Answers by chokostar / GATE Overflow for GATE CSE

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1

GATE CSE 2023 | Question: 38
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if ... $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^{2}$

Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|...

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answered Jul 27, 2023

0 votes

2

GATE CSE 2017 Set 2 | Question: 31
For any discrete random variable $X$, with probability mass function $P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain ... . The expectation of $Y$ is $N \beta(1-\beta)$ $N \beta$ $N (1-\beta)$ Not expressible in terms of $N$ and $\beta$ alone

For any discrete random variable $X$, with probability mass function$P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomi...

16.2k views

answered May 18, 2023

0 votes

3

NIELIT 2021 Dec Scientist A - Section B: 117
Worst case scenario in case of linear search algorithm is ______________ . Item is somewhere in the middle of the array. Item is not in the array at all. Item is the last element in the array. Item is the last element in the array or is not there at all.

Worst case scenario in case of linear search algorithm is ______________ .Item is somewhere in the middle of the array.Item is not in the array at all.Item is the last el...

530 views

answered Apr 27, 2023

0 votes

4

GATE CSE 1989 | Question: 3-v
Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$

Which of the following well-formed formulas are equivalent?$P \rightarrow Q$$\neg Q \rightarrow \neg P$$\neg P \vee Q$$\neg Q \rightarrow P$

3.8k views

answered Apr 14, 2023

0 votes

5

GATE CSE 1988 | Question: 2vii
Define the validity of a well-formed formula(wff)?

Define the validity of a well-formed formula(wff)?

2.0k views

answered Apr 14, 2023

0 votes

6

GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$

Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$

5.4k views

answered Apr 14, 2023

1 votes

7

GATE CSE 2023 | Question: 8
Let \[ A=\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{array}\right] \] and \[ B=\left[\begin{array}{llll} 3 & 4 & ... $\operatorname{det}(B)=-\operatorname{det}(A)$ $\operatorname{det}(A)=0$ $\operatorname{det}(A B)=\operatorname{det}(A)+\operatorname{det}(B)$

Let\[A=\left[\begin{array}{llll}1 & 2 & 3 & 4 \\4 & 1 & 2 & 3 \\3 & 4 & 1 & 2 \\2 & 3 & 4 & 1\end{array}\right]\]and\[B=\left[\begin{array}{llll}3 & 4 & 1 & 2 \\4 & 1 & 2...

11.6k views

answered Apr 9, 2023

1 votes

8

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 4
Consider the following arguments. $\text{Argument 1:}$ ... ? Only Argument $1$ is valid. Only Argument $2$ is valid. Both Arguments are valid. No Argument is valid.

Consider the following arguments.$\text{Argument 1:}$ Kerry errs or Myrna fails to show. If Kerry errs, then he does not break the record. Myrna fails to show. Therefore,...

524 views

answered Apr 6, 2023

4 votes

9

GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 5
Suppose that the characteristic polynomial of $\text{A}$ is $ p(\lambda)=\lambda(\lambda-2)(\lambda-3)^2. $ Which of the following can you determine from this information? The rank of $\text{A}$. Whether $\text{A}$ is symmetric. Whether $\text{A}$ is diagonalizable. The eigenvalues of $\text{A}$.

Suppose that the characteristic polynomial of $\text{A}$ is$$p(\lambda)=\lambda(\lambda-2)(\lambda-3)^2.$$Which of the following can you determine from this information?T...

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answered Apr 6, 2023

4 votes

10

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 3
Consider the following atomic propositions: $\text{R}$: It is Raining $\text{S}$ ... , and vice versa It is raining is equivalent to sonu is sick It is raining or sonu is sick but not both

Consider the following atomic propositions:$\text{R}$: It is Raining$\text{S}$: Sonu is SickWhich of the following is/are correct English Translation of the following log...

806 views

answered Apr 6, 2023

1 votes

11

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 2
Let’s consider the interpretation $v$ where $v(p) = F, v(q) = T, v(r) = T.$ Which of the following propositional formulas are satisfied by $v$? $(p \rightarrow \neg q) \vee \neg(r \wedge q)$ $(\neg p \vee \neg q) \rightarrow (p \vee \neg r)$ $\neg(\neg p \rightarrow \neg q) \wedge r$ $\neg (\neg p \rightarrow q \wedge \neg r)$

Let’s consider the interpretation $v$ where $v(p) = F, v(q) = T, v(r) = T.$ Which of the following propositional formulas are satisfied by $v$?$(p \rightarrow \neg q) \...

674 views

answered Apr 6, 2023

6 votes

12

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 1
Let $p,q$ be two atomic propositional assertions. Then which of the following is/are false? $(p \rightarrow q) \vee (p \rightarrow \neg q)$ is a tautology. $(p \rightarrow q) \vee (q \rightarrow p)$ ... $(p \rightarrow q) \vee (\neg q \rightarrow \neg p)$ is a tautology.

Let $p,q$ be two atomic propositional assertions. Then which of the following is/are false?$(p \rightarrow q) \vee (p \rightarrow \neg q)$ is a tautology.$(p \rightarrow ...

605 views

answered Apr 6, 2023

1 votes

13

Made Easy Test Series
p ->(q->r). Could you please tell me how it is a tautology?

p ->(q->r). Could you please tell me how it is a tautology?

376 views

answered Apr 5, 2023

0 votes

14

Testbook Test Series

327 views

answered Apr 5, 2023

1 votes

15

NPTEL Assignment Question

305 views

answered Apr 5, 2023

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