Recent questions tagged 1-mark / GATE Overflow for GATE CSE

3 votes

1 answer

61

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 4
Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then $2^{|A|} \leq|B|$ $2^{|A|} \geq|B|$ $2|A|<|B|$ $2^{|A|} \geq 2^{|B|}$

Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then$2^{|A|} \leq|B|$$2^{|A|} \geq|B|$$2|A|<|B|$$2^{|A|} \geq 2^{|B|}$

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GO Classes asked Apr 10

2 votes

3 answers

62

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...

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GO Classes asked Apr 10

6 votes

2 answers

63

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 1
Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”? The columns of $A$ are linearly independent. The rows of $A$ are linearly independent. The only solution of the homogeneous equations $Ax = 0$ is $x = 0$. The rank of $A$ is $n$.

Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”?The columns of $A$ a...

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98 views

GO Classes asked Apr 3

7 votes

3 answers

64

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 2
Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant $c$. Which (if any) any of the vectors must be an eigenvector of $M$ ... $W = \left[\begin{array}{l}1 \\ 1 \\ \end{array}\right]$ $U$ $V$ $W$ None of the above

Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rowsand also the sum of each of the columns is the same constant $c$. Which (if any) any of...

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138 views

GO Classes asked Apr 3

4 votes

1 answer

65

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 9
Let $A$ and $B$ be two $n \times n$ matrices. If $B$ is invertible and $(I+BA)^{-1} = 2B^2$, then which of the following is the correct definition of $A$ in terms of $B$? $A = (1/2)B^{-3} - B^{-1}$ $A = 2B^{-3}- B^{-1}$ $A = 2B^3-I$ None of the above

Let $A$ and $B$ be two $n \times n$ matrices. If $B$ is invertible and $(I+BA)^{-1} = 2B^2$, then which of the following is the correct definition of $A$ in terms of $B$?...

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70 views

GO Classes asked Apr 3

3 votes

1 answer

66

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 10
A $4 \times 4$ matrix $\mathrm{A}$ has rank 3 . Which of the following is/are true? 1. $A^{-1}$ does not exist 2. $A^{-1}$ may exist, and if it does, its rank must be less than 3 3. $A^{-1}$ may ... , and it can take any rank less than 5 Only 1 is correct Only 2,3 are correct Only 4 is correct None of the statements are correct.

A $4 \times 4$ matrix $\mathrm{A}$ has rank 3 . Which of the following is/are true?1. $A^{-1}$ does not exist2. $A^{-1}$ may exist, and if it does, its rank must be less ...

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62 views

GO Classes asked Apr 3

3 votes

1 answer

67

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 12
Consider two matrices $\mathrm{A}_{6 \times 3}$ and $\mathrm{B}_{3 \times 6}$, the non zero eigenvalues(EVs) of matrix $A B$ are $3,2,7,8$; see the following statements $\mathrm{S} 2$ : The EVs of BA must be all 0 for the ... false Both $\mathrm{S} 1$ and $\mathrm{S} 2$ are true Neither $\mathrm{S} 1$ nor $\mathrm{S} 2$ is true

Consider two matrices $\mathrm{A}_{6 \times 3}$ and $\mathrm{B}_{3 \times 6}$, the non zero eigenvalues(EVs) of matrix $A B$ are $3,2,7,8$; see the following statements$\...

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87 views

GO Classes asked Apr 3

3 votes

1 answer

68

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 1
What is the Cardinality of the Power set of the set $\{0,1,2\}$? $8$ $6$ $7$ $9$

What is the Cardinality of the Power set of the set $\{0,1,2\}$?$8$$6$$7$$9$

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91 views

GO Classes asked Apr 3

3 votes

1 answer

69

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 2
The symmetric difference of sets $\text{A}=\{1,2, 3,4, 5, 6, 7, 8\}$ and $\text{B}= \{1, 3, 5, 6, 7,8,9\}$ is: $\{1, 3, 5, 6, 7,8\}$ $\{2, 4, 9\}$ $\{2, 4\}$ $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$

The symmetric difference of sets $\text{A}=\{1,2, 3,4, 5, 6, 7, 8\}$ and $\text{B}= \{1, 3, 5, 6, 7,8,9\}$ is:$\{1, 3, 5, 6, 7,8\}$$\{2, 4, 9\}$$\{2, 4\}$$\{1, 2, 3, 4, 5...

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74 views

GO Classes asked Apr 3

3 votes

1 answer

70

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 3
If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$. Then $(A \cup \overline{B}) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ x \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$

If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$. Then $(A \cup \overline{B}) \cap (A \cap B)$ is equal to$\{u,v,w,x\}$$\{ x \}$$\{u,v,w,x...

