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+3
votes
1
TIFR2019B13
A row of $10$ houses has to be painted using the colours red, blue, and green so that each house is a single colour, and any house that is immediately to the right of a red or a blue house must be green. How many ways are there to paint the houses? $199$ $683$ $1365$ $3^{10}2^{10}$ $3^{10}$
answered
Jun 26, 2019
in
Combinatory

639
views
tifr2019
engineeringmathematics
discretemathematics
permutationandcombination
medium
0
votes
2
Cormen Edition 3 Exercise 2.3 Question 7 (Page No. 39)
Describe a $\Theta(n\ lg\ n)$ time algorithm that, given a set $S$ of $n$ integers and another integer $x$, determines whether or not there exist two elements in $S$ whose sum is exactly $x$.
answered
Jun 26, 2019
in
Algorithms

12
views
cormen
algorithms
algorithmdesigntechniques
descriptive
difficult
+1
vote
3
A FIRST COURSE IN PROBABILITY (SHELDON ROSS),CHAPTER 4 RANDOM VARIABLES, QUESTION#43
answered
Jun 26, 2019
in
Probability

108
views
probability
sheldonross
randomvariable
+3
votes
4
GATE198812iic
Using Armstrong’s axioms of functional dependency derive the following rules: $\{ x \rightarrow y, \: z \subset y \} \mid= x \rightarrow z$ (Note: $x \rightarrow y$ denotes $y$ is functionally dependent on $x$, $z \subseteq y$ denotes $z$ is subset of $y$, and $\mid =$ means derives).
answered
Jun 14, 2019
in
Databases

172
views
gate1988
normal
descriptive
databases
databasenormalization
0
votes
5
Goschedule information
As per Gate Overflow Schedule for 2020 for the first week we have to study " Logical Reasoning and Data Interpretation: Verbal reasoning deriving conclusion from passage, conclusions as in puzzles (can be in mathematical logic also) ". So which topics are covered under this and what questions to practice from GO PDF?
answered
Jun 12, 2019
in
Verbal Ability

158
views
goclassroom
verbalability
+3
votes
6
Self doubt DIGITAL LOGIC
Is Y' + Z' same as (YZ)' ? Please explain this concept of compliments..!!
answered
Jun 11, 2019
in
Digital Logic

85
views
+2
votes
7
TIFR2011A13
If $z=\dfrac{\sqrt{3}i}{2}$ and $\large(z^{95}+ i^{67})^{97}= z^{n}$, then the smallest value of $n$ is? $1$ $10$ $11$ $12$ None of the above.
answered
Jun 10, 2019
in
Numerical Ability

343
views
tifr2011
numericalability
complexnumber
0
votes
8
Theory of Computation: Context Free Languages
Hi, I am having a doubt understanding the result of CFL  Regular: Here's my approach: CFL  Regular = CFL INTERSECTION Regular' = CFL INTERSECTION Regular = CFL Suppose some CFL L1= {a^n b^n  n>=1} and some Regular R1= (a+b)* ... to say CFL  Regular = Regular or CFL  Regular = CFL ? If both are separate options, which one should I go for? Thanks
answered
Jun 9, 2019
in
Theory of Computation

58
views
theoryofcomputation
contextfreelanguages
selfdoubt
+1
vote
9
GEEKS FOR GEEKS GATE 2017 MOCK
If Kruskal’s algorithm is used for finding a minimum spanning tree of a weighted graph G with n vertices and m edges and edge weights are already given in a sorted list, then, What will be the time complexity to compute the minimum cost spanning tree given that union and find operations take amortized O(1) ? A O(m logn) B O(n) C O(m) D O(n logm)
answered
Jun 9, 2019
in
Algorithms

148
views
kruskalsalgorithm
graphalgorithms
greedyalgorithm
datastructures
0
votes
10
GATE2017 CE2: GA9
Budhan covers a distance of $19$ km in $2$ hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers $26$ km in $2$ hours. The speed in km/h at which Budhan walk is $1$ $4$ $5$ $6$
answered
Jun 7, 2019
in
Numerical Ability

202
views
gate2017ce2
speedtimedistance
numericalability
+1
vote
11
Self doubt in percentage and mixtures
In a mixture of 80 litres of milk and water, 25% of the mixture is milk. How much water should be added to the mixture so that milk becomes 20% of the mixture? (a) 20 litres (b) 15 litres (c) 25 litres (d) None of these
answered
Jun 4, 2019
in
Numerical Ability

55
views
+3
votes
12
Doubt on Bipartite Graph
What is T.C. to find maximum number of edges to be added to a tree so that it stays as a bipartite graph? Now my question is, why do we need to add edges to make a tree bipartite? A tree is already bipartite graph. Right?? Again how do we add edges in it?? Is BFS or DFS do any improvement in such a tree?? How to think such a question??
answered
Jun 2, 2019
in
Algorithms

86
views
graphtheory
algorithms
+8
votes
13
GATE2015 EC1: GA8
Fill in the missing value
answered
May 28, 2019
in
Numerical Ability

