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6
answers
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? $199$ $683$ $1365$ $3^{10}2^{10}$ $3^{10}$
commented
Oct 15
in
Combinatory

545
views
tifr2019
engineeringmathematics
discretemathematics
permutationandcombination
medium
1
answer
2
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 $\binom{n}{m}/n^m\\$ $\binom{n}{m}/m^n\\$ $\binom{m+n1}{m1}/n^m\\$ $\binom{m+n1}{m}/m^n$
commented
Jun 29
in
Probability

96
views
isi2018mma
engineeringmathematics
probability
1
answer
3
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
in
Algorithms

11
views
cormen
algorithms
algorithmdesigntechniques
descriptive
difficult
1
answer
4
A FIRST COURSE IN PROBABILITY (SHELDON ROSS),CHAPTER 4 RANDOM VARIABLES, QUESTION#43
answered
Jun 26
in
Probability

94
views
probability
sheldonross
randomvariable
1
answer
5
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 ?
commented
Jun 15
in
Theory of Computation

57
views
theoryofcomputation
pumpinglemma
1
answer
6
GATE199012b
Consider the following problem. Given $n$ positive integers $a_{1}, a_{2}\dots a_n,$ it is required to partition them in to two parts $A$ and $B$ such that $\sum_{i \in A} a_{i}  \sum_{i \in B} a_{i}$ is minimised Consider a greedy ... in that part whose sum in smaller at that step. Give an example with $n=5$ for which the solution produced by the greedy algorithm is not optimal.
commented
Jun 14
in
Algorithms

203
views
gate1990
descriptive
algorithms
algorithmdesigntechniques
1
answer
7
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
in
Databases

143
views
gate1988
normal
descriptive
databases
functionaldependencies
1
answer
8
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
in
Verbal Ability

146
views
goclassroom
verbalability
3
answers
9
Self doubt DIGITAL LOGIC
Is Y' + Z' same as (YZ)' ? Please explain this concept of compliments..!!
answered
Jun 11
in
Digital Logic

74
views
1
answer
10
TIFR2012A4
Let $\text{ABC}$ be a triangle with $\text{n} $ distinct points inside. A triangulation of $\text{ABC}$ with respect to the $\text{n}$ ... $n$ points inside it? $3n  1$ $n^{2} + 1$ $n + 3$ $2n + 1$ $4n  3$
commented
Jun 11
in
Numerical Ability

267
views
tifr2012
numericalability
geometry
2
answers
11
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
in
Numerical Ability

316
views
tifr2011
numericalability
complexnumber
1
answer
12
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
in
Theory of Computation

51
views
theoryofcomputation
contextfreelanguage
selfdoubt
2
answers
13
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
in
Algorithms

119
views
kruskalsalgorithm
graphalgorithms
greedyalgorithm
datastructure
4
answers
14
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 $1$ $4$ $5$ $6$
commented
Jun 7
in
Numerical Ability

129
views
gate2017ce2
speedtimedistance
numericalability
4
answers
15
Nfa dfa toc ace 1
commented
Jun 6
in
Theory of Computation

90
views
1
answer
16
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
answer edited
Jun 4
in
Numerical Ability

46
views
1
answer
17
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??
commented
Jun 2
in
Algorithms

71
views
graphtheory
algorithms
0
answers
18
#Rosen exercise1 ,question71 counting
use mathematical induction to prove the sum rule for m tasks from the sum rule for two tasks.
commented
Jun 2
in
Combinatory

40
views
counting
2
answers
19
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?
commented
Jun 2
in
Algorithms

158
views
madeeasytestseries
algorithms
0
answers
20
Descrete Mathematic ACE Text Book Practice Question #16
A women's health clinic has four doctors and each patient is assigned to one of them. If a patient givs birth btween 8 am and 4 pm, then her chance of being attended by her assigned doctor is 3/4, otherwise it is 1/4. What is the probability that ... is attended by the assigned doctor when she gives birth? (A) 25/144 (B) 5/12 (C) 7/12 (D) 1/12
commented
May 30
in
Mathematical Logic

