Recent questions tagged cmi2014 / GATE Overflow for GATE CSE

3 votes

2 answers

1

CMI2014-B-07c
Consider the code below, defining the function $A$: A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if (n == 0) return m; else return A(m, A(m,n-1,p), p-1); } Compute $A(2, 2, 3)$ and $A(2, 3, 3)$.

Consider the code below, defining the function $A$:A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if ...

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635 views

go_editor asked May 27, 2016

3 votes

2 answers

2

CMI2014-B-07b
Consider the code below, defining the function $A$: A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if (n == 0) return m; else return A(m, A(m,n-1,p), p-1); } Express $A(m, n, 2)$ as a function of $m$ and $n$.

Consider the code below, defining the function $A$:A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if ...

go_editor

646 views

go_editor asked May 27, 2016

3 votes

2 answers

3

CMI2014-B-07a
Consider the code below, defining the function $A$: A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if (n == 0) return m; else return A(m, A(m,n-1,p), p-1); } Express $A(m, n, 1)$ as a function of $m$ and $n$.

Consider the code below, defining the function $A$:A(m, n, p) { if (p == 0) return m+n; else if (n == 0 && p == 1) return 0; else if (n == 0 && p == 2) return 1; else if ...

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661 views

go_editor asked May 27, 2016

2 votes

2 answers

4

CMI2014-B-06b
Let $A$ be array of $n$ integers that is not assumed to be sorted. You are given a number $x$. The aim is to find out if there are indices $k,\: l$ and $m$ such that $A[k] + A[l] + A[m] = x$. Design an algorithm for this problem that works in time $O(n^2)$.

Let $A$ be array of $n$ integers that is not assumed to be sorted. You are given a number $x$. The aim is to find out if there are indices $k,\: l$ and $m$ such that $A[...

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443 views

go_editor asked May 27, 2016

2 votes

1 answer

5

CMI2014-B-06a
Let $A$ be an array of $n$ integers, sorted so that $A[1] \leq A[2] \leq \dots \leq A[n]$. You are given a number $x$x. The aim is to find out if there are indices $k$ and $l$ such that $A[k] + A[l] = x$. Design an algorithm for this problem that works in time $O(n)$.

Let $A$ be an array of $n$ integers, sorted so that $A \leq A \leq \dots \leq A[n]$. You are given a number $x$x. The aim is to find out if there are indices $k$ and $l...

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435 views

go_editor asked May 27, 2016

2 votes

1 answer

6

CMI2014-B-05
At the end of its fifth successful season, the Siruseri Premier League is planning to give an award to the Most Improved Batsman over the five years. For this, an Improvement Index will be computed for each batsman. This is defined as the longest ... to compute the Improvement Index for a batsman with an overall sequence of $n$ scores. Analyze the complexity of your algorithm.

At the end of its fifth successful season, the Siruseri Premier League is planning to give an award to the Most Improved Batsman over the five years. For this, an Improve...

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530 views

go_editor asked May 27, 2016

1 votes

2 answers

7

CMI2014-B-04
The frequency of a number in an array is the number of times it appears in the array. Describe an algorithm that finds the most frequent number in an array of $n$ numbers. If there are multiple numbers with highest frequency then list them all. Analyze the complexity of your algorithm.

The frequency of a number in an array is the number of times it appears in the array. Describe an algorithm that finds the most frequent number in an array of $n$ numbers...

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465 views

go_editor asked May 27, 2016

1 votes

1 answer

8

CMI2014-B-03
$\text{Air CMI }$operates direct flights between different cities. For any pair of cities $A$ and $B$, there is at most one flight in a day from $A$ to $B$. The online site $FakeTrip$ is tryingto compile a list of all routes available ... list all pairs of cities connected by a route on which all connections are feasible within the same day. Analyze the complexity of your algorithm.

$\text{Air CMI }$operates direct flights between different cities. For any pair of cities $A$ and $B$, there is at most one flight in a day from $A$ to $B$. The online si...

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480 views

go_editor asked May 27, 2016

1 votes

1 answer

9

CMI2014-B-02
There are $n$ students in a class. The students have formed $k$ committees. Each committee consists of more than half of the students. Show that there is at least one student who is a member of more than half of the committees.

There are $n$ students in a class. The students have formed $k$ committees. Each committee consists of more than half of the students. Show that there is at least one stu...

go_editor

568 views

go_editor asked May 27, 2016

1 votes

2 answers

10

CMI2014-B-01
Let $A$ be a regular language. Consider the following operations on $A$: $2A:=\{xy \mid x, \: y \in A \text{ and } x=y\}$ $A^2 :=\{xy \mid x, \: y \in A\}$ One of these operations necessarily leads to a regular language and the ... that it is regular. For the non-regular operation, give an example of an $A$ such that applying the operation on it results in a non-regular language.

Let $A$ be a regular language. Consider the following operations on $A$:$2A:=\{xy \mid x, \: y \in A \text{ and } x=y\}$$A^2 :=\{xy \mid x, \: y \in A\}$One of these oper...

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825 views

go_editor asked May 27, 2016

2 votes

3 answers

11

CMI2014-A-10
Avinash is taller than Abhay. Bharat is taller than Vinu and Vinay is taller than Bharat. Which of the following is a minimal set of additional information that can determine the tallest person? Vinay is taller than Avinash and Abhay is taller than Bharat. Avinash is taller than Vinay. Abhay is shorter than Vinay. None of the above.

