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Previous GATE Questions in Engineering Mathematics
4
votes
2
answers
61
GATE CSE 2021 Set 1 | Question: 20
Consider the following expression.$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$The value of the above expression (rounded to 2 decimal places) is ___________.
Consider the following expression.$$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$$The value of the above expression (rounded to 2 decimal places) is ____...
Arjun
6.4k
views
Arjun
asked
Feb 18, 2021
Calculus
gatecse-2021-set1
calculus
limits
numerical-answers
1-mark
+
–
23
votes
4
answers
62
GATE CSE 2021 Set 1 | Question: 34
Let $G$ be a group of order $6$, and $H$ be a subgroup of $G$ such that $1<|H|<6$. Which one of the following options is correct? Both $G$ and $H$ are always cyclic $G$ may not be cyclic, but $H$ is always cyclic $G$ is always cyclic, but $H$ may not be cyclic Both $G$ and $H$ may not be cyclic
Let $G$ be a group of order $6$, and $H$ be a subgroup of $G$ such that $1<|H|<6$. Which one of the following options is correct?Both $G$ and $H$ are always cyclic$G$ may...
Arjun
8.3k
views
Arjun
asked
Feb 18, 2021
Set Theory & Algebra
gatecse-2021-set1
set-theory&algebra
group-theory
2-marks
+
–
10
votes
1
answer
63
GATE CSE 2021 Set 1 | Question: 35
Consider the two statements. $S_1:\quad$ There exist random variables $X$ and $Y$ such that $ \left(\mathbb E[(X-\mathbb E(X))(Y-\mathbb E(Y))]\right)^2>\textsf{Var}[X]\textsf{Var}[Y]$ $S_2:\quad$ For all random variables $X$ ... $S_2$ are true $S_1$ is true, but $S_2$ is false $S_1$ is false, but $S_2$ is true Both $S_1$ and $S_2$ are false
Consider the two statements.$S_1:\quad$ There exist random variables $X$ and $Y$ such that $ \left(\mathbb E[(X-\mathbb E(X))(Y-\mathbb E(Y))]\right)^2>\textsf{Var}[X]\t...
Arjun
7.4k
views
Arjun
asked
Feb 18, 2021
Probability
gatecse-2021-set1
probability
random-variable
difficult
2-marks
+
–
35
votes
6
answers
64
GATE CSE 2021 Set 1 | Question: 36
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as: $\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortest path between $u$ and $v$}\}$ Let $M$ be the adjacency matrix of $G$. Define graph $G_2$ ... $\text{diam}(G_2) = \text{diam}(G)$ $\text{diam}(G)< \text{diam}(G_2)\leq 2\; \text{diam}(G)$
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as:$$\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortes...
Arjun
10.0k
views
Arjun
asked
Feb 18, 2021
Graph Theory
gatecse-2021-set1
graph-theory
graph-connectivity
2-marks
+
–
27
votes
5
answers
65
GATE CSE 2021 Set 1 | Question: 43
A relation $R$ is said to be circular if $a\text{R}b$ and $b\text{R}c$ together imply $c\text{R}a$. Which of the following options is/are correct? If a relation $S$ is reflexive and symmetric, then $S$ is an equivalence relation ... and circular, then $S$ is an equivalence relation. If a relation $S$ is transitive and circular, then $S$ is an equivalence relation.
A relation $R$ is said to be circular if $a\text{R}b$ and $b\text{R}c$ together imply $c\text{R}a$.Which of the following options is/are correct?If a relation $S$ is refl...
Arjun
8.3k
views
Arjun
asked
Feb 18, 2021
Set Theory & Algebra
gatecse-2021-set1
multiple-selects
set-theory&algebra
relations
2-marks
+
–
18
votes
5
answers
66
GATE CSE 2021 Set 1 | Question: 52
Consider the following matrix.$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$The largest eigenvalue of the above matrix is __________.
Consider the following matrix.$$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$$The largest eigenvalue of the above matrix is __...
Arjun
15.8k
views
Arjun
asked
Feb 18, 2021
Linear Algebra
gatecse-2021-set1
linear-algebra
matrix
eigen-value
numerical-answers
2-marks
+
–
21
votes
2
answers
67
GATE CSE 2021 Set 1 | Question: 54
A sender $(\textsf{S})$ transmits a signal, which can be one of the two kinds: $H$ and $L$ with probabilities $0.1$ and $0.9$ respectively, to a receiver $(\textsf{R})$. In the graph below, the weight of edge $(u,v)$ is the ... $0.7$. If the received signal is $H,$ the probability that the transmitted signal was $H$ (rounded to $2$ decimal places) is __________.
A sender $(\textsf{S})$ transmits a signal, which can be one of the two kinds: $H$ and $L$ with probabilities $0.1$ and $0.9$ respectively, to a receiver $(\textsf{R})$.I...
Arjun
5.7k
views
Arjun
asked
Feb 18, 2021
Probability
gatecse-2021-set1
probability
conditional-probability
numerical-answers
2-marks
+
–
23
votes
3
answers
68
GATE CSE 2020 | Question: 1
Consider the functions $e^{-x}$ $x^{2}-\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only
Consider the functions $e^{-x}$$x^{2}-\sin x$$\sqrt{x^{3}+1}$Which of the above functions is/are increasing everywhere in $[ 0,1]$?Ⅲ onlyⅡ onlyⅡ and Ⅲ onlyⅠ a...
