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Recent questions in Engineering Mathematics
6
votes
2
answers
81
GATE CSE 2024 | Set 2 | Question: 37
Let $A$ be an $n \times n$ matrix over the set of all real numbers $\mathbb{R}$. Let $B$ be a matrix obtained from $A$ by swapping two rows. Which of the following statements is/are TRUE? The determinant of $B$ is the negative of the ... If $A$ is symmetric, then $B$ is also symmetric If the trace of $A$ is zero, then the trace of $B$ is also zero
Let $A$ be an $n \times n$ matrix over the set of all real numbers $\mathbb{R}$. Let $B$ be a matrix obtained from $A$ by swapping two rows. Which of the f...
Arjun
2.1k
views
Arjun
asked
Feb 16
Linear Algebra
gatecse2024-set2
linear-algebra
multiple-selects
+
–
1
votes
3
answers
82
GATE CSE 2024 | Set 2 | Question: 50
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.
Arjun
1.9k
views
Arjun
asked
Feb 16
Graph Theory
gatecse2024-set2
graph-theory
numerical-answers
+
–
2
votes
2
answers
83
GATE CSE 2024 | Set 2 | Question: 53
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ that are their own inverses is ___________.
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \ti...
Arjun
2.1k
views
Arjun
asked
Feb 16
Set Theory & Algebra
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
+
–
2
votes
2
answers
84
GATE CSE 2024 | Set 1 | Question: 1
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x)=\max \left\{x, x^3\right\}, x \in \mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers. The set of all points where $f(x)$ is NOT differentiable is $\{-1,1,2\}$ $\{-2,-1,1\}$ $\{0,1\}$ $\{-1,0,1\}$
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x)=\max \left\{x, x^3\right\}, x \in \mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers....
Arjun
3.5k
views
Arjun
asked
Feb 16
Calculus
gatecse2024-set1
calculus
+
–
5
votes
8
answers
85
GATE CSE 2024 | Set 1 | Question: 2
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is $-1$ $0$ $1$ $2$
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is$-1$$0$$1$$2$
Arjun
2.9k
views
Arjun
asked
Feb 16
Linear Algebra
gatecse2024-set1
linear-algebra
+
–
0
votes
1
answer
86
GATE CSE 2024 | Set 1 | Question: 4
Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs before $2$ in the permutation, and $Y$ the event that $3$ occurs before ... The events $X$ and $Y$ are independent Either event $X$ or $Y$ must occur Event $X$ is more likely than event $Y$
Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs be...
Arjun
2.3k
views
Arjun
asked
Feb 16
Probability
gatecse2024-set1
probability
+
–
1
votes
1
answer
87
GATE CSE 2024 | Set 1 | Question: 17
Let $A$ and $B$ be two events in a probability space with $P(A)=0.3, P(B)=0.5$, and $P(A \cap B)=0.1$. Which of the following statements is/are TRUE? The two events $A$ and $B$ are independent $P(A \cup B)=0.7$ ... $B$ $P\left(A^c \cap B^c\right)=0.4$, where $A^c$ and $B^c$ are the complements of the events $A$ and $B$, respectively
Let $A$ and $B$ be two events in a probability space with $P(A)=0.3, P(B)=0.5$, and $P(A \cap B)=0.1$. Which of the following statements is/are TRUE?The two events $A$ an...
Arjun
2.0k
views
Arjun
asked
Feb 16
Probability
gatecse2024-set1
multiple-selects
probability
+
–
0
votes
1
answer
88
GATE CSE 2024 | Set 1 | Question: 22
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B$. The number of possible values of $\text{|A|}$ is ___________.
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B...
Arjun
1.8k
views
Arjun
asked
Feb 16
Set Theory & Algebra
gatecse2024-set1
numerical-answers
set-theory&algebra
+
–
12
votes
3
answers
89
GATE CSE 2024 | Set 1 | Question: 39
Let $A$ be any $n \times m$ matrix, where $m>n$. Which of the following statements is/are TRUE about the system of linear equations $Ax=0$? There exist at least $m-n$ linearly independent solutions to this system There exist $m-n$ ... solution in which at least $m-n$ variables are $0$ There exists a solution in which at least $n$ variables are non-zero
Let $A$ be any $n \times m$ matrix, where $m>n$. Which of the following statements is/are TRUE about the system of linear equations $Ax=0$?There exist at least $m-n...
Arjun
3.2k
views
Arjun
asked
Feb 16
Linear Algebra
gatecse2024-set1
multiple-selects
linear-algebra
+
–
0
votes
1
answer
90
GATE CSE 2024 | Set 1 | Question: 41
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic number $k$. Which of the following statements is/are always TRUE? $G$ contains a complete subgraph with ... $n/k$ $G$ contains at least $k(k-1) / 2$ edges $G$ contains a vertex of degree at least $k$
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic nu...