Avinash is taller than Abhay. Bharat is taller than Vinu and Vinay is taller than Bharat. Which of the following is a minimal set of additional information that can deter...

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745 views

go_editor asked May 27, 2016

2 votes

2 answers

12

CMI2014-A-09
A company is due to send a shipment to a client and the CEO has resigned. To select a new CEO, some candidates have been interviewed. One of them will be chosen through a vote. If the workers union resort to a strike and the candidates have to be ... B). If the workers union resorted to a strike, then the number of voters was greater than or equal to the number of abstainers.

A company is due to send a shipment to a client and the CEO has resigned. To select a new CEO, some candidates have been interviewed. One of them will be chosen through a...

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564 views

go_editor asked May 27, 2016

1 votes

1 answer

13

CMI2014-A-08
What are the possible values of $gcd(7p + 94,\: 7p^2 + 97p + 47)$, where $p$ is an arbitrary integer? Either $1$ or $94$ Either $94$ or $47$ Either $1$ or $47$ None of these

What are the possible values of $gcd(7p + 94,\: 7p^2 + 97p + 47)$, where $p$ is an arbitrary integer?Either $1$ or $94$Either $94$ or $47$Either $1$ or $47$None of these

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528 views

go_editor asked May 27, 2016

1 votes

1 answer

14

CMI2014-A-07
Let $M$ be the maximum number of unit disks (disks of radius $1$) that can be placed inside a disk of radius $10$ so that each unit disk lies entirely within the larger disk and no two unit disks overlap. Then: $M < 25$ $25 \leq M < 40$ $40 \leq M < 55$ $M \geq 55$

Let $M$ be the maximum number of unit disks (disks of radius $1$) that can be placed inside a disk of radius $10$ so that each unit disk lies entirely within the larger d...

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594 views

go_editor asked May 27, 2016

6 votes

1 answer

15

CMI2014-A-06
Suppose we are working with a programming language that supports automatic garbage collection. This means that: Uninitialized variables are assigned null values. Unreferenced dynamically allocated memory is added back to free space. Unreachable $\text{if – then – else}$ branches are pruned. Expressions where array indices exceed array bounds are flagged.

Suppose we are working with a programming language that supports automatic garbage collection. This means that:Uninitialized variables are assigned null values.Unreferenc...

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802 views

go_editor asked May 27, 2016

2 votes

2 answers

16

CMI2014-A-05
Let $\Sigma = \{a, b\}$. For a word $w \: \: \in \Sigma^*$ let $n_a(x)$ denote the number of $a$'s in $w$ and let $n_b(x)$ denote the number of $b$'s in $w$ ... $L$? $L$ is regular, but not context-free $L$ is context-free, but not regular $L$ is $\Sigma^*$ None of these

Let $\Sigma = \{a, b\}$. For a word $w \: \: \in \Sigma^*$ let $n_a(x)$ denote the number of $a$'s in $w$ and let $n_b(x)$ denote the number of $b$'s in $w$. Consider the...

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645 views

go_editor asked May 27, 2016

1 votes

1 answer

17

CMI2014-A-04
Alan's task is to design an algorithm for a decision problem $P$. He knows that there is an algorithm $A$ that transforms instances of $P$ to instances of the Halting Problem such that $\text{yes}$ instances of $P$ map to $\text{yes}$ instances of the ... $A$ says nothing about whether there is an algorithm for $P$. The Halting Problem can be solved using $A$.

Alan’s task is to design an algorithm for a decision problem $P$. He knows that there is an algorithm $A$ that transforms instances of $P$ to instances of the Halting P...

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669 views

go_editor asked May 27, 2016

3 votes

3 answers

18

CMI2014-A-03
In the code fragment on the right, start and end are integer values and $\text{prime}(x)$ is a function that returns true if $x$ is a prime number and $\text{false}$ otherwise. At the end of the loop: i := 0; j := 0; k := 0; for (m := start; m <= end; m := m+1){ k := k + m ... + m; }else{ j := j + m; } } $k < i+j$ $k = i+j$ $k > i+j$ Depends on $\text{start}$ and $\text{end}$

In the code fragment on the right, start and end are integer values and $\text{prime}(x)$ is a function that returns true if $x$ is a prime number and $\text{false}$ othe...

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905 views

go_editor asked May 27, 2016

12 votes

3 answers

19

CMI2014-A-02
The $12$ houses on one side of a street are numbered with even numbers starting at $2$ and going up to $24$. A free newspaper is delivered on Monday to $3$ different houses chosen at random from these $12$. Find the probability that at least $2$ of these newspapers are delivered to ... with numbers strictly greater than $14$. $\frac{7}{11}$ $\frac{5}{12}$ $\frac{4}{11}$ $\frac{5}{22}$

The $12$ houses on one side of a street are numbered with even numbers starting at $2$ and going up to $24$. A free newspaper is delivered on Monday to $3$ different hous...

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2.2k views

go_editor asked May 27, 2016

20 votes

4 answers

20

CMI2014-A-01
For the inter-hostel six-a-side football tournament, a team of $6$ players is to be chosen from $11$ players consisting of $5$ forwards, $4$ defenders and $2$ goalkeepers. The team must include at least $2$ forwards, at least $2$ defenders and at least $1$ goalkeeper. Find the number of different ways in which the team can be chosen. $260$ $340$ $720$ $440$

For the inter-hostel six-a-side football tournament, a team of $6$ players is to be chosen from $11$ players consisting of $5$ forwards, $4$ defenders and $2$ goalkeepers...

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2.3k views

go_editor asked May 27, 2016

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title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true