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Recent questions tagged cmi2015

5 votes
1 answer
1
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 $(b, c) ∈ R$, for every $a, b, c ∈ S$ ... $R$ is Euclidean, $(a, b) ∈ R$ and $(b, c) ∈ R$, then $(a, c) ∈ R$, for every $a, b, c ∈ S$ None of the above.
asked May 12, 2018 in Set Theory & Algebra Mk Utkarsh 271 views
2 votes
0 answers
2
A college prepares its timetable by grouping courses in slots A, B, C, . . . All courses in a slot meet at the same time, and courses in different slots have disjoint timings. Course registration has been completed and the administration now knows which ... courses with an overlapping audience. In this setting, the graph theoretic question to be answered is: Find a maximum size independent set.
asked May 29, 2016 in Graph Theory jothee 163 views
4 votes
0 answers
3
A college prepares its timetable by grouping courses in slots A, B, C, . . . All courses in a slot meet at the same time, and courses in different slots have disjoint timings. Course registration has been completed and the administration now knows which ... spanning tree with minimum number of edges. Find a minimal colouring. Find a minimum size vertex cover. Find a maximum size independent set
asked May 29, 2016 in Graph Theory jothee 243 views
3 votes
0 answers
4
A college prepares its timetable by grouping courses in slots A, B, C, . . . All courses in a slot meet at the same time, and courses in different slots have disjoint timings. Course registration has been completed and the administration now knows which ... pairs of courses with an overlapping audience. In this setting, the graph theoretic question to be answered is: Find a minimal colouring.
asked May 29, 2016 in Graph Theory jothee 219 views
3 votes
0 answers
5
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 along the ... if a single virus could possibly have produced the given sequence. Use dynamic programming, checking smaller subsequences before checking bigger subsequences.
asked May 27, 2016 in Algorithms jothee 164 views
4 votes
1 answer
6
Consider the code below, defining the functions $f$ and $g$: f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n == 0) return m; else { q = m div 10; r = m mod 10; return g(f(f(q, 0), r), n-1); } } How much time does it take to compute $f(m, n)$ and $g(m, n)$?
asked May 27, 2016 in Algorithms jothee 232 views
5 votes
1 answer
7
Consider the code below, defining the functions $f$ and $g$: f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n == 0) return m; else { q = m div 10; r = m mod 10; return g(f(f(q, 0), r), n-1); } } What does $g(m, n)$ compute, for nonnegative numbers $m$ and $n$?
asked May 27, 2016 in Algorithms jothee 121 views
2 votes
1 answer
8
Consider the code below, defining the functions $f$ and $g$: f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n == 0) return m; else { q = m div 10; r = m mod 10; return g(f(f(q, 0), r), n-1); } } Compute $g(3, 7), \: g(345, 1), \: g(345, 4) \text{ and } \: g(345, 0)$.
asked May 27, 2016 in Algorithms jothee 113 views
2 votes
0 answers
9
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 the ... change flights at most $k_1$ times. You can assume that the procedure can add or multiply two numbers in a single operation.
asked May 27, 2016 in Algorithms jothee 118 views
16 votes
1 answer
10
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].
asked May 27, 2016 in Algorithms jothee 637 views
2 votes
1 answer
11
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 ... If 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?
asked May 27, 2016 in Numerical Ability jothee 111 views
3 votes
1 answer
12
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?
asked May 27, 2016 in Numerical Ability jothee 101 views
2 votes
1 answer
13
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 $F_1$ ... friends. It is known that there are $k$ persons such that no pair among them is connected. What is the maximum number of friendships possible?
asked May 27, 2016 in Combinatory jothee 205 views
4 votes
2 answers
14
The school athletics coach has to choose $4$ students for the relay team. He calculates that there are $3876$ ways of choosing the team if the order in which the runners are placed is not considered. How many ways are there of choosing the team if the order of the runners is to be ... Between $12,000$ and $25,000$ Between $75,000$ and $99,999$ Between $30,000$ and $60,000$ More than $100,000$
asked May 27, 2016 in Combinatory jothee 208 views
12 votes
2 answers
15
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.
asked May 27, 2016 in Theory of Computation jothee 647 views
12 votes
4 answers
16
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; } } $40$ $41$ $42$ $43$
asked May 27, 2016 in Algorithms jothee 1.4k views
10 votes
2 answers
17
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 the die ... is the probability that you end up ordering a lime juice? $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$
asked May 27, 2016 in Probability jothee 500 views
7 votes
2 answers
18
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 we don't know whether there is a polynomial time algorithm for $B$, there cannot be a polynomial time algorithm for $A$.
asked May 27, 2016 in Algorithms jothee 491 views
15 votes
1 answer
19
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 $10$ ? $5$ $6$ $7$ $8$
asked May 27, 2016 in Graph Theory jothee 513 views
2 votes
0 answers
20
A college prepares its timetable by grouping courses in slots A, B, C, . . . All courses in a slot meet at the same time, and courses in different slots have disjoint timings. Course registration has been completed and the administration now knows which ... overlapping audience. In this setting, the graph theoretic question to be answered is: Find a spanning tree with minimum number of edges.
asked May 27, 2016 in Graph Theory jothee 168 views
3 votes
1 answer
21
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 an endpoint ... an endpoint of any blue coloured edge but is an endpoint of a green coloured edge and a red coloured edge. (A) and (C).
asked May 27, 2016 in Graph Theory jothee 196 views
5 votes
1 answer
22
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 $\text{TwinPrime}(n)$ be a predicate that is true if $n$ ... $\exists m \cdot \forall n \cdot \text{TwinPrime}(n) \text{ implies }n \leq m$
asked May 27, 2016 in Mathematical Logic jothee 316 views
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