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Previous GATE
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Previous GATE Questions in Engineering Mathematics
14
votes
3
answers
41
GATE CSE 2022 | Question: 27
Consider a simple undirected unweighted graph with at least three vertices. If $\textit{A}$ is the adjacency matrix of the graph, then the number of $3–$cycles in the graph is given by the trace of $\textit{A}^{3}$ $\textit{A}^{3}$ divided by $2$ $\textit{A}^{3}$ divided by $3$ $\textit{A}^{3}$ divided by $6$
Arjun
asked
in
Graph Theory
Feb 15, 2022
by
Arjun
7.4k
views
gatecse-2022
graph-theory
graph-connectivity
2-marks
21
votes
5
answers
42
GATE CSE 2022 | Question: 35
Consider solving the following system of simultaneous equations using $\text{LU}$ decomposition. $x_{1} + x_{2} - 2x_{3} = 4$ $x_{1} + 3x_{2} - x_{3} = 7$ $2x_{1} + x_{2} - 5x_{3} = 7$ where $\textit{L}$ and $\textit{U}$ ... $\textit{L}_{32}= - \frac{1}{2}, \textit{U}_{33}= - \frac{1}{2}, x_{1}= 0$
Arjun
asked
in
Linear Algebra
Feb 15, 2022
by
Arjun
11.1k
views
gatecse-2022
linear-algebra
matrix
system-of-equations
2-marks
14
votes
2
answers
43
GATE CSE 2022 | Question: 40
The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are $\text{TRUE}?$ The chromatic number of the graph is $3.$ The graph has a Hamiltonian path. The following graph is isomorphic to the Peterson ... $3.$ (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
Arjun
asked
in
Graph Theory
Feb 15, 2022
by
Arjun
7.4k
views
gatecse-2022
graph-theory
graph-isomorphism
multiple-selects
2-marks
hard
15
votes
6
answers
44
GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$
Arjun
asked
in
Combinatory
Feb 15, 2022
by
Arjun
7.7k
views
gatecse-2022
combinatory
recurrence-relation
multiple-selects
2-marks
16
votes
4
answers
45
GATE CSE 2022 | Question: 42
Which of the properties hold for the adjacency matrix $A$ of a simple undirected unweighted graph having $n$ vertices? The diagonal entries of $A^{2}$ ... . If there is at least a $1$ in each of $A\text{'s}$ rows and columns, then the graph must be connected.
Arjun
asked
in
Graph Theory
Feb 15, 2022
by
Arjun
7.3k
views
gatecse-2022
graph-theory
graph-connectivity
multiple-selects
2-marks
24
votes
1
answer
46
GATE CSE 2022 | Question: 43
Which of the following is/are the eigenvector(s) for the matrix given below? $\begin{pmatrix} - 9 & - 6 & - 2 & - 4 \\ - 8 & - 6 & - 3 & - 1 \\ 20 & 15 & 8 & 5 \\ 32 & 21 & 7 & 12 \end{pmatrix}$ ... $\begin{pmatrix} - 1 \\ 0 \\ 2 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 0 \\ 1 \\ - 3 \\ 0 \end{pmatrix}$
Arjun
asked
in
Linear Algebra
Feb 15, 2022
by
Arjun
10.2k
views
gatecse-2022
linear-algebra
eigen-value
multiple-selects
2-marks
4
votes
1
answer
47
GATE CSE 1995 | Question: 7(B)
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
admin
asked
in
Calculus
Apr 25, 2021
by
admin
1.4k
views
gate1995
calculus
limits
numerical-answers
24
votes
3
answers
48
GATE CSE 2021 Set 2 | Question: 11
Consider the following sets, where $n \geq 2$: $S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$ $S_2$: Set of all functions from the set $\{0,1,2, \dots, n^2-1\}$ ... There exists a surjection from $S_1$ to $S_2$ There exists a bijection from $S_1$ to $S_2$ There does not exist an injection from $S_1$ to $S_2$
Arjun
asked
in
Set Theory & Algebra
Feb 18, 2021
by
Arjun
6.3k
views
gatecse-2021-set2
