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Highest voted questions in Engineering Mathematics

60 votes
6 answers
61
GATE CSE 2000 | Question: 2.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true?$P(P(S)) = P(S)$$P(S) ∩ P(P(S)) = \{ Ø \}$$P(S) ∩ S = P(S)$$S ∉ P(S)$
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58 votes
9 answers
65
GATE CSE 2017 Set 2 | Question: 47
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
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58 votes
7 answers
66
GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?$5$$4$$3$$2$
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57 votes
10 answers
71
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleas...
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57 votes
17 answers
72
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 ___________.
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57 votes
11 answers
74
GATE CSE 2014 Set 3 | Question: 51
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $n-k$ $n-k+1$
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have?$\left\lfloor\frac {n}{k}\right\rfloor$$\left\lceil \frac{n}{k} \right\r...
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56 votes
6 answers
77
GATE CSE 2011 | Question: 30
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$, and a predicate$$P\left(x\right) = \neg \left(x=1\right)\wedge \forall y \left...
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56 votes
3 answers
78
GATE CSE 2010 | Question: 27
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$? $\left(\dfrac{1}{625}\right)$ $\left(\dfrac{4}{625}\right)$ $\left(\dfrac{12}{625}\right)$ $\left(\dfrac{16}{625}\right)$
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$?$\left(\dfrac{1}{625}\right)$$\left(\dfrac{4}{625}\right)$$\left(\dfrac{12}{625}\right)$$\lef...
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55 votes
6 answers
80
GATE CSE 1997 | Question: 6.3
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
The number of equivalence relations of the set $\{1,2,3,4\}$ is$15$$16$$24$$4$
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