Recent questions tagged 2-marks / GATE Overflow for GATE CSE

4 votes

1 answer

1441

GO Classes Scholarship 2023 | Test | Question: 1
A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$. Which of the following options is/are false? Every Total relation is ... total and transitive, then $\mathrm{S}$ is an equivalence relation. The number of total relations on a set of $5$ elements is $1024.$

A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$.Which of the following optio...

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964 views

GO Classes asked Aug 6, 2022

2 votes

3 answers

1442

GO Classes Scholarship 2023 | Test | Question: 2
Let $\text{S}$ be the set of all bit-strings of length $7 .$ We define a relation $\mathrm{R}$ on the set $\mathrm{S}$ by the rule that $x\mathrm{R}y$ iff $x$ and $y$ ... such that $\forall j \neq i, x_{j}=y_{j}$ and $x_{i} \neq y_{i}$. What is the cardinality of relation $\mathrm{R}$?

Let $\text{S}$ be the set of all bit-strings of length $7 .$ We define a relation $\mathrm{R}$ on the set $\mathrm{S}$ by the rule that $x\mathrm{R}y$ iff $x$ and $y$ dif...

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948 views

GO Classes asked Aug 6, 2022

4 votes

1 answer

1443

GO Classes Scholarship 2023 | Test | Question: 3
Let $\text{A, B}$ be two disjoint non-empty sets. Let $\text{M}$ be the universal set and $\text{A} \cup \text{B}$ is a proper subset of $\mathrm{M}$. For any set $\mathrm{S}$, let $\mathrm{S}^{\prime}$ be the set of those elements ...

Let $\text{A, B}$ be two disjoint non-empty sets. Let $\text{M}$ be the universal set and $\text{A} \cup \text{B}$ is a proper subset of $\mathrm{M}$. For any set $\mathr...

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518 views

GO Classes asked Aug 6, 2022

4 votes

1 answer

1444

GO Classes Scholarship 2023 | Test | Question: 5
Consider $5$ cards, each has a distinct value from the set $\{2,3,4,5,6\},$ so there are $5$ different values, and we put them face down on the table. There are $5$ players and each player is given a number from $2$ ... with the value that player has. If no player loses, then the dealer loses. How many ways are there so that the dealer loses?

Consider $5$ cards, each has a distinct value from the set $\{2,3,4,5,6\},$ so there are $5$ different values, and we put them face down on the table. There are $5$ playe...

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492 views

GO Classes asked Aug 6, 2022

4 votes

1 answer

1445

GO Classes Scholarship 2023 | Test | Question: 6
Consider three boxes and $12$ balls of the same size. We have $3$ indistinguishable red balls and $9$ distinguishable blue balls. The first box can fit at most three balls, the second box can fit at most four balls and the third box can fit ... all the red balls go into the same box. What is the total number of ways to put all the balls in the boxes?

Consider three boxes and $12$ balls of the same size. We have $3$ indistinguishable red balls and $9$ distinguishable blue balls. The first box can fit at most three ball...

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788 views

GO Classes asked Aug 6, 2022

3 votes

1 answer

1446

GO Classes Scholarship 2023 | Test | Question: 7
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ ... $x^{5}$ is $\mathrm{G}(x)?$

Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ is ...

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652 views

GO Classes asked Aug 6, 2022

5 votes

2 answers

1447

GO Classes Scholarship 2023 | Test | Question: 9
Consider the following graph $\text{G:}$ Let $\text{M, C, I, S, B, E}$ be the Matching number, chromatic number, independence number, Clique number, Vertex cover number, and edge cover number, respectively of $\text{G}.$ What is $\text{M+C+I+S+B+E}?$

Consider the following graph $\text{G:}$Let $\text{M, C, I, S, B, E}$ be the Matching number, chromatic number, independence number, Clique number, Vertex cover number, a...

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715 views

GO Classes asked Aug 6, 2022

3 votes

1 answer

1448

GO Classes Scholarship 2023 | Test | Question: 10
For which of the following does there exist a graph satisfying the specified conditions? A tree with six vertices and six edges. A tree with three or more vertices, two vertices of degree one, and all the other vertices with degree three or ... with $10$ vertices and $8$ edges. A disconnected graph with $12$ vertices and $11$ edges and no cycle.