74
views
probability
acebooklet
1
answer
21
GATE2015 EC1: GA8
Fill in the missing value
answered
May 28
in
Numerical Ability

182
views
gate2015ec1
generalaptitude
numericalability
sequenceseries
1
answer
22
Probability question of CLRS
In a restaurant each of $n$ customer gives a hat to the hat check person. The hat check person gives the hat back to the customer in a random order. What is expected number of customer who get back their own hat?
commented
May 27
in
Probability

112
views
algorithms
probability
2
answers
23
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
in
Digital Logic

211
views
gatebook
digitallogic
booleanalgebra
3
answers
24
Self DoubtCombinatory
In how many ways we can put $n$ distinct balls in $k$ dintinct bins?? Will it be $n^{k}$ or $k^{n}$?? Taking example will be easy way to remove this doubt or some other ways possible??
commented
May 25
in
Combinatory

103
views
discretemathematics
permutationandcombination
1
answer
25
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$ × $50^5$
commented
May 23
in
Theory of Computation

87
views
theoryofcomputation
numberofdfa
1
answer
26
self doubt: TOC
is union of regular language and context free language always regular?
answered
May 22
in
Theory of Computation

54
views
theoryofcomputation
regularlanguages
contextfreelanguage
1
answer
27
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 .
commented
May 20
in
Set Theory & Algebra

37
views
#discrete
#lattice
0
answers
28
Recurrence RelationSelf Doubt(Discrete Math+Algo)
Let $A(n)$ denotes the number of $n$ bit binary strings which have no pair of consecutive $1’s.$ what will be recurrence relation for it and what will be it’s Time Complexity??
commented
May 20
in
Algorithms

71
views
discretemathematics
recurrenceeqation
algorithms
4
answers
29
GATE2011 AG: GA10
The horse has played a little known but very important role in the field of medicine. Horses were injected with toxins of diseases until their blood built up immunities. Then a serum was made from their blood. Serums to fight with ... that horses were given immunity to diseases generally quite immune to diseases given medicines to fight toxins given diphtheria and tetanus serums
commented
May 15
in
Verbal Ability

128
views
generalaptitude
verbalability
gate2011ag
passagereading
2
answers
30
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
in
Verbal Ability

69
views
generalaptitude
verbalability
gate2011ag
mostappropriateword
1
answer
31
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
in
Verbal Ability

55
views
generalaptitude
verbalability
gate2010tf
mostappropriateword
1
answer
32
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.
commented
May 14
in
Algorithms

46
views
isi2018pcbcs
algorithms
recurrenceeqation
descriptive
3
answers
33
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
in
Numerical Ability

102
views
generalaptitude
numericalability
gate2010tf
numberseries
2
answers
34
#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
in
Combinatory

50
views
probability
1
answer
35
self doubt dfa
Given an algorithm to tell whether a regular language L contains at least 100 strings
commented
May 13
in
Theory of Computation

52
views
theoryofcomputation
1
answer
36
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
in
Set Theory & Algebra

29
views
isi2018pcbcs
engineeringmathematics
discretemathematics
settheory&algebra
functions
descriptive
1
answer
37
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 $S$.
answer edited
May 12
in
Set Theory & Algebra

30
views
isi2018pcba
engineeringmathematics
discretemathematics
settheory&algebra
descriptive
1
answer
38
ISI2018MMA27
Number of real solutions of the equation $x^7 + 2x^5 + 3x^3 + 4x = 2018$ is $1$ $3$ $5$ $7$
answered
May 11
in
Numerical Ability

44
views
isi2018mma
generalaptitude
numericalability
1
answer
39
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
in
Numerical Ability

17
views
isi2018mma
generalaptitude
numericalability
1
answer
40
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
in
Numerical Ability

54
views
isi2018mma
generalaptitude
numericalability
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