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Questions without a selected answer in Engineering Mathematics
3
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0
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1
#linear algebra
why Eigen Vectors can not be zero ?
srijankarak_123
asked
in
Linear Algebra
Mar 23
by
srijankarak_123
25
views
0
votes
0
answers
2
#discrete
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 24
by
Çșȇ ʛấẗẻ
61
views
discrete-mathematics
kenneth-rosen
0
votes
0
answers
3
Question on Quotient set
What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?
rick55
asked
in
Set Theory & Algebra
Feb 23
by
rick55
56
views
1
vote
1
answer
4
if p implies q is true then the truth value of which of the following cannot be determined
a) ~p\/q b) ~q=>~p c) ~p=>~q d) ~(p/\~q) can someone provide the solution?
swapnil sahu
asked
in
Mathematical Logic
Feb 20
by
swapnil sahu
127
views
engineering-mathematics
propositional-logic
0
votes
1
answer
5
#GATE
Is Vector Subspace, Span, Basis, Dimension part of the gate CSE engineering mathematics linear algebra syllabus ?
sup739
asked
in
Linear Algebra
Feb 18
by
sup739
133
views
0
votes
1
answer
6
GATE DS&AI 2024 | Question: 1
Consider the following statements: The mean and variance of a Poisson random variable are equal. For a standard normal random variable, the mean is zero and the variance is one. Which ONE of the following options is correct? Both $\text{(i)}$ and $\text{(ii)}$ are true ... $\text{(i)}$ is false Both $\text{(i)}$ and $\text{(ii)}$ are false
Arjun
asked
in
Probability
Feb 16
by
Arjun
1.2k
views
gate-ds-ai-2024
probability
0
votes
1
answer
7
GATE DS&AI 2024 | Question: 26
A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently. What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen? $2$ $4$ $6$ $8$
Arjun
asked
in
Probability
Feb 16
by
Arjun
978
views
gate-ds-ai-2024
probability
0
votes
1
answer
8
GATE DS&AI 2024 | Question: 47
Let $X$ be a random variable exponentially distributed with parameter $\lambda>0$. The probability density function of $X$ is given by: \[ f_{X}(x)=\left\{\begin{array}{ll} \lambda e^{-\lambda x}, \quad x \geq 0 \\ 0, & \text { otherwise } \end ... variance of $X$, respectively, the value of $\lambda$ is $\_\_\_\_\_\_\_\_$ (rounded off to one decimal place).
Arjun
asked
in
Probability
Feb 16
by
Arjun
599
views
gate-ds-ai-2024
numerical-answers
probability
random-variable
0
votes
1
answer
9
GATE DS&AI 2024 | Question: 48
Consider two events $T$ and $S$. Let $\bar{T}$ denote the complement of the event $T$. The probability associated with different events are given as follows: \[ P(\bar{T})=0.6, \quad P(S \mid T)=0.3, \quad P(S \mid \bar{T})=0.6 \] Then, $P(T \mid S)$ is $\_\_\_\_\_\_\_\_$ (rounded off to two decimal places).
Arjun
asked
in
Probability
Feb 16
by
Arjun
640
views
gate-ds-ai-2024
numerical-answers
probability
1
vote
1
answer
10
GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
Arjun
asked
in
Calculus
Feb 16
by
Arjun
769
views
gate-ds-ai-2024
numerical-answers
limits
engineering-mathematics
2
votes
3
answers
11
GATE CSE 2024 | Set 2 | Question: 2
Let $p$ and $q$ be the following propositions: $p$ : Fail grade can be given. $q$ : Student scores more than $50 \%$ marks. Consider the statement: "Fail grade cannot be given when student scores more than $50 \%$ marks." ... above statement in propositional logic? $q \rightarrow \neg p$ $q \rightarrow p$ $p \rightarrow q$ $\neg p \rightarrow q$
Arjun
asked
in
Mathematical Logic
Feb 16
by
Arjun
3.0k
views
gatecse2024-set2
mathematical-logic
4
votes
1
answer
12
GATE CSE 2024 | Set 2 | Question: 6
Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that \[ f(x)=1-f(2-x) \] Which one of the following options is the CORRECT value of $\int_{0}^{2} f(x) d x$ ? $0$ $1$ $2$ $-1$
Arjun
asked
in
Calculus
Feb 16
by
Arjun
2.0k
views
gatecse2024-set2
calculus
definite-integral
2
votes
2
answers
13
GATE CSE 2024 | Set 2 | Question: 7
Let $\text{A}$ be the adjacency matrix of a simple undirected graph $\text{G}$. Suppose $\text{A}$ is its own inverse. Which one of the following statements is always TRUE? $\text{G}$ is a cycle $\text{G}$ is a perfect matching $\text{G}$ is a complete graph There is no such graph $\text{G}$
Arjun
asked
in
Graph Theory
Feb 16
by
Arjun
2.5k
views
gatecse2024-set2
graph-theory
1
vote
1
answer
14
GATE CSE 2024 | Set 2 | Question: 8
When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers $(i.e., 1, 2, 3, 4, 5, \text{and } 6)$ is $\frac{1}{324}$ $\frac{5}{324}$ $\frac{7}{324}$ $\frac{11}{324}$
Arjun
asked
in
Probability
Feb 16
by
Arjun
1.7k
views
gatecse2024-set2
probability
1
vote
2
answers
15
GATE CSE 2024 | Set 2 | Question: 24
Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows \[ P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\} \] The number of total orders on $\{1,2,3,4\}$ that contain $\text{P}$ is __________.
