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7
answers
1
GATE CSE 2006 | Question: 24
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = \min(\pi(B))$, where $\min(S)$ is the smallest integer in the set of integers $S$, and $\pi$(S) is the set of ... $n! \frac{|A ∩ B|}{|A ∪ B|}$ $\dfrac{|A ∩ B|^2}{^n \mathrm{C}_{|A ∪ B|}}$
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = ...
11.1k
views
answer edited
Feb 5, 2021
Set Theory & Algebra
gatecse-2006
set-theory&algebra
normal
set-theory
+
–
1
answer
2
ISI2017-PCB-CS-8-b
Consider a simple code $\mathcal{C}$ for error detection and correction. Each codeword in $\mathcal{C}$ consists of $2$ data bits $[d_1, d_0]$ followed by check bits $[c_2, c_1, c_0]$ ... . Write down all the codewords for $\mathcal{C}$ Determine the minimum Hamming distance between any two distinct codewords of $\mathcal{C}$
Consider a simple code $\mathcal{C}$ for error detection and correction. Each codeword in $\mathcal{C}$ consists of $2$ data bits $[d_1, d_0]$ followed by check bits $[c_...
761
views
answered
Aug 24, 2020
Digital Logic
isi2017-pcb-cs
digital-logic
error-detection
programming
descriptive
+
–
2
answers
3
ISI-2017-PCB-C6
Let $A = \{a_1,a_2, \dots ,a_n\}$ be an array of $n$ distinct numbers. The array may not be sorted. The first element $a_1$ is said to be a blip if $a_1 > a_2$. Similar, the last element an is said to be a blip if $a_n > a_{n-1}$. Among the ... $O(\log n)$ time algorithm for finding a blip in $A$. Justify the complexity of your algorithm.
Let $A = \{a_1,a_2, \dots ,a_n\}$ be an array of $n$ distinct numbers. The array may not be sorted. The first element $a_1$ is said to be a blip if $a_1 a_2$. Similar, t...
956
views
commented
Aug 20, 2020
Algorithms
isi2017
algorithms
algorithm-design
descriptive
+
–
5
answers
4
GATE CSE 2020 | Question: 31
Let $G = (V, E)$ be a weighted undirected graph and let $T$ be a Minimum Spanning Tree (MST) of $G$ maintained using adjacency lists. Suppose a new weighed edge $(u, v) \in V \times V$ is added to $G$. The worst case time complexity of determining if $T$ is still an MST ... $\Theta (\mid E \mid \mid V \mid) \\$ $\Theta(E \mid \log \mid V \mid) \\$ $\Theta( \mid V \mid)$
Let $G = (V, E)$ be a weighted undirected graph and let $T$ be a Minimum Spanning Tree (MST) of $G$ maintained using adjacency lists. Suppose a new weighed edge $(u, v) ...
18.8k
views
commented
Jul 2, 2020
Algorithms
gatecse-2020
algorithms
minimum-spanning-tree
graph-algorithm
2-marks
+
–
3
answers
5
GATE CSE 1989 | Question: 13b
Find a solution to the following recurrence equation: $T(n)=\sqrt{n}+T\left(\frac{n}{2}\right)$ $T(1)=1$
Find a solution to the following recurrence equation:$T(n)=\sqrt{n}+T\left(\frac{n}{2}\right)$$T(1)=1$
4.2k
views
comment edited
Jun 29, 2020
Algorithms
gate1989
descriptive
algorithms
recurrence-relation
+
–
0
answers
6
Kenneth Rosen Edition 7 Exercise 2.5 Question 32 (Page No. 177)
Show that when you substitute $(3n + 1)^{2}$ for each occurrence of $n$ and $(3m + 1)^{2}$ for each occurrence of m in the right-hand side of the formula for the function $f (m, n)$ in question $31,$ you ... $Q \times Q \rightarrow Q.$
Show that when you substitute $(3n + 1)^{2}$ for each occurrence of $n$ and $(3m + 1)^{2}$ for each occurrence of m in the right-hand side of the formula for the function...
184
views
commented
Apr 28, 2020
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
descriptive
+
–
2
answers
7
Kenneth Rosen Edition 7 Exercise 6.1 Question 6 (Page No. 396)
There are four major auto routes from Boston to Detroit and six from Detroit to Los Angeles. How many major auto routes are there from Boston to Los Angeles via Detroit?
There are four major auto routes from Boston to Detroit and six from Detroit to Los Angeles. How many major auto routes are there from Boston to Los Angeles via Detroit?
