
asked
May 7, 2017
in
Mathematical Logic
by
sh!va
Boss
(
33k
points)

3k
views
isro2017
booleanalgebra
mathematicallogic
+39
votes
9
answers
17
GATE19941.6, ISRO200829
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
asked
Oct 4, 2014
in
Graph Theory
by
Kathleen
Veteran
(
52.2k
points)

10.5k
views
gate1994
graphtheory
permutationandcombination
normal
isro2008
counting
+11
votes
8
answers
18
GATE201935
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... Set of all positive integers $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
asked
Feb 7, 2019
in
Mathematical Logic
by
Arjun
Veteran
(
431k
points)

5.9k
views
gate2019
engineeringmathematics
discretemathematics
mathematicallogic
firstorderlogic
+6
votes
8
answers
19
TIFR2018B1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
asked
Dec 10, 2017
in
Combinatory
by
Arjun
Veteran
(
431k
points)

575
views
tifr2018
modulararithmetic
permutationandcombination
+30
votes
8
answers
20
GATE2017223
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
asked
Feb 14, 2017
in
Graph Theory
by
Madhav
Active
(
1.6k
points)

4.9k
views
gate20172
graphtheory
numericalanswers
degreeofgraph
+16
votes
8
answers
21
GATE2017147
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
asked
Feb 14, 2017
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

3.8k
views
gate20171
settheory&algebra
normal
numericalanswers
sets
+41
votes
8
answers
22
GATE2016127
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
asked
Feb 12, 2016
in
Combinatory
by
Sandeep Singh
Loyal
(
7.2k
points)

8k
views
gate20161
permutationandcombination
recurrence
normal
numericalanswers
+55
votes
8
answers
23
GATE2016228
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an odd number ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
asked
Feb 12, 2016
in
Set Theory & Algebra
by
Akash Kanase
Boss
(
41.9k
points)

5.5k
views
gate20162
settheory&algebra
difficult
sets
+7
votes
8
answers
24
ISRO201473
How many different trees are there with four nodes $A, B, C$ and $D$? 30 60 90 120
asked
Sep 23, 2015
in
Combinatory
by
ajit
Active
(
2.5k
points)

7k
views
permutationandcombination
isro2014
+8
votes
8
answers
25
Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?
asked
Jul 13, 2015
in
Combinatory
by
Anu
Loyal
(
5.8k
points)

2.4k
views
permutationandcombination
counting
+31
votes
8
answers
26
GATE2005IT36
Let $P(x)$ and $Q(x)$ ...
asked
Nov 3, 2014
in
Mathematical Logic
by
Ishrat Jahan
Boss
(
16.3k
points)

4.6k
views
gate2005it
mathematicallogic
firstorderlogic
normal
+28
votes
8
answers
27
GATE2004IT35
In how many ways can we distribute $5$ distinct balls, $B_1, B_2, \ldots, B_5$ in $5$ distinct cells, $C_1, C_2, \ldots, C_5$ such that Ball $B_i$ is not in cell $C_i$, $\forall i= 1,2,\ldots 5$ and each cell contains exactly one ball? $44$ $96$ $120$ $3125$
asked
Nov 2, 2014
in
Combinatory
by
Ishrat Jahan
Boss
(
16.3k
points)

3.2k
views
gate2004it
permutationandcombination
normal
ballsinbins
+15
votes
8
answers
28
GATE19962.3
Which of the following is false? Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication $((x \rightarrow y) \wedge x) \rightarrow y$ $((\neg x \rightarrow y) \wedge (\neg x \rightarrow \neg y)) \rightarrow x$ $(x \rightarrow (x \vee y))$ $((x \vee y) \leftrightarrow (\neg x \rightarrow \neg y))$
asked
Oct 9, 2014
in
Mathematical Logic
by
Kathleen
Veteran
(
52.2k
points)

1.8k
views
gate1996
mathematicallogic
normal
propositionallogic
+28
votes
8
answers
29
GATE2014153
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ $( (p \to q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $
asked
Sep 28, 2014
in
Mathematical Logic
by
jothee
Veteran
(
105k
points)

3.6k
views
gate20141
mathematicallogic
normal
propositionallogic
+68
votes
8
answers
30
GATE2014151
Consider an undirected graph $G$ where selfloops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $ac \leq 1$ and $bd \leq 1$. The number of edges in this graph is______.
asked
Sep 28, 2014
in
Graph Theory
by
jothee
Veteran
(
105k
points)

8.6k
views
gate20141
graphtheory
numericalanswers
normal
graphconnectivity
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