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Hot questions in Engineering Mathematics
26
votes
1
answer
151
GATE CSE 2022 | Question: 43
Which of the following is/are the eigenvector(s) for the matrix given below? $\begin{pmatrix} - 9 & - 6 & - 2 & - 4 \\ - 8 & - 6 & - 3 & - 1 \\ 20 & 15 & 8 & 5 \\ 32 & 21 & 7 & 12 \end{pmatrix}$ ... $\begin{pmatrix} - 1 \\ 0 \\ 2 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 0 \\ 1 \\ - 3 \\ 0 \end{pmatrix}$
Which of the following is/are the eigenvector(s) for the matrix given below?$$\begin{pmatrix} – 9 & – 6 & – 2 & – 4 \\ – 8 & – 6 & – 3 & – ...
Arjun
10.5k
views
Arjun
asked
Feb 15, 2022
Linear Algebra
gatecse-2022
linear-algebra
eigen-value
multiple-selects
2-marks
+
–
50
votes
4
answers
152
GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
What is the first order predicate calculus statement equivalent to the following?"Every teacher is liked by some student"$∀(x)\left[\text{teacher}\left(x\right) → ∃...
gatecse
11.8k
views
gatecse
asked
Sep 21, 2014
Mathematical Logic
gatecse-2005
mathematical-logic
easy
first-order-logic
+
–
5
votes
8
answers
153
GATE CSE 2024 | Set 1 | Question: 2
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is $-1$ $0$ $1$ $2$
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is$-1$$0$$1$$2$
Arjun
3.0k
views
Arjun
asked
Feb 16
Linear Algebra
gatecse2024-set1
linear-algebra
+
–
38
votes
3
answers
154
GATE CSE 2021 Set 1 | Question: 19
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that:The fastest computer g...
Arjun
11.9k
views
Arjun
asked
Feb 18, 2021
Combinatory
gatecse-2021-set1
combinatory
counting
numerical-answers
1-mark
+
–
18
votes
3
answers
155
GATE CSE 2022 | Question: 22
The number of arrangements of six identical balls in three identical bins is _____________ .
The number of arrangements of six identical balls in three identical bins is _____________ .
Arjun
10.5k
views
Arjun
asked
Feb 15, 2022
Combinatory
gatecse-2022
numerical-answers
combinatory
balls-in-bins
1-mark
+
–
43
votes
10
answers
156
GATE CSE 2003 | Question: 3
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right),{1}$ ${1},\left(\dfrac{1}{2}\right)$
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are$\left(\dfrac{1}{4...
Kathleen
11.8k
views
Kathleen
asked
Sep 16, 2014
Probability
gatecse-2003
probability
easy
conditional-probability
+
–
46
votes
3
answers
157
GATE CSE 2013 | Question: 47
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ? $∀ x(∃ z(¬β )→∀ y(α))$ $∀x(∀ z(β )→∃ y(¬α))$ $∀x(∀ y(α)→∃z(¬β ))$ $∀x(∃ y(¬α)→∃z(¬β ))$
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ?$∀ x(∃ z(¬β )→∀ y(α))$$∀x(∀ z(β )→∃ y(¬α))$$∀x(∀ y(�...
gatecse
12.0k
views
gatecse
asked
Aug 21, 2014
Mathematical Logic
mathematical-logic
normal
marks-to-all
gatecse-2013
first-order-logic
+
–
26
votes
4
answers
158
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 _______
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 ...
Arjun
19.7k
views
Arjun
asked
Feb 7, 2019
Linear Algebra
gatecse-2019
numerical-answers
engineering-mathematics
linear-algebra
eigen-value
2-marks
+
–
16
votes
3
answers
159
GATE CSE 2021 Set 2 | Question: 25
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that fo...
