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Recent activity in Engineering Mathematics
77
votes
9
answers
1
GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
viral8702
commented
in
Linear Algebra
5 hours
ago
by
viral8702
28.4k
views
gatecse-2014-set2
linear-algebra
eigen-value
normal
numerical-answers
0
votes
1
answer
2
graph theory ,discrete math
how many subgraph with atleast 1 vertex does k2 have? (graph theory question)
shuham kumar
answered
in
Mathematical Logic
9 hours
ago
by
shuham kumar
80
views
discrete-mathematics
graph-theory
2
votes
1
answer
3
Kenneth Rosen Edition 6th Exercise 1.1 Question 10 (Page No. 17)
Let p, q, and r be the propositions p : You get an A on the final exam. q : You do every exercise in this book. r : You get an A in this class. Write these propositions using p, q, and r and logical connectives (including ... get an A in this class if and only if you either do every exercise in this book or you get an A on the final.
pavan singh
comment edited
in
Mathematical Logic
22 hours
ago
by
pavan singh
3.1k
views
kenneth-rosen
mathematical-logic
discrete-mathematics
4
votes
1
answer
4
Kenneth Rosen Edition 6th Exercise 1.1 Question 11 (Page No. 17)
Let p, q, and r be the propositions p : Grizzly bears have been seen in the area. q : Hiking is safe on the trail. r : Berries are ripe along the trail. Write these propositions using p, q, and r and logical ... . Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are ripe along the trail.
pavan singh
comment edited
in
Mathematical Logic
22 hours
ago
by
pavan singh
4.7k
views
kenneth-rosen
mathematical-logic
42
votes
7
answers
5
GATE CSE 2011 | Question: 34
A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number ... $\left(\dfrac{4}{25}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{2}{5}\right)$
Umair alvi
commented
in
Probability
1 day
ago
by
Umair alvi
12.9k
views
gatecse-2011
probability
normal
82
votes
8
answers
6
GATE CSE 2016 Set 1 | Question: 28
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.
Souvik33
commented
in
Set Theory & Algebra
1 day
ago
by
Souvik33
16.0k
views
gatecse-2016-set1
set-theory&algebra
functions
normal
numerical-answers
37
votes
12
answers
7
GATE CSE 2007 | Question: 24
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these
Umair alvi
commented
in
Probability
2 days
ago
by
Umair alvi
11.3k
views
gatecse-2007
probability
easy
uniform-distribution
0
votes
1
answer
8
Discrete mathematics kenneth rosen
Determine whether the premises If I do not leave my home early or get stuck in a traffic jam, I will be late to my class and get scolded by my teacher , If I am late to my class, I will miss the attendance for the day , and ... today lead to the conclusion Therefore, I have left my home early today . Explain which rules of inference are used for each step.
Sunnidhya Roy
answer edited
in
Mathematical Logic
2 days
ago
by
Sunnidhya Roy
142
views
discrete-mathematics
mathematical-logic
kenneth-rosen
11
votes
5
answers
9
GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$
Shubham8415
commented
in
Mathematical Logic
2 days
ago
by
Shubham8415
4.0k
views
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
28
votes
3
answers
10
GATE CSE 2018 | Question: 44
Consider Guwahati, $(G)$ and Delhi $(D)$ whose temperatures can be classified as high $(H)$, medium $(M)$ and low $(L)$. Let $P(H_G)$ denote the probability that Guwahati has high temperature. Similarly, $P(M_G)$ ... , then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is ________.
Lakshman Patel RJIT
retagged
in
Probability
2 days
ago
by
Lakshman Patel RJIT
10.1k
views
gatecse-2018
probability
conditional-probability
numerical-answers
2-marks
2
votes
1
answer
11
Kenneth Rosen Edition 6th Exercise 1.1 Question 8 (Page No. 17)
Let p, q, and r be the propositions p : You have the flu. q : You miss the final examination. r : You pass the course. Express each of these propositions as an English sentence. $p \rightarrow q$ $\neg q \leftrightarrow r$ ... $(p \rightarrow \neg r) \vee (q \rightarrow \neg r)$ $(p \wedge q) \vee (\neg q \wedge r)$
pavan singh
commented
in
Mathematical Logic
2 days
ago
by
pavan singh
2.0k
views
kenneth-rosen
discrete-mathematics
mathematical-logic
63
votes
3
answers
12
GATE CSE 2018 | Question: 28
Consider the first-order logic sentence $\varphi \equiv \exists \: s \: \exists \: t \: \exists \: u \: \forall \: v \: \forall \: w \forall \: x \: \forall \: y \: \psi(s, t, u, v, w, x, y)$ ... or equal to $3$ There exists no model of $\varphi$ with universe size of greater than $7$ Every model of $\varphi$ has a universe of size equal to $7$
Lakshman Patel RJIT
retagged
in
Mathematical Logic
2 days
ago
by
Lakshman Patel RJIT
16.9k
views
gatecse-2018
mathematical-logic
normal
first-order-logic
2-marks
42
votes
6
answers
13
GATE CSE 2018 | Question: 27
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
Lakshman Patel RJIT
retagged
in
Set Theory & Algebra
2 days
ago
by
Lakshman Patel RJIT
16.3k
views
gatecse-2018
set-theory&algebra
countable-uncountable-set
normal
2-marks
59
votes
5
answers
14
GATE CSE 2018 | Question: 26
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the ... III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
Lakshman Patel RJIT
edited
in
Linear Algebra
2 days
ago
by
Lakshman Patel RJIT
19.6k
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gatecse-2018
linear-algebra
matrix
eigen-value
normal
2-marks
23
votes
4
answers
15
GATE CSE 2018 | Question: 19
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
Lakshman Patel RJIT
retagged
in
Set Theory & Algebra
3 days
ago
by
Lakshman Patel RJIT
10.1k
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gatecse-2018
group-theory
numerical-answers
set-theory&algebra
1-mark
28
votes
5
answers
16
GATE CSE 2018 | Question: 18
The chromatic number of the following graph is _____
Lakshman Patel RJIT
retagged
in
Graph Theory
3 days
ago
by
Lakshman Patel RJIT
9.1k
views
graph-theory
graph-coloring
numerical-answers
gatecse-2018
1-mark
