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Recent questions and answers in Engineering Mathematics
25
votes
4
answers
1
TIFR CSE 2010 | Part A | Question: 8
Which of the following is NOT necessarily true? { Notation: The symbol ''$\neg$''notes negation; $P (x, y)$ means that for given $x$ and $y$, the property $P(x, y)$ is true }. $(∀x∀y P(x, y)) \Rightarrow (∀y∀x P(x, y))$ ... $(∃x∀y P(x, y)) \Rightarrow (∀y∃x P(x, y))$ $(∀x∃y P(x, y)) \Rightarrow (∃y∀x P(x, y))$
Sahil5635
answered
in
Mathematical Logic
Mar 24
by
Sahil5635
3.3k
views
tifr2010
mathematical-logic
first-order-logic
23
votes
6
answers
2
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 ____
dharmik_3103
answered
in
Linear Algebra
Mar 23
by
dharmik_3103
10.1k
views
gatecse-2018
linear-algebra
eigen-value
normal
numerical-answers
1-mark
3
votes
0
answers
3
#linear algebra
why Eigen Vectors can not be zero ?
srijankarak_123
asked
in
Linear Algebra
Mar 23
by
srijankarak_123
25
views
0
votes
1
answer
4
Discrete mathematics Ch 1 : Propositional logic , Topic 2 : Logical operators or connectives
Which of the following is the negation of x is even iff x is divisible by 2 a) (x is even or x is not divisible by 2) and (x is not even or x is divisible by 2) b) (x is even and x is not divisible by 2) ... is divisible by 2) c) x is not even iff x is not divisible by 2 d) x is even if x is divisible by 2
KraVLonE
answered
in
Mathematical Logic
Mar 20
by
KraVLonE
62
views
41
votes
9
answers
5
GATE CSE 1996 | Question: 2.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is given by $f^{-1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{x-y}\right)$ ... $f^{-1}(x,y)=\left [ 2\left(x-y\right),2\left(x+y\right) \right ]$
ritiksri8
answered
in
Set Theory & Algebra
Mar 20
by
ritiksri8
9.7k
views
gate1996
set-theory&algebra
functions
normal
42
votes
8
answers
6
GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
Rohit139
answered
in
Mathematical Logic
Mar 20
by
Rohit139
17.0k
views
gatecse-2020
first-order-logic
mathematical-logic
2-marks
49
votes
10
answers
7
GATE CSE 2016 Set 1 | Question: 05
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
reccurGautam
answered
in
Linear Algebra
Mar 20
by
reccurGautam
14.5k
views
gatecse-2016-set1
linear-algebra
eigen-value
numerical-answers
normal
0
votes
1
answer
8
Memory Based GATE DA 2024 | Question: 53
Consider the following scenarios involving linear algebra: For a \(3 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution? For a \(3 \times 3\) matrix, if some vector p ... 2 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution?
Ajay Sreenivas
answered
in
Linear Algebra
Mar 19
by
Ajay Sreenivas
118
views
gate2024-da-memory-based
goclasses
linear-algebra
system-of-equations
43
votes
14
answers
9
GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
artrides
answered
in
Linear Algebra
Mar 18
by
artrides
18.1k
views
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
4
votes
4
answers
10
Self Doubt: Mathematical Logic
Is the assertion "This statement is false" a proposition?
TusharRana
answered
in
Mathematical Logic
Mar 18
by
TusharRana
2.1k
views
mathematical-logic
7
votes
3
answers
11
Mathematics GATE 2011 probability
A fair die is tossed two times. the probability that 2nd toss results in value greater than first toss is ?
Creatorpk
answered
in
Probability
Mar 17
by
Creatorpk
2.4k
views
gate-ec
probability
expectation
36
votes
6
answers
12
GATE CSE 2017 Set 2 | Question: 21
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
ritiksri8
answered
in
Set Theory & Algebra
Mar 17
by
ritiksri8
11.8k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
6
votes
3
answers
13
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 2
Which of the following expressions is false? $p \rightarrow q \equiv q \rightarrow p$ $\neg(p \vee q) \equiv \neg p \wedge \neg q$ $p \rightarrow q \equiv \neg q \rightarrow \neg p$ none of the above
i_m_sudip
answered
in
Mathematical Logic
Mar 15
by
i_m_sudip
316
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
1-mark
3
votes
2
answers
14
GO Classes Weekly Quiz 5 | Propositional Logic | Question: 13
Let $p,q,r$ be three propositional variables. Which of the following statements is/are false? $p \rightarrow(q \vee r)) \equiv((p \wedge \neg q) \rightarrow r)$ $(p \wedge q) \vee r \equiv p \wedge(q \vee r)$ ... is FALSE then $(q \rightarrow p)$ is TRUE. If $(p \rightarrow q)$ is TRUE then $(q \rightarrow p)$ is FALSE.