Arjun
6.3k
views
Arjun
asked
Feb 18, 2021
Calculus
gatecse-2021-set2
numerical-answers
calculus
continuity
1-mark
+
–
2
votes
2
answers
160
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 $\{-1,1,2\}$ $\{-2,-1,1\}$ $\{0,1\}$ $\{-1,0,1\}$
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....
Arjun
3.5k
views
Arjun
asked
Feb 16
Calculus
gatecse2024-set1
calculus
+
–
37
votes
7
answers
161
GATE CSE 2004 | Question: 77
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is$2$$3$$4$$5$
Kathleen
12.7k
views
Kathleen
asked
Sep 18, 2014
Graph Theory
gatecse-2004
graph-theory
graph-coloring
easy
+
–
43
votes
9
answers
162
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 ]$
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 ...
Kathleen
9.9k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
functions
normal
+
–
51
votes
4
answers
163
GATE CSE 1991 | Question: 01,xv
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
Kathleen
11.6k
views
Kathleen
asked
Sep 12, 2014
Graph Theory
gate1991
graph-theory
graph-connectivity
normal
fill-in-the-blanks
+
–
19
votes
5
answers
164
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 _______________ .
Consider a simple undirected graph of $10$ vertices. If the graph is disconnected, then the maximum number of edges it can have is _______________ .
Arjun
8.9k
views
Arjun
asked
Feb 15, 2022
Graph Theory
gatecse-2022
numerical-answers
graph-theory
graph-connectivity
1-mark
+
–
63
votes
14
answers
165
GATE CSE 2014 Set 1 | Question: 49
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. The set of all possible $1-$pennants is ${(1)}$, the set of all possible ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10-$pennants is________
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. ...
go_editor
11.6k
views
go_editor
asked
Sep 28, 2014
Combinatory
gatecse-2014-set1
combinatory
numerical-answers
normal
+
–
49
votes
5
answers
166
GATE CSE 2001 | Question: 2.3
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images. $S_1: f(E \cup F) = f(E) \cup f(F)$ $S_2: f(E \cap F)=f(E) \cap f(F)$ Which of the following is true about S1 and S2? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images.$S_1: f(E \cup F) = f(E) \cup f(F)$$S_2: f(E \cap F...
Kathleen
11.3k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
functions
normal
+
–
41
votes
4
answers
167
GATE CSE 2012 | Question: 21
Consider a random variable $X$ that takes values $+1$ and $−1$ with probability $0.5$ each. The values of the cumulative distribution function $F(x)$ at $x = −1$ and $+1$ are $0$ and $0.5$ $0$ and $1$ $0.5$ and $1$ $0.25$ and $0.75$
Consider a random variable $X$ that takes values $+1$ and $−1$ with probability $0.5$ each. The values of the cumulative distribution function $F(x)$ at $x = −1$ and ...
Arjun
12.7k
views
Arjun
asked
Sep 24, 2014
Probability
gatecse-2012
probability
random-variable
easy
+
–
29
votes
6
answers
168
GATE CSE 2002 | Question: 2.17
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetric Symmetric and reflexive Transitive and reflexive Transitive and symmetric
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetricSymmetric and reflexiveTransitive and reflexive...
Kathleen
13.0k
views
Kathleen
asked
Sep 15, 2014
Set Theory & Algebra
gatecse-2002
set-theory&algebra
normal
relations
+
–
60
votes
5
answers
169
GATE CSE 2007 | Question: 21
How many different non-isomorphic Abelian groups of order $4$ are there? $2$ $3$ $4$ $5$
How many different non-isomorphic Abelian groups of order $4$ are there?$2$$3$$4$$5$
Kathleen
19.7k
views
Kathleen
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2007
group-theory
normal
+
–
54
votes
7
answers
170
GATE CSE 2009 | Question: 3
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices have the same degree. At least three vertices have the same degree. All vertices have the same degree.
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices ...
gatecse
11.4k
views
gatecse
asked
Sep 15, 2014
Graph Theory
gatecse-2009
graph-theory
normal
degree-of-graph
+
–
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