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Most answered questions in Engineering Mathematics
97
votes
8
answers
91
GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
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 & ...
go_editor
36.9k
views
go_editor
asked
Sep 28, 2014
Linear Algebra
gatecse-2014-set2
linear-algebra
eigen-value
normal
numerical-answers
+
–
43
votes
8
answers
92
GATE CSE 2014 Set 2 | Question: 4
If the matrix $A$ is such that $A= \begin{bmatrix} 2\\ −4\\7\end{bmatrix}\begin{bmatrix}1& 9& 5\end{bmatrix}$ then the determinant of $A$ is equal to ______.
If the matrix $A$ is such that $$A= \begin{bmatrix} 2\\ −4\\7\end{bmatrix}\begin{bmatrix}1& 9& 5\end{bmatrix}$$ then the determinant of $A$ is equal to ______.
go_editor
12.7k
views
go_editor
asked
Sep 28, 2014
Linear Algebra
gatecse-2014-set2
linear-algebra
numerical-answers
easy
determinant
+
–
30
votes
8
answers
93
GATE CSE 1998 | Question: 1.1
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is $\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{8}$ $\dfrac{1}{2}$
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is$\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{8}$ $\dfrac{1}{2}...
Kathleen
8.4k
views
Kathleen
asked
Sep 25, 2014
Probability
gate1998
probability
easy
+
–
52
votes
8
answers
94
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
13.9k
views
Arjun
asked
Sep 24, 2014
Mathematical Logic
gatecse-2013
mathematical-logic
easy
first-order-logic
+
–
59
votes
8
answers
95
GATE CSE 2013 | Question: 26
The line graph $L(G)$ of a simple graph $G$ is defined as follows: There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$. For any two edges $e$ and $e'$ in $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if ... planar graph is planar. (S) The line graph of a tree is a tree. $P$ only $P$ and $R$ only $R$ only $P, Q$ and $S$ only
The line graph $L(G)$ of a simple graph $G$ is defined as follows:There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$.For any two edges $e$ and $e'$ in ...
Arjun
18.9k
views
Arjun
asked
Sep 24, 2014
Graph Theory
gatecse-2013
graph-theory
normal
graph-connectivity
+
–
48
votes
8
answers
96
GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move...
Kathleen
12.4k
views
Kathleen
asked
Sep 21, 2014
Combinatory
gatecse-2007
combinatory
+
–
43
votes
8
answers
97
GATE CSE 2007 | Question: 22
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ ... $\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ is connected. Which of the follo...
Kathleen
8.8k
views
Kathleen
asked
Sep 21, 2014
Mathematical Logic
gatecse-2007
mathematical-logic
easy
first-order-logic
+
–
27
votes
8
answers
98
GATE CSE 2005 | Question: 50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$?$i$$i+1$$2i$$2^i$
gatecse
8.1k
views
gatecse
asked
Sep 21, 2014
Combinatory
gatecse-2005
normal
generating-functions
+
–
31
votes
8
answers
99
GATE CSE 2010 | Question: 5
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? $0$ $e^{-2}$ $e^{-1/2}$ $1$
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ?$0$$e^{-2}$$e^{-1/2}$$1$
gatecse
8.9k
views
gatecse
asked
Sep 21, 2014
Calculus
gatecse-2010
calculus
limits
normal
+
–
86
votes
8
answers
100
GATE CSE 2004 | Question: 79
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k$ $^{\left(\frac{n^2-n}{2}\right)}C_n$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ?$^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$$^{{\l...
Kathleen
14.3k
views
Kathleen
asked
Sep 18, 2014
Graph Theory
gatecse-2004
graph-theory
combinatory
normal
counting
+
–
42
votes
8
answers
101
GATE CSE 2004 | Question: 73
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
The inclusion of which of the following sets into$S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3,...
Kathleen
12.8k
views
Kathleen
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2004
set-theory&algebra
partial-order
normal
+
–
37
votes
8
answers
102
GATE CSE 2006 | Question: 28
A logical binary relation $\odot$ ... $(\sim A\odot B)$ $\sim(A \odot \sim B)$ $\sim(\sim A\odot\sim B)$ $\sim(\sim A\odot B)$
A logical binary relation $\odot$, is defined as follows: $$\begin{array}{|l|l|l|} \hline \textbf{A} & \textbf{B}& \textbf{A} \odot \textbf{B}\\\hline \text{True} & \text...
