Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

1 votes

1 answer

41

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

3 votes

1 answer

42

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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GO Classes asked Apr 3

2 votes

1 answer

43

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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GO Classes asked Apr 3

4 votes

1 answer

44

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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66 views

GO Classes asked Apr 3

1 votes

1 answer

45

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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97 views

GO Classes asked Apr 3

3 votes

1 answer

46

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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60 views

GO Classes asked Apr 3

3 votes

1 answer

47

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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50 views

GO Classes asked Apr 3

3 votes

1 answer

48

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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85 views

GO Classes asked Apr 3

5 votes

1 answer

49

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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56 views

GO Classes asked Apr 3

5 votes

1 answer

50

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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69 views

GO Classes asked Apr 3

5 votes

2 answers

51

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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74 views

GO Classes asked Apr 3

11 votes

1 answer

52

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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176 views

GO Classes asked Apr 3

20 votes

2 answers

53

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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231 views

GO Classes asked Apr 3

6 votes

1 answer

54

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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69 views

GO Classes asked Apr 3

12 votes

1 answer

55

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...

GO Classes

244 views

GO Classes asked Apr 3

0 votes

0 answers

56

BME entrance exam
A data file of 1,000,000 records must be stored using bucket hashing. Record length is 350 bytes, the net capacity of a block is 2000 bytes. Keys occupy 32 bytes, while pointers need 8 bytes. Each bucket consists of 2 blocks. How many blocks are needed at least to store the whole structure (i.e. data file + hash table) on disc? Select one:

A data file of 1,000,000 records must be stored using bucket hashing. Record length is 350 bytes, the net capacity of a block is 2000 bytes. Keys occupy 32 bytes, while p...

Ilqar

66 views

Ilqar asked Apr 2

0 votes

1 answer

57

BME entrance exam
A hash function h maps 16-bit inputs to 8-bit hash values. What is the largest k such that in any set of 1000 inputs, there are at least k inputs that h maps to the same hash value?

A hash function h maps 16-bit inputs to 8-bit hash values. What is the largest k such that in any set of 1000 inputs, there are at least k inputs that h maps to the same ...

Ilqar

64 views

Ilqar asked Apr 2

0 votes

1 answer

58

Permutation and combination
Your mother-in-law buys 1000 small gifts to give to relatives for Christmas. Each of the 1000 things in different. There are 25 relatives to give gifts to. How many ways are there to distribute the gifts? The correct answer is $25^{1000}$. I ... ? I know some people may feel its silly question but please trust me many people like me are confused with this doubt.

Your mother-in-law buys 1000 small gifts to give to relatives for Christmas. Each of the 1000 things in different. There are 25 relatives to give gifts to. How many ways ...

rajishu07

91 views

rajishu07 asked Apr 2

0 votes

1 answer

59

Practice Material Question
If G is a connected graph with 6 vertices and maximum number of edges, then which of the following is true ? (a) Euler path exists, but Euler circuit does not exist in G. (b) Only Euler path exists in G. (c) Euler circuit does not exists in G (d) G is not traversable.

If G is a connected graph with 6 vertices and maximum number of edges, then which of the following is true ? (a) Euler path exists, but Euler circuit does not exist in G....

Akash Chakraborty

98 views

Akash Chakraborty asked Mar 30

5 votes

2 answers

60

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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95 views

GO Classes asked Mar 29

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