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Previous GATE Questions in Engineering Mathematics
45
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 _______
Madhav
asked
in
Linear Algebra
Feb 14, 2017
by
Madhav
15.4k
views
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 _________ .
Madhav
asked
in
Graph Theory
Feb 14, 2017
by
Madhav
17.3k
views
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 ___.
Kantikumar
asked
in
Probability
Feb 14, 2017
by
Kantikumar
16.3k
views
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 ___________ .
Arjun
asked
in
Combinatory
Feb 14, 2017
by
Arjun
17.6k
views
gatecse-2017-set2
combinatory
generating-functions
numerical-answers
normal
49
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
Arjun
asked
in
Probability
Feb 14, 2017
by
Arjun
16.0k
views
gatecse-2017-set2
probability
random-variable
difficult
63
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 ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{7}{8}\right)$ $\left(\dfrac{11}{12}\right)$
Arjun
asked
in
Probability
Feb 14, 2017
by
Arjun
12.4k
views
gatecse-2017-set2
probability
conditional-probability
31
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 ___________ .
Arjun
asked
in
Linear Algebra
Feb 14, 2017
by
Arjun
11.8k
views
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 ____________ .
Arjun
asked
in
Set Theory & Algebra
Feb 14, 2017
by
Arjun
11.6k
views
gatecse-2017-set1
set-theory&algebra
normal
numerical-answers
set-theory
83
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
Arjun
asked
in
Linear Algebra
Feb 14, 2017
by
Arjun
44.4k
views
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 $v$? $2$ $\frac{1}{2}$ $1$ $\frac{ -1}{2}$
Arjun
asked
in
Linear Algebra
Feb 14, 2017
by
Arjun
14.0k
views
gatecse-2017-set1
linear-algebra
normal
vector-space
48
votes
10
answers
111
GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE
Arjun
asked
in
Mathematical Logic
Feb 14, 2017
by
Arjun
10.5k
views
gatecse-2017-set1
mathematical-logic
propositional-logic
22
votes
4
answers
112
GATE CSE 2017 Set 1 | Question: 28
The value of $\displaystyle \lim_{x\rightarrow 1} \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2}$ is $0$ is $-1$ is $1$ does not exist
Arjun
asked
in
Calculus
Feb 14, 2017
by
Arjun
6.1k
views
gatecse-2017-set1
calculus
limits
normal
48
votes
5
answers
113
GATE CSE 2017 Set 1 | Question: 19
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .
Arjun
asked
in
Probability
Feb 14, 2017
by
Arjun
20.5k
views
gatecse-2017-set1
probability
numerical-answers
normal-distribution
67
votes
9
answers
114
GATE CSE 2017 Set 1 | Question: 3
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ ... has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$-dimensional vector of all 1. no solution infinitely many solutions finitely many solutions
Arjun
asked
in
Linear Algebra
Feb 14, 2017
by
Arjun
20.2k
views
gatecse-2017-set1
linear-algebra
system-of-equations
normal
36
votes
6
answers
115
GATE CSE 2017 Set 2 | Question: 21
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
khushtak
asked
in
Set Theory & Algebra
Feb 14, 2017
by
khushtak
11.8k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
27
votes
2
answers
116
GATE CSE 2017 Set 2 | Question: 10
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are $\frac{2}{\pi}$ and $\frac{16}{\pi}$ $\frac{2}{\pi}$ and 0 $\frac{4}{\pi}$ and 0 $\frac{4}{\pi}$ and $\frac{16}{\pi}$
Madhav
asked
in
Calculus
Feb 14, 2017
by
Madhav
8.5k
views
gatecse-2017-set2
engineering-mathematics
calculus
differentiation
39
votes
5
answers
117
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 $b=$ _____
khushtak
asked
in
Set Theory & Algebra
Feb 14, 2017
by
khushtak
14.3k
views
gatecse-2017-set2
polynomials
numerical-answers
set-theory&algebra
57
votes
10
answers
118
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
khushtak
asked
in
Mathematical Logic
Feb 14, 2017
by
khushtak
12.1k
views
gatecse-2017-set2
mathematical-logic
propositional-logic
0
votes
0
answers
119
GATE CSE 1988 | Question: 16ii-iii
If $x \| \underline{x} \| \infty = 1< i^{max} < n \: \: max \: \: ( \mid x1 \mid ) $ for the vector $\underline{x} = (x1, x2 \dots x_n)$ ... known property of this norm. Although this norm is very easy to calculate for any matrix, explain why the condition number is difficult (i.e. expensive) to calculate.
go_editor
asked
in
Linear Algebra
Dec 20, 2016
by
go_editor
735
views
gate1988
descriptive
matrix
out-of-gate-syllabus
8
votes
3
answers
120
GATE CSE 1988 | Question: 16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangular, and $P$ ... $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
go_editor
asked
in
Linear Algebra
Dec 20, 2016
by
go_editor
3.3k
views
gate1988
normal
descriptive
linear-algebra
matrix
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