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Answers by soujanyareddy13
0
votes
151
CMI2015-A-09
Let $L_1$ and $L_2$ be languages over an alphabet $\Sigma$ such that $L_1 \subseteq L_2$. Which of the following is true: If $L_2$ is regular, then $L_1$ must also be regular. If $L_1$ is regular, then $L_2$ must also be regular. Either both $L_1$ and $L_2$ are regular, or both are not regular. None of the above.
answered
in
Theory of Computation
May 6, 2021
944
views
cmi2015
theory-of-computation
regular-language
1
vote
152
CMI2015-A-08
How many times is the comparison $i \geq n$ performed in the following program? int i=85, n=5; main() { while (i >= n) { i=i-1; n=n+1; } } $40$ $41$ $42$ $43$
answered
in
Algorithms
May 6, 2021
4.3k
views
cmi2015
algorithms
time-complexity
0
votes
153
CMI2015-A-07
You arrive at a snack bar and you can't decide whether to order a lime juice or a lassi. You decide to throw a fair $6$-sided die to make the choice, as follows. If you throw $2$ or $6$ you order a lime juice. If you throw a $4$, you order a lassi. Otherwise, you throw ... is the probability that you end up ordering a lime juice? $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$
answered
in
Probability
May 6, 2021
927
views
cmi2015
probability
0
votes
154
CMI2015-A-06
Suppose we have constructed a polynomial time reduction from problem $A$ to problem $B$. Which of the following can we infer from this fact? If the best algorithm for $B$ takes exponential time, there is no polynomial time algorithm for $A$. If the best ... we don't know whether there is a polynomial time algorithm for $B$, there cannot be a polynomial time algorithm for $A$.
answered
in
Algorithms
May 6, 2021
1.4k
views
cmi2015
algorithms
p-np-npc-nph
0
votes
155
CMI2015-A-05
An undirected graph has $10$ vertices labelled $1, 2,\dots , 10$ and $37$ edges. Vertices $1, 3, 5, 7, 9$ have degree $8$ and vertices $2, 4, 6, 8$ have degree $7.$ What is the degree of vertex $10$ ? $5$ $6$ $7$ $8$
answered
in
Graph Theory
May 6, 2021
1.5k
views
cmi2015
graph-theory
degree-of-graph
easy
0
votes
156
CMI2015-A-03
Suppose each edge of an undirected graph is coloured using one of three colours - red, blue or green. Consider the following property of such graphs: if any vertex is the endpoint of a red coloured edge, then it is either an endpoint of a blue coloured edge or not ... endpoint of any blue coloured edge but is an endpoint of a green coloured edge and a red coloured edge. (A) and (C).
answered
in
Graph Theory
May 6, 2021
413
views
cmi2015
graph-theory
graph-coloring
0
votes
157
CMI2015-A-02
A binary relation $R ⊆ (S S)$ is said to be Euclidean if for every $a, b, c ∈ S, (a, b) ∈ R$ and $(a, c) ∈ R$ implies $(b, c) ∈ R$. Which of the following statements is valid? If $R$ is Euclidean, $(b, a) ∈ R$ and $(c, a) ∈ R$, then $(b, c) ∈ R$ ... $R$ is Euclidean, $(a, b) ∈ R$ and $(b, c) ∈ R$, then $(a, c) ∈ R$, for every $a, b, c ∈ S$ None of the above.
answered
in
Set Theory & Algebra
May 6, 2021
654
views
cmi2015
relations
set-theory&algebra
1
vote
158
CMI2015-A-01
Twin primes are pairs of numbers $p$ and $p+2$ such that both are primes-for instance, $5$ and $7$, $11$ and $13$, $41$ and $43$. The Twin Prime Conjecture says that there are infinitely many twin primes. Let $\text{TwinPrime}(n)$ ... $\exists m \cdot \forall n \cdot \text{TwinPrime}(n) \text{ implies }n \leq m$
answered
in
Mathematical Logic
May 6, 2021
847
views
cmi2015
mathematical-logic
first-order-logic
0
votes
159
CMI2015-B-07
There is a thin, long and hollow fibre with a virus in the centre. The virus occasionally becomes active and secretes some side products. The fibre is so thin that new side products secreted by the virus push the old products ... a single virus could possibly have produced the given sequence. Use dynamic programming, checking smaller subsequences before checking bigger subsequences.
answered
in
Algorithms
May 6, 2021
329
views
cmi2015
descriptive
algorithms
dynamic-programming
0
votes
160
CMI2015-B-05
An airline runs flights between several cities of the world. Every flight connects two cities. A millionaire wants to travel from Chennai to Timbuktu by changing at most $k_1$ flights. Being a millionaire with plenty of time and money, he does not mind revisiting ... flights at most $k_1$ times. You can assume that the procedure can add or multiply two numbers in a single operation.
