Recent questions tagged 2-marks / GATE Overflow for GATE CSE

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61

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 4
Consider the following matrix A: $\left[\begin{array}{lll}2 & -1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2\end{array}\right]$ Which of the following regarding the matrix $A$ ... $x$ is the eigenvector corresponding to eigenvalue $\lambda$ of $A$ then $x$ is also the eigenvector of $A^{-1}$.

Consider the following matrix A:$\left[\begin{array}{lll}2 & -1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2\end{array}\right]$Which of the following regarding the matrix $A$ is/are cor...

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GO Classes asked Apr 3

1 votes

1 answer

62

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 5
Suppose a $3 \times 5$ matrix $A$ has rank $r = 3$. Then the equation $Ax = b$ $\textbf{BLANK 1}$ has $\textbf{BLANK 2}$ ... BLANK 2: Infinitely many solutions BLANK 1: Sometimes, BLANK 2: Unique solution BLANK 1: Sometimes, BLANK 2: Infinitely many solutions

Suppose a $3 \times 5$ matrix $A$ has rank $r = 3$. Then the equation $Ax = b$ $\textbf{BLANK 1}$ has $\textbf{BLANK 2}$.Which of the following are appropriate words ...

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GO Classes asked Apr 3

3 votes

2 answers

63

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 6
Which of the following statements is/are $\textbf{NOT CORRECT}$? If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue. If $A$ is a nilpotent matrix, meaning that $A^k = 0$ for the ... is an eigenvalue of an invertible matrix $A$ then $\lambda ^{-1}$ is an eigenvalue of $A^{-1}$.

Which of the following statements is/are $\textbf{NOT CORRECT}$?If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue.If ...

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GO Classes asked Apr 3

2 votes

1 answer

64

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 7
Given an $m \times n$ matrix $A$ whose rows are linearly independent. Now, consider following statements regarding $A$: $S1:$ The system of equations $Ax = b$ for any $b$ is consistent. $S2:$ $Ax = b$ always has a unique solution. ... $S2$ is FALSE. $S1$ is FALSE and $S2$ is TRUE. Both $S1$ and $S2$ are FALSE.

Given an $m \times n$ matrix $A$ whose rows are linearly independent. Now, consider following statements regarding $A$: $S1:$ The system of equations $Ax = b$ for any ...

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GO Classes asked Apr 3

3 votes

1 answer

65

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 8
Which of the following statements is/are $\textbf{FALSE}$? For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvalues. For $n \times n$ matrices $A$ and $B$ with $B$ ... eigenvectors. For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvectors.

Which of the following statements is/are $\textbf{FALSE}$?For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvalues.For $n \tim...

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105 views

GO Classes asked Apr 3

1 votes

1 answer

66

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 11
The rank and nullity of a matrix $A$ are 4 and 2 , respectively. The nullity of $A^{\top}$ is 3 . What are the dimensions of $A$ ? $6 \times 7$ $4 \times 5$ $7 \times 6$ $5 \times 4$

The rank and nullity of a matrix $A$ are 4 and 2 , respectively. The nullity of $A^{\top}$ is 3 . What are the dimensions of $A$ ?$6 \times 7$$4 \times 5$$7 \times 6$$5 \...

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GO Classes asked Apr 3

2 votes

1 answer

67

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 13
Which of the followings(s) is/are TRUE ? If a system of linear equations has no free variables, then it has a unique solution. If an augmented matrix $[A \mid b]$ is transformed into $[C \mid d]$ by elementary row operations, ... equation $A x=b$ has $a$ unique solution for every $b$ in the set of real numbers of dimension $m$.

Which of the followings(s) is/are TRUE ?If a system of linear equations has no free variables, then it has a unique solution.If an augmented matrix $[A \mid b]$ is transf...

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74 views

GO Classes asked Apr 3

4 votes

1 answer

68

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 14
Which of the following(s) is/are TRUE ? If none of the vectors in the set $S=\left\{\vec{v}_1, \vec{v}_2, \vec{v}_3\right\}$ in $\mathbb{R}^3$ is a multiple of one of the other vectors, then $S$ ... $\vec{v}_2$. Then $\left\{\vec{v}_1, \vec{v}_2, \vec{v}_3\right\}$ is linearly independent.

Which of the following(s) is/are TRUE ?If none of the vectors in the set $S=\left\{\vec{v}_1, \vec{v}_2, \vec{v}_3\right\}$ in $\mathbb{R}^3$ is a multiple of one of the ...

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95 views

GO Classes asked Apr 3

1 votes

1 answer

69

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 15
Consider the following two statements: $S 1$. If $A B=I$, then $A$ is invertible. $S 2$. If $A$ is a $3 \times 3$ matrix and the equation $A \vec{x}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has a unique ... $S 2$ is false $\mathrm{S} 1$ is false but $\mathrm{S} 2$ is true Both are true Both are false

Consider the following two statements:$S 1$. If $A B=I$, then $A$ is invertible.$S 2$. If $A$ is a $3 \times 3$ matrix and the equation $A \vec{x}=\left[\begin{array}{l}1...

