Recent questions tagged numerical-answers / GATE Overflow for GATE CSE

9 votes

1 answer

301

GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 17
You have a matrix $A$ ... $3$ eigenvalues of $A?$

You have a matrix $A$ with the factorization:$$A=\underbrace{\left(\begin{array}{ccc}1 & & \\3 & 2 & \\1 & -1 & 2\end{array}\right)}_B \quad \underbrace{\left(\begin{arra...

GO Classes

565 views

GO Classes asked Apr 5, 2023

14 votes

2 answers

302

GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 18
In this problem, consider the $4 \times 4$ matrix $A$ whose columns are vectors $\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3, \mathbf{a}_4 \in \mathbb{R}^4$ ... a element in matrix $\text{A}$ at $\mathrm{i}^{\text {th }}$ row and $\mathrm{j}^{\text{th}}$ column.

In this problem, consider the $4 \times 4$ matrix $A$ whose columns are vectors $\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3, \mathbf{a}_4 \in \mathbb{R}^4$ :$$A=\left[\math...

GO Classes

765 views

GO Classes asked Apr 5, 2023

18 votes

2 answers

303

GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 20
Consider Three matrices $A, B$ and $C$ ... $\alpha_1$, then: The Entries which are not shown in matrices are zeros. What is the rank of $B ?$

Consider Three matrices $A, B$ and $C$ such that -$$\underbrace{\left(\begin{array}{lllll}1 & 2 & 4 & 2 & 5 \\& 2 & 3 & 5 & 6 \\& & 3 & 4 & 3 \\& & & 4 & 3 \\& & & 5\end{...

GO Classes

1.1k views

GO Classes asked Apr 5, 2023

10 votes

3 answers

304

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 2
Consider a matrix $A_{4 \times 5}$. Where all the solutions of $A x=0$ has the following form - $ \left[\begin{array}{c} 6 c-12 e \\ -4 c+10 e \\ c \\ -5 e \\ e \end{array}\right] $ What will be the rank of $A?$

Consider a matrix $A_{4 \times 5}$. Where all the solutions of $A x=0$ has the following form -$$\left[\begin{array}{c}6 c-12 e \\-4 c+10 e \\c \\-5 e \\e\end{array}\righ...

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769 views

GO Classes asked Mar 29, 2023

32 votes

2 answers

305

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 7
Let $\mathrm{A}$ be a $3 \times 3$ matrix. Let $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are linearly independent $3$ ... $\mathrm{A}$.

Let $\mathrm{A}$ be a $3 \times 3$ matrix. Let $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are linearly independent $3$-dimensional vectors. Suppose that we have$$A \mathbf{x}=\...

GO Classes

1.5k views

GO Classes asked Mar 29, 2023

10 votes

2 answers

306

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 10
The given system has infinitely many solutions for $k=?$ $ \left[\begin{array}{ccc} 2 & 2 & -4 \\ 1 & 3 & -2 \\ -4 & k & 8 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 3 \\ 4 \\ -6 \end{array}\right] $

The given system has infinitely many solutions for $k=?$ $$\left[\begin{array}{ccc}2 & 2 & -4 \\1 & 3 & -2 \\-4 & k & 8\end{array}\right]\left[\begin{array}{l}x \\y \\z\e...

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685 views

GO Classes asked Mar 29, 2023

27 votes

4 answers

307

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 12
If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ matrix $\mathrm{A},$ and $\operatorname{det(A)}=4,$ then $\alpha$ equals to?

If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ matrix $\mathrm{A},$ and $\operatorname{det(A)}...

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1.3k views

GO Classes asked Mar 29, 2023

17 votes

3 answers

308

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 25
Let $u \in \mathbb{R}^n$ be such that $u^T u=1$ and set $A=u u^T$. What will be the sum of all eigenvalues of $A?$

Let $u \in \mathbb{R}^n$ be such that $u^T u=1$ and set $A=u u^T$. What will be the sum of all eigenvalues of $A?$

GO Classes

1.1k views

GO Classes asked Mar 29, 2023

35 votes

4 answers

309

GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 12
Two compound propositions are logically equivalent if they have the same truth table. For example, the following two compound propositions are logically equivalent: $\mathrm{p} \rightarrow \mathrm{q}$ ... propositional variables, how many compound propositions are there that are Not logically equivalent to each other?

Two compound propositions are logically equivalent if they have the same truth table.For example, the following two compound propositions are logically equivalent: $\math...

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1.3k views

GO Classes asked Mar 26, 2023

1 votes

1 answer

310

GO Classes 2023 | IIITH Mock Test 1 | Question: 40
In an $\textsf{IPv4}$ datagram, the value of $\textsf{HLEN}$ is $15,$ the value of total length is $300$ and the fragment offset value is $200.$ The sum of the sequence numbers of the first and the last bytes of the payload is _________

In an $\textsf{IPv4}$ datagram, the value of $\textsf{HLEN}$ is $15,$ the value of total length is $300$ and the fragment offset value is $200.$ The sum of the sequence n...

