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Most viewed questions in Engineering Mathematics
61
votes
8
answers
91
GATE IT 2007 | Question: 2
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvectors of $A?$ $5$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5 - √5)}{2}$
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvect...
Ishrat Jahan
16.5k
views
Ishrat Jahan
asked
Oct 29, 2014
Linear Algebra
gateit-2007
linear-algebra
eigen-value
normal
+
–
34
votes
4
answers
92
GATE CSE 2019 | Question: 47
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal place) _______
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal...
Arjun
16.5k
views
Arjun
asked
Feb 7, 2019
Probability
gatecse-2019
numerical-answers
engineering-mathematics
probability
uniform-distribution
2-marks
+
–
28
votes
4
answers
93
GATE CSE 2018 | Question: 16
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
gatecse
16.5k
views
gatecse
asked
Feb 14, 2018
Calculus
gatecse-2018
calculus
integration
normal
numerical-answers
1-mark
+
–
6
votes
1
answer
94
The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain a) exactly one vowel? b) exactly two vowels? c) at least one vowel? d) at least two vowels?
Hi Answer to each option is given as:a) 122,523,030b) 72,930,375c) 223,149,655d) 100,626,625And I used the following approach to each option but answers don't match.a) C(...
Sahil Gupta
16.5k
views
Sahil Gupta
asked
Nov 23, 2014
24
votes
6
answers
95
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
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
Kathleen
16.4k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
normal
set-theory
+
–
10
votes
3
answers
96
ISRO2007-29
The set of all Equivalence Classes of a set A of Cardinality C is of cardinality $2^c$ have the same cardinality as A forms a partition of A is of cardinality $C^2$
The set of all Equivalence Classes of a set A of Cardinality Cis of cardinality $2^c$have the same cardinality as Aforms a partition of Ais of cardinality $C^2$
go_editor
16.4k
views
go_editor
asked
Jun 10, 2016
Set Theory & Algebra
isro2007
set-theory&algebra
equivalence-class
+
–
50
votes
7
answers
97
GATE CSE 2017 Set 2 | Question: 31
For any discrete random variable $X$, with probability mass function $P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain ... . The expectation of $Y$ is $N \beta(1-\beta)$ $N \beta$ $N (1-\beta)$ Not expressible in terms of $N$ and $\beta$ alone
For any discrete random variable $X$, with probability mass function$P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomi...
Arjun
16.2k
views
Arjun
asked
Feb 14, 2017
Probability
gatecse-2017-set2
probability
random-variable
difficult
+
–
41
votes
5
answers
98
GATE CSE 2006 | Question: 18
We are given a set $X = \{X_1,\ldots,X_n\}$ where $X_i=2^i$. A sample $S\subseteq X$ is drawn by selecting each $X_i$ independently with probability $P_i = \frac{1}{2}$ . The expected value of the smallest number in sample $S$ is: $\left(\frac{1}{n}\right)$ $2$ $\sqrt n$ $n$
We are given a set $X = \{X_1,\ldots,X_n\}$ where $X_i=2^i$. A sample $S\subseteq X$ is drawn by selecting each $X_i$ independently with probability $P_i = \frac{1}{2...
Rucha Shelke
16.2k
views
Rucha Shelke
asked
Sep 17, 2014
Probability
gatecse-2006
probability
expectation
normal
+
–
116
votes
6
answers
99
GATE CSE 2003 | Question: 33
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: ... I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
Consider the following formula and its two interpretations \(I_1\) and \(I_2\).\(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg...
Kathleen
16.2k
views
Kathleen
asked
Sep 16, 2014
Mathematical Logic
gatecse-2003
mathematical-logic
difficult
first-order-logic
+
–
77
votes
8
answers
100
GATE CSE 2014 Set 2 | Question: 50
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the ... $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum ...
go_editor
16.1k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set2
set-theory&algebra
normal
set-theory
+
–
25
votes
2
answers
101
GATE CSE 2013 | Question: 25
Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. P only Q only Both P and Q Neither P nor Q
Which of the following statements is/are TRUE for undirected graphs?P: Number of odd degree vertices is even.Q: Sum of degrees of all vertices is even. P only Q only Both...
Arjun
16.1k
views
Arjun
asked
Sep 24, 2014
Graph Theory
gatecse-2013
graph-theory
easy
degree-of-graph
+
–
56
votes
7
answers
102
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.
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...
Akash Kanase
16.1k
views
Akash Kanase
asked
Feb 12, 2016
Linear Algebra
gatecse-2016-set2
linear-algebra
system-of-equations
normal
+
–
18
votes
5
answers
103
GATE CSE 2021 Set 1 | Question: 52
Consider the following matrix.$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$The largest eigenvalue of the above matrix is __________.
Consider the following matrix.$$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$$The largest eigenvalue of the above matrix is __...
Arjun
16.0k
views
Arjun
asked
Feb 18, 2021
Linear Algebra
gatecse-2021-set1
linear-algebra
matrix
eigen-value
numerical-answers
2-marks
+
–
65
votes
9
answers
104
GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-d...
Kathleen
15.9k
views
Kathleen
asked
Sep 17, 2014
Graph Theory
gatecse-2003
graph-theory
normal
degree-of-graph
+
–
65
votes
16
answers
105
GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ___...
go_editor
15.9k
views
go_editor
asked
Feb 14, 2015
Combinatory
gatecse-2015-set3
combinatory
normal
numerical-answers
+
–
77
votes
6
answers
106
GATE CSE 2014 Set 3 | Question: 50
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is ...
go_editor
15.8k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
group-theory
numerical-answers
normal
+
–
78
votes
6
answers
107
GATE CSE 2014 Set 3 | Question: 49
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$. For each such function it must be the case that for every ... is CORRECT? $P, Q$ and $R$ are true Only $Q$ and $R$ are true Only $P$ and $Q$ are true Only $R$ is true
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider th...
go_editor
15.8k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
functions
normal
+
–
47
votes
8
answers
108
GATE CSE 2017 Set 2 | Question: 52
If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is $2,$ then the largest among the absolute values of the eigenvalues of $M$ is _______
If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \ma...
Madhav
15.8k
views
Madhav
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set2
engineering-mathematics
linear-algebra
numerical-answers
eigen-value
+
–
66
votes
6
answers
109
GATE CSE 2015 Set 1 | Question: 16
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\varnothing \in 2^{A}$ $\varnothing \subseteq 2^{A}$ ... I and III only II and III only I, II and III only I, II and IV only
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE?$\varnoth...
makhdoom ghaya
15.7k
views
makhdoom ghaya
asked
Feb 13, 2015
Set Theory & Algebra
gatecse-2015-set1
set-theory&algebra
set-theory
normal
+
–
43
votes
4
answers
110
GATE CSE 2016 Set 2 | Question: 03
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________.
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________.
Akash Kanase
15.6k
views
Akash Kanase
asked
Feb 12, 2016
Graph Theory
gatecse-2016-set2
graph-theory
graph-coloring
normal
numerical-answers
+
–
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