Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Previous GATE Questions in Engineering Mathematics
79
votes
7
answers
91
GATE CSE 2018 | Question: 26
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the ... III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$.Consider the following statements.P does not have an inverseP has ...
gatecse
27.4k
views
gatecse
asked
Feb 14, 2018
Linear Algebra
gatecse-2018
linear-algebra
matrix
eigen-value
normal
2-marks
+
–
28
votes
4
answers
92
GATE CSE 2018 | Question: 19
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
gatecse
12.3k
views
gatecse
asked
Feb 14, 2018
Set Theory & Algebra
gatecse-2018
group-theory
numerical-answers
set-theory&algebra
1-mark
+
–
32
votes
5
answers
93
GATE CSE 2018 | Question: 18
The chromatic number of the following graph is _____
The chromatic number of the following graph is _____
gatecse
12.2k
views
gatecse
asked
Feb 14, 2018
Graph Theory
graph-theory
graph-coloring
numerical-answers
gatecse-2018
1-mark
+
–
24
votes
6
answers
94
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 ____
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 larg...
gatecse
10.3k
views
gatecse
asked
Feb 14, 2018
Linear Algebra
gatecse-2018
linear-algebra
eigen-value
normal
numerical-answers
1-mark
+
–
28
votes
4
answers
95
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
16.2k
views
gatecse
asked
Feb 14, 2018
Calculus
gatecse-2018
calculus
integration
normal
numerical-answers
1-mark
+
–
35
votes
8
answers
96
GATE CSE 2018 | Question: 15
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a ... and that all trials are independent. The probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a ti...
gatecse
11.0k
views
gatecse
asked
Feb 14, 2018
Probability
gatecse-2018
probability
normal
numerical-answers
1-mark
+
–
42
votes
11
answers
97
GATE CSE 2018 | Question: 1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$?$\frac...
gatecse
22.7k
views
gatecse
asked
Feb 14, 2018
Combinatory
gatecse-2018
generating-functions
normal
combinatory
1-mark
+
–
2
votes
1
answer
98
GATE CSE 2017 Set 1 | Question: 31
https://gateoverflow.in/118312/gate2017-1-31 In the explanation of how 1st statement is true they have said that $\lambda$12 + $\lambda$22 <=50 How is this statement arrived at?
https://gateoverflow.in/118312/gate2017-1-31In the explanation of how 1st statement is truethey have said that $\lambda$12 + $\lambda$22 <=50How is this statement arrived...
A_i_$_h
757
views
A_i_$_h
asked
Oct 25, 2017
73
votes
8
answers
99
GATE CSE 2017 Set 1 | Question: 02
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ IV only I and IV only II only II and III only
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$?$\exists y(\ex...
khushtak
17.3k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
first-order-logic
+
–
30
votes
8
answers
100
GATE CSE 2017 Set 1 | Question: 01
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$ I only I and IV only II only II and III only
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below?$p \Rightarrow q$$q \Rightarrow p$$\left ( ...
khushtak
9.0k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
propositional-logic
easy
+
–
47
votes
8
answers
101
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
15.6k
views
Madhav
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set2
engineering-mathematics
linear-algebra
numerical-answers
eigen-value
+
–
44
votes
9
answers
102
GATE CSE 2017 Set 2 | Question: 23
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
Madhav
17.5k
views
Madhav
asked
Feb 14, 2017
Graph Theory
gatecse-2017-set2
graph-theory
numerical-answers
degree-of-graph
+
–
47
votes
4
answers
103
GATE CSE 2017 Set 2 | Question: 48
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
Kantikumar
16.4k
views
Kantikumar
asked
Feb 14, 2017
Probability
gatecse-2017-set2
expectation
poisson-distribution
numerical-answers
probability
+
–
58
votes
9
answers
104
GATE CSE 2017 Set 2 | Question: 47
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
Arjun
17.7k
views
Arjun
asked
Feb 14, 2017
Combinatory
gatecse-2017-set2
combinatory
generating-functions
numerical-answers
normal
+
–
50
votes
7
answers
105
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
16.1k
views
Arjun
asked
Feb 14, 2017
Probability
gatecse-2017-set2
probability
random-variable
difficult
+
–
65
votes
6
answers
106
GATE CSE 2017 Set 2 | Question: 26
$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q$ applies for the job is $\dfrac{1}{2},$ and the probability that $Q$ applies for the ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{7}{8}\right)$ $\left(\dfrac{11}{12}\right)$
$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q...
Arjun
12.5k
views
Arjun
asked
Feb 14, 2017
Probability
gatecse-2017-set2
probability
conditional-probability
+
–
33
votes
2
answers
107
GATE CSE 2017 Set 2 | Question: 22
Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices. Then the rank of $ P+Q$ is ___________ .
Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices.Th...
Arjun
11.9k
views
Arjun
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set2
linear-algebra
eigen-value
numerical-answers
+
–
25
votes
9
answers
108
GATE CSE 2017 Set 1 | Question: 47
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
Arjun
11.7k
views
Arjun
asked
Feb 14, 2017
Set Theory & Algebra
gatecse-2017-set1
set-theory&algebra
normal
numerical-answers
set-theory
+
–
88
votes
6
answers
109
GATE CSE 2017 Set 1 | Question: 31
Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements. One eigenvalue must be in $\left [ -5,5 \right ]$ The eigenvalue ... than $5$ Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II
Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements.One eigenvalu...
Arjun
49.6k
views
Arjun
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set1
linear-algebra
eigen-value
normal
+
–
30
votes
5
answers
110
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
14.0k
views
Arjun
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set1
linear-algebra
normal
vector-space
+
–
Page:
« prev
1
2
3
4
5
6
7
8
9
10
...
28
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register