Recent questions tagged numerical-answers / GATE Overflow for GATE CSE

3 votes

1 answer

631

GO Classes Test Series 2023 | Theory of Computation | Test 2 | Question: 8
Consider the following non-deterministic finite automaton(NFA), where $\Sigma = \{a, b, c\}.$ How many strings of length $6$ are accepted by the given NFA over the alphabet $\Sigma=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$ ?

Consider the following non-deterministic finite automaton(NFA), where $\Sigma = \{a, b, c\}.$How many strings of length $6$ are accepted by the given NFA over the alphabe...

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569 views

GO Classes asked Jun 22, 2022

4 votes

1 answer

632

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 4
We go to a pizza party, and there are $5$ types of pizza. We have been starving for days, so we can eat $13$ slices, but we want to sample each type at least once. In how many ways can we do this? Order does not matter.

We go to a pizza party, and there are $5$ types of pizza. We have been starving for days, so we can eat $13$ slices, but we want to sample each type at least once. In how...

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625 views

GO Classes asked Jun 14, 2022

3 votes

1 answer

633

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 5
How many integer solutions does the equation $ x_{1}+x_{2}+x_{3}+x_{4}=15 $ have, if we require that $x_{1} \geq 2, x_{2} \geq 3, x_{3} \geq 10$ and $x_{4} \geq-3 ?$

How many integer solutions does the equation$$x_{1}+x_{2}+x_{3}+x_{4}=15$$have, if we require that $x_{1} \geq 2, x_{2} \geq 3, x_{3} \geq 10$ and $x_{4} \geq-3 ?$

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389 views

GO Classes asked Jun 14, 2022

5 votes

1 answer

634

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 6
How many integer solutions are there to the system of inequalities $ x_{1}+x_{2}+x_{3}+x_{4} \leq 15, \quad x_{1}, \ldots, x_{4} \geq 0 ? $

How many integer solutions are there to the system of inequalities$$x_{1}+x_{2}+x_{3}+x_{4} \leq 15, \quad x_{1}, \ldots, x_{4} \geq 0 ?$$

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517 views

GO Classes asked Jun 14, 2022

6 votes

3 answers

635

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 7
We want those bit strings of length $10$ which Start and end with the symbol $1.$ No two zeroes are consecutive. How many such bit strings are there?

We want those bit strings of length $10$ whichStart and end with the symbol $1.$No two zeroes are consecutive.How many such bit strings are there?

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1.2k views

GO Classes asked Jun 14, 2022

3 votes

1 answer

636

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 8
How many ways are there to split a dozen people into $3$ teams, where one team has $2$ people, and the other two teams have $5$ people each?

How many ways are there to split a dozen people into $3$ teams, where one team has $2$ people, and the other two teams have $5$ people each?

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784 views

GO Classes asked Jun 14, 2022

2 votes

1 answer

637

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 12
How many rectangles are there in a chess board?

How many rectangles are there in a chess board?

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430 views

GO Classes asked Jun 14, 2022

4 votes

3 answers

638

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 14
The number of ways of selecting at least one Indian and at least one American for a debate from a group comprising $3$ Indians and $4$ Americans and no one else?

The number of ways of selecting at least one Indian and at least one American for a debate from a group comprising $3$ Indians and $4$ Americans and no one else?

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673 views

GO Classes asked Jun 14, 2022

3 votes

2 answers

639

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 15
In an examination, a question paper consists of $12$ questions divided into two parts i.e, Part I and Part II, containing $5$ and $7$ questions respectively. A student is required to attempt $8$ questions in all, selecting at least $3$ from each part. In how many ways can a student select the questions?

In an examination, a question paper consists of $12$ questions divided into two parts i.e, Part I and Part II, containing $5$ and $7$ questions respectively. A student is...

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436 views

GO Classes asked Jun 14, 2022

7 votes

1 answer

640

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 16
Count the number of non-negative integer solutions to $ 3 x_{1}+3 x_{2}+3 x_{3}+7 x_{4}=22 . $

Count the number of non-negative integer solutions to$$3 x_{1}+3 x_{2}+3 x_{3}+7 x_{4}=22 .$$

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557 views

GO Classes asked Jun 14, 2022

4 votes

2 answers

641

GO Classes Test Series 2023 | Theory of Computation | Test 1 | Question: 14
Let $L$ be the language accepted by the following non-deterministic finite automaton with $\epsilon$-transitions: The number of states in the minimal DFA that accepts the language that is recognized by the above NFA over alphabet $\{a\},$ is ________

Let $L$ be the language accepted by the following non-deterministic finite automaton with $\epsilon$-transitions:The number of states in the minimal DFA that accepts the ...

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531 views

GO Classes asked Jun 9, 2022

3 votes

1 answer

642

GO Classes Test Series 2023 | Theory of Computation | Test 1 | Question: 25
Let $L$ be a language over an alphabet $\Sigma$. The equivalence relation $\sim_{L}$ on the set $\Sigma^{\ast }$ of finite strings over $\Sigma$ is defined by $u \sim_{L} v$ ... the regular expression $a ^\ast b(a \mid b)$. Number of $\sim_{L}$-equivalence classes for this $L$ is ________

Let $L$ be a language over an alphabet $\Sigma$. The equivalence relation $\sim_{L}$ on the set $\Sigma^{\ast }$ of finite strings over $\Sigma$ is defined by $u \sim_{L}...

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452 views

GO Classes asked Jun 9, 2022

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