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138 views

GO Classes asked Apr 3

5 votes

2 answers

70

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 6
Let $S$ be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$. Then at least one of the sets $S_i$ is a finite set not more than one of the sets $S_i$ can be finite at least one of the sets $S_i$ is an infinite None of the above

Let $S$ be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$. Thenat least one of the sets $S_i$ is a finite setnot more than...

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GO Classes asked Apr 3

11 votes

1 answer

71

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 7
Power set of empty set has exactly _______ subsets. One Two Zero Three

Power set of empty set has exactly _______ subsets.OneTwoZeroThree

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235 views

GO Classes asked Apr 3

20 votes

2 answers

72

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 8
Which of the following is/are true? If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$. If $S$ is a set and $|S| = 103$, then $S$ is a power set ... $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.

Which of the following is/are true?If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.If ...

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309 views

GO Classes asked Apr 3

7 votes

1 answer

73

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 9
Which of the following statements is /are TRUE? $2 \in A \cup B$ implies that if $2 \notin A$ then $2 \in B$. $\{2,3\} \subseteq A$ implies that $2 \in A$ and $3 \in A$. $A \cap B \supseteq\{2,3\}$ ... $A-B \supseteq\{3\}$ and $\{2\} \subseteq B$ implies that $\{2,3\} \subseteq A \cup B$.

Which of the following statements is /are TRUE?$2 \in A \cup B$ implies that if $2 \notin A$ then $2 \in B$.$\{2,3\} \subseteq A$ implies that $2 \in A$ and $3 \in A$.$A ...

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99 views

GO Classes asked Apr 3

13 votes

1 answer

74

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 10
Which of the following statements is /are False? $\{2,3,4\} \in A$ and $\{2,3\} \in B$ implies that $\{4\} \subseteq A-B$. $A \cap B \supseteq\{2,3,4\}$ implies that $\{2,3,4\} \subseteq A$ and $\{2,3,4\} \subseteq B$ ... $\{2,3\} \subseteq A \cup B$ implies that if $\{2,3\} \cap A=\emptyset$ then $\{2,3\} \subseteq B$.

Which of the following statements is /are False?$\{2,3,4\} \in A$ and $\{2,3\} \in B$ implies that $\{4\} \subseteq A-B$.$A \cap B \supseteq\{2,3,4\}$ implies that $\{2,3...

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321 views

GO Classes asked Apr 3

3 votes

2 answers

75

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 6
Select the grammatically incorrect sentence from the options given. The case holding the plates are broken. Either Ravi or Reena is attempting to come today. Both Ali and Anjana will have to take the test. The overall sentiment in the office is negative regarding the reports.

Select the grammatically incorrect sentence from the options given.The case holding the plates are broken.Either Ravi or Reena is attempting to come today.Both Ali and An...

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413 views

GO Classes asked Feb 5

4 votes

1 answer

76

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 7
A class of 30 students was asked what they did on their winter holiday. 20 students said that they went skating. 9 students said that they went skiing. Exactly 5 students said that they went skating and went skiing. How many students did not go skating and did not go skiing? 1 6 11 19

A class of 30 students was asked what they did on their winter holiday. 20 students said that they went skating. 9 students said that they went skiing. Exactly 5 students...

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306 views

GO Classes asked Feb 5

8 votes

1 answer

77

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 8
In her last basketball game, Jackie scored 36 points. These points raised the average (mean) number of points that she scored per game from 20 to 21. To raise this average to 22 points, how many points must Jackie score in her next game? 38 22 23 36

In her last basketball game, Jackie scored 36 points. These points raised the average (mean) number of points that she scored per game from 20 to 21. To raise this averag...

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368 views

GO Classes asked Feb 5

6 votes

1 answer

78

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 9
The positive integers are arranged in rows and columns, as shown, and described below. The odd numbered rows list six positive integers in order from left to right beginning in column B. The even numbered rows list six positive integers in order from ... row = 836) row $=837$, column $=\mathrm{D}$ row $=837$, column $=\mathrm{E}$

The positive integers are arranged in rows and columns, as shown, and described below.The odd numbered rows list six positive integers in order from left to right beginni...

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993 views

GO Classes asked Feb 5

3 votes

1 answer

79

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 10
In the diagram, a figure is formed dividing a square into eight identical pieces using its two diagonals and the two lines joining the midpoints of opposite sides, and then drawing a circle in the square as shown. This figure is reflected in line L. Which of the following shows the final position of the figure?

In the diagram, a figure is formed dividing a square into eight identical pieces using its two diagonals and the two lines joining the midpoints of opposite sides, and th...

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321 views

GO Classes asked Feb 5

9 votes

2 answers

80

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 36
Assume a linear page table, with a 1-byte page-table entry. Assume physical and virtual address spaces of size 128 bytes with 32-byte pages. The page-table base register is set to physical address 16. The contents of ... What are the physical addresses that will get referred in fetch and execute of the above instruction? 10 42 102 70

Assume a linear page table, with a 1-byte page-table entry. Assume physical and virtual address spaces of size 128 bytes with 32-byte pages. The page-table base register ...

