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Recent questions tagged cmi2016
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CMI2016B7ai
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(101)$
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Dec 31, 2016
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Calculus
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jothee
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cmi2016
calculus
functions
descriptive
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2
CMI2016B7b
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Give a constant time algorithm that computes $M(n)$ on input $n$. (A constanttime algorithm is one whose running time is independent of the input $n$)
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Dec 31, 2016
in
Calculus
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jothee
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cmi2016
calculus
functions
descriptive
0
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1
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3
CMI2016B7aiii
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(87)$
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Dec 31, 2016
in
Calculus
by
jothee
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51
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cmi2016
calculus
functions
descriptive
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2
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4
CMI2016B7aii
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(99)$
asked
Dec 31, 2016
in
Calculus
by
jothee
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105k
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69
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cmi2016
calculus
functions
descriptive
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1
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5
CMI2016B6
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 $y)?$
asked
Dec 31, 2016
in
Algorithms
by
jothee
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105k
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73
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cmi2016
dynamicprogramming
algorithmdesign
descriptive
0
votes
2
answers
6
CMI2016B5
For a string $x=a_0a_1 \ldots a_{n1}$ 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.
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Dec 30, 2016
in
Theory of Computation
by
jothee
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cmi2016
descriptive
finiteautomata
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0
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7
CMI2016B4
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.
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Dec 30, 2016
in
Theory of Computation
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jothee
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35
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cmi2016
closureproperty
proof
descriptive
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1
answer
8
CMI2016B3
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.
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Dec 30, 2016
in
Graph Theory
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jothee
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cmi2016
descriptive
graphtheory
graphconnectivity
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9
CMI2016B2b
A $\textit{simple path}$ (respectively cycle) in a graph is a path (respectively cycle) in which no edge or vertex is repeated. The $length$ of such a path (respectively cycle) is the number of edges in the path (respectively cycle). Let $G$ be an undirected graph with minimum degree $k \geq 2$. Show that $G$ contains a simple cycle of length at least $k+1$.
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Dec 30, 2016
in
Graph Theory
by
jothee
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105k
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cmi2016
graphtheory
graphconnectivity
descriptive
+1
vote
1
answer
10
CMI2016B2a
A $\textit{simple path}$ (respectively cycle) in a graph is a path (respectively cycle) in which no edge or vertex is repeated. The $\textit{length}$ of such a path (respectively cycle) is the number of edges in the path (respectively cycle). Let $G$ be an undirected graph with minimum degree $k \geq 2$. Show that $G$ contains a simple path of length at least $k$.
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Dec 30, 2016
in
Graph Theory
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jothee
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cmi2016
graphtheory
descriptive
graphconnectivity
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0
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11
CMI2016B1
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.)
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Dec 30, 2016
in
Algorithms
by
jothee
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286
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cmi2016
algorithms
descriptive
algorithmdesign
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vote
1
answer
12
CMI2016A10
Which of the following relationships holds in general between the $\text{scope}$ of a variable and the $\text{lifetime}$ of a variable (in a language like C or Java)? The scope of a variable is contained in the lifetime of the variable The scope of a variable is same as the lifetime of the variable The lifetime of a variable is disjoint from the scope of the variable None of the above
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Dec 30, 2016
in
Programming
by
jothee
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cmi2016
programminginc
scopingrule
lifetime
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vote
1
answer
13
CMI2016A9
ScamTel has won a state government contract to connect $17$ cities by highspeed fibre optic links. Each link will connect a pair of cities so that the entire network is connectedthere is a path from each city to every other city. The contract requires the network to remain ... $34$ $32$ $17$ $16$
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Dec 30, 2016
in
Graph Theory
by
jothee
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105k
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62
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cmi2016
graphtheory
graphconnectivity
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vote
1
answer
14
CMI2016A8
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
asked
Dec 30, 2016
in
Numerical Ability
by
jothee
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105k
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86
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cmi2016
logicalreasoning
conjunction
0
votes
1
answer
15
CMI2016A7
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 $\text{Kababs Unlimited}$? $\frac{1}{5}$ $\frac{1}{3}$ $\frac{2}{5}$ $\frac{1}{2}$
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Dec 30, 2016
in
Probability
by
jothee
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105k
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100
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cmi2016
conditionalprobability
randomvariable
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1
answer
16
CMI2016A6
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: $k == ij.$ $k == ji.$ $k == ji.$ Depends on $\mathsf{start}$ and $\mathsf{end}$
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Dec 30, 2016
in
Programming
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jothee
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105k
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46
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cmi2016
identifyfunction
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1
answer
17
CMI2016A5
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
asked
Dec 30, 2016
in
Graph Theory
by
jothee
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105k
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45
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cmi2016
graphtheory
undirectedgraph
regularpentagon
faces
0
votes
1
answer
18
CMI2016A4
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 $(u, v)$
asked
Dec 30, 2016
in
Graph Theory
by
jothee
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105k
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99
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cmi2016
graphtheory
shortestpath
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vote
1
answer
19
CMI2016A3
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
asked
Dec 30, 2016
in
Theory of Computation
by
jothee
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105k
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73
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cmi2016
regularlanguages
regularexpressions
closureproperty
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vote
1
answer
20
CMI2016A2
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
asked
Dec 30, 2016
in
Numerical Ability
by
jothee
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105k
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63
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cmi2016
numericalability
numbersystem
+1
vote
1
answer
21
CMI2016A1
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
asked
Dec 30, 2016
in
Graph Theory
by
jothee
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105k
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109
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cmi2016
graphtheory
shortestpath
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