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1 votes
3 answers
5371
GATE Overflow | Mathematics | Test 1 | Question: 29
According to the principle of logic, an implication and it's contrapositive must be both true or both false both true both false none
According to the principle of logic, an implication and it's contrapositive must beboth true or both falseboth trueboth falsenone
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0 votes
2 answers
5372
GATE Overflow | Mathematics | Test 1 | Question: 26
Which of the following propositions is a tautology ? $(p \vee q) \to p$ $p \vee (q \to p )$ $p \vee ( p \to q )$ $p \to (p \to q )$
Which of the following propositions is a tautology ?$(p \vee q) \to p$ $p \vee (q \to p )$$p \vee ( p \to q )$ $p \to (p \to q )$
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4 votes
2 answers
5373
GATE Overflow | Mathematics | Test 1 | Question: 25
A 6 digit number 123ABC is exactly divisible by $5,7$ and $9$. How many such possible numbers are there ? 2 3 4 5
A 6 digit number 123ABC is exactly divisible by $5,7$ and $9$. How many such possible numbers are there ?2 3 4 5
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1 votes
2 answers
5374
GATE Overflow | Mathematics | Test 1 | Question: 24
Rama wrote 5 different letters. He prepared 5 different envelopes for the 5 letters. If he randomly distributes the 5 letters to the 5 envelops what is the probability that each letter gets into correct envelope ? 1/2 1/5 1/60 1/120
Rama wrote 5 different letters. He prepared 5 different envelopes for the 5 letters. If he randomly distributes the 5 letters to the 5 envelops what is the probability th...
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3 votes
2 answers
5375
GATE Overflow | Mathematics | Test 1 | Question: 22
Total number of Equivalent Relations that can be defined on set $\{1,2,3\}$ ? 8 64 5 3
Total number of Equivalent Relations that can be defined on set $\{1,2,3\}$ ?8 64 5 3
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3 votes
1 answer
5376
GATE Overflow | Mathematics | Test 1 | Question: 21
A subset of a countable set is countable is finite may or may not be countable none of the options above are true
A subset of a countable setis countable is finite may or may not be countable none of the options above are true
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2 votes
1 answer
5377
GATE Overflow | Mathematics | Test 1 | Question: 20
Every element of some ring $(R,+,*)$ is such that $a*a=a.$ This ring is commutative is non-commutative may or may not be commutative none
Every element of some ring $(R,+,*)$ is such that $a*a=a.$ This ringis commutative is non-commutative may or may not be commutative none
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2 votes
2 answers
5378
GATE Overflow | Mathematics | Test 1 | Question: 19
A group has 11 elements. The number of proper sub-groups it can have is 0 11 5 4
A group has 11 elements. The number of proper sub-groups it can have is0 11 5 4
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1 votes
1 answer
5379
GATE Overflow | Mathematics | Test 1 | Question: 18
Let $A$ be a finite set of size $n$, the number of elements in the power set of $A \times A$ is $2^{2^n}$ $2^{n^2}$ ${(2^n)}^2$ ${(2^2)}^n$
Let $A$ be a finite set of size $n$, the number of elements in the power set of $A \times A$ is$2^{2^n}$ $2^{n^2}$ ${(2^n)}^2$ ${(2^2)}^n$
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1 votes
1 answer
5380
GATE Overflow | Mathematics | Test 1 | Question: 17
The set $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM and GCD represents which of the following algebraic structure? group ring lattice field
The set $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM and GCD represents which of the following algebraic structure?group ring lattice field
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1 votes
1 answer
5381
GATE Overflow | Mathematics | Test 1 | Question: 16
A relation $R$ is defined on $N \times N$, such that $(a,b) R (c,d)$ iff $a+d = b+c.$ The relation $R$ is reflexive but not transitive reflexive and transitive but not symmetric an equivalence relation a partial order
A relation $R$ is defined on $N \times N$, such that $(a,b) R (c,d)$ iff $a+d = b+c.$ The relation $R$ isreflexive but not transitive reflexive and transitive ...
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2 votes
2 answers
5382
GATE Overflow | Mathematics | Test 1 | Question: 15
At any time total number of persons on earth who have shaken hands an odd number of times has to be an even number an odd number a prime number a perfect square
At any time total number of persons on earth who have shaken hands an odd number of times has to bean even number an odd numbera prime number a perfect square
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0 votes
1 answer
5383
GATE Overflow | Mathematics | Test 1 | Question: 14
In any undirected graph the sum of degree of all the nodes must be even is twice the number of edges need not be even both A and B
In any undirected graph the sum of degree of all the nodesmust be even is twice the number of edges need not be evenboth A and B
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0 votes
2 answers
5384
GATE Overflow | Mathematics | Test 1 | Question: 13
For a function to be invertible it has to be one to one onto both one to one and onto none
For a function to be invertible it has to beone to one onto both one to one and ontonone
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1 votes
1 answer
5385
GATE Overflow | Mathematics | Test 1 | Question: 12
The set $\{1,2,3\}$ is equal to $\{2,1,3\}$ $\{3,2,1\}$ $\{1,2,3,1\}$ All of the above
The set $\{1,2,3\}$ is equal to$\{2,1,3\}$ $\{3,2,1\}$ $\{1,2,3,1\}$ All of the above
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1 votes
1 answer
5386
GATE Overflow | Mathematics | Test 1 | Question: 11
For a game in which $2$ partners oppose $2$ other partners, seven men are available. If every possible pair must play against every other pair, then the number of games to be played is 90 120 140 105
For a game in which $2$ partners oppose $2$ other partners, seven men are available. If every possible pair must play against every other pair, then the number of games t...
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0 votes
1 answer
5387
GATE Overflow | Mathematics | Test 1 | Question: 10
The number of elements in the power set of the set $\{ \{\{\}\}, 1, (2,3) \}$ is 2 4 8 3
The number of elements in the power set of the set $\{ \{\{\}\}, 1, (2,3) \}$ is2 4 8 3
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0 votes
2 answers
5388
GATE Overflow | Mathematics | Test 1 | Question: 9
A student taking a History examination is directed to answer any seven of 10 essay questions. There is no concern about Order here, so the student can answer the examination in how many ways? 110 129 120 140
A student taking a History examination is directed to answer any seven of 10 essay questions. There is no concern about Order here, so the student can answer the examinat...
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0 votes
1 answer
5390
GATE Overflow | Mathematics | Test 1 | Question: 5
Let $X = \{2,3,6,12,24\}$ and $£$ be the partial order defined by $X £ Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X,£)$ is? 3 4 9 None of the above
Let $X = \{2,3,6,12,24\}$ and $£$ be the partial order defined by $X £ Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X,&po...
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