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Previous GATE Questions in Engineering Mathematics
5
votes
2
answers
1
GATE CSE 2022 | Question: 10
Consider the following two statements with respect to the matrices $\textit{A}_{m \times n}, \textit{B}_{n \times m}, \textit{C}_{n \times n}$ and $ \textit{D}_{n \times n}.$ Statement $1: tr \text{(AB)} = tr \text{(BA)}$ ... $2$ is correct. Both Statement $1$ and Statement $2$ are correct. Both Statement $1$ and Statement $2$ are wrong.
Arjun
asked
in
Linear Algebra
Feb 15
by
Arjun
2.1k
views
gatecse-2022
linear-algebra
matrix
5
votes
2
answers
2
GATE CSE 2022 | Question: 17
Which of the following statements is/are $\text{TRUE}$ for a group $\textit{G}?$ If for all $x,y \in \textit{G}, \; (xy)^{2} = x^{2} y^{2},$ then $\textit{G}$ is commutative. If for all $x \in \textit{G}, \; x^{2} = 1,$ then ... $2,$ then $\textit{G}$ is commutative. If $\textit{G}$ is commutative, then a subgroup of $\textit{G}$ need not be commutative.
Arjun
asked
in
Set Theory & Algebra
Feb 15
by
Arjun
2.0k
views
gatecse-2022
set-theory&algebra
group-theory
multiple-selects
6
votes
4
answers
3
GATE CSE 2022 | Question: 20
Consider a simple undirected graph of $10$ vertices. If the graph is disconnected, then the maximum number of edges it can have is _______________ .
Arjun
asked
in
Graph Theory
Feb 15
by
Arjun
2.2k
views
gatecse-2022
numerical-answers
graph-theory
graph-connectivity
4
votes
3
answers
4
GATE CSE 2022 | Question: 22
The number of arrangements of six identical balls in three identical bins is _____________ .
Arjun
asked
in
Combinatory
Feb 15
by
Arjun
2.4k
views
gatecse-2022
numerical-answers
combinatory
balls-in-bins
3
votes
4
answers
5
GATE CSE 2022 | Question: 24
The value of the following limit is ________________. $\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$
Arjun
asked
in
Calculus
Feb 15
by
Arjun
1.4k
views
gatecse-2022
numerical-answers
calculus
limits
9
votes
5
answers
6
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Arjun
asked
in
Combinatory
Feb 15
by
Arjun
2.1k
views
gatecse-2022
combinatory
generating-functions
4
votes
2
answers
7
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 $3â$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
by
Arjun
1.8k
views
gatecse-2022
graph-theory
graph-connectivity
6
votes
3
answers
8
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
by
Arjun
2.0k
views
gatecse-2022
linear-algebra
matrix
5
votes
2
answers
9
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
by
Arjun
2.2k
views
gatecse-2022
graph-theory
graph-isomorphism
multiple-selects
7
votes
6
answers
10
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
by
Arjun
2.5k
views
gatecse-2022
combinatory
recurrence-relation
multiple-selects
6
votes
3
answers
11
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
by
Arjun
1.9k
views
gatecse-2022
graph-theory
graph-connectivity
multiple-selects
4
votes
1
answer
12
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
by
Arjun
2.0k
views
gatecse-2022
linear-algebra
eigen-value
multiple-selects
3
votes
1
answer
13
GATE CSE 1995 | Question: 7(B)
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
Lakshman Patel RJIT
asked
in
Calculus
Apr 25, 2021
by
Lakshman Patel RJIT
700
views
gate1995
calculus
limits
numerical-answers
16
votes
3
answers
14
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
3.5k
views
gatecse-2021-set2
multiple-selects
set-theory&algebra
functions
11
votes
5
answers
15
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
3.9k
views
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
9
votes
1
answer
16
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
2.9k
views
gatecse-2021-set2
numerical-answers
probability
random-variable
20
votes
6
answers
17
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
8.0k
views
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
9
votes
2
answers
18
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, $fâ(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
Arjun
asked
in
Calculus
Feb 18, 2021
by
Arjun
2.9k
views
gatecse-2021-set2
numerical-answers
calculus
continuity
12
votes
4
answers
19
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
3.4k
views
gatecse-2021-set2
probability
expectation
20
votes
4
answers
20
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
5.5k
views
gatecse-2021-set2
probability
normal
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