Arjun
12.3k
views
Arjun
asked
Feb 12, 2020
Calculus
gatecse-2020
engineering-mathematics
calculus
maxima-minima
1-mark
+
–
15
votes
5
answers
69
GATE CSE 2020 | Question: 17
Let $\mathcal{R}$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $\mathcal{R}$ at random. The probability that the chosen relation is reflexive (round off to $3$ decimal places) is ______.
Let $\mathcal{R}$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $\mathcal{R}$ at random. The probability that the chosen re...
Arjun
9.2k
views
Arjun
asked
Feb 12, 2020
Set Theory & Algebra
gatecse-2020
numerical-answers
probability
relations
1-mark
+
–
15
votes
4
answers
70
GATE CSE 2020 | Question: 18
Let $G$ be a group of $35$ elements. Then the largest possible size of a subgroup of $G$ other than $G$ itself is _______.
Let $G$ be a group of $35$ elements. Then the largest possible size of a subgroup of $G$ other than $G$ itself is _______.
Arjun
9.4k
views
Arjun
asked
Feb 12, 2020
Set Theory & Algebra
gatecse-2020
numerical-answers
group-theory
easy
1-mark
+
–
15
votes
3
answers
71
GATE CSE 2020 | Question: 27
Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let rank($M$) and $\text{det}(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider the following statements. $\text{rank}(AB) = \text{rank }(A) \text{rank }(B)$ ... Which of the above statements are TRUE? I and II only I and IV only II and III only III and IV only
Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let rank($M$) and $\text{det}(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider...
Arjun
10.2k
views
Arjun
asked
Feb 12, 2020
Linear Algebra
gatecse-2020
linear-algebra
matrix
2-marks
+
–
42
votes
9
answers
72
GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
Which one of the following predicate formulae is NOT logically valid?Note that $W$ is a predicate formula without any free occurrence of $x$.$\forall x (p(x) \vee W) \equ...
Arjun
17.3k
views
Arjun
asked
Feb 12, 2020
Mathematical Logic
gatecse-2020
first-order-logic
mathematical-logic
2-marks
+
–
28
votes
8
answers
73
GATE CSE 2020 | Question: 42
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
Arjun
16.6k
views
Arjun
asked
Feb 12, 2020
Combinatory
gatecse-2020
numerical-answers
combinatory
2-marks
+
–
24
votes
2
answers
74
GATE CSE 2020 | Question: 45
For $n>2$, let $a \in \{0,1\}^n$ be a non-zero vector. Suppose that $x$ is chosen uniformly at random from $\{0,1\}^n$. Then, the probability that $\displaystyle{} \Sigma_{i=1}^n a_i x_i$ is an odd number is______________
For $n>2$, let $a \in \{0,1\}^n$ be a non-zero vector. Suppose that $x$ is chosen uniformly at random from $\{0,1\}^n$. Then, the probability that $\displaystyle{} \Sigm...
Arjun
12.3k
views
Arjun
asked
Feb 12, 2020
Probability
gatecse-2020
numerical-answers
probability
uniform-distribution
2-marks
+
–
28
votes
6
answers
75
GATE CSE 2020 | Question: 52
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is _______
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is...
Arjun
13.7k
views
Arjun
asked
Feb 12, 2020
Graph Theory
gatecse-2020
numerical-answers
graph-theory
graph-coloring
2-marks
+
–
19
votes
2
answers
76
GATE CSE 1995 | Question: 25b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
Arjun
4.4k
views
Arjun
asked
Jun 6, 2019
Set Theory & Algebra
gate1995
set-theory&algebra
set-theory
numerical-answers
+
–
28
votes
4
answers
77
GATE CSE 2019 | Question: 5
Let $U = \{1, 2, \dots , n\}$ Let $A=\{(x, X) \mid x \in X, X \subseteq U \}$. Consider the following two statements on $\mid A \mid$. $\mid A \mid = n2^{n-1}$ $\mid A \mid = \Sigma_{k=1}^{n} k \begin{pmatrix} n \\ k \end{pmatrix}$ Which of the above statements is/are TRUE? Only I Only II Both I and II Neither I nor II
Let $U = \{1, 2, \dots , n\}$ Let $A=\{(x, X) \mid x \in X, X \subseteq U \}$. Consider the following two statements on $\mid A \mid$.$\mid A \mid = n2^{n-1}$$\mid A \mi...
Arjun
11.6k
views
Arjun
asked
Feb 7, 2019
Combinatory
gatecse-2019
engineering-mathematics
discrete-mathematics
combinatory
1-mark
+
–
27
votes
7
answers
78
GATE CSE 2019 | Question: 9
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is non-zero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
Let $X$ be a square matrix. Consider the following two statements on $X$.$X$ is invertibleDeterminant of $X$ is non-zeroWhich one of the following is TRUE?I implies II; I...
Arjun
10.7k
views
Arjun
asked
Feb 7, 2019
Linear Algebra
gatecse-2019
engineering-mathematics
linear-algebra
determinant
1-mark
+
–
38
votes
9
answers
79
GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
Let $G$ be an arbitrary group. Consider the following relations on $G$:$R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a ...
Arjun
17.4k
views
Arjun
asked
Feb 7, 2019
Set Theory & Algebra
gatecse-2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1-mark
+
–
33
votes
14
answers
80
GATE CSE 2019 | Question: 12
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$
Let $G$ be an undirected complete graph on $n$ vertices, where $n 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to$n!$$(n-1)!$$1$$\frac{(n-1)!}{2}...
Arjun
21.4k
views
Arjun
asked
Feb 7, 2019
Graph Theory
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
1-mark
+
–
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