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38 votes
3 answers
8962
GATE IT 2008 | Question: 25
In how many ways can $b$ blue balls and $r$ red balls be distributed in $n$ distinct boxes? $\frac{(n+b-1)!\,(n+r-1)!}{(n-1)!\,b!\,(n-1)!\,r!}$ $\frac{(n+(b+r)-1)!}{(n-1)!\,(n-1)!\,(b+r)!}$ $\frac{n!}{b!\,r!}$ $\frac{(n + (b + r) - 1)!} {n!\,(b + r - 1)}$
In how many ways can $b$ blue balls and $r$ red balls be distributed in $n$ distinct boxes?$\frac{(n+b-1)!\,(n+r-1)!}{(n-1)!\,b!\,(n-1)!\,r!}$$\frac{(n+(b+r)-1)!}{(n-1)!\...
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14 votes
3 answers
8963
GATE IT 2008 | Question: 24
The exponent of $11$ in the prime factorization of $300!$ is $27$ $28$ $29$ $30$
The exponent of $11$ in the prime factorization of $300!$ is$27$$28$$29$$30$
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34 votes
5 answers
8964
GATE IT 2008 | Question: 23
What is the probability that in a randomly chosen group of $r$ people at least three people have the same birthday? $1-\dfrac{365-364 \dots (365-r+1)}{365^{r}}$ ... $\dfrac{365 \cdot 364 \dots (365-r+1)}{365^{r}}$
What is the probability that in a randomly chosen group of $r$ people at least three people have the same birthday?$1-\dfrac{365-364 \dots (365-r+1)}{365^{r}}$$\dfrac{365...
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68 votes
9 answers
8966
GATE IT 2008 | Question: 21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ is a first order formul...
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58 votes
7 answers
8967
GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?$5$$4$$3$$2$
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34 votes
4 answers
8968
GATE IT 2008 | Question: 3
What is the chromatic number of the following graph? $2$ $3$ $4$ $5$
What is the chromatic number of the following graph? $2$$3$$4$$5$
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19 votes
2 answers
8970
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric? Please explain how to calculate .
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?Please explain how to calculate .
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6 votes
1 answer
8972
GATE CSE 1996 | Question: 9
The Fibonacci sequence $\{f_1, f_2, f_3 \ldots f_n\}$ is defined by the following recurrence:$f_{n+2} = f_{n+1} + f_n, n \geq 1; f_2 =1:f_1=1$Prove by induction that every third element of the sequence is even.
The Fibonacci sequence $\{f_1, f_2, f_3 \ldots f_n\}$ is defined by the following recurrence:$$f_{n+2} = f_{n+1} + f_n, n \geq 1; f_2 =1:f_1=1$$Prove by induction that ev...
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23 votes
4 answers
8975
GATE CSE 1996 | Question: 2.7
The probability that top and bottom cards of a randomly shuffled deck are both aces is $\frac{4}{52} \times \frac{4}{52}$ $\frac{4}{52} \times \frac{3}{52}$ $\frac{4}{52} \times \frac{3}{51}$ $\frac{4}{52} \times \frac{4}{51}$
The probability that top and bottom cards of a randomly shuffled deck are both aces is$\frac{4}{52} \times \frac{4}{52}$$\frac{4}{52} \times \frac{3}{52}$$\frac{4}{52} \t...
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