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907 views

GO Classes asked Mar 26, 2023

4 votes

1 answer

311

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 1
What will be the value of the following expression? $ \frac{1}{\log _a a b c}+\frac{1}{\log _b a b c}+\frac{1}{\log _c a b c} $

What will be the value of the following expression?$$\frac{1}{\log _a a b c}+\frac{1}{\log _b a b c}+\frac{1}{\log _c a b c}$$

GO Classes

558 views

GO Classes asked Mar 14, 2023

16 votes

2 answers

312

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 2
If $n!$ denotes the product of the integers $1$ through $n,$ what is the remainder when $(1 !+2 !+3 !+4 !+5 !+6 !+\ldots +9 ! )$ is divided by $9 ?$

If $n!$ denotes the product of the integers $1$ through $n,$ what is the remainder when $(1 !+2 !+3 !+4 !+5 !+6 !+\ldots +9 ! )$ is divided by $9 ?$

GO Classes

788 views

GO Classes asked Mar 14, 2023

12 votes

2 answers

313

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 6
Consider a set of $n$ linearly independent vectors $\left\{\vec{w}_1, \ldots, \vec{w}_n\right\} \in \mathbb{R}^n$. A vector $\vec{u} \in \mathbb{R}^n$ will: Option $1.$ Always be a linear ... $2$ is correct then enter $\text{ 2 }.$

Consider a set of $n$ linearly independent vectors $\left\{\vec{w}_1, \ldots, \vec{w}_n\right\} \in \mathbb{R}^n$. A vector $\vec{u} \in \mathbb{R}^n$ will:Option $1.$ Al...

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784 views

GO Classes asked Mar 14, 2023

13 votes

4 answers

314

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 13
What will be value of $x$ satisfying the below equation? $ \sqrt{\log _2 x^4}+4 \log _4 \sqrt{\frac{2}{x}}=2 $

What will be value of $x$ satisfying the below equation?$$\sqrt{\log _2 x^4}+4 \log _4 \sqrt{\frac{2}{x}}=2$$

GO Classes

856 views

GO Classes asked Mar 14, 2023

0 votes

0 answers

315

Gate 2023
Consider the language L over the alphabet {0, 1}, given below: L = {w ∈ {0, 1}* | w does not contain three or more consecutive 1’s}. The minimum number of states in a Deterministic Finite-State Automaton (DFA) for L is ______ .

Consider the language L over the alphabet {0, 1}, given below:L = {w ∈ {0, 1}* | w does not contain three or more consecutive 1’s}. The minimum number of states in ...

ic3rror

1.6k views

ic3rror asked Feb 16, 2023

9 votes

4 answers

316

GATE CSE 2023 | Question: 20
Let $A$ be the adjacency matrix of the graph with vertices $\{1,2,3,4,5\}.$ Let $\lambda_{1}, \lambda_{2}, \lambda_{3}, \lambda_{4}$, and $\lambda_{5}$ be the five eigenvalues of $A$. Note that these eigenvalues need not be distinct. The value of $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________

Let $A$ be the adjacency matrix of the graph with vertices $\{1,2,3,4,5\}.$Let $\lambda_{1}, \lambda_{2}, \lambda_{3}, \lambda_{4}$, and $\lambda_{5}$ be the five eigenva...

admin

13.3k views

admin asked Feb 15, 2023

5 votes

2 answers

317

GATE CSE 2023 | Question: 21
The value of the definite integral \[ \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x \] is _________. (Rounded off to the nearest integer)

The value of the definite integral \[\int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x\]is _________. (Rounde...

admin

9.0k views

admin asked Feb 15, 2023

6 votes

2 answers

318

GATE CSE 2023 | Question: 22
A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is _____________.

A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is _____________.

admin

12.7k views

admin asked Feb 15, 2023

9 votes

4 answers

319

GATE CSE 2023 | Question: 23
Consider a $3$-stage pipelined processor having a delay of $10 \mathrm{~ns}$ (nanoseconds), $20 \mathrm{~ns}$, and $14 \mathrm{~ns},$ for the first, second, and the third stages, respectively. Assume that there is no other ... instruction is fetched every cycle. The total execution time for executing $100$ instructions on this processor is _____________ $\mathrm{ns}.$

Consider a $3$-stage pipelined processor having a delay of $10 \mathrm{~ns}$ (nanoseconds), $20 \mathrm{~ns}$, and $14 \mathrm{~ns},$ for the first, second, and the third...

admin

9.6k views

admin asked Feb 15, 2023

11 votes

2 answers

320

GATE CSE 2023 | Question: 24
A keyboard connected to a computer is used at a rate of $1$ keystroke per second. The computer system polls the keyboard every $10 \mathrm{~ms}$ (milli seconds) to check for a keystroke and consumes $100\; \mu \mathrm{s}$ (micro seconds) for ... interrupt and processing a keystroke. The ratio $\dfrac{T_{1}}{T_{2}}$ is _____________. (Rounded off to one decimal place)

