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GATE CSE 2020 | Question: 9
Consider the following statements. Symbol table is accessed only during lexical analysis and syntax analysis. Compilers for programming languages that support recursion necessarily need heap storage for memory allocation in the run-time environment. Errors violating the condition any ... the above statements is/are TRUE? I only I and III only Ⅱ only None of Ⅰ, Ⅱ and Ⅲ

commented in Compiler Design May 9, 2020

9.6k views

3 answers

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GATE CSE 2019 | Question: 52
Consider the following C program: #include <stdio.h> int main() { float sum = 0.0, j=1.0, i=2.0; while (i/j > 0.0625) { j=j+j; sum=sum+i/j; printf("%f\n", sum); } return 0; } The number of times the variable sum will be printed, when the above program is executed, is _________

answered in Programming Apr 21, 2019

9.0k views

12 answers

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GATE CSE 2017 Set 2 | Question: 55
Consider the following C program. #include<stdio.h> #include<string.h> int main() { char* c="GATECSIT2017"; char* p=c; printf("%d", (int)strlen(c+2[p]-6[p]-1)); return 0; } The output of the program is _______

comment edited in Programming Dec 28, 2018

21.2k views

8 answers

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GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$

answered in Mathematical Logic Dec 9, 2018

3.2k views

5 answers

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GATE CSE 1999 | Question: 1.13
Suppose we want to arrange the $n$ numbers stored in any array such that all negative values occur before all positive ones. Minimum number of exchanges required in the worst case is $n-1$ $n$ $n+1$ None of the above

answer edited in Algorithms Nov 28, 2018

16.1k views

2 answers

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CMI2017-B-7
Consider the following function that takes as input a sequence $A$ of integers with n elements,$A[1],A[2], \dots ,A[n]$ and an integer $k$ and returns an integer value. The function length$(S)$ returns the length of the sequence $S$. Comments ... complexity of this algorithm in terms of the length of the input sequence $A$? Give an example of a worst-case input for this algorithm.

commented in Algorithms Nov 24, 2018

975 views

3 answers

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CMI2013-A-10
The below question is based on following program: procedure mystery (A : array [1..100] of int) int i,j,position,tmp; begin for j := 1 to 100 do position := j; for i := j to 100 do if (A[i] > A[position]) then position := i; endfor tmp := A[j]; ... endfor end The number of times the test $A[i] > A[\text{position}]$ is executed is: $100$ $5050$ $10000$ Depends on contents of $A$

commented in Algorithms Nov 23, 2018

1.1k views

6 answers

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TIFR CSE 2018 | Part A | Question: 9
How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$

answer edited in Graph Theory Nov 23, 2018

3.7k views

6 answers

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GATE CSE 2004 | Question: 78
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to $d$ is $\dfrac{^{n}C_{d}}{2^{n}}$ $\dfrac{^{n}C_{d}}{2^{d}}$ $\dfrac{d}{2^{n}}$ $\dfrac{1}{2^{d}}$

answer edited in Probability Nov 21, 2018

5.6k views

8 answers

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GATE IT 2006 | Question: 25
Consider the undirected graph $G$ defined as follows. The vertices of $G$ are bit strings of length $n$. We have an edge between vertex $u$ and vertex $v$ if and only if $u$ and $v$ differ in exactly one bit position (in other words, $v$ can be obtained from $u$ by ... $\left(\frac{1}{n}\right)$ $\left(\frac{2}{n}\right)$ $\left(\frac{3}{n}\right)$

commented in Graph Theory Oct 27, 2018

10.3k views

3 answers

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TIFR CSE 2018 | Part B | Question: 8
In an undirected graph $G$ with $n$ vertices, vertex $1$ has degree $1$, while each vertex $2,\ldots,n-1$ has degree $10$ and the degree of vertex $n$ is unknown, Which of the following statement must be TRUE on the graph $G$? There is a path ... Vertex $n$ has degree $1$. The diameter of the graph is at most $\frac{n}{10}$ All of the above choices must be TRUE

answered in Graph Theory Oct 12, 2018

4.2k views

8 answers

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GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$

commented in Graph Theory Oct 10, 2018

12.3k views

4 answers

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GATE CSE 1998 | Question: 11
Suppose $A = \{a, b, c, d\}$ and $\Pi_1$ is the following partition of A $\Pi_1 = \left\{\left\{a, b, c\right\}\left\{d\right\}\right\}$ List the ordered pairs of the equivalence relations induced by $\Pi_1$. Draw the graph of the above ... $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.

commented in Set Theory & Algebra Sep 15, 2018

9.4k views

6 answers

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GATE IT 2004 | Question: 85
Consider a simplified time slotted MAC protocol, where each host always has data to send and transmits with probability $p$ = $0.2$ in every slot. There is no backoff and one frame can be transmitted in one slot. If more than one host transmits in the same slot, then ... if each host has to be provided a minimum throughput of $0.16$ frames per time slot? $1$ $2$ $3$ $4$

answered in Computer Networks Sep 12, 2018

12.4k views

5 answers

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GATE CSE 1991 | Question: 15,a
Show that the product of the least common multiple and the greatest common divisor of two positive integers $a$ and $b$ is $a\times b$.

