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Most viewed questions in Engineering Mathematics
49
votes
10
answers
121
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 _______
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
Sandeep Singh
14.5k
views
Sandeep Singh
asked
Feb 12, 2016
Linear Algebra
gatecse-2016-set1
linear-algebra
eigen-value
numerical-answers
normal
+
–
23
votes
3
answers
122
GATE CSE 1998 | Question: 1.23
How many sub strings of different lengths (non-zero) can be formed from a character string of length $n$? $n$ $n^2$ $2^n$ $\frac{n(n+1)}{2}$
How many sub strings of different lengths (non-zero) can be formed from a character string of length $n$?$n$$n^2$$2^n$$\frac{n(n+1)}{2}$
Kathleen
14.4k
views
Kathleen
asked
Sep 25, 2014
Combinatory
gate1998
combinatory
normal
+
–
60
votes
4
answers
123
GATE CSE 2014 Set 1 | Question: 5
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________
go_editor
14.3k
views
go_editor
asked
Sep 26, 2014
Linear Algebra
gatecse-2014-set1
linear-algebra
eigen-value
numerical-answers
normal
+
–
86
votes
8
answers
124
GATE CSE 2004 | Question: 79
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k$ $^{\left(\frac{n^2-n}{2}\right)}C_n$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ?$^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$$^{{\l...
Kathleen
14.3k
views
Kathleen
asked
Sep 18, 2014
Graph Theory
gatecse-2004
graph-theory
combinatory
normal
counting
+
–
39
votes
5
answers
125
GATE CSE 2017 Set 2 | Question: 24
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
khushtak
14.3k
views
khushtak
asked
Feb 14, 2017
Set Theory & Algebra
gatecse-2017-set2
polynomials
numerical-answers
set-theory&algebra
+
–
28
votes
6
answers
126
GATE CSE 1995 | Question: 1.19
Let $R$ be a symmetric and transitive relation on a set $A$. Then $R$ is reflexive and hence an equivalence relation $R$ is reflexive and hence a partial order $R$ is reflexive and hence not an equivalence relation None of the above
Let $R$ be a symmetric and transitive relation on a set $A$. Then$R$ is reflexive and hence an equivalence relation$R$ is reflexive and hence a partial order$R$ is reflex...
Kathleen
14.2k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
relations
normal
+
–
0
votes
2
answers
127
How many subgraphs with at least one vertex does K3 have?
Piyush Kapoor
14.0k
views
Piyush Kapoor
asked
Oct 8, 2015
Graph Theory
graph-theory
+
–
9
votes
2
answers
128
Please explain this question .. Number of trivial substrings in “GATE2013” are: A. 37 B. 35 C. 2 D. 36
vijay dwivedi
14.0k
views
vijay dwivedi
asked
Jun 7, 2015
Combinatory
combinatory
counting
+
–
52
votes
6
answers
129
GATE CSE 2001 | Question: 2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices?$\frac{n(n-1)} {2}$$2^n$$n!$$2^\f...
Kathleen
14.0k
views
Kathleen
asked
Sep 14, 2014
Graph Theory
gatecse-2001
graph-theory
normal
counting
+
–
52
votes
8
answers
130
GATE CSE 2013 | Question: 27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
What is the logical translation of the following statement?"None of my friends are perfect."$∃x(F (x)∧ ¬P(x))$$∃ x(¬ F (x)∧ P(x))$$ ∃x(¬F (x)∧¬P(x))$$ ¬�...
Arjun
14.0k
views
Arjun
asked
Sep 24, 2014
Mathematical Logic
gatecse-2013
mathematical-logic
easy
first-order-logic
+
–
57
votes
6
answers
131
GATE CSE 2003 | Question: 72
The following resolution rule is used in logic programming. Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$ Which of the following statements related to this rule is FALSE? $((P ∨ R)∧(Q ∨ ¬R))⇒(P ∨ Q)$ ... if $(P ∨ R)∧(Q ∨ ¬R)$ is satisfiable $(P ∨ Q)⇒ \text{FALSE}$ if and only if both $P$ and $Q$ are unsatisfiable
The following resolution rule is used in logic programming.Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$Which of the following statements related to th...