multiple-selects
set-theory&algebra
functions
1-mark
27
votes
9
answers
49
GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$
Arjun
asked
in
Mathematical Logic
Feb 18, 2021
by
Arjun
8.7k
views
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
14
votes
1
answer
50
GATE CSE 2021 Set 2 | Question: 22
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________
Arjun
asked
in
Probability
Feb 18, 2021
by
Arjun
6.0k
views
gatecse-2021-set2
numerical-answers
probability
random-variable
1-mark
43
votes
14
answers
51
GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
Arjun
asked
in
Linear Algebra
Feb 18, 2021
by
Arjun
18.1k
views
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
16
votes
3
answers
52
GATE CSE 2021 Set 2 | Question: 25
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
Arjun
asked
in
Calculus
Feb 18, 2021
by
Arjun
6.2k
views
gatecse-2021-set2
numerical-answers
calculus
continuity
1-mark
26
votes
4
answers
53
GATE CSE 2021 Set 2 | Question: 29
In an examination, a student can choose the order in which two questions ($\textsf{QuesA}$ and $\textsf{QuesB}$) must be attempted. If the first question is answered wrong, the student gets zero marks. If the first question is answered correctly and the ... $22$. First $\textsf{QuesA}$ and then $\textsf{QuesB}$. Expected marks $16$.
Arjun
asked
in
Probability
Feb 18, 2021
by
Arjun
7.4k
views
gatecse-2021-set2
probability
expectation
2-marks
36
votes
4
answers
54
GATE CSE 2021 Set 2 | Question: 33
A bag has $r$ red balls and $b$ black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of ...
Arjun
asked
in
Probability
Feb 18, 2021
by
Arjun
10.7k
views
gatecse-2021-set2
probability
normal
2-marks
21
votes
1
answer
55
GATE CSE 2021 Set 2 | Question: 37
For two $n$-dimensional real vectors $P$ and $Q$, the operation $s(P,Q)$ is defined as follows: $s(P,Q) = \displaystyle \sum_{i=1}^n (P[i] \cdot Q[i])$ Let $\mathcal{L}$ be a set of $10$-dimensional non-zero real vectors such that for every pair ... $s(P,Q)=0$. What is the maximum cardinality possible for the set $\mathcal{L}$? $9$ $10$ $11$ $100$
Arjun
asked
in
Set Theory & Algebra
Feb 18, 2021
by
Arjun
7.0k
views
gatecse-2021-set2
set-theory&algebra
set-theory
2-marks
25
votes
6
answers
56
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Arjun
asked
in
Combinatory
Feb 18, 2021
by
Arjun
11.8k
views
gatecse-2021-set2
combinatory
counting
numerical-answers
2-marks
14
votes
8
answers
57
GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
Arjun
asked
in
Mathematical Logic
Feb 18, 2021
by
Arjun
8.1k
views
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
13
votes
5
answers
58
GATE CSE 2021 Set 1 | Question: 16
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.
Arjun
asked
in
Graph Theory
Feb 18, 2021
by
Arjun
8.0k
views
gatecse-2021-set1
graph-theory
graph-planarity
numerical-answers
easy
1-mark
16
votes
2
answers
59
GATE CSE 2021 Set 1 | Question: 18
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
Arjun
asked
in
Probability
Feb 18, 2021
by
Arjun
9.2k
views
gatecse-2021-set1
probability
random-variable
numerical-answers
1-mark
38
votes
3
answers
60
GATE CSE 2021 Set 1 | Question: 19
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
Arjun
asked
in
Combinatory
Feb 18, 2021
by
Arjun
11.7k
views
gatecse-2021-set1
combinatory
counting
numerical-answers
1-mark
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