3.7k
views
answered
Apr 28, 2020
Combinatory
kenneth-rosen
discrete-mathematics
counting
descriptive
+
–
0
answers
8
ISI2018-PCB-A3
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r-1$ divides $n^s-1$ if and only if $r$ divides $s$.
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r-1$ divides $n^s-1$ if and only if $r$ divides $s$.
430
views
commented
Apr 14, 2020
Quantitative Aptitude
isi2018-pcb-a
general-aptitude
quantitative-aptitude
descriptive
+
–
5
answers
9
ISRO2016-15
The Excess-$3$ code is also called Cyclic Redundancy Code Weighted Code Self-Complementing Code Algebraic Code
The Excess-$3$ code is also calledCyclic Redundancy CodeWeighted CodeSelf-Complementing CodeAlgebraic Code
8.3k
views
comment edited
Mar 14, 2020
Digital Logic
isro2016
digital-logic
binary-codes
+
–
0
answers
10
In an examination, the score in each of the four languages
In an examination, the score in each of the four languages – Bengali, Hindi, Urdu and Telegu- can be integers between 0 and 10. Then the number of ways in which a student can secure a total score of 21 is (A) 880; (B) 760; (C) 450; (D) 1360.
In an examination, the score in each of the four languages – Bengali, Hindi, Urdu and Telegu- can be integers between 0 and 10. Then the number of ways in which a stude...
1.6k
views
commented
Mar 12, 2020
Combinatory
combinatory
+
–
3
answers
11
GATE CSE 2004 | Question: 56
Consider three IP networks $A, B$ and $C$. Host $H_A$ in network $A$ sends messages each containing $180$ bytes of application data to a host $H_C$ in network $C$. The $\text{TCP}$ layer prefixes $20$ byte header to the message. This passes ... $200$ $220$ $240$ $260$
Consider three IP networks $A, B$ and $C$. Host $H_A$ in network $A$ sends messages each containing $180$ bytes of application data to a host $H_C$ in network $C$. The $\...
22.8k
views
comment edited
Mar 4, 2020
Computer Networks
gatecse-2004
computer-networks
ip-addressing
tcp
normal
+
–
8
answers
12
GATE CSE 2004 | Question: 57
Consider three IP networks $A, B$ and $C$. Host $H_A$ in network $A$ sends messages each containing $180$ $bytes$ of application data to a host $H_C$ in network $C$. The TCP layer prefixes $20$ byte header to the message. This passes through an intermediate network $B$ ... overheads. $325.5$ $\text{Kbps}$ $354.5$ $\text{Kbps}$ $409.6$ $\text{Kbps}$ $512.0$ $\text{Kbps}$
Consider three IP networks $A, B$ and $C$. Host $H_A$ in network $A$ sends messages each containing $180$ $bytes$ of application data to a host $H_C$ in network $C$. The ...
18.8k
views
comment edited
Mar 4, 2020
Computer Networks
gatecse-2004
computer-networks
ip-addressing
tcp
normal
+
–
1
answer
13
JEST 2020
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-one For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-oneFor all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, ...
841
views
commented
Feb 17, 2020
Set Theory & Algebra
jest
functions
set-theory
+
–
1
answer
14
TIFR CSE 2019 | Part B | Question: 12
Let $G=(V,E)$ be a directed graph with $n(\geq 2)$ vertices, including a special vertex $r$. Each edge $e \in E$ has a strictly positive edge weight $w(e)$. An arborescence in $G$ rooted at $r$ is a subgraph $H$ of $G$ ... is acyclic $w^*$ is less than the weight of the minimum weight directed Hamiltonian cycle in $G$, when $G$ has a directed Hamiltonian cycle
Let $G=(V,E)$ be a directed graph with $n(\geq 2)$ vertices, including a special vertex $r$. Each edge $e \in E$ has a strictly positive edge weight $w(e)$. An arborescen...
2.4k
views
comment edited
Feb 15, 2020
Graph Theory
tifr2019
graph-connectivity
graph-theory
difficult
+
–
1
answer
15
TIFR CSE 2020 | Part A | Question: 6
What is the maximum number of regions that the plane $\mathbb{R}^{2}$ can be partitioned into using $10$ lines? $25$ $50$ $55$ $56$ $1024$ Hint: Let $A(n)$ be the maximum number of partitions that can be made by $n$ lines. Observe that $A(0) = 1, A(2) = 2, A(2) = 4$ etc. Come up with a recurrence equation for $A(n)$.
What is the maximum number of regions that the plane $\mathbb{R}^{2}$ can be partitioned into using $10$ lines?$25$$50$$55$$56$$1024$Hint: Let $A(n)$ be the maximum numbe...
