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Questions by Arjun
6
votes
3
answers
41
GATE CSE 2022 | Question: 35
Consider solving the following system of simultaneous equations using $\text{LU}$ decomposition. $x_{1} + x_{2} - 2x_{3} = 4$ $x_{1} + 3x_{2} - x_{3} = 7$ $2x_{1} + x_{2} - 5x_{3} = 7$ where $\textit{L}$ and $\textit{U}$ ... $\textit{L}_{32}= - \frac{1}{2}, \textit{U}_{33}= - \frac{1}{2}, x_{1}= 0$
asked
in
Linear Algebra
Feb 15
2.0k
views
gatecse-2022
linear-algebra
matrix
system-of-equations
2-marks
5
votes
2
answers
42
GATE CSE 2022 | Question: 36
Which of the following is/are undecidable? Given two Turing machines $\textit{M}_{1}$ and $\textit{M}_{2},$ decide if $\textit{L(M}_{1}) = \textit{L(M}_{2}).$ Given a Turing machine $\textit{M},$ decide if $\textit{L(M)}$ is ... $\textit{M},$ decide if $\textit{M}$ takes more than $1073$ steps on every string.
asked
in
Theory of Computation
Feb 15
2.3k
views
gatecse-2022
theory-of-computation
turing-machine
decidability
multiple-selects
2-marks
8
votes
2
answers
43
GATE CSE 2022 | Question: 37
Consider the following languages: $L_{1} = \{ a^{n} wa^{n} | w \in \{a,b\}^{\ast}\}$ $L_{2} = \{wxw^{R} | w, x \in \{a,b\}^{*}, |w|, |x| > 0 \}$ Note that $w^{R}$ is the reversal of the string $w.$ Which of the following is/are ... $L_{2}$ are context-free. $L_{1}$ is regular and $L_{2}$ is context-free. $L_{1}$ and $L_{2}$ are context-free but not regular.
asked
in
Theory of Computation
Feb 15
1.7k
views
gatecse-2022
theory-of-computation
identify-class-language
context-free-language
multiple-selects
2-marks
7
votes
2
answers
44
GATE CSE 2022 | Question: 38
Consider the following languages: $L_{1} = \{ ww | w \in \{a,b\}^{\ast} \}$ $L_{2} = \{a^{n} b^{n} c^{m} | m,n \geq 0 \}$ $L_{3} = \{a^{m} b^{n} c^{n} | m,n \geq 0 \}$ Which of the following statements is/are $\text{FALSE}?$ ... $L_{2}$ is context-free. $L_{2}, L_{3}$ and $L_{2} \cap L_{3}$ all are context-free. Neither $L_{1}$ nor its complement is context-free.
asked
in
Theory of Computation
Feb 15
3.0k
views
gatecse-2022
theory-of-computation
context-free-language
multiple-selects
2-marks
7
votes
1
answer
45
GATE CSE 2022 | Question: 39
Consider a simple undirected weighted graph $\textit{G},$ all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of $\textit{G}$ is/are $\text{TRUE}?$ The edge with the second smallest weight is ... always be part of any minimum spanning tree of $\textit{G}.$ $\textit{G}$ can have multiple minimum spanning trees.
asked
in
Algorithms
Feb 15
4.5k
views
gatecse-2022
algorithms
spanning-tree
minimum-spanning-tree
multiple-selects
2-marks
5
votes
2
answers
46
GATE CSE 2022 | Question: 40
The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are $\text{TRUE}?$ The chromatic number of the graph is $3.$ The graph has a Hamiltonian path. The following graph is isomorphic to the Peterson ... $3.$ (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
asked
in
Graph Theory
Feb 15
2.2k
views
gatecse-2022
graph-theory
graph-isomorphism
multiple-selects
2-marks
7
votes
6
answers
47
GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$
asked
in
Combinatory
Feb 15
2.5k
views
gatecse-2022
combinatory
recurrence-relation
multiple-selects
2-marks
6
votes
3
answers
48
GATE CSE 2022 | Question: 42
Which of the properties hold for the adjacency matrix $A$ of a simple undirected unweighted graph having $n$ vertices? The diagonal entries of $A^{2}$ ... . If there is at least a $1$ in each of $A\text{'s}$ rows and columns, then the graph must be connected.
asked
in
Graph Theory
Feb 15
1.9k
views
gatecse-2022
graph-theory
graph-connectivity
multiple-selects
2-marks
4
votes
1
answer
49
GATE CSE 2022 | Question: 43
Which of the following is/are the eigenvector(s) for the matrix given below? $\begin{pmatrix} - 9 & - 6 & - 2 & - 4 \\ - 8 & - 6 & - 3 & - 1 \\ 20 & 15 & 8 & 5 \\ 32 & 21 & 7 & 12 \end{pmatrix}$ ... $\begin{pmatrix} - 1 \\ 0 \\ 2 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 0 \\ 1 \\ - 3 \\ 0 \end{pmatrix}$
asked
in
Linear Algebra
Feb 15
2.0k
views
gatecse-2022
linear-algebra
eigen-value
multiple-selects
2-marks
4
votes
2
answers
50
GATE CSE 2022 | Question: 44
Consider a system with $2 \;\text{KB}$ direct mapped data cache with a block size of $64 \; \text{bytes}.$ The system has a physical address space of $64 \; \text{KB}$ and a word length of $16 \; \text{bits.}$ During the execution of a program, four data ... only $\text{R}$ and $\text{S}$ reside in the cache. Every access to $\text{R}$ evicts $\text{Q}$ from the cache.
