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Highest voted questions in Discrete Mathematics

1 votes
1 answer
2551
Narsingh Deo Problem 2-28
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1 votes
1 answer
2553
Graph Theory
Let G be a simple graph in which every vertex has degree 3. Prove that G decomposes into claws iff G is bipartite.
Let G be a simple graph in which every vertex has degree 3. Prove that G decomposes into claws iff G is bipartite.
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1 answer
2554
Testbook Test Series: Combinatory - Permutations And Combinations
NUMBER OF WAYS WE CAN ARRAYS LETTERS OF THE WORD "TESTBOOK" SO THAT NO TWO VOWELS ARE TOGETHER IS
NUMBER OF WAYS WE CAN ARRAYS LETTERS OF THE WORD "TESTBOOK" SO THAT NO TWO VOWELS ARE TOGETHER IS
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1 votes
0 answers
2555
Permutation of 4 Gs out of 5 Gs
Given symbols:- $GGGGGAAATTTECCS$ No of ways such that exactly 4 Gs out of 5 Gs are together. I am getting$ \frac{11! × 11}{3!×3!×2!} $. Some one verify it?
Given symbols:- $GGGGGAAATTTECCS$No of ways such that exactly 4 Gs out of 5 Gs are together. I am getting$ \frac{11! × 11}{3!×3!×2!} $.Some one verify it?
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1 votes
1 answer
2556
Kenneth Rosen Edition 6th Exercise 6.4 Question 33 (Page No. 442)
Use generating function to solve the recurrence relation $a_k=3{a_{k-1}} + 2$ with initial conditions $a_0=1 $.
Use generating function to solve the recurrence relation $a_k=3{a_{k-1}} + 2$ with initial conditions $a_0=1 $.
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2557
ISI-SAMPLE-2014-22
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1 votes
0 answers
2558
Propositional Logic
Number of nonequivalent propositional functions ( different truth tables ) possible with 'n' atomic propositions is ? and explain also a) $2^n$ b) $n^2$ c) 2^2^n (means 2 raise to power 2 raise to power n) d) 2^n^2
Number of nonequivalent propositional functions ( different truth tables ) possible with 'n' atomic propositions is ? and explain alsoa) $2^n$b) $n^2$c) 2^2^n (means 2 ...
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2559
Graph Book
The maximum number of edges in a n-node undirected graph WITH self-loops is?
The maximum number of edges in a n-node undirected graph WITH self-loops is?
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1 votes
2 answers
2562
Graph Theory
Can someone solve this? Also please attempt this question on Algorithms time complexity if interested :) https://gateoverflow.in/210836/algorithms-time-complexity
Can someone solve this?Also please attempt this question on Algorithms time complexity if interested :)https://gateoverflow.in/210836/algorithms-time-complexity
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1 votes
1 answer
2563
Permutations
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1 votes
2 answers
2565
counting
Using the letters PQRST , without repetition , how many 4 letters strings can be formed that, 1) start or end with P.. 2) start with either P or Q. 3) start with Q or end with T. 4) contain the letter R.. 5) don't have the letter P. 6) contain S and T.
Using the letters PQRST , without repetition , how many 4 letters strings can be formed that,1) start or end with P..2) start with either P or Q.3) start with Q or end wi...
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1 votes
1 answer
2567
#test series
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1 votes
3 answers
2568
ISI-2016-02
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid = 5$ ? $0$ $1$ $2$ $3$
How many complex numbers $z$ are there such that $\mid z+1 \mid = \mid z+i \mid$ and $\mid z \mid = 5$ ?$0$$1$$2$$3$
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1 votes
1 answer
2569
ISI-2017-23
What is the smallest degree of a polynomial with real coefficients and having roots $2\omega, 2+3\omega, 2{\omega}^2, -1-3\omega \text{ and } 2-\omega-{\omega}^2$? [Here $\omega \neq 1$ is a cube root of unity.] $5$ $7$ $9$ $10$
What is the smallest degree of a polynomial with real coefficients and having roots $2\omega, 2+3\omega, 2{\omega}^2, -1-3\omega \text{ and } 2-\omega-{\omega}^2$?[Here $...
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1 votes
2 answers
2570
ISI-2017-6
In a class of $80$ students, $40$ are girls and $40$ are boys. Also, exactly $50$ students wear glasses. Then the set of all possible number of boys without glasses is $\{0,.....,30\}$ $\{10,....,30\}$ $\{0,.....,40\}$ $\text{none of these}$
In a class of $80$ students, $40$ are girls and $40$ are boys. Also, exactly $50$ students wear glasses. Then the set of all possible number of boys without glasses is$\{...
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