808
views
answered
Feb 11, 2020
Quantitative Aptitude
tifr2020
general-aptitude
quantitative-aptitude
number-theory
+
–
2
answers
16
TIFR CSE 2020 | Part A | Question: 10
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall that January has $31$ days)? Sunday Monday Wednesday Friday None of the others
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall th...
2.1k
views
answered
Feb 11, 2020
Probability
tifr2020
engineering-mathematics
probability
+
–
2
answers
17
TIFR CSE 2020 | Part A | Question: 9
A contiguous part, i.e., a set of adjacent sheets, is missing from Tharoor's GRE preparation book. The number on the first missing page is $183$, and it is known that the number on the last missing page has the same three digits, but in a different ... front and one at the back. How many pages are missing from Tharoor's book? $45$ $135$ $136$ $198$ $450$
A contiguous part, i.e., a set of adjacent sheets, is missing from Tharoor’s GRE preparation book. The number on the first missing page is $183$, and it is known that t...
872
views
answered
Feb 11, 2020
Quantitative Aptitude
tifr2020
quantitative-aptitude
number-theory
+
–
5
answers
18
GATE IT 2007 | Question: 84
Consider the $B^+$ tree in the adjoining figure, where each node has at most two keys and three links. Keys $K15$ and then $K25$ are inserted into this tree in that order. Exactly how many of the following nodes (disregarding the links) will be present in the tree after the two insertions? $1$ $2$ $3$ $4$
Consider the $B^+$ tree in the adjoining figure, where each node has at most two keys and three links.Keys $K15$ and then $K25$ are inserted into this tree in that order....
16.0k
views
commented
Feb 1, 2020
Databases
gateit-2007
databases
b-tree
normal
+
–
2
answers
19
Is L CFL or not?
L ={ww | w ∈{a, b}∗} Is compliment of L, CFL? Support with reason
L ={ww | w ∈{a, b}∗}Is compliment of L, CFL? Support with reason
2.9k
views
answer edited
Jan 21, 2020
6
answers
20
GATE IT 2008 | Question: 27
$G$ is a simple undirected graph. Some vertices of $G$ are of odd degree. Add a node $v$ to $G$ and make it adjacent to each odd degree vertex of $G$. The resultant graph is sure to be regular complete Hamiltonian Euler
$G$ is a simple undirected graph. Some vertices of $G$ are of odd degree. Add a node $v$ to $G$ and make it adjacent to each odd degree vertex of $G$. The resultant graph...
13.9k
views
commented
Jan 19, 2020
Graph Theory
gateit-2008
graph-theory
graph-connectivity
normal
+
–
7
answers
21
GATE CSE 2018 | Question: 51
A processor has $16$ integer registers $\text{(R0, R1}, \ldots ,\text{ R15)}$ and $64$ floating point registers $\text{(F0, F1}, \ldots , \text{F63)}.$ It uses a $2\text{- byte}$ instruction format. There are four categories of ... $\text{(1F)}.$ The maximum value of $\text{N}$ is _________.
A processor has $16$ integer registers $\text{(R0, R1}, \ldots ,\text{ R15)}$ and $64$ floating point registers $\text{(F0, F1}, \ldots , \text{F63)}.$ It uses a $2\text{...
24.0k
views
commented
Jan 17, 2020
CO and Architecture
gatecse-2018
co-and-architecture
machine-instruction
instruction-format
numerical-answers
2-marks
+
–
5
answers
22
#ADDRESS INSTRUCTION
Consider the hypothetical processor is supports both 2 address and one address instructions.It has 128 word memory A 16-bit instruction is placed in the one memory word. Q1.What is the range of two address and one address instructions are supported. A)1 to ... 2-address instructions are already existed.How many one address instructions can be supported ? A)128 B)2 C)256 D)32
Consider the hypothetical processor is supports both 2 address and one address instructions.It has 128 word memory A 16-bit instruction is placed in the one memory word.Q...
16.6k
views
answer edited
Jan 17, 2020
CO and Architecture
co-and-architecture
cache-memory
machine-instruction
instruction-format
computer-architecture
+
–
3
answers
23
GATE IT 2008 | Question: 85
Host $X$ has $IP$ address $192.168.1.97$ and is connected through two routers $R1$ and $R2$ to another host $Y$ with $IP$ address $192.168.1.80$. Router $R1$ has $IP$ addresses $192.168.1.135$ and $192.168.1.110$. $R2$ has $IP$ ... . Which $IP$ address should $X$ configure its gateway as? $192.168.1.67$ $192.168.1.110$ $192.168.1.135$ $192.168.1.155$
Host $X$ has $IP$ address $192.168.1.97$ and is connected through two routers $R1$ and $R2$ to another host $Y$ with $IP$ address $192.168.1.80$. Router $R1$ has $IP$ a...