For which of the following does there exist a graph satisfying the specified conditions?A tree with six vertices and six edges.A tree with three or more vertices, two ver...

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520 views

GO Classes asked Aug 6, 2022

6 votes

2 answers

1449

GO Classes Scholarship 2023 | Test | Question: 11
Let $\text{U}$ be a set and $\text{X, Y} \subseteq \text{U}$. Define operation twist by $ \operatorname{twist}\text{(X, Y)} =(\text{X} \cap \text{Y}) \cup(\overline{\text{X}} \cap \overline{\text{Y}}). $ Which of the following ... $\operatorname{twist}\text{(X, Y)}=\operatorname{twist}(\overline{\text{X}}, \overline{\text{Y}})$

Let $\text{U}$ be a set and $\text{X, Y} \subseteq \text{U}$. Define operation twist by$$\operatorname{twist}\text{(X, Y)} =(\text{X} \cap \text{Y}) \cup(\overline{\text{...

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431 views

GO Classes asked Aug 6, 2022

4 votes

1 answer

1450

GO Classes Scholarship 2023 | Test | Question: 12
How many non-isomorphic simple undirected graphs are there, each with four vertices and without a cycle?

How many non-isomorphic simple undirected graphs are there, each with four vertices and without a cycle?

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749 views

GO Classes asked Aug 6, 2022

4 votes

2 answers

1451

GO Classes Scholarship 2023 | Test | Question: 13
Let $\text{T}_{n}$ be the number of ways to arrange cars in a row with $n$ parking spaces if we can use sedans, SUVs, trucks to park such that a truck requires two spaces, whereas a sedan or SUV requires just one space each, and No two ... i.e. initial conditions are already given, hence no need to compute them)

Let $\text{T}_{n}$ be the number of ways to arrange cars in a row with $n$ parking spaces if we can use sedans, SUVs, trucks to park such that a truck requires two spaces...

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988 views

GO Classes asked Aug 6, 2022

3 votes

1 answer

1452

GO Classes Scholarship 2023 | Test | Question: 15
Consider Figure $\text{A}$ and Figure $\text{B}$ which represent $4$ bit signed and unsigned numbers respectively in $2's$ complement system. Assume that a few variables are defined below and initialized in such a way that places them in the spot shown in Figure ... of the following(s) is/are true? $s3 > u3$ $s1 > s3$ $u1 > u3$ $s1 > u3$

Consider Figure $\text{A}$ and Figure $\text{B}$ which represent $4$ bit signed and unsigned numbers respectively in $2’s$ complement system.Assume that a few variables...

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734 views

GO Classes asked Aug 6, 2022

4 votes

3 answers

1453

GO Classes Scholarship 2023 | Test | Question: 16
Consider the following declaration of variables $a$ and $b.$ int a = 1, b = 0; Which of the following is/are will evaluate to TRUE? b++ && b == a b++ && a == 0 a || b == --a a || ++b == 0

Consider the following declaration of variables $a$ and $b.$int a = 1, b = 0;Which of the following is/are will evaluate to TRUE?b++ && b == ab++ && a == 0a || b == aa |...

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721 views

GO Classes asked Aug 6, 2022

5 votes

3 answers

1454

GO Classes Scholarship 2023 | Test | Question: 17
Consider the following pair of mutually recursive functions. int f(int n){ if (n==0) return 1; return f(n-1)+g(n-1); } int g(int n){ if (n==0) return 1; return g(n-1) - f(n); } Which of the following is/are will evaluate to TRUE? $f(2) == g(0)$ $g(2)+f(1) == 0$ $g(4)+g(1) == 0$ $f(3)+f(0) == 0$

Consider the following pair of mutually recursive functions.int f(int n){ if (n==0) return 1; return f(n-1)+g(n-1); } int g(int n){ if (n==0) return 1; return g(n-1) - f(...