asked
in
CO and Architecture
Feb 15
2.1k
views
gatecse-2022
co-and-architecture
direct-mapping
multiple-selects
2-marks
12
votes
4
answers
51
GATE CSE 2022 | Question: 45
Consider routing table of an organization's router shown below: ... of the subnets in the routing table? $12.20.164.0/20$ $12.20.164.0/22$ $12.20.164.0/21$ $12.20.168.0/22$
asked
in
Computer Networks
Feb 15
5.1k
views
gatecse-2022
computer-networks
subnetting
multiple-selects
2-marks
10
votes
4
answers
52
GATE CSE 2022 | Question: 46
Consider the relational database with the following four schemas and their respective instances. Student(sNo, sName, dNo) Dept(dNo, dName) Course(cNo, cName, dNo) Register(sNo, cNo) ... SELECT cNo FROM Register WHERE sNo = S.sNo) The number of rows returned by the above $\text{SQL}$ query is ____________.
asked
in
Databases
Feb 15
2.5k
views
gatecse-2022
numerical-answers
databases
sql
2-marks
10
votes
2
answers
53
GATE CSE 2022 | Question: 47
Consider a network with three routers $\text{P, Q, R}$ shown in the figure below. All the links have cost of unity. The routers exchange distance vector routing information and have converged on the routing tables, after which the link $\text{Q-R}$ ... off to one decimal place) between $\text{P}$ and $\text{Q},$ leading to count-to-infinity problem, is _______________.
asked
in
Computer Networks
Feb 15
3.0k
views
gatecse-2022
numerical-answers
computer-networks
routing
distance-vector-routing
2-marks
5
votes
2
answers
54
GATE CSE 2022 | Question: 48
Let $\textit{G(V,E)}$ be a directed graph, where $\textit{V} = \{ 1, 2, 3, 4, 5 \}$ is the set of vertices and $\textit{E}$ is the set of directed edges, as defined by the following adjacency matrix $\textit{A}.$ ... contains a directed path from $r$ to every other vertex in $V.$ The number of such directed spanning trees rooted at vertex $5$ is __________________.
asked
in
Algorithms
Feb 15
1.8k
views
gatecse-2022
numerical-answers
algorithms
spanning-tree
2-marks
2
votes
2
answers
55
GATE CSE 2022 | Question: 49
Consider a $100 \; \text{Mbps}$ link between an earth station (sender) and a satellite (receiver) at an altitude of $2100 \; \text{km}.$ The signal propagates at a speed of $3 \times 10^{8} \; \text{m/s.}$ ... $1000 \; \text{bytes}$ transmitted by the sender is _______________.
asked
in
Computer Networks
Feb 15
2.0k
views
gatecse-2022
numerical-answers
computer-networks
2-marks
2
votes
3
answers
56
GATE CSE 2022 | Question: 50
Consider the data transfer using $\text{TCP}$ over a $1 \; \text{Gbps}$ link. Assuming that the maximum segment lifetime $\text{(MSL)}$ is set to $60 \; \text{seconds},$ the minimum number of bits required for the sequence number field of the $\text{TCP}$ header, to prevent the sequence number space from wrapping around during the $\text{MSL}$ is ________________.
asked
in
Computer Networks
Feb 15
1.7k
views
gatecse-2022
numerical-answers
computer-networks
tcp
2-marks
7
votes
3
answers
57
GATE CSE 2022 | Question: 51
A processor $\text{X}_{1}$ operating at $2 \; \text{GHz}$ has a standard $5-$stage $\text{RISC}$ instruction pipeline having a base $\text{CPI (cycles per instruction)}$ of one without any pipeline hazards. For a given program $\text{P}$ ... $\text{X}_{2}$ over $\text{X}_{1}$ in executing $\text{P}$ is _______________.
asked
in
CO and Architecture
Feb 15
2.5k
views
gatecse-2022
numerical-answers
co-and-architecture
pipelining
stall
2-marks
11
votes
7
answers
58
GATE CSE 2022 | Question: 52
Consider the queues $Q_{1}$ containing four elements and $Q_{2}$ containing none (shown as the $\textsf{Initial State}$ in the figure). The only operations allowed on these two queues are $\textsf{Enqueue (Q, element)}$ ... $\textsf{Final State}$ in the figure) without using any additional storage is________________.
asked
in
DS
Feb 15
6.3k
views
gatecse-2022
numerical-answers
data-structures
queue
2-marks
9
votes
1
answer
59
GATE CSE 2022 | Question: 53
Consider two files systems $\text{A}$ and $\text{B}$, that use contiguous allocation and linked allocation, respectively. A file of size $100$ blocks is already stored in $\text{A}$ and also in $\text{B}$. Now, consider inserting a new block in the middle of ... $\text{B}$ are $n_{A}$ and $n_{B}$, respectively, then the value of $n_{A} + n_{B}$ is__________________.
asked
in
Operating System
Feb 15
2.2k
views
gatecse-2022
numerical-answers
operating-system
file-system
2-marks
4
votes
3
answers
60
GATE CSE 2022 | Question: 54
Consider a demand paging system with four page frames (initially empty) and $\text{LRU}$ page replacement policy. For the following page reference string $7, 2, 7, 3, 2, 5, 3, 4, 6, 7, 7, 1, 5, 6, 1$ the page fault rate, defined as the ratio of number of page faults to the number of memory accesses $\textit{(rounded off to one decimal place)}$ is _____________.
asked
in
Operating System
Feb 15
2.5k
views
gatecse-2022
numerical-answers
operating-system
page-replacement
demand-paging
2-marks
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