251
views
gate2015ec1
generalaptitude
numericalability
numericalanswers
sequenceseries
0
votes
14
GateBook Test Series: Digital Logic  Boolean Algebra
What is the time complexity for checking whether an assignment of truth values to variables $x_1,\dots ,x_n$ satisfies a given formula $f(x_1\dots,x_n)$? $O(2^n)$ $O(g(n))$ where $g$ is a polynomial $O(log(n))$ None of the above
answered
May 25, 2019
in
Digital Logic

255
views
gatebook
digitallogic
booleanalgebra
+1
vote
15
Ace Academy Question Bank: Automata
Find the no. of DFA’s that can be constructed over the alphabet Σ with 5 symbols, and with 10 states. (a) $2^5$^0$ × $50^5$ (b) $2^1$^0$ × $10^5$^0$ (c) $2^5$ × $10^5$^0$ (d) $2^5$^0$ × $50^5$
answered
May 22, 2019
in
Theory of Computation

94
views
theoryofcomputation
numberofdfa
0
votes
16
self doubt: TOC
is union of regular language and context free language always regular?
answered
May 22, 2019
in
Theory of Computation

58
views
theoryofcomputation
regularlanguages
contextfreelanguages
+1
vote
17
Discrete mathematics #TEST_BOOK
I Have doubt about the language. Is it asking about the sum of elements if we make the GBL set for the given lattice .
answered
May 20, 2019
in
Set Theory & Algebra

40
views
#discrete
#lattice
0
votes
18
GateBook Test Series: Digital Logic  Boolean Algebra
What is the time complexity for checking whether an assignment of truth values to variables $x_1,\dots ,x_n$ satisfies a given formula $f(x_1\dots,x_n)$? $O(2^n)$ $O(g(n))$ where $g$ is a polynomial $O(log(n))$ None of the above
answered
May 15, 2019
in
Digital Logic

255
views
gatebook
digitallogic
booleanalgebra
+2
votes
19
GATE2011 AG: GA3
Choose the most appropriate word from the options given below to complete the following sentence: It was her view that the country’s problem had been _________ by foreign technocrats, so that to invite them to come back would be counterproductive. identified ascertained exacerbated analysed
answered
May 14, 2019
in
Verbal Ability

109
views
generalaptitude
verbalability
gate2011ag
mostappropriateword
+1
vote
20
GATE2010 TF: GA3
Choose the most appropriate word from the options given below to complete the following sentence: The two child norm with _______ for the violators will have significant implications for oar demographic profile$.$ disincentives incitements restrictions restraints
answered
May 14, 2019
in
Verbal Ability

82
views
generalaptitude
verbalability
gate2010tf
mostappropriateword
+1
vote
21
GATE2010 TF: GA7
Consider the series $\frac{1}{2}+\frac{1}{3}\frac{1}{4}+\frac{1}{8}+\frac{1}{9}\frac{1}{16}+\frac{1}{32}+\frac{1}{27}\frac{1}{64}+\ldots.$ The sum of the infinite series above is$:$ $\infty$ $\frac{5}{6}$ $\frac{1}{2}$ $0$
answered
May 14, 2019
in
Numerical Ability

135
views
generalaptitude
numericalability
gate2010tf
numberseries
0
votes
22
#probability(self doubt)
An automobile showroom has 10 cars, 2 of which are defective. If you are going to buy the 6th car sold that day at random, then the probability of selecting a defective car is??
answered
May 13, 2019
in
Combinatory

53
views
probability
+2
votes
23
ISI2018PCBCS2
You can climb up a staircase of $n$ stairs by taking steps of one or two stairs at a time. Formulate a recurrence relation for counting $a_n$, the number of distinct ways in which you can climb up the staircase. Mention the boundary conditions for your recurrence relation. Find a closed form expression for $a_n$ by solving your recurrence.
answered
May 13, 2019
in
Algorithms

57
views
isi2018pcbcs
algorithms
recurrence
descriptive
+1
vote
24
self doubt dfa
Given an algorithm to tell whether a regular language L contains at least 100 strings
answered
May 12, 2019
in
Theory of Computation

56
views
theoryofcomputation
+3
votes
25
ISI2018MMA20
Consider the set of all functions from $\{1, 2, . . . ,m\}$ to $\{1, 2, . . . , n\}$,where $n > m$. If a function is chosen from this set at random, the probability that it will be strictly increasing is $\binom{n}{m}/n^m\\$ $\binom{n}{m}/m^n\\$ $\binom{m+n1}{m1}/n^m\\$ $\binom{m+n1}{m}/m^n$
answered
May 12, 2019
in
Probability

116
views
isi2018mma
engineeringmathematics
probability
0
votes
26
ISI2018PCBCS3
An $n$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ denote the number of such functions. Calculate the value of $\sigma_4$. Derive an expression for $\sigma_n$ in terms of $n$.
answered
May 12, 2019
in
Set Theory & Algebra