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105 views

GO Classes asked Apr 3

5 votes

1 answer

71

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 4
The power set of the set $\{ \Phi \}$ is $\{ \Phi \}$ $\{ \Phi, \{ \Phi \} \}$ $\{ 0 \}$ $\{ 0, \Phi , \{ \Phi \} \}$

The power set of the set $\{ \Phi \}$ is$\{ \Phi \}$$\{ \Phi, \{ \Phi \} \}$$\{ 0 \}$$\{ 0, \Phi , \{ \Phi \} \}$

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74 views

GO Classes asked Apr 3

5 votes

1 answer

72

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 5
Let $A, B$ be two sets. Let $\bar{A}$ denote the complement of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are not in $B$. Set $(A - (A - B))$ is equal to: $B$ $A\cap \bar{B}$ $A - B$ $A\cap B$

Let $A, B$ be two sets. Let $\bar{A}$ denote the complement of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are n...

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94 views

GO Classes asked Apr 3

6 votes

2 answers

73

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 5
Which of the following compound propositions is/are a tautology? $[p \land (p \rightarrow q)] \rightarrow q$ $[q \land (p \rightarrow q)] \rightarrow p$ $[(p \lor q) \land (r \rightarrow p) \land (r \rightarrow q)] \rightarrow r$ $[(p \lor q) \land (p \rightarrow r) \land (q \rightarrow r)] \rightarrow r$

Which of the following compound propositions is/are a tautology?$[p \land (p \rightarrow q)] \rightarrow q$$[q \land (p \rightarrow q)] \rightarrow p$$[(p \lor q) \land (...

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125 views

GO Classes asked Mar 29

6 votes

1 answer

74

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 1
The graph shows styles of music on a playlist. Country music songs are added to the playlist so that now $40\%$ of the songs are Country. If the ratio of Hip Hop songs to Pop songs remains the same, what percentage of the total number of songs are now Hip Hop? 7 21 35 39

The graph shows styles of music on a playlist. Country music songs are added to the playlist so that now $40\%$ of the songs are Country. If the ratio of Hip Hop songs to...

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749 views

GO Classes asked Feb 5

6 votes

1 answer

75

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 2
The numbered net shown is folded to form a cube. What is the product of the numbers on the four faces sharing an edge with the face numbered 1? 120 144 180 240

The numbered net shown is folded to form a cube. What is the product of the numbers on the four faces sharing an edge with the face numbered 1?120144180240

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609 views

GO Classes asked Feb 5

6 votes

1 answer

76

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 3
In the diagram, there are 26 levels, labelled A, B, C, . . . , Z. There is one dot on level A. Each of levels B, D, F, H, J, . . ., and Z contains twice as many dots as the level immediately above. ... ., and Y contains the same number of dots as the level immediately above. How many dots does level Z contain? 2048 4096 8192 16384

In the diagram, there are 26 levels, labelled A, B, C, . . . , Z. There is one dot on level A. Each of levels B, D, F, H, J, . . ., and Z contains twice as many dots as t...

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463 views

GO Classes asked Feb 5

4 votes

1 answer

77

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 4
Choose the most appropriate alternative from the options given below to complete the following sentence: Mistakes involving wrong posting are called as errors of _______. Compensating Omission Principle Posting clerical error

Choose the most appropriate alternative from the options given below to complete the following sentence:Mistakes involving wrong posting are called as errors of _______.C...

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425 views

GO Classes asked Feb 5

4 votes

1 answer

78

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 5
The diagram shows a square divided into eight pieces. Which shape is not one of those pieces?

The diagram shows a square divided into eight pieces. Which shape is not one of those pieces?

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276 views

GO Classes asked Feb 5

4 votes

2 answers

79

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 11
Consider the following network, which consists of two routers (R1 and R2), two switches (S1 and S2), and four hosts (H1, H2, H3, and H4). Suppose H1 wants to send packet to H3, which of the following is ... address of R1 Packet leaving R1 will have destination mac address of R2 Packet leaving R2 will have destination mac address of S2

Consider the following network, which consists of two routers (R1 and R2), two switches (S1 and S2), and four hosts (H1, H2, H3, and H4).Suppose H1 wants to send packet t...

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665 views

GO Classes asked Feb 5

4 votes

1 answer

80

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 12
Consider the sender's view of the sequence numbers in Go-Back-N protocol. Suppose the first sequence number in the sender's window is $k$, and the last sequence number in the sender's window is $k+3$. Let a packet with sequence ... must have been sent. If $p_{k+2}$ is not sent, then $p_{k+1}$ must not have been sent.

Consider the sender's view of the sequence numbers in Go-Back-N protocol. Suppose the first sequence number in the sender's window is $k$, and the last sequence number in...

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395 views

GO Classes asked Feb 5

4 votes

1 answer

81

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 13
Division operator in relational algebra is appropriate to handle which of the following query types? employees work on at most one of the critical projects employees work on any one of the critical projects employees work on at least one of the critical projects employees work on all the critical projects

Division operator in relational algebra is appropriate to handle which of the following query types?employees work on at most one of the critical projectsemployees work o...

