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Highest voted questions in Discrete Mathematics

38 votes
9 answers
161
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
How many $4$-digit even numbers have all $4$ digits distinct?$2240$$2296$$2620$$4536$
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37 votes
5 answers
162
GATE CSE 1989 | Question: 4-i
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
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37 votes
7 answers
164
GATE IT 2006 | Question: 11
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a Hamiltonian cycle grid hypercube tree
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is aHamiltonian cyclegri...
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37 votes
7 answers
166
GATE CSE 2004 | Question: 77
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is$2$$3$$4$$5$
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37 votes
8 answers
167
GATE CSE 2006 | Question: 28
A logical binary relation $\odot$ ... $(\sim A\odot B)$ $\sim(A \odot \sim B)$ $\sim(\sim A\odot\sim B)$ $\sim(\sim A\odot B)$
A logical binary relation $\odot$, is defined as follows: $$\begin{array}{|l|l|l|} \hline \textbf{A} & \textbf{B}& \textbf{A} \odot \textbf{B}\\\hline \text{True} & \text...
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37 votes
6 answers
168
GATE CSE 2014 Set 1 | Question: 1
Consider the statement "Not all that glitters is gold Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ ... $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$
Consider the statement "Not all that glitters is gold”Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ is gold. Which one of the ...
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37 votes
4 answers
169
GATE CSE 2000 | Question: 2.4
A polynomial $p(x)$ satisfies the following: $p(1) = p(3) = p(5) = 1$ $p(2) = p(4) = -1$ The minimum degree of such a polynomial is $1$ $2$ $3$ $4$
A polynomial $p(x)$ satisfies the following:$p(1) = p(3) = p(5) = 1$ $p(2) = p(4) = -1$The minimum degree of such a polynomial is$1$$2$$3$$4$
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36 votes
8 answers
172
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
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36 votes
6 answers
175
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: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
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)...
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36 votes
4 answers
176
GATE CSE 2006 | Question: 2
Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is $z^{2^{xy}}$ $z \times 2^{xy}$ $z^{2^{x+y}}$ $2^{xyz}$
Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is$z^{2^{...
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35 votes
4 answers
180
GATE CSE 2007 | Question: 3
What is the maximum number of different Boolean functions involving $n$ Boolean variables? $n^2$ $2^n$ $2^{2^n}$ $2^{n^2}$
What is the maximum number of different Boolean functions involving $n$ Boolean variables?$n^2$$2^n$$2^{2^n}$$2^{n^2}$
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