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Questions by GO Classes
3
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1
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1
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 $1024.$
asked
in
Set Theory & Algebra
Aug 7
477
views
goclasses-scholarship-test1
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
2
votes
3
answers
2
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 $\mathrm{R}$?
asked
in
Set Theory & Algebra
Aug 7
372
views
goclasses-scholarship-test1
numerical-answers
goclasses
set-theory&algebra
relations
2-marks
4
votes
1
answer
3
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 ...
asked
in
Set Theory & Algebra
Aug 7
227
views
goclasses-scholarship-test1
goclasses
set-theory&algebra
set-theory
multiple-selects
2-marks
5
votes
2
answers
4
GO Classes Scholarship 2023 | Test | Question: 4
Consider a $3 \times 11$ rectangular grid as depicted in Figure $1,$ formed by $33$ tiles of area $1\text{m}^2.$ A staircase walk is a path in the grid which moves only right or up. How many staircase walks are there from $\text{A}$ to $\text{B}$ which start by going to the right two times?
asked
in
Combinatory
Aug 7
226
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
1-mark
3
votes
1
answer
5
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?
asked
in
Combinatory
Aug 7
164
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
2-marks
4
votes
1
answer
6
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?
asked
in
Combinatory
Aug 7
177
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
2-marks
3
votes
1
answer
7
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 $\mathrm{G}(x)?$
asked
in
Combinatory
Aug 7
154
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
generating-functions
2-marks
3
votes
1
answer
8
GO Classes Scholarship 2023 | Test | Question: 8
In a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$, two nodes $u$ and $v$ are strongly connected if and only if they are mutually reachable i.e. there is a path from u to $v$ and a path from $v$ to $u$. ... connected components $\dots?$ can not increase can not decrease by more than $1$ can not decrease by more than $2$ may remain unchanged
asked
in
Graph Theory
Aug 7
159
views
goclasses-scholarship-test1
goclasses
graph-theory
graph-connectivity
multiple-selects
1-mark
4
votes
2
answers
9
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 $\text{M+C+I+S+B+E}?$
asked
in
Graph Theory
Aug 7
218
views
goclasses-scholarship-test1
numerical-answers
goclasses
graph-theory
graph-connectivity
vertex-cover
2-marks
3
votes
1
answer
10
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.
asked
in
Graph Theory
Aug 7
141
views
goclasses-scholarship-test1
goclasses
graph-theory
graph-connectivity
multiple-selects
2-marks
3
votes
2
answers
11
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 ... $\operatorname{twist}\text{(X, Y)}=\operatorname{twist}(\overline{\text{X}}, \overline{\text{Y}})$
asked
in
Set Theory & Algebra
Aug 7
147
views
goclasses-scholarship-test1
goclasses
set-theory&algebra
set-theory
multiple-selects
2-marks
4
votes
1
answer
12
GO Classes Scholarship 2023 | Test | Question: 12
How many non-isomorphic simple undirected graphs are there, each with four vertices and without a cycle?
asked
in
Graph Theory
Aug 7
150
views
goclasses-scholarship-test1
numerical-answers
goclasses
graph-theory
graph-isomorphism
2-marks
4
votes
2
answers
13
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)
asked
in
Combinatory
Aug 7
309
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
recurrence-relation
2-marks
3
votes
1
answer
14
GO Classes Scholarship 2023 | Test | Question: 14
Consider the following C program given below. #include<stdio.h> main() { int a = 4; switch (a) { a--; case 4: printf("Science "); break; default: printf("Technology "); case ... ;Philosophy"); } } What will be the output of the program? Science Knowledge Philosophy Technology Knowledge Philosophy Science Knowledge
asked
in
Programming
Aug 7
263
views
goclasses-scholarship-test1
goclasses
programming
programming-in-c
output
1-mark
3
votes
1
answer
15
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? $s3 > u3$ $s1 > s3$ $u1 > u3$ $s1 > u3$
asked
in
Programming
Aug 7
249
views
goclasses-scholarship-test1
goclasses
programming
programming-in-c
number-representation
multiple-selects
2-marks
2
votes
2
answers
16
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
asked
in
Programming
Aug 7
206
views
goclasses-scholarship-test1
goclasses
programming
programming-in-c
multiple-selects
2-marks
2
votes
3
answers
17
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? $f(2) == g(0)$ $g(2)+f(1) == 0$ $g(4)+g(1) == 0$ $f(3)+f(0) == 0$
asked
in
Programming
Aug 7
222
views
goclasses-scholarship-test1
goclasses
programming
programming-in-c
functions
recursion
multiple-selects
2-marks
3
votes
2
answers
18
GO Classes Scholarship 2023 | Test | Question: 18
Consider the following declaration of pointer variable $p.$ int (*p)[10][5]; If the initial value of $p$ is $1000,$ then what will be the value of $p+1?$ It is given that system has $8$ bytes of address size and $4$ bytes of integer size.
asked
in
Programming
Aug 7
222
views
goclasses-scholarship-test1
numerical-answers
goclasses
programming
programming-in-c
pointers
1-mark
2
votes
1
answer
19
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 $5$
asked
in
Programming
Aug 7
202
views
goclasses-scholarship-test1
goclasses
programming
programming-in-c
array
multiple-selects
2-marks
1
vote
1
answer
20
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
asked
in
Programming
Aug 7
169
views
goclasses-scholarship-test1
goclasses
programming
programming-in-c
pointers
array-of-pointers
2-marks
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