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Most answered questions in Discrete Mathematics

1 votes
1 answer
2164
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 6
The following propositional statement simplifies to $\ (\neg P\leftrightarrow \neg Q)\vee (\neg P\leftrightarrow Q)$ $P\wedge Q$ True $P\rightarrow Q$ False
The following propositional statement simplifies to$\ (\neg P\leftrightarrow \neg Q)\vee (\neg P\leftrightarrow Q)$$P\wedge Q$True$P\rightarrow Q$False
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1 votes
1 answer
2165
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 8
The following propositional statement is a $\ \neg(\neg A \wedge B)\leftrightarrow (A\rightarrow B)$ Tautology Contradiction Contingent More than one of these
The following propositional statement is a$\ \neg(\neg A \wedge B)\leftrightarrow (A\rightarrow B)$TautologyContradictionContingentMore than one of these
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2 votes
1 answer
2167
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 10
How many permutations of the letters ABCDEFGHIJKL contain the string ACDKL? $7!$ $\frac{12!}{5!}$ $8!$ None of these
How many permutations of the letters ABCDEFGHIJKL contain the string ACDKL?$7!$$\frac{12!}{5!}$$8!$None of these
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1 votes
1 answer
2168
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 12
How many triangles can be formed by $15$ points of which $6$ are collinear? $455$ $445$ $452$ $435$
How many triangles can be formed by $15$ points of which $6$ are collinear?$455$$445$$452$$435$
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4 votes
1 answer
2169
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 13
Which of the following statements is VALID? $\neg \forall x\exists y[(x\leq y)\rightarrow(x+y)<0]\Longleftrightarrow \exists x\forall y[(x>y)\wedge(x+y)\leq 0]$ ...
Which of the following statements is VALID?$\neg \forall x\exists y[(x\leq y)\rightarrow(x+y)<0]\Longleftrightarrow \exists x\forall y[(x>y)\wedge(x+y)\leq 0]$$\forall x\...
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2 votes
1 answer
2171
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 15
The total number of ways in which $4$ notes of different denominations can be put into the purses of $3$ persons so that no purse is empty is ________
The total number of ways in which $4$ notes of different denominations can be put into the purses of $3$ persons so that no purse is empty is ________
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2 votes
1 answer
2172
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 16
The generating function corresponding to $4,5,7,10,14,19,25,\dots $ is ? $\frac{4}{1-x} + \frac{x}{(1-x)^3}$ $\frac{2}{1-x} + \frac{x}{(1-x)^3}$ $\frac{4}{1-x} + \frac{x}{(1-x)^2}$ $\frac{x}{(1-x)^3}$
The generating function corresponding to $4,5,7,10,14,19,25,\dots $ is ?$\frac{4}{1-x} + \frac{x}{(1-x)^3}$$\frac{2}{1-x} + \frac{x}{(1-x)^3}$$\frac{4}{1-x} + \frac{x}{(1...
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1 votes
1 answer
2173
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 17
You are at a party with $8$ of your friends and you order a $16$-cut pizza ($16$ identical slices). How many distributions of pizza slices are there if each person gets at least one slice of pizza? $6435$ $6433$ $6437$ $6439$
You are at a party with $8$ of your friends and you order a $16$-cut pizza ($16$ identical slices). How many distributions of pizza slices are there if each person gets a...
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2 votes
1 answer
2176
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 20
Let $X$ and $Y$ be two sets containing four and three elements respectively. Then the number of subsets of the set $X\times Y,$ each having at least four elements? $2048$ $4096$ $3797$ $3410$
Let $X$ and $Y$ be two sets containing four and three elements respectively. Then the number of subsets of the set $X\times Y,$ each having at least four elements?$2048$$...
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4 votes
1 answer
2177
GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 21
Let $A=\{a,b,c,d,e\}$. The total number of unordered pairs of disjoint subsets of $A$ is equal to? $3^{5}$ $5^{3}$ $102$ $122$
Let $A=\{a,b,c,d,e\}$. The total number of unordered pairs of disjoint subsets of $A$ is equal to?$3^{5}$$5^{3}$$102$$122$
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