i_m_sudip
answered
in
Mathematical Logic
Mar 15
by
i_m_sudip
358
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
34
votes
4
answers
15
GATE CSE 2005 | Question: 40
Let $P, Q,$ and $R$ be three atomic propositional assertions. Let $X$ denote $( P ∨ Q ) → R$ and $Y$ denote $(P → R) ∨ (Q → R).$ Which one of the following is a tautology? $X ≡ Y$ $X → Y$ $Y → X$ $¬Y → X$
i_m_sudip
answered
in
Mathematical Logic
Mar 13
by
i_m_sudip
6.5k
views
gatecse-2005
mathematical-logic
propositional-logic
normal
0
votes
2
answers
16
Find no of sets A and B such that A n B = {3,5} and A U B = {2,3,5,7,8)
I_M_CK
answered
in
Set Theory & Algebra
Mar 13
by
I_M_CK
99
views
0
votes
1
answer
17
Does Either...Or means Exclusive Or or Inclusive Or?
Let's take a compound propositions Either it is below freezing or it is snowing. Now if $p$: it is below freezing $q$: it is snowing Will it be $p \vee q$ or $p \oplus q$? There are some instances where semantics are ... both cases can't be true, because if you are ill you can't appear for example and you must be in one state.
I_M_CK
answered
in
Mathematical Logic
Mar 12
by
I_M_CK
106
views
propositional-logic
mathematical-logic
18
votes
4
answers
18
GATE CSE 2022 | Question: 10
Consider the following two statements with respect to the matrices $\textit{A}_{m \times n}, \textit{B}_{n \times m}, \textit{C}_{n \times n}$ and $ \textit{D}_{n \times n}.$ Statement $1: tr \text{(AB)} = tr \text{(BA)}$ ... $2$ is correct. Both Statement $1$ and Statement $2$ are correct. Both Statement $1$ and Statement $2$ are wrong.
Rohit139
answered
in
Linear Algebra
Mar 10
by
Rohit139
10.4k
views
gatecse-2022
linear-algebra
matrix
1-mark
14
votes
8
answers
19
GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
ritiksri8
answered
in
Mathematical Logic
Mar 9
by
ritiksri8
8.1k
views
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
24
votes
6
answers
20
GATE CSE 1995 | Question: 1.20
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is: $2$ $4$ $8$ None of the above
ritiksri8
answered
in
Set Theory & Algebra
Mar 9
by
ritiksri8
16.2k
views
gate1995
set-theory&algebra
normal
set-theory
29
votes
8
answers
21
GATE IT 2005 | Question: 3
The determinant of the matrix given below is $\begin{bmatrix} 0 &1 &0 &2 \\ -1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& -2& 0& 1 \end{bmatrix}$ $-1$ $0$ $1$ $2$
EagerLearner
answered
in
Linear Algebra
Mar 8
by
EagerLearner
20.3k
views
gateit-2005
linear-algebra
normal
determinant
2
votes
3
answers
22
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? $q \rightarrow \neg p$ $q \rightarrow p$ $p \rightarrow q$ $\neg p \rightarrow q$
Rohit139
answered
in
Mathematical Logic
Mar 6
by
Rohit139
3.0k
views
gatecse2024-set2
mathematical-logic
1
vote
1
answer
23
Why (p ∨ T) is not a tautology?
tbhaxor
answered
in
Mathematical Logic
Mar 6
by
tbhaxor
137
views
mathematical-logic
propositional-logic
0
votes
2
answers
24
Kenneth Rosen Edition 7 Exercise 6.1 Question 57 (Page No. 398)
The name of a variable in the JAVA programming language is a string of between $1$ and $65,535$ characters, inclusive, where each character can be an uppercase or a lowercase letter, a dollar sign, an underscore, or a digit, except that the first character must not be a digit. Determine the number of different variable names in JAVA.
Shriram BM
answered
in
Combinatory
Mar 3
by
Shriram BM
1.1k
views
kenneth-rosen
discrete-mathematics
counting
descriptive
87
votes
7
answers
25
GATE CSE 2004 | Question: 23, ISRO2007-32
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$ ... $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
ritiksri8
answered
in
Mathematical Logic
Mar 3
by
ritiksri8
110k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
1
vote
2
answers
26
Evaluate the limit without using L' Hospital Rule.