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386 views

GO Classes asked Feb 5

6 votes

3 answers

82

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 14
A B-Tree of order $m$ is an $m$-way search tree. What is the minimum number of keys that can be stored on the leaf level of a B-Tree of order 20 with 3 levels? (Note: the root of a tree counts as its first level)

A B-Tree of order $m$ is an $m$-way search tree. What is the minimum number of keys that can be stored on the leaf level of a B-Tree of order 20 with 3 levels? (Note: th...

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680 views

GO Classes asked Feb 5

13 votes

1 answer

83

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 15
Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , a vertex of degree 4, a vertex of degree 5 , a vertex of degree 6 and ... of degree 7. Which of the following can be the degree of the last vertex? (Select all that are possible) 0 3 4 8

Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , a vertex of degree 4, ...

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665 views

GO Classes asked Feb 5

7 votes

1 answer

84

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 16
Consider the following C code: double A[2][3] = {{1, 2, 3}, {4, 5, 6}}; Assume that A[0] = 0xFFAA0000 and the sizeof(double) is 8. What will be the value of `A[1]`? 0xFFAA0024 0xFFAA0003 0xFFAA000C 0xFFAA0018

Consider the following C code:double A [3] = {{1, 2, 3}, {4, 5, 6}};Assume that A[0] = 0xFFAA0000 and the sizeof(double) is 8.What will be the value of A ?0xFFAA00240x...

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591 views

GO Classes asked Feb 5

5 votes

1 answer

85

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 17
Consider the following function. If $n$ and $\mathrm{k}$ are positive integers, then the least value of $\mathrm{k}$ such that $\mathrm{f}(\mathrm{k})>n$ is approximately $\log _2\left(\log _2 n\right)$ $\log _2 n$ $n \log _2 n$ $2^n$

Consider the following function.If $n$ and $\mathrm{k}$ are positive integers, then the least value of $\mathrm{k}$ such that $\mathrm{f}(\mathrm{k})>n$ is approximately$...

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504 views

GO Classes asked Feb 5

4 votes

2 answers

86

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 18
Bob writes down a number between 1 and 1,000. Mary must identify that number by asking "yes/no" questions of Bob. Mary knows that Bob always tells the truth. If Mary uses an optimal strategy then she will determine that answer at the end of exactly how many questions on the worst case? 999 500 32 10

Bob writes down a number between 1 and 1,000. Mary must identify that number by asking "yes/no" questions of Bob. Mary knows that Bob always tells the truth. If Mary uses...

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500 views

GO Classes asked Feb 5

4 votes

1 answer

87

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 19
Which of the following frequencies for A,B,C and D can generate the following Huffman tree? (Select all that apply.) $p_A=0.4, p_B=0.3, p_C=0.2, p_D=0.1$ $p_A=0.35, p_B=0.25, p_C=0.2, p_D=0.2$ $p_A=0.25, p_B=0.25, p_C=0.25, p_D=0.25$ $p_A=0.2, p_B=0.35, p_C=0.2, p_D=0.25$

Which of the following frequencies for A,B,C and D can generate the following Huffman tree? (Select all that apply.)$p_A=0.4, p_B=0.3, p_C=0.2, p_D=0.1$$p_A=0.35, p_B=0.2...

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475 views

GO Classes asked Feb 5

2 votes

2 answers

88

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 20
Consider the following array$: [32, 33, 5, 2, 14, -4, 22, 39, 34, -9].$ ... sorting algorithms could we possibly have applied? Merge sort (top-down approach) Bubble sort Quicksort (Using First element as pivot) Insertion sort

Consider the following array$: [32, 33, 5, 2, 14, -4, 22, 39, 34, -9].$ We apply a certain sorting algorithm and observe that the array has been modified to $[2, 5, 14, 3...

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584 views

GO Classes asked Feb 5

2 votes

2 answers

89

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 21
Suppose we have events $A, B$ in a sample space. And we know that $\mathrm{P}(\mathrm{A})=0.3, \mathrm{P}\left(\mathrm{B} \mid \mathrm{A}^c\right)=0.25, \mathrm{P}(\mathrm{B} \mid \mathrm{A})=0.45$. What is $\mathrm{P}\left(\mathrm{A}^c \mid \mathrm{B}\right) ?$ 0.75 0.55 0.2 0.56

Suppose we have events $A, B$ in a sample space. And we know that $\mathrm{P}(\mathrm{A})=0.3, \mathrm{P}\left(\mathrm{B} \mid \mathrm{A}^c\right)=0.25, \mathrm{P}(\mathr...

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549 views

GO Classes asked Feb 5

5 votes

1 answer

90

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 22
Let $A$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $A$, we get a matrix $B$ which has 12 nonzero rows. Which of the following is/are always true? The rank of $A$ is 12. The ranks of $A$ and $B$ are ... . If $v$ is a vector such that $A v=0$ then $B v$ is also 0. The rank of $B$ is at most 11.

Let $A$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $A$, we get a matrix $B$ which has 12 nonzero rows. Which of the following i...

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GO Classes asked Feb 5

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