Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Recent questions tagged cmi2016
1
votes
2
answers
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(...
go_editor
527
views
go_editor
asked
Dec 31, 2016
Calculus
cmi2016
calculus
functions
descriptive
+
–
1
votes
1
answer
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 algor...
go_editor
386
views
go_editor
asked
Dec 31, 2016
Calculus
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(...
go_editor
488
views
go_editor
asked
Dec 31, 2016
Calculus
cmi2016
calculus
functions
descriptive
+
–
2
votes
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(...
go_editor
469
views
go_editor
asked
Dec 31, 2016
Calculus
cmi2016
calculus
functions
descriptive
+
–
1
votes
2
answers
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 ent...
go_editor
809
views
go_editor
asked
Dec 31, 2016
Algorithms
cmi2016
dynamic-programming
algorithm-design
descriptive
+
–
0
votes
3
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 si...
go_editor
502
views
go_editor
asked
Dec 30, 2016
Theory of Computation
cmi2016
descriptive
finite-automata
+
–
1
votes
2
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...
go_editor
530
views
go_editor
asked
Dec 30, 2016
Theory of Computation
cmi2016
closure-property
proof
descriptive
+
–
1
votes
2
answers
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...
go_editor
782
views
go_editor
asked
Dec 30, 2016
Graph Theory
cmi2016
descriptive
graph-theory
graph-connectivity
+
–
1
votes
1
answer
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 ...
go_editor
474
views
go_editor
asked
Dec 30, 2016
Graph Theory
cmi2016
graph-theory
graph-connectivity
descriptive
+
–
1
votes
2
answers
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 (resp...
go_editor
525
views
go_editor
asked
Dec 30, 2016
Graph Theory
cmi2016
graph-theory
descriptive
graph-connectivity
+
–
1
votes
1
answer
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...
go_editor
1.1k
views
go_editor
asked
Dec 30, 2016
Algorithms
cmi2016
algorithms
descriptive
algorithm-design
+
–
2
votes
2
answers
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 ...
go_editor
1.2k
views
go_editor
asked
Dec 30, 2016
Programming in C
cmi2016
programming-in-c
scoping-rule
lifetime
+
–
1
votes
2
answers
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 ...
go_editor
919
views
go_editor
asked
Dec 30, 2016
Graph Theory
cmi2016
graph-theory
graph-connectivity
+
–
1
votes
2
answers
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 t...
go_editor
981
views
go_editor
asked
Dec 30, 2016
Analytical Aptitude
cmi2016
logical-reasoning
conjunction
+
–
4
votes
2
answers
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 $\text{Kababs Unlimited}$...
go_editor
730
views
go_editor
asked
Dec 30, 2016
Probability
cmi2016
conditional-probability
random-variable
+
–
2
votes
3
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}...
go_editor
629
views
go_editor
asked
Dec 30, 2016
Programming in C
cmi2016
identify-function
+
–
1
votes
2
answers
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$30$ ed...
go_editor
581
views
go_editor
asked
Dec 30, 2016
Graph Theory
cmi2016
graph-theory
undirected-graph
regular-pentagon
+
–
0
votes
2
answers
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...
go_editor
873
views
go_editor
asked
Dec 30, 2016
Graph Theory
cmi2016
graph-theory
shortest-path
+
–
2
votes
2
answers
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 ...
go_editor
865
views
go_editor
asked
Dec 30, 2016
Theory of Computation
cmi2016
regular-language
regular-expression
closure-property
+
–
1
votes
2
answers
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 statemen...
go_editor
488
views
go_editor
asked
Dec 30, 2016
Quantitative Aptitude
cmi2016
quantitative-aptitude
number-system
+
–
1
votes
2
answers
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 proper...
go_editor
1.1k
views
go_editor
asked
Dec 30, 2016
Graph Theory
cmi2016
graph-theory
shortest-path
+
–
To see more, click for the
full list of questions
or
popular tags
.
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register