Priyam Garg
answered
in
Calculus
Feb 28
by
Priyam Garg
253
views
limits
calculus
1
vote
2
answers
27
Memory Based GATE DA 2024 | Question: 3
Evaluate the limit: \[ \lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2} \]
Sonu123x
answered
in
Calculus
Feb 28
by
Sonu123x
461
views
gate2024-da-memory-based
goclasses
calculus
limits
numerical-answers
20
votes
5
answers
28
TIFR CSE 2016 | Part A | Question: 8
Let $A$ and $B$ be finite sets such that $A \subseteq B$. Then, what is the value of the expression: $ \sum \limits_{C:A \subseteq C \subseteq B} (-1)^{\mid C \setminus A \mid,}$ Where $C \setminus A=\{x \in C : x \notin A \}$? Always $0$ Always $1$ $0$ if $A=B$ and $1$ otherwise $1$ if $A=B$ and $0$ otherwise Depends on the size of the universe
Priyam Garg
answered
in
Set Theory & Algebra
Feb 28
by
Priyam Garg
2.7k
views
tifr2016
set-theory&algebra
set-theory
7
votes
4
answers
29
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
Priyam Garg
answered
in
Combinatory
Feb 27
by
Priyam Garg
7.8k
views
gatecse-2023
combinatory
recurrence-relation
1-mark
19
votes
18
answers
30
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
ravi2002
answered
in
Combinatory
Feb 26
by
ravi2002
18.1k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
16
votes
3
answers
31
TIFR CSE 2014 | Part A | Question: 17
A fair dice (with faces numbered $1, . . . , 6$) is independently rolled repeatedly. Let $X$ denote the number of rolls till an even number is seen and let $Y$ denote the number of rolls till $3$ is seen. Evaluate $E(Y |X = 2)$. $6\frac{5}{6}$ $6$ $5\frac{1}{2}$ $6\frac{1}{3}$ $5\frac{2}{3}$
Priyam Garg
answered
in
Probability
Feb 25
by
Priyam Garg
4.0k
views
tifr2014
expectation
54
votes
7
answers
32
GATE CSE 2016 Set 2 | Question: 04
Consider the systems, each consisting of $m$ linear equations in $n$ variables. If $m < n$, then all such systems have a solution. If $m > n$, then none of these systems has a solution. If $m = n$, then there exists a system which has a solution. ... $\text{II}$ and $\text{III}$ are true. Only $\text{III}$ is true. None of them is true.
SASIDHAR_1
answered
in
Linear Algebra
Feb 25
by
SASIDHAR_1
15.7k
views
gatecse-2016-set2
linear-algebra
system-of-equations
normal
19
votes
4
answers
33
GATE CSE 2005 | Question: 48
Consider the following system of linear equations : $2x_1 - x_2 + 3x_3 = 1$ $3x_1 + 2x_2 + 5x_3 = 2$ $-x_1+4x_2+x_3 = 3$ The system of equations has no solution a unique solution more than one but a finite number of solutions an infinite number of solutions
SASIDHAR_1
answered
in
Linear Algebra
Feb 25
by
SASIDHAR_1
7.2k
views
gatecse-2005
linear-algebra
system-of-equations
normal
19
votes
7
answers
34
TIFR CSE 2013 | Part A | Question: 6
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise two-thirds of the population the park and give a correct answer to requests for directions with probability $\dfrac{3}{4}$. The air of Kabrastan has an ... $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{2}{3}\right)$ $\left(\dfrac{3}{4}\right)$
Priyam Garg
answered
in
Probability
Feb 25
by
Priyam Garg
3.2k
views
tifr2013
probability
conditional-probability
48
votes
7
answers
35
GATE CSE 1996 | Question: 1.7
Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false? The system has a solution if and ... a unique solution. The system will have only a trivial solution when $m=n$, $b$ is the zero vector and $\text{rank}(A) =n$.
SASIDHAR_1
answered
in
Linear Algebra
Feb 25
by
SASIDHAR_1
21.3k
views
gate1996
linear-algebra
system-of-equations
normal
0
votes
0
answers
36
#discrete
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 24
by
Çșȇ ʛấẗẻ
61
views
discrete-mathematics
kenneth-rosen
0
votes
0
answers
37
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
38
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
124
views
engineering-mathematics
propositional-logic
0
votes
1
answer
39
#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
40
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
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