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638 views

GO Classes asked Aug 6, 2022

5 votes

1 answer

1455

GO Classes Scholarship 2023 | Test | Question: 19
Consider the following declaration of variable a in C program (row-major order). int a[3][4][5]; Which of the following(s) is/are TRUE about pointer arithmetic operations? Value of $a[2]-a[1]$ is $4$ Value of $a[1][2]-a[0][3]$ is $15$ Value of $a[0][10]-a[1][0]$ is $30$ Value of $a[2]-a[1]$ is $5$

Consider the following declaration of variable a in C program (row-major order).int a[3][4][5];Which of the following(s) is/are TRUE about pointer arithmetic operations?V...

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753 views

GO Classes asked Aug 6, 2022

2 votes

1 answer

1456

GO Classes Scholarship 2023 | Test | Question: 20
Consider the following declarations of a few variables. int (*p1)[3]; int (*p2)[3]; int (*t1)[2]; int (*t2)[2]; Let the initial values of $p1, p2, t2$ and $t1$ are $1000, 1036, 2000$ and $2040$ respectively. Consider ... is correct but $\text{S2}$ is incorrect $\text{S2}$ is correct but $\text{S1}$ is incorrect Both are correct Both are incorrect

Consider the following declarations of a few variables.int (*p1)[3]; int (*p2)[3]; int (*t1) ; int (*t2) ;Let the initial values of $p1, p2, t2$ and $t1$ are $1000, 1036,...

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565 views

GO Classes asked Aug 6, 2022

4 votes

1 answer

1457

GO Classes Scholarship 2023 | Test | Question: 22
Consider below two program fragments. Assume malloc is always successful, and sizes are as follows - sizeof (int *)=8 bytes sizeof ( double)=8 bytes sizeof ( char )=1 byte sizeof ( int )=4 byte Program 1 int **p; p = (int ... run time error, but Program $1$ will run fine. Both programs will always run fine. Both programs may produce run time errors.

Consider below two program fragments.Assume malloc is always successful, and sizes are as follows -sizeof (int *)=8 bytes sizeof ( double)=8 bytes sizeof ( char )=1 byte ...

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647 views

GO Classes asked Aug 6, 2022

3 votes

3 answers

1458

GO Classes Scholarship 2023 | Test | Question: 25
Consider struct alignment rules as described below - Each primitive data (int, char, float, etc.) type requiring $\text{K}$ bytes must be stored at the address must be multiple of $\text{K}.$ ... a [5]; long int b; } What will be $\text{sizeof(struct s)}?$ $24$ $18$ $32$ $20$

Consider struct alignment rules as described below –Each primitive data (int, char, float, etc.) type requiring $\text{K}$ bytes must be stored at the address must be m...

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492 views

GO Classes asked Aug 6, 2022

3 votes

3 answers

1459

GO Classes Scholarship 2023 | Test | Question: 26
What will be the output of the following C program? int sum = 0; for (int i = 1; i <= 10; i++) for (int j = 1; j <= 10; j++){ sum += i * j; }

What will be the output of the following C program?int sum = 0; for (int i = 1; i <= 10; i++) for (int j = 1; j <= 10; j++){ sum += i * j; }

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435 views

GO Classes asked Aug 6, 2022

3 votes

1 answer

1460

GO Classes Scholarship 2023 | Test | Question: 28
What will be the output of the following program? #include<stdio.h> struct _go{ char b[20]; char *a; struct _go *c; }x[2] = {"GATE", "2023", x+1, "GO", "Classes", x}, *p = x; typedef struct_go go; go ... ;c, n-2); } int main() { printf("%s",mystry(p,2023)->a); } GATE $2023$ Run time error GO

What will be the output of the following program?#include<stdio.h struct _go{ char b[20]; char *a; struct _go *c; }x = {"GATE", "2023", x+1, "GO", "Classes", x}, *p = x;...

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734 views

GO Classes asked Aug 6, 2022

5 votes

1 answer

1461

GO Classes Test Series 2023 | Theory of Computation | Test 5 | Question: 8
Consider the following instance of Post's Correspondence Problem: ... The above instance of Post's Correspondence Problem has : Exactly one solution At least one solution Infinite solutions No solution

Consider the following instance of Post's Correspondence Problem:$$\begin{array}{c|c|c} \text{Index} & \text{A} & \text{B} \\\hline 1 & 10 & 101 \\2 & 101 & 011 \\3 & 110...

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272 views

GO Classes asked Aug 1, 2022

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