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Search results for combinatory
19
votes
3
answers
1
How to construct an automata with even number of a's and odd number of b's?
The alphabets are a and b. Construct a DFA
The alphabets are a and b.Construct a DFA
Gourab_Classic
109k
views
Gourab_Classic
asked
Mar 14, 2016
Theory of Computation
minimal-state-automata
theory-of-computation
finite-automata
combinatory
+
–
67
votes
14
answers
2
GATE CSE 2018 | Question: 46
The number of possible min-heaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
The number of possible min-heaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
gatecse
39.1k
views
gatecse
asked
Feb 14, 2018
DS
gatecse-2018
binary-heap
numerical-answers
combinatory
2-marks
+
–
77
votes
12
answers
3
GATE CSE 1994 | Question: 1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
The number of distinct simple graphs with up to three nodes is$15$$10$$7$$9$
Kathleen
34.8k
views
Kathleen
asked
Oct 4, 2014
Graph Theory
gate1994
graph-theory
graph-connectivity
combinatory
normal
isro2008
counting
+
–
57
votes
17
answers
4
GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
Sandeep Singh
25.9k
views
Sandeep Singh
asked
Feb 12, 2016
Combinatory
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
+
–
19
votes
18
answers
5
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
The value of $3^{51} \text{ mod } 5$ is _____
Arjun
18.2k
views
Arjun
asked
Feb 7, 2019
Combinatory
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
+
–
67
votes
10
answers
6
GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Sandeep Singh
29.3k
views
Sandeep Singh
asked
Feb 12, 2016
Combinatory
gatecse-2016-set1
combinatory
recurrence-relation
normal
numerical-answers
+
–
55
votes
9
answers
7
GATE CSE 2010 | Question: 65
Given digits $ 2, 2, 3, 3, 3, 4, 4, 4, 4$ how many distinct $4$ digit numbers greater than $3000$ can be formed? $50$ $51$ $52$ $54$
Given digits $ 2, 2, 3, 3, 3, 4, 4, 4, 4$ how many distinct $4$ digit numbers greater than $3000$ can be formed?$50$$51$$52$$54$
go_editor
17.4k
views
go_editor
asked
Sep 30, 2014
Quantitative Aptitude
gatecse-2010
quantitative-aptitude
combinatory
normal
+
–
26
votes
6
answers
8
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Arjun
12.0k
views
Arjun
asked
Feb 18, 2021
Combinatory
gatecse-2021-set2
combinatory
counting
numerical-answers
2-marks
+
–
28
votes
8
answers
9
GATE CSE 2020 | Question: 42
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
Arjun
16.5k
views
Arjun
asked
Feb 12, 2020
Combinatory
gatecse-2020
numerical-answers
combinatory
2-marks
+
–
42
votes
11
answers
10
GATE CSE 2018 | Question: 1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
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...
gatecse
22.7k
views
gatecse
asked
Feb 14, 2018
Combinatory
gatecse-2018
generating-functions
normal
combinatory
1-mark
+
–
86
votes
8
answers
11
GATE CSE 2004 | Question: 79
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k$ $^{\left(\frac{n^2-n}{2}\right)}C_n$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ?$^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$$^{{\l...
Kathleen
14.4k
views
Kathleen
asked
Sep 18, 2014
Graph Theory
gatecse-2004
graph-theory
combinatory
normal
counting
+
–
7
votes
4
answers
12
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
The Lucas sequence $L_{n}$ is defined by the recurrence relation:\[L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3,\]with $L_{1}=1$ and $L_{2}=3$.Which one of t...
admin
8.0k
views
admin
asked
Feb 15, 2023
Combinatory
gatecse-2023
combinatory
recurrence-relation
1-mark
+
–
65
votes
16
answers
13
GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ___...
go_editor
15.7k
views
go_editor
asked
Feb 14, 2015
Combinatory
gatecse-2015-set3
combinatory
normal
numerical-answers
+
–
26
votes
6
answers
14
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below?$$ a_{n} = \left\{\begin{matrix} n + 1, &...
Arjun
9.5k
views
Arjun
asked
Feb 15, 2022
Combinatory
gatecse-2022
combinatory
generating-functions
2-marks
+
–
9
votes
9
answers
15
ISRO2014-73
How many different trees are there with four nodes $\text{A, B, C}$ and $\text{D}?$ $30$ $60$ $90$ $120$
How many different trees are there with four nodes $\text{A, B, C}$ and $\text{D}?$$30$$60$$90$$120$
ajit
14.7k
views
ajit
asked
Sep 23, 2015
DS
isro2014
data-structures
tree
combinatory
+
–
60
votes
6
answers
16
GATE CSE 2014 Set 1 | Question: 50
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is...
go_editor
12.5k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set1
set-theory&algebra
functions
combinatory
numerical-answers
+
–
38
votes
7
answers
17
GATE CSE 1999 | Question: 2.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves?$1638$$2100$$2640$None of th...
Kathleen
12.3k
views
Kathleen
asked
Sep 23, 2014
Combinatory
gate1999
combinatory
normal
+
–
14
votes
3
answers
18
GATE CSE 2023 | Question: 38
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if ... $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^{2}$
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|...
admin
6.6k
views
admin
asked
Feb 15, 2023
Combinatory
gatecse-2023
combinatory
counting
2-marks
+
–
38
votes
3
answers
19
GATE CSE 2021 Set 1 | Question: 19
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that:The fastest computer g...
Arjun
11.8k
views
Arjun
asked
Feb 18, 2021
Combinatory
gatecse-2021-set1
combinatory
counting
numerical-answers
1-mark
+
–
63
votes
14
answers
20
GATE CSE 2014 Set 1 | Question: 49
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 ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10-$pennants is________
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. ...
go_editor
11.5k
views
go_editor
asked
Sep 28, 2014
Combinatory
gatecse-2014-set1
combinatory
numerical-answers
normal
+
–
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