answered
in
Algorithms
May 6, 2021
309
views
cmi2015
descriptive
algorithms
algorithm-design
0
votes
161
CMI2015-B-04
You are given $n$ positive integers, $d_1, d_2 \dots d_n$, each greater than $0$. Design a greedy algorithm to test whether these integers correspond to the degrees of some $n$-vertex simple undirected graph $G = (V, E)$. [A simple graph has no self-loops and at most one edge between any pair of vertices].
answered
in
Algorithms
May 6, 2021
1.1k
views
cmi2015
descriptive
algorithms
greedy-algorithm
0
votes
162
CMI2015-B-03b
A cook has a kitchen at the top of a hill, where she can prepare rotis. Each roti costs one rupee to prepare. She can sell rotis for two rupees a piece at a stall down the hill. Once she goes down the steep hill, she can not climb back in time make more ... she starts at the top with $P$ paans and $1$ rupee, what is the minimum and maximum amount of money she can have at the end?
answered
in
Quantitative Aptitude
May 6, 2021
313
views
cmi2015
descriptive
quantitative-aptitude
0
votes
163
CMI2015-B-03a
A cook has a kitchen at the top of a hill, where she can prepare rotis. Each roti costs one rupee to prepare. She can sell rotis for two rupees a piece at a stall down the hill. Once she goes down the steep hill, she can not climb back in time make more rotis. Suppose the cook starts at the top with $R$ rupees. What are all the possible amounts of money she can have at the end?
answered
in
Quantitative Aptitude
May 6, 2021
283
views
cmi2015
quantitative-aptitude
descriptive
0
votes
164
CMI2015-B-02
Consider a social network with $n$ persons. Two persons $A$ and $B$ are said to be connected if either they are friends or they are related through a sequence of friends: that is, there exists a set of persons $F_1, \dots, F_m$ such that $A$ and ... . It is known that there are $k$ persons such that no pair among them is connected. What is the maximum number of friendships possible?
answered
in
Combinatory
May 6, 2021
438
views
descriptive
cmi2015
combinatory
0
votes
165
CMI2016-B-7b
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Give a constant time algorithm that computes $M(n)$ on input $n$. (A constant-time algorithm is one whose running time is independent of the input $n$)
answered
in
Calculus
May 6, 2021
220
views
cmi2016
calculus
functions
descriptive
0
votes
166
CMI2016-B-6
An automatic spelling checker works as follows. Given a word $w$, first check if $w$ is found in the dictionary. If $w$ is not in the dictionary, compute a dictionary entry that is close to $w$. For instance if the user types $\mathsf{ocurrance}$, the spelling checker ... alignments of $x$ and $y$. What is the running time of your algorithm (in terms of the lengths of $x$ and $y)?$
answered
in
Algorithms
May 6, 2021
496
views
cmi2016
dynamic-programming
algorithm-design
descriptive
0
votes
167
CMI2016-B-5
For a string $x=a_0a_1 \ldots a_{n-1}$ over the alphabet $\{0, 1, 2\}$, define $val(x)$ to be the value of $x$ interpreted as a ternary number, where $a_0$ is the most significant digit. More formally, $val(x)$ ... $ x \in \{0, 1, 2\}^*$ such that $val(x)$ is divisible by 4.
answered
in
Theory of Computation
May 6, 2021
307
views
cmi2016
descriptive
finite-automata
0
votes
168
CMI2016-B-4
Let $\Sigma = \{0, 1\}$. Let $A, \: B$ be arbitrary subsets of $\Sigma^\ast$. We define the following operations on such sets: $ A+B := \{ w \in \Sigma^\ast \mid w \in A \text{ or } w \in B \}$ ... $A$ and $B$? If yes, give a proof. If not, provide suitable $A$ and $B$ for which this equation fails.
answered
in
Theory of Computation
May 6, 2021
267
views
cmi2016
closure-property
proof
descriptive
0
votes
169
CMI2016-B-3
An undirected graph can be converted into a directed graph by choosing a direction for every edge. Here is an example: Show that for every undirected graph, there is a way of choosing directions for its edges so that the resulting directed graph has no directed cycles.
answered
in
Graph Theory
May 6, 2021
521
views
cmi2016
descriptive
graph-theory
graph-connectivity
0
votes
170
CMI2016-B-1
A group of war prisoners are trying to escape from a prison. They have thoroughly planned the escape from the prison itself, and after that they hope to find shelter in a nearby village. However, the village (marked as $B$, see picture below) and the ... and assuming that soldiers do not change their locations ($Hint$: Model this as a graph, with soldiers represented by the vertices.)