Arjun
2.0k
views
Arjun
asked
Feb 16
Graph Theory
gatecse2024-set1
multiple-selects
graph-theory
+
–
3
votes
2
answers
91
GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE? Operator $\diamond$ ... $\square$ obeys the distributive law Operator $\square$ over the operator $\diamond$ obeys the distributive law
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE?Ope...
Arjun
1.8k
views
Arjun
asked
Feb 16
Set Theory & Algebra
gatecse2024-set1
multiple-selects
set-theory&algebra
+
–
2
votes
2
answers
92
GATE CSE 2024 | Set 1 | Question: 53
A bag contains $10$ red balls and $15$ blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to $3$ decimal places) that both balls drawn are red is ___________.
A bag contains $10$ red balls and $15$ blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off ...
Arjun
2.1k
views
Arjun
asked
Feb 16
Probability
gatecse2024-set1
numerical-answers
probability
+
–
0
votes
0
answers
93
Regular expression to finite automata
Çșȇ ʛấẗẻ
216
views
Çșȇ ʛấẗẻ
asked
Feb 15
Mathematical Logic
finite-automata
theory-of-computation
regular-expression
+
–
0
votes
0
answers
94
COA Self doubt
Çșȇ ʛấẗẻ
97
views
Çșȇ ʛấẗẻ
asked
Feb 15
Mathematical Logic
co-and-architecture
self-doubt
+
–
0
votes
1
answer
95
Permutation and combination
Çșȇ ʛấẗẻ
137
views
Çșȇ ʛấẗẻ
asked
Feb 15
Mathematical Logic
combinatory
engineering-mathematics
discrete-mathematics
+
–
1
votes
0
answers
96
Gate 2016
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________. I am confused with the question's language. please correct me if I have a wrong assumption. We need to tell the minimum colors required for a planar graph. Suppose I start ... is only fixed to 4. I understand the answer not to be less than 4. What does the word "any" means here?
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________.I am confused with the question's language.please correct me if I have a wr...
TusharRana
203
views
TusharRana
asked
Feb 8
0
votes
0
answers
97
Combinatorics & Probability
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyone except the individual who just called. (a) By how many different paths can a rumor ... in $N$ calls? (c) What is the probability that if $A$ starts the rumor, then $A$ receives the third calls?
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyo...
Debargha Mitra Roy
166
views
Debargha Mitra Roy
asked
Feb 8
Combinatory
combinatory
counting
+
–
0
votes
0
answers
98
#self doubt
Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/ Let S={ϕ,{ϕ},{ϕ,{ϕ}}} P(s)= Power Set of set S P(s)={ϕ,{ϕ},{ϕ,{ϕ}},{ϕ,{ϕ,{ϕ}}},{{ϕ},{ϕ,{ϕ}}},{ϕ,{ϕ},{ϕ,{ϕ}}}} n(P(s))=6.
Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/Let S={ϕ,{�...
Dknights
131
views
Dknights
asked
Feb 6
Set Theory & Algebra
discrete-mathematics
+
–
13
votes
1
answer
99
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 15
Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , a vertex of degree 4, a vertex of degree 5 , a vertex of degree 6 and ... of degree 7. Which of the following can be the degree of the last vertex? (Select all that are possible) 0 3 4 8
Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , a vertex of degree 4, ...
GO Classes
652
views
GO Classes
asked
Feb 5
Graph Theory
goclasses2024-mockgate-14
graph-theory
degree-of-graph
multiple-selects
1-mark
+
–
2
votes
2
answers
100
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 21
Suppose we have events $A, B$ in a sample space. And we know that $\mathrm{P}(\mathrm{A})=0.3, \mathrm{P}\left(\mathrm{B} \mid \mathrm{A}^c\right)=0.25, \mathrm{P}(\mathrm{B} \mid \mathrm{A})=0.45$. What is $\mathrm{P}\left(\mathrm{A}^c \mid \mathrm{B}\right) ?$ 0.75 0.55 0.2 0.56
Suppose we have events $A, B$ in a sample space. And we know that $\mathrm{P}(\mathrm{A})=0.3, \mathrm{P}\left(\mathrm{B} \mid \mathrm{A}^c\right)=0.25, \mathrm{P}(\mathr...
GO Classes
541
views
GO Classes
asked
Feb 5
Probability
goclasses2024-mockgate-14
probability
conditional-probability
1-mark
+
–
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