45
views
isi2018pcbcs
engineeringmathematics
discretemathematics
settheory&algebra
functions
descriptive
0
votes
27
ISI2018PCBA4
Let $A$ and $B$ are two nonempty finite subsets of $\mathbb{Z}$, the set of all integers. Define $A+B=\{a+b:a\in A,b\in B\}$.Prove that $\mid A+B \mid \geq \mid A \mid + \mid B \mid 1 $, where $\mid S \mid$ denotes the cardinality of finite set $S$.
answered
May 12, 2019
in
Set Theory & Algebra

43
views
isi2018pcba
settheory&algebra
descriptive
+1
vote
28
ISI2018MMA27
Number of real solutions of the equation $x^7 + 2x^5 + 3x^3 + 4x = 2018$ is $1$ $3$ $5$ $7$
answered
May 11, 2019
in
Numerical Ability

59
views
isi2018mma
generalaptitude
numericalability
0
votes
29
ISI2018MMA7
The greatest common divisor of all numbers of the form $p^2 − 1$, where $p \geq 7$ is a prime, is $6$ $12$ $24$ $48$
answered
May 11, 2019
in
Numerical Ability

27
views
isi2018mma
generalaptitude
numericalability
+3
votes
30
ISI2018MMA24
The sum of the infinite series $1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+\dots $ is $2$ $3$ $4$ $6$
answered
May 11, 2019
in
Numerical Ability

67
views
isi2018mma
generalaptitude
numericalability
+2
votes
31
Made Easy Test Series:Algorithm Minimum Weight Path
Consider the following statement: $A)$ If all edge weight of a graph are positive then any subset of edges that connect all vertices and has minimum total weight is a tree. $B)$ ... minimum weight graph?? and what about B)?? Is it just saying each minimum path between $2$ vertices makes total shortest path??
answered
May 10, 2019
in
Algorithms

67
views
algorithms
madeeasytestseries
+1
vote
32
Made Easy Test Series:AlgorithmRecurrence Relation
What is the solution of recurrence relation $T\left ( n \right )=T\left ( n1 \right )+n$
answered
May 10, 2019
in
Algorithms

158
views
algorithms
timecomplexity
recurrenceeqation
0
votes
33
Self doubt:Pumping Lemma
How by Pumping Lemma we can prove that “context free grammar generate an infinite number of strings” and here what could be pumping length ?
answered
May 9, 2019
in
Theory of Computation

70
views
theoryofcomputation
pumpinglemma
+1
vote
34
Made Easy Test Series:Algo Asymptotic Complexity
$1)n^{2019}=O\left (n^{2020} \right )$ $2)O(n^{2019})=O\left (n^{2020} \right )$ Which one is correct?? If $1)$ is correct, why $2)$ not correct?
answered
May 9, 2019
in
Algorithms

169
views
madeeasytestseries
algorithms
0
votes
35
Michael Sipser Edition 3 Exercise 2 Question 26 (Page No. 157)
Show that if $G$ is a $CFG$ in Chomsky normal form$,$ then for any string $w\in L(G)$ of length $n\geq 1,$ exactly $2n − 1$ steps are required for any derivation of $w.$
answered
May 8, 2019
in
Theory of Computation

28
views
michaelsipser
theoryofcomputation
contextfreegrammars
cnf
proof
0
votes
36
Michael Sipser Edition 3 Exercise 2 Question 35 (Page No. 157)
Let $G$ be a $CFG$ in Chomsky normal form that contains $b$ variables$.$ Show that if $G$ generates some string with a derivation having at least $2^{b}$ steps$, L(G)$ is infinite$.$
answered
May 8, 2019
in
Theory of Computation

37
views
michaelsipser
theoryofcomputation
contextfreelanguages
cnf
proof
0
votes
37
Kenneth Rosen Edition 7th Exercise 2.3 Question 72 (Page No. 155)
Suppose that $f$ is a function from $A$ to $B$, where $A$ and $B$ are finite sets with $A=B$. Show that $f$ is onetoone if and only if it is onto.
answered
May 8, 2019
in
Set Theory & Algebra

40
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
38
Michael Sipser Edition 3 Exercise 0 Question 11 (Page No. 27)
Let $S(n) = 1 + 2 + · · · + n$ be the sum of the first $n$ natural numbers and let $C(n) = 1^{3} + 2^{3} + · · · + n^{3}$ be the sum of the first $n$ cubes. Prove the following equalities by induction on $n,$ ... $C(n)=\frac{1}{4}(n^{4}+2n^{3}+n^{2}=\frac{1}{4}n^{2}(n+1)^{2}.$
answered
May 8, 2019
in
Theory of Computation

25
views
michaelsipser
theoryofcomputation
proof
+1
vote
39
Michael Sipser Edition 3 Exercise 1 Question 11 (Page No. 85)
Prove that every $\text{NFA}$ can be converted to an equivalent one that has a single accept state.
answered
May 8, 2019
in
Theory of Computation

51
views
michaelsipser
theoryofcomputation
nfadfa
proof
+2
votes
40
GATE2016EC_2
answered
May 8, 2019
in
Numerical Ability

71
views
generalaptitude
numericalability
worktime
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