19.6k
views
commented
Jan 16, 2020
Computer Networks
gateit-2008
computer-networks
subnetting
normal
+
–
1
answer
24
topological ordering of DAG
What is the method to find no of topological ordering of a Directed Acyclic Graph? For an instance, i found two graphs on internet, whose no of topological ordering is given but how to quickly calculate the total no of ordering? Graph 1 For graph 1, no of ... . If I try to solve it by brute force method, then it's taking lot's of time. Is there any faster way?
What is the method to find no of topological ordering of a Directed Acyclic Graph?For an instance, i found two graphs on internet, whose no of topological ordering is giv...
956
views
comment edited
Jan 10, 2020
DS
topological-sort
data-structures
directed-acyclic-graph
no-of-topological-ordering
+
–
10
answers
25
GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
17.5k
views
comment edited
Jan 6, 2020
Combinatory
gatecse-2016-set2
modular-arithmetic
normal
numerical-answers
+
–
2
answers
26
UGC NET CSE | December 2019 | Part 2 | Question: 52
Let $A= \{001, 0011, 11, 101\}$ and $B=\{01, 111, 111, 010\}$. Similarly, let $C= \{00, 001, 1000\}$ and $D=\{0, 11, 011\}$. Which of the following pairs have a post-correspondence solution? Only pair $(A, B)$ Only pair $(C, D)$ Both $(A, B)$ and $(C, D)$ Neither $(A, B)$ nor $(C, D)$
Let $A= \{001, 0011, 11, 101\}$ and $B=\{01, 111, 111, 010\}$. Similarly, let $C= \{00, 001, 1000\}$ and $D=\{0, 11, 011\}$.Which of the following pairs have a post-corre...
1.2k
views
comment edited
Jan 3, 2020
Others
ugcnetcse-dec2019-paper2
+
–
4
answers
27
DMA Cycle Stealing Mode Transfer
A DMA controller transfers $16$-bit word to memory using cycle stealing. The words are assembled from a device that transmits characters at a rate of $2400$ characters per second. The CPU is fetching and executing instructions at an average rate ... ASCII? How much more percent the CPU slows down when $32$ -bits words are transferred to memory using cycle stealing?
A DMA controller transfers $16$-bit word to memory using cycle stealing. The words are assembled from a device that transmits characters at a rate of $2400$ characters pe...
10.8k
views
commented
Dec 31, 2019
CO and Architecture
dma
co-and-architecture
+
–
2
answers
28
Hamacher-DMA
The average seek time and rotational delay in a disk system are 6ms and 3ms, respectively. The rate of data transfer to or from the disk is 30 Mbytes/sec and all disk accesses are for 8 Kbytes of data. Disk DMA controller, the processor and the main ... stolen by a disk unit, on average over a long period of time during which a sequence of independent 8K-byte transfers takes place?
The average seek time and rotational delay in a disk system are 6ms and 3ms, respectively. The rate of data transfer to or from the disk is 30 Mbytes/sec and all disk ac...
5.2k
views
commented
Dec 31, 2019
CO and Architecture
co-and-architecture
dma
+
–
5
answers
29
How much time will the processor be slowed down due to DMA activity?
A processor is fetching instructions at the rate of 1 MIPS.A DMA module is used to transfer characters to RAM from a device transmitting at 9600 bps.How much time will the processor be slowed down due to DMA activity? a)9.6 ms b)4.8 ms c)2.4 ms d)1.2 ms
A processor is fetching instructions at the rate of 1 MIPS.A DMA module is used to transfer characters to RAM from a device transmitting at 9600 bps.How much time will th...
10.9k
views
answer edited
Dec 30, 2019
CO and Architecture
co-and-architecture
dma
+
–
2
answers
30
Andrew S. Tanenbaum (OS) Edition 4 Exercise 5 Question 5 (Page No. 429)
A DMA controller has five channels. The controller is capable of requesting a $32$-bit word every $40\: nsec.$ A response takes equally long. How fast does the bus have to be to avoid being a bottleneck?
A DMA controller has five channels. The controller is capable of requesting a $32$-bit word every $40\: nsec.$ A response takes equally long. How fast does the bus have t...
2.2k
views
commented
Dec 29, 2019
Operating System
tanenbaum
operating-system
input-output
dma
descriptive
+
–
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