Recent questions without a selected answer / GATE Overflow for GATE CSE

4 votes

1 answer

31

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 7
Consider a $4 \times 4$ matrix $A$ and a vector $\mathbf{v} \in \mathbb{R}^{4}$ such that $A^{4} \mathbf{v}=\mathbf{0}$ but $A^{3} \mathbf{v} \neq \mathbf{0}$ ... $\mathbb{R}^{4}$. $\mathcal{B}$ is a basis of $\mathbb{R}^{4}$. $\mathcal{B}$ is not linearly independent.

Consider a $4 \times 4$ matrix $A$ and a vector $\mathbf{v} \in \mathbb{R}^{4}$ such that $A^{4} \mathbf{v}=\mathbf{0}$ but $A^{3} \mathbf{v} \neq \mathbf{0}$.Set $\mathc...

GO Classes

27 views

GO Classes asked Apr 11

1 votes

1 answer

32

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 8
Consider a linear system $A \mathbf{x}=\mathbf{b}$, where $A$ is a $3 \times 4$ matrix with $\operatorname{Rank}(A)=2$ ... unique solution. (i) infinitely many solutions, (ii) no solution. (i) infinitely many solutions, (ii) unique solution.

Consider a linear system $A \mathbf{x}=\mathbf{b}$, where $A$ is a $3 \times 4$ matrix with $\operatorname{Rank}(A)=2$.How many solutions does this system have if $(i) \o...

GO Classes

17 views

GO Classes asked Apr 11

2 votes

1 answer

33

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 9
Suppose that $a \neq 0$ and $a \neq b$. Which equation below is the equation relating $a, b$ and $c$ ... $4 a-3 b+c \neq 0$ $3 a-4 b-c \neq 0$ $4 a-3 b-c \neq 0$

Suppose that $a \neq 0$ and $a \neq b$. Which equation below is the equation relating $a, b$ and $c$ so that the vectors$$\left[\begin{array}{l}1 \\1 \\a\end{array}\right...

GO Classes

18 views

GO Classes asked Apr 11

1 votes

1 answer

34

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 10
Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ ... $\left(\begin{array}{lll}2 & 1 & 3 \\ 6 & 3 & 9\end{array}\right)$

Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ be a linear transformation such that $T\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]=\left[\begin{array}{l}2 \\ 6...

GO Classes

16 views

GO Classes asked Apr 11

2 votes

1 answer

35

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 11
Which of the following statements are true? There exists a $3 \times 3$ matrix $A$ and vectors $b, c \in \mathbb{R}^{3}$ such that the linear system $A x=b$ has a unique solution but $A x=c$ has infinitely ... $n$, then the column space of $A$ is equal to the column space of $B$.

Which of the following statements are true?There exists a $3 \times 3$ matrix $A$ and vectors $b, c \in \mathbb{R}^{3}$ such that the linear system $A x=b$ has a unique s...

GO Classes

21 views

GO Classes asked Apr 11

3 votes

2 answers

36

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 12
Consider two statements S1 and S2. S1: If $\left\{v_{1}, \ldots, v_{n}\right\}$ are linearly INDEPENDENT vectors in $V$, then $\left\{T\left(v_{1}\right), \ldots, T\left(v_{n}\right)\right\}$ are linearly ... $\mathrm{S} 2$ is true. Both S1 and S2 are true. Both S1 and S2 are false.

Consider two statements S1 and S2.S1: If $\left\{v_{1}, \ldots, v_{n}\right\}$ are linearly INDEPENDENT vectors in $V$, then $\left\{T\left(v_{1}\right), \ldots, T\left(v...

GO Classes

25 views

GO Classes asked Apr 11

4 votes

2 answers

37

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 13
Suppose $A$ is a $4 \times 3$ matrix and $B$ is a $3 \times 2$ matrix, and let $T$ be the matrix transformation $T(x)=A B x$. Which of the following must be true? The column space of $A B$ ... space of $A$. $T$ has domain $\mathbf{R}^{2}$ and codomain $\mathbf{R}^{4}$. $T$ cannot be onto.

Suppose $A$ is a $4 \times 3$ matrix and $B$ is a $3 \times 2$ matrix, and let $T$ be the matrix transformation $T(x)=A B x$. Which of the following must be true?The colu...

