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Recent questions tagged cmi2016
1
vote
1
answer
1
CMI2016-B-7ai
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(101)$
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(101)$
asked
Dec 31, 2016
in
Calculus
jothee
124
views
cmi2016
calculus
functions
descriptive
1
vote
0
answers
2
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 $n$)
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 $n$)
asked
Dec 31, 2016
in
Calculus
jothee
89
views
cmi2016
calculus
functions
descriptive
0
votes
1
answer
3
CMI2016-B-7aiii
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(87)$
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(87)$
asked
Dec 31, 2016
in
Calculus
jothee
120
views
cmi2016
calculus
functions
descriptive
1
vote
2
answers
4
CMI2016-B-7aii
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(99)$
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(99)$
asked
Dec 31, 2016
in
Calculus
jothee
114
views
cmi2016
calculus
functions
descriptive
1
vote
1
answer
5
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 $y)?$
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 should ... all 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
jothee
239
views
cmi2016
dynamic-programming
algorithm-design
descriptive
0
votes
2
answers
6
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.
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, $val(x)$ is given by $ \Sigma_{0 \leq i < n} 3^{n-1-i} \cdot a_i.$ Design a finite automaton that accepts exactly the set of strings $ x \in \{0, 1, 2\}^*$ such that $val(x)$ is divisible by 4.
asked
Dec 30, 2016
in
Theory of Computation
jothee
138
views
cmi2016
descriptive
finite-automata
1
vote
0
answers
7
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.
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.
asked
Dec 30, 2016
in
Theory of Computation
jothee
110
views
cmi2016
closure-property
proof
descriptive
1
vote
1
answer
8
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.
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.
asked
Dec 30, 2016
in
Graph Theory
jothee
301
views
cmi2016
descriptive
graph-theory
graph-connectivity
1
vote
0
answers
9
CMI2016-B-2b
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 $k+1$.
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 $k+1$.
asked
Dec 30, 2016
in
Graph Theory
jothee
106
views
cmi2016
graph-theory
graph-connectivity
descriptive
1
vote
1
answer
10
CMI2016-B-2a
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 $k$.
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 $k$.
asked
Dec 30, 2016
in
Graph Theory
jothee
132
views
cmi2016
graph-theory
descriptive
graph-connectivity
1
vote
0
answers
11
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.)
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 prison ... , and assuming that soldiers do not change their locations ($Hint$: Model this as a graph, with soldiers represented by the vertices.)
asked
Dec 30, 2016
in
Algorithms
jothee
498
views
cmi2016
algorithms
descriptive
algorithm-design
2
votes
1
answer
12
CMI2016-A-10
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
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
asked
Dec 30, 2016
in
Programming
jothee
189
views
cmi2016
programming-in-c
scoping-rule
lifetime
1
vote
1
answer
13
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 ... $34$ $32$ $17$ $16$
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 connected if $any$ single link fails. What is the minimum number of links that ScamTel needs to set up? $34$ $32$ $17$ $16$
asked
Dec 30, 2016
in
Graph Theory
jothee
264
views
cmi2016
graph-theory
graph-connectivity
1
vote
1
answer
14
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
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
Quantitative Aptitude
jothee
194
views
cmi2016
logical-reasoning
conjunction
2
votes
1
answer
15
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 $\text{Kababs Unlimited}$? $\frac{1}{5}$ $\frac{1}{3}$ $\frac{2}{5}$ $\frac{1}{2}$
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 $10$ minutes, at $0, 10, 20, 30, 40$ ... ends up eating in $\text{Kababs Unlimited}$? $\frac{1}{5}$ $\frac{1}{3}$ $\frac{2}{5}$ $\frac{1}{2}$
asked
Dec 30, 2016
in
Probability
jothee
222
views
cmi2016
conditional-probability
random-variable
2
votes
2
answers
16
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 $\mathsf{end}$
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+1){ if ( ... } } At the end of the loop: $k == i-j.$ $k == j-i.$ $k == -j-i.$ Depends on $\mathsf{start}$ and $\mathsf{end}$
asked
Dec 30, 2016
in
Programming
jothee
153
views
cmi2016
identify-function
1
vote
1
answer
17
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
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
jothee
119
views
cmi2016
graph-theory
undirected-graph
regular-pentagon
0
votes
1
answer
18
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 $(u, v)$
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? Weight ... $(u, v) = 12$ Weight of $(u, v) \geq 12$ Nothing can be said about the weight of $(u, v)$
asked
Dec 30, 2016
in
Graph Theory
jothee
254
views
cmi2016
graph-theory
shortest-path
2
votes
1
answer
19
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
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
jothee
189
views
cmi2016
regular-languages
regular-expressions
closure-property
1
vote
1
answer
20
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
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 $a$ such that $(2 \mid (a^3 -1))$ and $( 2 \mid a)$. ... . 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
Quantitative Aptitude
jothee
142
views
cmi2016
numerical-ability
number-system
1
vote
1
answer
21
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
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 $P$ ... 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
Graph Theory
jothee
254
views
cmi2016
graph-theory
shortest-path
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