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Recent questions and answers in Engineering Mathematics
40
votes
14
answers
1
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
7 hours
ago
by
artrides
17.8k
views
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
4
votes
4
answers
2
Self Doubt: Mathematical Logic
Is the assertion "This statement is false" a proposition?
TusharRana
answered
in
Mathematical Logic
21 hours
ago
by
TusharRana
2.1k
views
mathematical-logic
7
votes
3
answers
3
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
1 day
ago
by
Creatorpk
2.3k
views
gate-ec
probability
expectation
36
votes
6
answers
4
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
1 day
ago
by
ritiksri8
11.6k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
6
votes
3
answers
5
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
4 days
ago
by
i_m_sudip
290
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
1-mark
3
votes
2
answers
6
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
4 days
ago
by
i_m_sudip
332
views
goclasses2024_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
34
votes
4
answers
7
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
5 days
ago
by
i_m_sudip
6.4k
views
gatecse-2005
mathematical-logic
propositional-logic
normal
0
votes
2
answers
8
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
5 days
ago
by
I_M_CK
63
views
0
votes
1
answer
9
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 required. For ... this 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
6 days
ago
by
I_M_CK
64
views
propositional-logic
mathematical-logic
23
votes
5
answers
10
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 ____
Rohit139
answered
in
Linear Algebra
Mar 10
by
Rohit139
10.0k
views
gatecse-2018
linear-algebra
eigen-value
normal
numerical-answers
1-mark
17
votes
4
answers
11
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
9.7k
views
gatecse-2022
linear-algebra
matrix
1-mark
14
votes
8
answers
12
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
7.9k
views
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
24
votes
6
answers
13
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
16.1k
views
gate1995
set-theory&algebra
normal
set-theory
29
votes
8
answers
14
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
17.6k
views
gateit-2005
linear-algebra
normal
determinant
2
votes
3
answers
15
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
2.8k
views
gatecse2024-set2
mathematical-logic
1
vote
1
answer
16
Why (p ∨ T) is not a tautology?
tbhaxor
answered
in
Mathematical Logic
Mar 6
by
tbhaxor
107
views
mathematical-logic
propositional-logic
0
votes
2
answers
17
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 4
by
Shriram BM
1.1k
views
kenneth-rosen
discrete-mathematics
counting
descriptive
87
votes
7
answers
18
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
88.2k
views
gatecse-2004
mathematical-logic
easy
isro2007
first-order-logic
1
vote
2
answers
19
Evaluate the limit without using L' Hospital Rule.
Priyam Garg
answered
in
Calculus
Feb 28
by
Priyam Garg
233
views
limits
calculus
1
vote
2
answers
20
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
424
views
gate2024-da-memory-based
goclasses
calculus
limits
numerical-answers
20
votes
5
answers
21
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
2.6k
views
tifr2016
set-theory&algebra
set-theory
7
votes
4
answers
22
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 28
by
Priyam Garg
7.7k
views
gatecse-2023
combinatory
recurrence-relation
1-mark
19
votes
18
answers
23
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
ravi2002
answered
in
Combinatory
Feb 26
by
ravi2002
17.9k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
16
votes
3
answers
24
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
3.9k
views
tifr2014
expectation
53
votes
7
answers
25
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
15.5k
views
gatecse-2016-set2
linear-algebra
system-of-equations
normal
19
votes
4
answers
26
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
6.2k
views
gatecse-2005
