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0 votes
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151
Kenneth Rosen Edition 7 Exercise 6.3 Question 11 (Page No. 413)
How many bit strings of length $10$ contain exactly four $1s?$ at most four $1s?$ at least four $1s?$ an equal number of $0s$ and $1s?$
How many bit strings of length $10$ containexactly four $1s?$at most four $1s?$at least four $1s?$an equal number of $0s$ and $1s?$
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60 votes
6 answers
152
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)$$S ∉ P(S)$
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60 votes
9 answers
154
GATE CSE 2005 | Question: 44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such th...
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8 votes
1 answer
155
application of pigeonhole principle
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days during which the team must play exactly 14 games
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days...
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22 votes
5 answers
158
GATE CSE 1996 | Question: 1.2
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is $3$ $4$ $9$ None of the above
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is$3$$4$$9$No...
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56 votes
6 answers
161
GATE CSE 2011 | Question: 30
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$, and a predicate$$P\left(x\right) = \neg \left(x=1\right)\wedge \forall y \left...
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32 votes
6 answers
162
GATE CSE 2015 Set 3 | Question: 9
The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is $0$ $\frac{1}{2}$ $1$ $\infty$
The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is$0$$\frac{1}{2}$$1$$\infty$
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36 votes
4 answers
163
GATE CSE 2014 Set 2 | Question: 48
The probability that a given positive integer lying between $1$ and $100$ (both inclusive) is NOT divisible by $2$, $3$ or $5$ is ______ .
The probability that a given positive integer lying between $1$ and $100$ (both inclusive) is NOT divisible by $2$, $3$ or $5$ is ______ .
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3 votes
3 answers
165
Kenneth Rosen Edition 7 Exercise 1.1 Question 4 (Page No. 12)
What is the negation of each of these propositions? Jennifer and Teja are friends. There are 13 items in a baker’s dozen. Abby sent more than 100 text messages every day. 121 is a perfect square.
What is the negation of each of these propositions?Jennifer and Teja are friends.There are 13 items in a baker’s dozen.Abby sent more than 100 text messages every day.1...
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49 votes
11 answers
166
GATE CSE 2009 | Question: 2
What is the chromatic number of an $n$ vertex simple connected graph which does not contain any odd length cycle? Assume $n > 2$. $2$ $3$ $n-1$ $n$
What is the chromatic number of an $n$ vertex simple connected graph which does not contain any odd length cycle? Assume $n 2$.$2$$3$$n-1$ $n$
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35 votes
6 answers
169
GATE CSE 2014 Set 1 | Question: 4
Consider the following system of equations: $3x + 2y = 1 $ $4x + 7z = 1 $ $x + y + z = 3$ $x - 2y + 7z = 0$ The number of solutions for this system is ______________
Consider the following system of equations: $3x + 2y = 1 $$4x + 7z = 1 $$x + y + z = 3$$x - 2y + 7z = 0$The number of solutions for this system is ______________
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34 votes
2 answers
170
GATE IT 2004 | Question: 37
What is the number of vertices in an undirected connected graph with $27$ edges, $6$ vertices of degree $2, 3$ vertices of degree $4$ and remaining of degree $3$? $10$ $11$ $18$ $19$
What is the number of vertices in an undirected connected graph with $27$ edges, $6$ vertices of degree $2, 3$ vertices of degree $4$ and remaining of degree $3$?$10$$11$...
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