GO Classes

27 views

GO Classes asked Apr 11

2 votes

1 answer

38

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 14
Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$ ... the matrix equation $A x=0$ has infinitely many solutions, then $\operatorname{rank}(A) \leq 4$.

Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$. Which of the following statements are true?$\op...

GO Classes

23 views

GO Classes asked Apr 11

2 votes

1 answer

39

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 15
The matrix $ \left(\begin{array}{rr} -2 & 11 \\ 4 & 2 \end{array}\right) $ represents a linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ ... $\left(\begin{array}{rr}-2 & 11 \\ 4 & 2\end{array}\right)$

The matrix$$\left(\begin{array}{rr}-2 & 11 \\4 & 2\end{array}\right)$$represents a linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ with respect to th...

GO Classes

24 views

GO Classes asked Apr 11

4 votes

1 answer

40

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 16
Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$ ... the matrix equation $A x=0$ has infinitely many solutions, then $\operatorname{rank}(A) \leq 4$.

Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$. Which of the following statements are true?$\op...

GO Classes

30 views

GO Classes asked Apr 11

0 votes

0 answers

41

Graph Theory
A vertex colouring with three colours of a graph G = (V, E) is a mapping V → {R, G, B }. So that any two adjacent vertices does not same colour. Consider the below graphs:

A vertex colouring with three colours of a graph G = (V, E) is a mapping V → {R, G, B }. So that any two adjacent vertices does not same colour. Consider the below grap...

alexa16

70 views

alexa16 asked Apr 11

0 votes

1 answer

42

Consider the following program: #include <stdio.h> int main(){ int a=2, i; static int b=a++; for(i=0;i<a+b;i++) printf("GATE Wallah"); return 0; } Which of the following is/are CORRECT? (a) GATE Wallah is printed 3 times. (b) GATE Wallah is printed 4 times. (c) GATE Wallah is printed 5 times. (d) Compilation Error.

Consider the following program: #include <stdio.h int main(){ int a=2, i; static int b=a++; for(i=0;i<a+b;i++) printf("GATE Wallah"); return 0; }Which of the following is...

Pradeep kori 73

58 views

Pradeep kori 73 asked Apr 11

0 votes

1 answer

43

Can anyone explain how we can write this regular langugae for the following diagram ?(in depth)

programmer1218

69 views

programmer1218 asked Apr 11

0 votes

0 answers

44

IIT BHUBANESHWAR MTECH WRITTEN EXAM AND INTERVIEW
PLEASE ANYONE GUIDE ME HOW I SHOULD PREPARE FOR MTECH WRITTEN TEST OF IIT BHUBANESHWAR ?

PLEASE ANYONE GUIDE ME HOW I SHOULD PREPARE FOR MTECH WRITTEN TEST OF IIT BHUBANESHWAR ?

Ray Tomlinson

45 views

Ray Tomlinson asked Apr 11

1 votes

1 answer

45

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 1
If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then $A=\phi$ $B=\phi$ $A\neq B$ $A=B$

If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then$A=\phi$$B=\phi$$A\neq B$$A=B$

GO Classes

41 views

GO Classes asked Apr 10

1 votes

2 answers

46

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 2
The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?

The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?

GO Classes

40 views

GO Classes asked Apr 10

2 votes

1 answer

47

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 3
What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ? $\{(1, a),(1, b),(2, a),(b, b)\}$ $\{(1,1),(2,2),(a, a),(b, b)\}$ $\{(1, a),(2, a),(1, b),(2, b)\}$ $\{(1,1),(a, a),(2, a),(1, b)\}$

What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ?$\{(1, a),(1, b),(2, a),(b, b)\}$$\{(1,1),(2,2),(a, a),(b, b)\}$$\{(1, a),(2, a),(1, b),(2, b)\}$$\{(1,1),(...

GO Classes

37 views

GO Classes asked Apr 10

2 votes

3 answers

48

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 5
Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is: $2^{n^2}$ $\left(2^n\right)^2$ $\left(2^2\right)^n$ None of the above

Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is:$2^{n^2}$$\left(2^n\right)^2$$\left(2^2\right)^n$None of...