Rucha Shelke
5.8k
views
Rucha Shelke
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2006
set-theory&algebra
binary-operation
+
–
34
votes
8
answers
103
GATE CSE 2002 | Question: 13
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$, the number of ways is $2$, i.e., $1+2, 2+1$. Give only ... $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$, th...
Kathleen
7.2k
views
Kathleen
asked
Sep 15, 2014
Combinatory
gatecse-2002
combinatory
normal
descriptive
balls-in-bins
+
–
39
votes
8
answers
104
GATE CSE 2002 | Question: 1.25, ISRO2008-30, ISRO2016-6
The maximum number of edges in a $n$-node undirected graph without self loops is $n^2$ $\frac{n(n-1)}{2}$ $n-1$ $\frac{(n+1)(n)}{2}$
The maximum number of edges in a $n$-node undirected graph without self loops is$n^2$$\frac{n(n-1)}{2}$$n-1$$\frac{(n+1)(n)}{2}$
Kathleen
17.7k
views
Kathleen
asked
Sep 15, 2014
Graph Theory
gatecse-2002
graph-theory
easy
isro2008
isro2016
graph-connectivity
+
–
33
votes
8
answers
105
GATE CSE 2009 | Question: 24
The binary operation $\Box$ ... following is equivalent to $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$
The binary operation $\Box$ is defined as follows$$\begin{array}{|c|c|c|} \hline \textbf{P} & \textbf{Q} & \textbf{P} \Box \textbf{Q}\\\hline \text{T} & \text{T}& \text{T...
gatecse
8.4k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2009
mathematical-logic
easy
propositional-logic
+
–
40
votes
8
answers
106
GATE CSE 2009 | Question: 23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
Which one of the following is the most appropriate logical formula to represent the statement?"Gold and silver ornaments are precious".The following notations are used: ...
gatecse
8.3k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2009
mathematical-logic
easy
first-order-logic
+
–
37
votes
8
answers
107
GATE CSE 2008 | Question: 27
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is $0.6$. If she studies mathematics on a day, then the probability that she studies computer ... what is the probability that she studies computer science on Wednesday? $0.24$ $0.36$ $0.4$ $0.6$
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next da...
Kathleen
7.6k
views
Kathleen
asked
Sep 11, 2014
Probability
gatecse-2008
probability
normal
conditional-probability
+
–
17
votes
8
answers
108
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then$P = Q - k$$P = Q...
Kathleen
5.5k
views
Kathleen
asked
Sep 11, 2014
Combinatory
gatecse-2008
combinatory
easy
summation
+
–
28
votes
8
answers
109
GATE CSE 2008 | Question: 2
If $P, Q, R$ are subsets of the universal set U, then $(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$ is $Q^c \cup R^c$ $P \cup Q^c \cup R^c$ $P^c \cup Q^c \cup R^c$ U
If $P, Q, R$ are subsets of the universal set U, then $$(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$$ is$Q^c \cup R^c$$P \cup Q^c \cup R^c$$P^c \cup Q^c \c...
Kathleen
9.2k
views
Kathleen
asked
Sep 11, 2014
Set Theory & Algebra
gatecse-2008
normal
set-theory&algebra
set-theory
+
–
0
votes
7
answers
110
NIELIT 2017 July Scientist B (CS) - Section B: 13
For the graph shown, which of the following paths is a Hamilton circuit? $ABCDCFDEFAEA$ $AEDCBAF$ $AEFDCBA$ $AFCDEBA$
For the graph shown, which of the following paths is a Hamilton circuit?$ABCDCFDEFAEA$$AEDCBAF$$AEFDCBA$$AFCDEBA$
admin
2.1k
views
admin
asked
Mar 30, 2020
Graph Theory
nielit2017july-scientistb-cs
discrete-mathematics
graph-theory
+
–
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