A keyboard connected to a computer is used at a rate of $1$ keystroke per second. The computer system polls the keyboard every $10 \mathrm{~ms}$ (milli seconds) to check ...

admin

8.1k views

admin asked Feb 15, 2023

18 votes

4 answers

321

GATE CSE 2023 | Question: 25
The integer value printed by the $\textsf{ANSI-C}$ program given below is _______________ #include<stdio.h> int funcp(){ static int x = 1; x++; return x; } int main(){ int x,y; x = funcp(); y = funcp()+x; printf("%d\n", (x+y)); return 0; }

The integer value printed by the $\textsf{ANSI-C}$ program given below is _______________#include<stdio.h int funcp(){ static int x = 1; x++; return x; } int main(){ int ...

admin

11.1k views

admin asked Feb 15, 2023

10 votes

1 answer

322

GATE CSE 2023 | Question: 46
Let $U=\{1,2,3\}$. Let $2^{U}$ denote the powerset of $U$. Consider an undirected graph $G$ whose vertex set is $2^{U}$. For any $A, B \in 2^{U},(A, B)$ is an edge in $G$ if and only if (i) $A \neq B$, and (ii) ... $A$ is denoted by $\mathcal{B}(A)$. If $\emptyset$ denotes the empty set, then the cardinality of $\mathcal{B}(\emptyset)$ is ______________.

Let $U=\{1,2,3\}$. Let $2^{U}$ denote the powerset of $U$. Consider an undirected graph $G$ whose vertex set is $2^{U}$. For any $A, B \in 2^{U},(A, B)$ is an edge in $G$...

admin

6.5k views

admin asked Feb 15, 2023

21 votes

4 answers

323

GATE CSE 2023 | Question: 47
Consider the following two-dimensional array $\text{D}$ in the $\text{C}$ programming language, which is stored in row-major order: int D[128][128]; Demand paging is used for allocating memory and each physical page frame holds $512$ elements of the ... j++) D[j][i] *= 10; The number of page faults generated during the execution of this code snippet is _______________.

Consider the following two-dimensional array $\text{D}$ in the $\text{C}$ programming language, which is stored in row-major order:int D[128][128];Demand paging is used f...

admin

10.8k views

admin asked Feb 15, 2023

11 votes

2 answers

324

GATE CSE 2023 | Question: 48
Consider a computer system with $57$-bit virtual addressing using multi-level tree-structured page tables with $\mathrm{L}$ levels for virtual to physical address translation. The page size is $4 \mathrm{~KB}(1 \mathrm{~KB}=1024 \mathrm{~B})$ and a page table entry at any of the levels occupies $8$ bytes. The value of $\mathrm{L}$ is ______________.

Consider a computer system with $57$-bit virtual addressing using multi-level tree-structured page tables with $\mathrm{L}$ levels for virtual to physical address transla...

admin

12.2k views

admin asked Feb 15, 2023

6 votes

3 answers

325

GATE CSE 2023 | Question: 49
Consider a sequence $a$ of elements $a_{0}=1, a_{1}=5, a_{2}=7, a_{3}=8, a_{4}=9$, and $a_{5}=2$. The following operations are performed on a stack $S$ and a queue $Q,$ both of which are initially empty. $\textsf{push}$ the ... $S$. $\textsf{pop}$ an element from $S$. The top element of $S$ after executing the above operations is ______________.

Consider a sequence $a$ of elements $a_{0}=1, a_{1}=5, a_{2}=7, a_{3}=8, a_{4}=9$, and $a_{5}=2$. The following operations are performed on a stack $S$ and a queue $Q,$ b...

admin

7.0k views

admin asked Feb 15, 2023

4 votes

2 answers

326

GATE CSE 2023 | Question: 50
Consider the syntax directed translation given by the following grammar and semantic rules. Here $N, I, F$ and $B$ are non-terminals. $N$ is the starting non-terminal, and $\#, \mathbf{0}$ and $\mathbf{1}$ are lexical tokens ... \] The value computed by the translation scheme for the input string $10\#011$ is ____________. (Rounded off to three decimal places)

Consider the syntax directed translation given by the following grammar and semantic rules. Here $N, I, F$ and $B$ are non-terminals. $N$ is the starting non-terminal, an...

admin

7.5k views

admin asked Feb 15, 2023

9 votes

2 answers

327

GATE CSE 2023 | Question: 51
Consider the following table named $\text{Student}$ in a relational database. The primary key of this table is $\text{rollNum}.$ $\text{Student}$ ... . SELECT * FROM Student WHERE gender = 'F' AND marks > 65; The number of rows returned by the query is ___________.

Consider the following table named $\text{Student}$ in a relational database. The primary key of this table is $\text{rollNum}.$$\text{Student}$$\begin{array}{|c|l|c|c|}\...

admin

7.6k views

admin asked Feb 15, 2023

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