linear-algebra
system-of-equations
normal
19
votes
7
answers
27
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
28
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
21.2k
views
gate1996
linear-algebra
system-of-equations
normal
9
votes
5
answers
29
TIFR CSE 2013 | Part A | Question: 17
A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio $4:3$. What is the probability that the three sticks that are left CANNOT form a triangle? $1/4$ $1/3$ $5/6$ $1/2$ $\log_{e}(2)/2$
Priyam Garg
answered
in
Probability
Feb 24
by
Priyam Garg
1.8k
views
tifr2013
probability
0
votes
0
answers
30
#discrete
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Feb 24
by
Çșȇ ʛấẗẻ
50
views
discrete-mathematics
kenneth-rosen
2
votes
3
answers
31
ISI2016-MMA-27
Consider the function $f(x) = \dfrac{e^{- \mid x \mid}}{\text{max}\{e^x, e^{-x}\}}, \: \: x \in \mathbb{R}$. Then $f$ is not continuous at some points $f$ is continuous everywhere, but not differentiable anywhere $f$ is continuous everywhere, but not differentiable at exactly one point $f$ is differentiable everywhere
Sonu123x
answered
in
Calculus
Feb 24
by
Sonu123x
518
views
isi2016-mmamma
calculus
continuity
differentiation
0
votes
1
answer
32
ISI2016-MMA-24
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one the following is always true? The limits $\lim_{x \rightarrow a+} f(x) $ and $\lim_{x \rightarrow a-} f(x)$ exist for all real numbers $a$ If $f$ is differentiable at $a$ then ... such that $f(x)<B$ for all real $x$ There cannot be any real number $L$ such that $f(x)>L$ for all real $x$
Sonu123x
answered
in
Calculus
Feb 24
by
Sonu123x
458
views
isi2016-mmamma
calculus
continuity
differentiation
limits
0
votes
2
answers
33
ISI2016-PCB-A-2
Let $n$ be a fixed positive integer. For any real number $x,$ if for some integer $q,$ $x=qn+r, \: \: \: 0 \leq r < n,$ then we define $x \text{ mod } n=r$. Specify the points of discontinuity of the function $f(x)=x \text{ mod } 3$ with proper reasoning.
Sonu123x
answered
in
Calculus
Feb 24
by
Sonu123x
405
views
isi2016-pcb-a
calculus
continuity
non-gate
descriptive
0
votes
0
answers
34
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 24
by
rick55
44
views
1
vote
4
answers
35
ISI2018-MMA-28
Consider the following functions $f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ ... at $\pm1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $\pm2$ $h_1$ has discontinuity at $\pm 2$ and $h_2$ has discontinuity at $\pm1$.
Sonu123x
answered
in
Calculus
Feb 23
by
Sonu123x
1.2k
views
isi2018-mma
engineering-mathematics
calculus
continuity
12
votes
4
answers
36
TIFR CSE 2011 | Part A | Question: 14
The limit $\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$ is $0$ $2$ $1$ $\frac{1}{2}$ None of the above
Priyam Garg
answered
in
Calculus
Feb 23
by
Priyam Garg
2.2k
views
tifr2011
calculus
limits
25
votes
7
answers
37
TIFR CSE 2011 | Part A | Question: 19
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{9}\right)$ $\left(\dfrac{5}{18}\right)$ $\left(\dfrac{2}{9}\right)$
Priyam Garg
answered
in
Probability
Feb 23
by
Priyam Garg
2.8k
views
tifr2011
probability
independent-events
36
votes
2
answers
38
GATE CSE 2008 | Question: 25
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$
Sonu123x
answered
in
Calculus
Feb 23
by
Sonu123x
8.4k
views
gatecse-2008
calculus
maxima-minima
easy
0
votes
2
answers
39
ISI2015-DCG-57
Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and many-one $y$ is not differentiable and many-one $y$ is not differentiable $y$ is differentiable and many-one
Sonu123x
answered
in
Calculus
Feb 22
by
Sonu123x
402
views
isi2015-dcg
calculus
continuity
differentiation
1
vote
3
answers
40
NIELIT 2017 DEC Scientific Assistant A - Section B: 10
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is : Continuous and differentiable Continuous but not differentiable Differentiable but not continuous Neither continuous nor differentiable
Sonu123x
answered
in
Calculus
Feb 22
by
Sonu123x
1.1k
views
nielit2017dec-assistanta
engineering-mathematics
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