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621 views

GO Classes asked Feb 5

2 votes

1 answer

81

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 37
Suppose that an operating system provides two functions, block() which puts the calling process on the blocked queue, and wakeup(P) which moves process P to the ready queue if it is currently on the blocked queue. ... alternation printing ABABAB . A and B will always run forever with strick alternation printing BABABA . None of these

Suppose that an operating system provides two functions, block() which puts the calling process on the blocked queue, and wakeup(P) which moves process P to the ready que...

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503 views

GO Classes asked Feb 5

4 votes

1 answer

82

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 38
Consider a sliding window protocol with a window size of $5$ using cumulative ACKs (and ACK is being sent for each segment). Assume that the retransmission timeout timer is long enough and timeout has not occurred for any ... after data packet 5 Data packet 3 was duplicated by the network ACK packet A3 was duplicated by the network

Consider a sliding window protocol with a window size of $5$ using cumulative ACKs (and ACK is being sent for each segment).Assume that the retransmission timeout timer i...

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446 views

GO Classes asked Feb 5

4 votes

1 answer

83

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 39
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are correct? The function $f$ must be one-to-one. The function $f$ must be onto. The function g must be one-to-one. The function $g$ must be onto.

For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are...

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529 views

GO Classes asked Feb 5

4 votes

0 answers

84

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 40
Consider the following schema (primary keys are underlined): Which of the following queries returns the department numbers of those departments for which there are no courses being offered?

Consider the following schema (primary keys are underlined):Which of the following queries returns the department numbers of those departments for which there are no cour...

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328 views

GO Classes asked Feb 5

9 votes

1 answer

85

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 41
Consider the following lock requests in the Table below. And note that: $\mathrm{S}(\cdot)$ and $\mathrm{X}(\cdot)$ stand for 'shared lock' and 'exclusive lock', respectively. $T_1, T_2, T_3, T_4$, and $T_5$ represent five ... dead('-'). Select all that are correct. At t3: a At t6: b At t7: a At t8: -

Consider the following lock requests in the Table below. And note that:$\mathrm{S}(\cdot)$ and $\mathrm{X}(\cdot)$ stand for 'shared lock' and 'exclusive lock', respectiv...

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743 views

GO Classes asked Feb 5

4 votes

1 answer

86

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 42
The provided C code is a version of the C string library function strlen(), which calculates the length of a given string. unsigned int mystrlen(char *c) { unsigned int i = 0; /* Your code here. */ } Which line of code creates a working and ... != '\0') i++; return i; while (*(c + i) != '\0') ++i; return i;

The provided C code is a version of the C string library function strlen(), which calculates the length of a given string.unsigned int mystrlen(char *c) { unsigned in...

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431 views

GO Classes asked Feb 5

4 votes

1 answer

87

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 43
What will be the output of the following C program? #include <stdio.h> void Mickey(int**, int, int); void Mouse(int, int*); int main() { int a = 2, b = 3, c = 4; int *points = &a; Mickey(&points, b, c); printf("%d", ... x; *p = **points+1; Mouse(z, p); return; } void Mouse(int z, int *p) { *p = *p+1; return; }

What will be the output of the following C program?#include <stdio.h>void Mickey(int , int, int);void Mouse(int, int*);int main(){ int a = 2, b = 3, c = 4; int *poi...

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429 views

GO Classes asked Feb 5

5 votes

2 answers

88

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 44
Let $B$ be a binary search tree (BST) with eight nodes filled with the following set of eight integer keys $A=\{10,2,5,3,20,15,9,22\}$. The order in which these keys were inserted to create $B$ is not known. However ... are required to verify if all eight keys of $A$ are present in $B$. How many leaf nodes are present in B?

Let $B$ be a binary search tree (BST) with eight nodes filled with the following set of eight integer keys $A=\{10,2,5,3,20,15,9,22\}$. The order in which these keys were...

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506 views

GO Classes asked Feb 5

7 votes

1 answer

89

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 45
Consider a stack whose elements are unsigned integers and support the following operations: PUSH a: Pushes the element 'a' onto the stack. ADD: Adds the two topmost elements, removes them, and pushes the result. SQR: ... once, count it as many times as it is used. Your final count should include initial 3 PUSH instructions.

Consider a stack whose elements are unsigned integers and support the following operations:PUSH a: Pushes the element 'a' onto the stack.ADD: Adds the two topmost element...

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549 views

GO Classes asked Feb 5

4 votes

1 answer

90

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 46
We have a procedure $P(n)$ that makes multiple calls to a procedure $Q(m)$, and runs in polynomial time in $n$. Unfortunately, a significant flaw was discovered in $Q(m)$, and it had to be replaced by $R(m)$, which runs in exponential ... $P(n)$ runs in polynomial time in $n$ if, for each call $Q(m),m \underline<\log \;n.$

We have a procedure $P(n)$ that makes multiple calls to a procedure $Q(m)$, and runs in polynomial time in $n$. Unfortunately, a significant flaw was discovered in $Q(m)$...

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GO Classes asked Feb 5

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