answered in Set Theory & Algebra Sep 8, 2018

1.4k views

5 answers

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GATE CSE 2004 | Question: 24
Consider the binary relation: $S= \left\{\left(x, y\right) \mid y=x+1 \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$ The reflexive transitive closure is $S$ ... $\left\{\left(x, y\right) \mid y \leq x \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$

answer edited in Set Theory & Algebra Sep 8, 2018

7.3k views

5 answers

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GATE CSE 2002 | Question: 2.17
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetric Symmetric and reflexive Transitive and reflexive Transitive and symmetric

commented in Set Theory & Algebra Sep 7, 2018

10.5k views

4 answers

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GATE CSE 1999 | Question: 3
Mr. X claims the following: If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof: “From xRy, using symmetry we get yRx. Now because R is transitive xRy and yRx together imply xRx. Therefore, R is reflexive”. Give an example of a relation R which is symmetric and transitive but not reflexive.

commented in Set Theory & Algebra Sep 7, 2018

2.2k views

6 answers

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GATE CSE 1998 | Question: 10a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$

commented in Set Theory & Algebra Sep 6, 2018

2.9k views

9 answers

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GATE IT 2005 | Question: 33
Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $S_2\subset S_1$. What is the maximum cardinality of $C?$ $n$ $n+1$ $2^{n-1} + 1$ $n!$

answer edited in Set Theory & Algebra Sep 4, 2018

8.6k views

12 answers

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GATE CSE 2016 Set 1 | Question: 41
Let $Q$ denote a queue containing sixteen numbers and $S$ be an empty stack. $Head(Q)$ returns the element at the head of the queue $Q$ without removing it from $Q$. Similarly $Top(S)$ returns the element at the top of $S$ without removing ... = Pop(S); Enqueue (Q, x); end end The maximum possible number of iterations of the while loop in the algorithm is _______.

commented in DS Sep 2, 2018

24.8k views

7 answers

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GATE CSE 2006 | Question: 24
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = \min(\pi(B))$, where $\min(S)$ is the smallest integer in the set of integers $S$, and $\pi$(S) is the set of ... $n! \frac{|A ∩ B|}{|A ∪ B|}$ $\dfrac{|A ∩ B|^2}{^n \mathrm{C}_{|A ∪ B|}}$

comment edited in Set Theory & Algebra Sep 2, 2018

8.5k views

4 answers

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GATE CSE 2001 | Question: 2.2
Consider the following statements: $S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite. $S_2:$ There exists two irrational numbers $x$ and y such that $(x+y)$ ... $S_2$? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct

commented in Set Theory & Algebra Sep 1, 2018

6.8k views

4 answers

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GATE CSE 1994 | Question: 2.4
The number of subsets $\left\{ 1,2, \dots, n\right\}$ with odd cardinality is ___________

commented in Set Theory & Algebra Sep 1, 2018

4.0k views

8 answers

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GATE CSE 2009 | Question: 22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators

commented in Set Theory & Algebra Aug 30, 2018

6.7k views

3 answers

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GATE CSE 2005 | Question: 46
Consider the set $H$ of all $3 * 3$ matrices of the type $\left( \begin{array}{ccc} a & f & e \\ 0 & b & d \\ 0 & 0 & c \end{array} \right)$ where $a,b,c,d,e$ and $f$ ... the matrix multiplication operation, the set $H$ is: a group a monoid but not a group a semi group but not a monoid neither a group nor a semi group

commented in Set Theory & Algebra Aug 30, 2018

5.6k views

3 answers

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GATE CSE 1998 | Question: 12
Let $(A, *)$ be a semigroup, Furthermore, for every $a$ and $b$ in $A$, if $a \neq b$, then $a*b \neq b*a$. Show that for every $a$ in $A$, $a*a=a$ Show that for every $a$, $b$ in $A$, $a*b*a=a$ Show that for every $a,b,c$ in $A$, $a*b*c=a*c$

answered in Set Theory & Algebra Aug 29, 2018

5.5k views

8 answers

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GATE CSE 2016 Set 1 | Question: 28
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.

commented in Set Theory & Algebra Aug 29, 2018

16.7k views

6 answers

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GATE CSE 2003 | Question: 39
Let $\Sigma = \left\{a, b, c, d, e\right\}$ be an alphabet. We define an encoding scheme as follows: $g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11$. Let $p_i$ denote the i-th prime number $\left(p_1 = 2\right)$ ... numbers is the encoding, $h$, of a non-empty sequence of strings? $2^73^75^7$ $2^83^85^8$ $2^93^95^9$ $2^{10}3^{10}5^{10}$

commented in Set Theory & Algebra Aug 25, 2018

5.8k views

5 answers

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GATE CSE 2003 | Question: 37
Let \(f : A \to B\) be an injective (one-to-one) function. Define \(g : 2^A \to 2^B\) as: \(g(C) = \left \{f(x) \mid x \in C\right\} \), for all subsets $C$ of $A$. Define \(h : 2^B \to 2^A\) as: \(h(D) = \{x \mid x \in A, f(x) \in D\}\), for all ... always true? \(g(h(D)) \subseteq D\) \(g(h(D)) \supseteq D\) \(g(h(D)) \cap D = \phi\) \(g(h(D)) \cap (B - D) \ne \phi\)

answered in Set Theory & Algebra Aug 24, 2018

6.4k views