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.8k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
partial-order
1
vote
3
answers
16
GATE CSE 2024 | Set 2 | Question: 34
Let $x$ and $y$ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $z=x y$ and let the mean values of $x, y, z$ be $\bar{x}, \bar{y}, \bar{z}$ ... $\bar{z} \leq \bar{x} \bar{y}$ $\bar{z} \geq \bar{x} \bar{y}$ $\bar{z} \leq \bar{x}$
Arjun
asked
in
Probability
Feb 16
by
Arjun
2.3k
views
gatecse2024-set2
probability
random-variable
2
votes
0
answers
17
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
Arjun
asked
in
Linear Algebra
Feb 16
by
Arjun
1.8k
views
gatecse2024-set2
linear-algebra
multiple-selects
1
vote
2
answers
18
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 __________.
Arjun
asked
in
Graph Theory
Feb 16
by
Arjun
1.6k
views
gatecse2024-set2
graph-theory
numerical-answers
2
votes
2
answers
19
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 ___________.
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.8k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
1
vote
2
answers
20
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 $\{-1,1,2\}$ $\{-2,-1,1\}$ $\{0,1\}$ $\{-1,0,1\}$
Arjun
asked
in
Calculus
Feb 16
by
Arjun
3.3k
views
gatecse2024-set1
calculus
3
votes
7
answers
21
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 $-1$ $0$ $1$ $2$
Arjun
asked
in
Linear Algebra
Feb 16
by
Arjun
2.6k
views
gatecse2024-set1
linear-algebra
0
votes
1
answer
22
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 $Y$
Arjun
asked
in
Probability
Feb 16
by
Arjun
2.1k
views
gatecse2024-set1
probability
1
vote
1
answer
23
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
Arjun
asked
in
Probability
Feb 16
by
Arjun
1.7k
views
gatecse2024-set1
multiple-selects
probability
0
votes
1
answer
24
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 ___________.
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.6k
views
gatecse2024-set1
numerical-answers
set-theory&algebra
6
votes
1
answer
25
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
Arjun
asked
in
Linear Algebra
Feb 16
by
Arjun
2.6k
views
gatecse2024-set1
multiple-selects
linear-algebra
0
votes
1
answer
26
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 $k$
Arjun
asked
in
Graph Theory
Feb 16
by
Arjun
1.8k
views
gatecse2024-set1
multiple-selects
graph-theory
1
vote
1
answer
27
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
Arjun
asked
in
Set Theory & Algebra
Feb 16
by
Arjun
1.6k
views
gatecse2024-set1
multiple-selects
set-theory&algebra
0
votes
2
answers
28
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 ___________.
Arjun
asked
in
Probability
Feb 16
by
Arjun
1.8k
views
gatecse2024-set1
numerical-answers
probability
0
votes
0
answers
29
Regular expression to finite automata
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 15
by
Çșȇ ʛấẗẻ
200
views
finite-automata
theory-of-computation
regular-expression
0
votes
0
answers
30
COA Self doubt
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 15
by
Çșȇ ʛấẗẻ
87
views
co-and-architecture
self-doubt
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