answered
in
Algorithms
May 6, 2021
713
views
cmi2016
algorithms
descriptive
algorithm-design
0
votes
171
CMI2016-A-9
ScamTel has won a state government contract to connect $17$ cities by high-speed fibre optic links. Each link will connect a pair of cities so that the entire network is connected-there is a path from each city to every other city. The contract requires the network to remain ... $34$ $32$ $17$ $16$
answered
in
Graph Theory
May 6, 2021
640
views
cmi2016
graph-theory
graph-connectivity
0
votes
172
CMI2016-A-8
An advertisement for a tennis magazine states, "If I'm not playing tennis, I'm watching tennis. And If I'm not watching tennis, I'm reading about tennis." We can assume that the speaker can do at most one of these activities at a time. What is the speaker doing? Playing tennis Watching tennis Reading about tennis None of the above
answered
in
Analytical Aptitude
May 6, 2021
560
views
cmi2016
logical-reasoning
conjunction
0
votes
173
CMI2016-A-7
Varsha lives alone and dislikes cooking, so she goes out for dinner every evening. She has two favourite restaurants, $\text{Dosa Paradise}$ and $\text{Kababs Unlimited}$, to which she travels by local train. The train to $\text{Dosa Paradise}$ runs every $10$ ... up eating in $\text{Kababs Unlimited}$? $\frac{1}{5}$ $\frac{1}{3}$ $\frac{2}{5}$ $\frac{1}{2}$
answered
in
Probability
May 6, 2021
456
views
cmi2016
conditional-probability
random-variable
0
votes
174
CMI2016-A-6
In the code fragment given below, $\mathsf{start}$ and $\mathsf{end}$ are integer values and $\mathsf{prime(x)}$ is a function that returns $\mathsf{true}$ if $\mathsf{x}$ is a prime number and $\mathsf{false}$ otherwise. i:=0; j:=0; k:=0; from (m := start; m <= end; m := m ... At the end of the loop: $k == i-j.$ $k == j-i.$ $k == -j-i.$ Depends on $\mathsf{start}$ and $\mathsf{end}$
answered
in
Programming
May 6, 2021
391
views
cmi2016
identify-function
0
votes
175
CMI2016-A-5
A dodecahedron is a regular solid with $12$ faces, each face being a regular pentagon. How many edges are there? And how many vertices? $60$ edges and $20$ vertices $30$ edges and $20$ vertices $60$ edges and $50$ vertices $30$ edges and $50$ vertices
answered
in
Graph Theory
May 6, 2021
285
views
cmi2016
graph-theory
undirected-graph
regular-pentagon
0
votes
176
CMI2016-A-4
Consider a weighted undirected graph $G$ with positive edge weights. Let $(u, v)$ be an edge in the graph. It is known that the shortest path from a vertex $s$ to $u$ has weight $53$ and the shortest path from $s$ to $v$ has weight $65.$ Which of the statements is always true? ... $(u, v) = 12$ Weight of $(u, v) \geq 12$ Nothing can be said about the weight of $(u, v)$
answered
in
Graph Theory
May 6, 2021
538
views
cmi2016
graph-theory
shortest-path
0
votes
177
CMI2016-A-3
For a regular expression $e$, let $L(e)$ be the language generated by $e$. If $e$ is an expression that has no Kleene star $\ast$ occurring in it, which of the following is true about $e$ in general? $L(e)$ is empty $L(e)$ is finite Complement of $L(e)$ is empty Both $L(e)$ and its complement are infinite
answered
in
Theory of Computation
May 6, 2021
459
views
cmi2016
regular-language
regular-expression
closure-property
0
votes
178
CMI2016-A-2
The symbol $\mid$ reads as "divides", and $\nmid$ as "does not divide". For instance, $2 \: \mid \:6$ and $2 \: \nmid \: 5$ are both true. Consider the following statements. There exists a positive integer $a$ ... . What can you say about these statements? Only i is true Only ii is true Both i and ii are true Neither i nor ii is true
answered
in
Quantitative Aptitude
May 6, 2021
301
views
cmi2016
quantitative-aptitude
number-system
0
votes
179
CMI2016-A-1
In a connected undirected graph, the distance between two vertices is the number of edges in the shortest path between them. Suppose we denote bt $P$ the following property: there exists a vertex that is a neighbour of all other vertices. Consider the following statements: If ... say about these statements? Only i is true Only ii is true Both i and ii are true Neither i nor ii is true
answered
in
Graph Theory
May 6, 2021
724
views
cmi2016
graph-theory
shortest-path
0
votes
180
CMI2017-B-7
Consider the following function that takes as input a sequence $A$ of integers with n elements,$A[1],A[2], \dots ,A[n]$ and an integer $k$ and returns an integer value. The function length$(S)$ returns the length of the sequence $S$. Comments ... complexity of this algorithm in terms of the length of the input sequence $A$? Give an example of a worst-case input for this algorithm.
answered
in
Algorithms
May 6, 2021
954
views
cmi2017
algorithms
time-complexity
descriptive
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