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Recent questions in Engineering Mathematics
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31
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
32
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
33
Regular expression to finite automata
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 15
by
Çșȇ ʛấẗẻ
195
views
finite-automata
theory-of-computation
regular-expression
0
votes
0
answers
34
COA Self doubt
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 15
by
Çșȇ ʛấẗẻ
81
views
co-and-architecture
self-doubt
0
votes
1
answer
35
Permutation and combination
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 15
by
Çșȇ ʛấẗẻ
116
views
combinatory
engineering-mathematics
discrete-mathematics
1
vote
0
answers
36
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?
TusharRana
asked
in
Graph Theory
Feb 8
by
TusharRana
177
views
0
votes
0
answers
37
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?
Debargha Mitra Roy
asked
in
Combinatory
Feb 8
by
Debargha Mitra Roy
133
views
combinatory
counting
0
votes
0
answers
38
#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.
Dknights
asked
in
Set Theory & Algebra
Feb 6
by
Dknights
109
views
discrete-mathematics
13
votes
1
answer
39
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
GO Classes
asked
in
Graph Theory
Feb 5
by
GO Classes
551
views
goclasses2024-mockgate-14
graph-theory
degree-of-graph
multiple-selects
1-mark
2
votes
2
answers
40
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
GO Classes
asked
in
Probability
Feb 5
by
GO Classes
451
views
goclasses2024-mockgate-14
probability
conditional-probability
1-mark
5
votes
1
answer
41
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 22
Let $A$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $A$, we get a matrix $B$ which has 12 nonzero rows. Which of the following is/are always true? The rank of $A$ is 12. The ranks of $A$ and $B$ are ... . If $v$ is a vector such that $A v=0$ then $B v$ is also 0. The rank of $B$ is at most 11.
GO Classes
asked
in
Linear Algebra
Feb 5
by
GO Classes
316
views
goclasses2024-mockgate-14
linear-algebra
rank-of-matrix
multiple-selects
1-mark
3
votes
1
answer
42
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 39
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are correct? The function $f$ must be one-to-one. The function $f$ must be onto. The function g must be one-to-one. The function $g$ must be onto.
GO Classes
asked
in
Set Theory & Algebra
Feb 5
by
GO Classes
447
views
goclasses2024-mockgate-14
set-theory&algebra
functions
multiple-selects
2-marks
2
votes
1
answer
43
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 48
Consider the quadratic equation $x^2+\dfrac{x}{2}+c=0$, where $c$ is chosen uniformly randomly from the interval $[0,1]$. What is the probability that the given quadratic equation has a real solution? The solutions of $a x^2+b x+c=0$ are given by $x=\dfrac{-b \pm \sqrt{b^2-4 a c}}{2a}$. $1 / 2$ $1 / 4$ $1 / 8$ $1 / 16$
GO Classes
asked
in
Probability
Feb 5
by
GO Classes
325
views
goclasses2024-mockgate-14
probability
uniform-distribution
2-marks
6
votes
2
answers
44
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 49
Consider a $2 \times 2$ matrix M. Which of the following are NOT POSSIBLE for the system of equations $M x=p?$ no solutions for some but not all $\vec{p}$; exactly one solution for all other $\vec{p}$ exactly one solution for ... some $\vec{p}$, exactly one solution for some $\vec{p}$ and more than one solution for some $\vec{p}$
GO Classes
asked
in
Linear Algebra
Feb 5
by
GO Classes
478
views
goclasses2024-mockgate-14
linear-algebra
system-of-equations
multiple-selects
2-marks
6
votes
2
answers
45
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 56
The coefficient of $x^6$ in the expansion of $A(x)$ is, where $ A(x)=\frac{x(1+x)}{(1-x)^3} $
GO Classes
asked
in
Combinatory
Feb 5
by
GO Classes
490
views
goclasses2024-mockgate-14
numerical-answers
combinatory
recurrence-relation
2-marks
6
votes
1
answer
46
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 57
A strongly connected component $(\mathrm{SCC})$ of a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$ ... ; edges in its associated directed acyclic graph $G^{\prime}$ be $A, B$ respectively, then what is $A+B?$
GO Classes
asked
in
Graph Theory
Feb 5
by
GO Classes
488
views
goclasses2024-mockgate-14
numerical-answers
graph-theory
graph-connectivity
2-marks
11
votes
2
answers
47
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 58
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae. Which of the following is/are True? If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology. If $F \wedge G$ is a contradiction then at ... $G$ is a tautology. If $F \rightarrow G$ is a contradiction then $F$ is a tautology and $G$ is a contradiction.
GO Classes
asked
in
Mathematical Logic
Feb 5
by
GO Classes
711
views
goclasses2024-mockgate-14
mathematical-logic
propositional-logic
multiple-selects
2-marks
2
votes
1
answer
48
Memory Based GATE DA 2024 | Question: 1
Consider the probability density function \(f(x) = \lambda e^{-\lambda x}\) for \(x \geq 0\) and \(\lambda > 0\). Determine the value of \(\lambda\) such that \(5E(x) = V(x)\).
GO Classes
asked
in
Probability
Feb 4
by
GO Classes
291
views
gate2024-da-memory-based
goclasses
probability
expectation
numerical-answers
1
vote
2
answers
49
Memory Based GATE DA 2024 | Question: 3
Evaluate the limit: \[ \lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2} \]
GO Classes
asked
in
Calculus
Feb 4
by
GO Classes
434
views
gate2024-da-memory-based
goclasses
calculus
limits
numerical-answers
2
votes
2
answers
50
Memory Based GATE DA 2024 | Question: 4
Consider the matrix \[ \mathrm{M} = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6 \end{bmatrix} \] Find the value of \(|\mathrm{M}^2 + 12M|\).
GO Classes
asked
in
Linear Algebra
Feb 4
by
GO Classes
426
views
gate2024-da-memory-based
goclasses
linear-algebra
determinant
numerical-answers
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