19
votes
3
answers
17
GATE CSE 2018 | Question: 17
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ____
Lakshman Patel RJIT
retagged
in
Linear Algebra
3 days
ago
by
Lakshman Patel RJIT
6.9k
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gatecse-2018
linear-algebra
eigen-value
normal
numerical-answers
1-mark
26
votes
4
answers
18
GATE CSE 2018 | Question: 16
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
Lakshman Patel RJIT
retagged
in
Calculus
3 days
ago
by
Lakshman Patel RJIT
11.4k
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gatecse-2018
calculus
integration
normal
numerical-answers
1-mark
27
votes
8
answers
19
GATE CSE 2018 | Question: 15
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a ... and that all trials are independent. The probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____
Lakshman Patel RJIT
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in
Probability
3 days
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Lakshman Patel RJIT
7.9k
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gatecse-2018
probability
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numerical-answers
1-mark
34
votes
11
answers
20
GATE CSE 2018 | Question: 1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
Lakshman Patel RJIT
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Combinatory
3 days
ago
by
Lakshman Patel RJIT
17.3k
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gatecse-2018
generating-functions
normal
combinatory
1-mark
2
votes
1
answer
21
Kenneth Rosen Edition 6th Exercise 1.1 Question 5 (Page No. 16)
Let p and q be the propositions Swimming at the New Jersey shore is allowed and Sharks have been spotted near the shore, respectively. Express each of these compound propositions as an English sentence. $\neg q$ $p \wedge q$ ... $\neg p \rightarrow \neg q$ $p \leftrightarrow \neg q$ $\neg p \wedge (p \vee \neg q)$
pavan singh
comment edited
in
Mathematical Logic
3 days
ago
by
pavan singh
3.1k
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kenneth-rosen
mathematical-logic
discrete-mathematics
2
votes
1
answer
22
Kenneth Rosen Edition 6th Exercise 1.1 Question 6 (Page No. 17)
Let p and q be the propositions The election is decided and The votes have been counted, respectively. Express each of these compound propositions as an English sentence. $\neg p$ $p \vee q$ $\neg p \wedge q$ $q \rightarrow p$ ... $\neg p \rightarrow \neg q$ $p \leftrightarrow q$ $\neg q \vee (\neg p \wedge q)$
pavan singh
comment edited
in
Mathematical Logic
3 days
ago
by
pavan singh
2.7k
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mathematical-logic
kenneth-rosen
discrete-mathematics
2
votes
1
answer
23
Kenneth Rosen Edition 6th Exercise 1.1 Question 4 (Page No. 16)
Let p and q be the propositions p : I bought a lottery ticket this week. q : I won the million dollar jackpot. Express each of these propositions as an English sentence. $\neg p$ $p \vee q$ $p \rightarrow q$ $p \wedge q$ $p \leftrightarrow q$ $\neg p \rightarrow \neg q$ $\neg p \wedge \neg q$ $\neg p \vee (p \wedge q)$
pavan singh
commented
in
Mathematical Logic
3 days
ago
by
pavan singh
2.7k
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kenneth-rosen
mathematical-logic
0
votes
1
answer
24
Null Qunatification Rule
What is the meaning of NULL Quantification Rule in Predicate Calculus ?
Rusty_01
commented
in
Mathematical Logic
3 days
ago
by
Rusty_01
2.2k
views
discrete-mathematics
propositional-logic
7
votes
5
answers
25
GATE CSE 2022 | Question: 20
Consider a simple undirected graph of $10$ vertices. If the graph is disconnected, then the maximum number of edges it can have is _______________ .
dutta18
answered
in
Graph Theory
3 days
ago
by
dutta18
2.3k
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gatecse-2022
numerical-answers
graph-theory
graph-connectivity
1-mark
28
votes
3
answers
26
GATE CSE 2019 | Question: 47
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal place) _______
Lakshman Patel RJIT
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Probability
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Lakshman Patel RJIT
11.8k
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gatecse-2019
numerical-answers
engineering-mathematics
probability
uniform-distribution
2-marks
18
votes
4
answers
27
GATE CSE 2019 | Question: 44
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
Lakshman Patel RJIT
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Linear Algebra
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Lakshman Patel RJIT
12.7k
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numerical-answers
engineering-mathematics
linear-algebra
eigen-value
2-marks
30
votes
6
answers
28
GATE CSE 2019 | Question: 38
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
Lakshman Patel RJIT
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Graph Theory
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Lakshman Patel RJIT
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engineering-mathematics
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graph-theory
graph-connectivity
2-marks
44
votes
10
answers
29
GATE CSE 2019 | Question: 35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... of all integers Which of the above sets satisfy $\varphi$? $S_1$ and $S_2$ $S_1$ and $S_3$ $S_2$ and $S_3$ $S_1, S_2$ and $S_3$
Lakshman Patel RJIT
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Mathematical Logic
3 days
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Lakshman Patel RJIT
14.7k
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gatecse-2019
engineering-mathematics
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first-order-logic
2-marks
17
votes
15
answers
30
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
Lakshman Patel RJIT
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Combinatory
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Lakshman Patel RJIT
13.9k
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