GO Classes

42 views

GO Classes asked Apr 10

1 votes

1 answer

49

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 6
Which one of the following is/are true? $R \cap S=(R \cup S)-[(R-S) \cup(S-R)]$ $R \cup S=(R \cap S)-[(R-S) \cup(S-R)]$ $R \cap S=(R \cup S)-[(R-S) \cap(S-R)]$ $R \cap S=(R \cup S) \cup(R-S)$

Which one of the following is/are true?$R \cap S=(R \cup S)-[(R-S) \cup(S-R)]$$R \cup S=(R \cap S)-[(R-S) \cup(S-R)]$$R \cap S=(R \cup S)-[(R-S) \cap(S-R)]$$R \cap S=(R \...

GO Classes

23 views

GO Classes asked Apr 10

3 votes

1 answer

50

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 7
Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasing size ? $|A-B|<|A \oplus B|<|A|+|B|<|A \cup B|$ ... $|A-B|<|A \oplus B|<|A \cup B|<|A|+|B|$

Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasi...

GO Classes

59 views

GO Classes asked Apr 10

5 votes

1 answer

51

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 8
Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is listed in lexicographic order, then the next element after $((1,0), c,(1,1))$ is $((1,0), a,(0,0))$ $((1,1), c,(0,0))$ $((1,1), a,(0,0))$ $((1,1), a,(1,1))$

Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is...

GO Classes

64 views

GO Classes asked Apr 10

3 votes

0 answers

52

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 9
Which of the following statements is $\textbf{TRUE}$? For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=A-(B \cup C)$. For all sets $A, B$, and $C$, if $A \cap C=B \cap C$ then $A=B$.

Which of the following statements is $\textbf{TRUE}$?For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$.For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$.For all sets ...

GO Classes

51 views

GO Classes asked Apr 10

1 votes

0 answers

53

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 10
Which of the following statements is $\textbf{FALSE}$? $C-(B \cup A)=(C-B)-A$ $A-(C \cup B)=(A-B)-C$ $B-(A \cup C)=(B-C)-A$ $A-(B \cup C)=(B-C)-A$

Which of the following statements is $\textbf{FALSE}$?$C-(B \cup A)=(C-B)-A$$A-(C \cup B)=(A-B)-C$$B-(A \cup C)=(B-C)-A$$A-(B \cup C)=(B-C)-A$

GO Classes

38 views

GO Classes asked Apr 10

0 votes

0 answers

54

gate 2024
hello,my gate AIR is 645 and my category is OBC-NCL and my brach is CSE so my question is which top iits can i get at this score??

hello,my gate AIR is 645 and my category is OBC-NCL and my brach is CSE so my question is which top iits can i get at this score??

Viraj2412

65 views

Viraj2412 asked Apr 10

0 votes

0 answers

55

A/an ________ algorithm ensures no starvation. a. Altruistic b. Lock-free c.Test and set d.Compare and set

Mujahid s

28 views

Mujahid s asked Apr 10

0 votes

0 answers

56

#unacademyDPP

4nm01_

35 views

4nm01_ asked Apr 9

0 votes

0 answers

57

PGEE exam
What Bakery Algorithm improves: (a). throughput (b). latency (c). both (d). None

What Bakery Algorithm improves: (a). throughput (b). latency (c). both (d). None

Himanshu_2211

68 views

Himanshu_2211 asked Apr 8

0 votes

0 answers

58

If P and Q are predicates and P is the relational algebra expression, then which of the following equivalence are valid ? (1) σP(σQ(e)) = σQ(σP(e)). (2) σP(σQ(e)) = σP ∪ Q(e) (3) σP(σP(e)) = σP V Q (4) All of these

SandeepKumar147

48 views

SandeepKumar147 asked Apr 8

1 votes

1 answer

59

#Recursivefunctions
int bar(int val){ int x=0; while(val > 0){ x=x+bar(val -1); } return val; } Q: For bar(3) this function is supposed to be stuck in an infinite loop but I do not know how please can someone explain?

int bar(int val){int x=0;while(val 0){x=x+bar(val -1);}return val;}Q: For bar(3) this function is supposed to be stuck in an infinite loop but I do not know how please c...

sumitkumarsethi

82 views

sumitkumarsethi asked Apr 8

0 votes

0 answers

60

Why does the transmission rate in the reserved link gets divided when more concurrent connections are established?

I am reading Kurose Computer Networking book 8e, on page number 57, under 1.3.2 Circuit SwitchingBecause it link has $4$ circuits, for each link used by the end-to-end co...

tbhaxor

43 views

tbhaxor asked Apr 7

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