Kathleen
13.9k
views
Kathleen
asked
Sep 17, 2014
Mathematical Logic
gatecse-2003
mathematical-logic
normal
propositional-logic
+
–
7
votes
3
answers
132
ISRO2018-38
The number of edges in a regular graph of degree: $d$ and $n$ vertices is: maximum of $n$ and $d$ $n +d$ $nd$ $nd/2$
The number of edges in a regular graph of degree: $d$ and $n$ vertices is:maximum of $n$ and $d$ $n +d$$nd$$nd/2$
Arjun
13.9k
views
Arjun
asked
Apr 22, 2018
Graph Theory
isro2018
graph-theory
graph-connectivity
+
–
63
votes
5
answers
133
GATE CSE 2014 Set 3 | Question: 2
Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE? For any subsets $A$ and $B$ of $X, |f(A \cup B)| = |f(A)| + |f(B)|$ For any subsets $A$ and $B$ of $X, f(A \cap B) = f(A) \cap f(B)$ For any subsets $A$ ... $S$ and $T$ of $Y, f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$
Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE?For any subsets $A$ and $B$ of $X, |f(A \cup B)| = |f(A)| + |f...
go_editor
13.9k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
functions
normal
+
–
39
votes
5
answers
134
GATE CSE 2000 | Question: 2.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having $1$ equivalence class $R$ is an equivalence relation having $2$ equivalence classes $R$ is an equivalence relation having $3$ equivalence classes
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true?$R$ is not an equivalence relation$R$ is an equ...
Kathleen
13.9k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2000
set-theory&algebra
relations
normal
+
–
30
votes
5
answers
135
GATE CSE 2017 Set 1 | Question: 30
Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $w = u + \alpha v$ bisects the angle between $u$ and $v$? $2$ $\frac{1}{2}$ $1$ $\frac{ -1}{2}$
Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $...
Arjun
13.9k
views
Arjun
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set1
linear-algebra
normal
vector-space
+
–
43
votes
6
answers
136
GATE IT 2008 | Question: 27
$G$ is a simple undirected graph. Some vertices of $G$ are of odd degree. Add a node $v$ to $G$ and make it adjacent to each odd degree vertex of $G$. The resultant graph is sure to be regular complete Hamiltonian Euler
$G$ is a simple undirected graph. Some vertices of $G$ are of odd degree. Add a node $v$ to $G$ and make it adjacent to each odd degree vertex of $G$. The resultant graph...
Ishrat Jahan
13.9k
views
Ishrat Jahan
asked
Oct 28, 2014
Graph Theory
gateit-2008
graph-theory
graph-connectivity
normal
+
–
70
votes
5
answers
137
GATE CSE 2008 | Question: 30
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown automaton. Let $\text{equivalent}$ ...
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown autom...
Kathleen
13.9k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gatecse-2008
easy
mathematical-logic
first-order-logic
+
–
40
votes
5
answers
138
GATE CSE 1996 | Question: 2.2
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement)$A$ is reflexive and transi...
Kathleen
13.9k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
relations
normal
+
–
60
votes
4
answers
139
GATE CSE 2012 | Question: 9
Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local minima of this function are One, at $\dfrac{\pi}{2}$ One, at $\dfrac{3\pi}{2}$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2}$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$
Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local minima of this function are...
gatecse
13.8k
views
gatecse
asked
Aug 5, 2014
Calculus
gatecse-2012
calculus
maxima-minima
normal
+
–
35
votes
6
answers
140
GATE CSE 1994 | Question: 1.4, ISRO2017-2
Let $A$ and $B$ be any two arbitrary events, then, which one of the following is TRUE? $P (A \cap B) = P(A)P(B)$ $P (A \cup B) = P(A)+P(B)$ $P (A \mid B) = P(A \cap B)P(B)$ $P (A \cup B) \leq P(A) + P(B)$
Let $A$ and $B$ be any two arbitrary events, then, which one of the following is TRUE?$P (A \cap B) = P(A)P(B)$$P (A \cup B) = P(A)+P(B)$$P (A \mid B) = P(A \cap B)P(B)$$...
Kathleen
13.8k
views
Kathleen
asked
Oct 4, 2014
Probability
gate1994
probability
conditional-probability
normal
isro2017
+
–
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