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Previous GATE Questions in Engineering Mathematics
4
votes
2
answers
31
GATE CSE 2023 | Memory Based Question: 13
Let $ A=\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{array}\right] $ ... $\operatorname{det} \mathrm{B}=-\operatorname{det} \mathrm{A}$ $\operatorname{det} \mathrm{A}=\operatorname{det} \mathrm{B}$
Let$$A=\left[\begin{array}{llll}1 & 2 & 3 & 4 \\4 & 1 & 2 & 3 \\3 & 4 & 1 & 2 \\2 & 3 & 4 & 1\end{array}\right]$$And$$B=\left[\begin{array}{llll}3 & 4 & 1 & 2 \\4 & 1 & 2...
GO Classes
2.5k
views
GO Classes
asked
Feb 5, 2023
Linear Algebra
memorybased-gatecse2023
goclasses
linear-algebra
determinant
+
–
0
votes
1
answer
32
GATE CSE 2023 | Memory Based Question: 15
The Lucas sequence $L_n$ is defined by the recurrence relation: $L_n=L_{n-1}+L_{n-2}$, for $n \geq 3$ with $L_1=1$ and $L_2=3$. Which one of the options given is TRUE? $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{3}\right)^n$ ... $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{2}\right)^n$
The Lucas sequence $L_n$ is defined by the recurrence relation:$L_n=L_{n-1}+L_{n-2}$, for $n \geq 3$ with $L_1=1$ and $L_2=3$.Which one of the options given is TRUE?$L_n=...
GO Classes
1.5k
views
GO Classes
asked
Feb 5, 2023
Combinatory
memorybased-gatecse2023
goclasses
combinatory
recurrence-relation
+
–
1
votes
1
answer
33
GATE CSE 2023 | Memory Based Question: 16
How many permutations of $U$ separate $A$ from $B?$ $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k!)^2$ $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k)!(n!)$ $n!$ $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^2$
How many permutations of $U$ separate $A$ from $B?$$2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k!)^2$$\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2...
GO Classes
1.0k
views
GO Classes
asked
Feb 5, 2023
Combinatory
memorybased-gatecse2023
goclasses
combinatory
counting
+
–
1
votes
2
answers
34
GATE CSE 2023 | Memory Based Question: 17
Let $x$ be a set, $2^x=$ power $2 \mathrm{k}$ set of $\mathrm{X}$. define A binary operation $\Delta$ on $2^x$ as $A \Delta B=(A-B) \cup(B-A)$. Let $H=\left(2^x, \Delta\right)$, then for every $A \in 2^x$; inverse of $A$ ... $\mathrm{H}$ is a group. $\mathrm{H}$ satisfies inverse prop, but not a group for every $A \in 2^x$; the inverse of $A$ is $A$.
Let $x$ be a set, $2^x=$ power $2 \mathrm{k}$ set of $\mathrm{X}$. define A binary operation $\Delta$ on $2^x$ as $A \Delta B=(A-B) \cup(B-A)$. Let $H=\left(2^x, \Delta\r...
GO Classes
891
views
GO Classes
asked
Feb 5, 2023
Set Theory & Algebra
memorybased-gatecse2023
goclasses
set-theory&algebra
group-theory
multiple-selects
+
–
19
votes
4
answers
35
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.
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 ...
Arjun
10.9k
views
Arjun
asked
Feb 15, 2022
Linear Algebra
gatecse-2022
linear-algebra
matrix
1-mark
+
–
14
votes
2
answers
36
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.
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 commutati...
Arjun
7.6k
views
Arjun
asked
Feb 15, 2022
Set Theory & Algebra
gatecse-2022
set-theory&algebra
group-theory
multiple-selects
1-mark
+
–
19
votes
5
answers
37
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 _______________ .
Consider a simple undirected graph of $10$ vertices. If the graph is disconnected, then the maximum number of edges it can have is _______________ .
Arjun
8.8k
views
Arjun
asked
Feb 15, 2022
Graph Theory
gatecse-2022
numerical-answers
graph-theory
graph-connectivity
1-mark
+
–
17
votes
3
answers
38
GATE CSE 2022 | Question: 22
The number of arrangements of six identical balls in three identical bins is _____________ .
The number of arrangements of six identical balls in three identical bins is _____________ .
Arjun
10.4k
views
Arjun
asked
Feb 15, 2022
Combinatory
gatecse-2022
numerical-answers
combinatory
balls-in-bins
1-mark
+
–
11
votes
4
answers
39
GATE CSE 2022 | Question: 24
The value of the following limit is ________________. $\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$
The value of the following limit is ________________.$$\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$$
Arjun
6.4k
views
Arjun
asked
Feb 15, 2022
Calculus
gatecse-2022
numerical-answers
calculus
limits
1-mark
+
–
26
votes
6
answers
40
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below?$$ a_{n} = \left\{\begin{matrix} n + 1, &...
Arjun
9.5k
views
Arjun
asked
Feb 15, 2022
Combinatory
gatecse-2022
combinatory
generating-functions
2-marks
+
–
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 $6$
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 g...
Arjun
7.5k
views
Arjun
asked
Feb 15, 2022
Graph Theory
gatecse-2022
graph-theory
graph-connectivity
2-marks
+
–
22
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 $\textit{U}$ ... $\textit{L}_{32}= - \frac{1}{2}, \textit{U}_{33}= - \frac{1}{2}, x_{1}= 0$
Consider solving the following system of simultaneous equations using $\text{LU}$ decomposition.$$x_{1} + x_{2} – 2x_{3} = 4$$$$x_{1} + 3x_{2} – x_{3} = 7$$$$2x_{1} +...
Arjun
11.4k
views
Arjun
asked
Feb 15, 2022
Linear Algebra
gatecse-2022
linear-algebra
matrix
system-of-equations
2-marks
+
–
14
votes
2
answers
43
GATE CSE 2022 | Question: 40
The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are $\text{TRUE}?$ The chromatic number of the graph is $3.$ The graph has a Hamiltonian path. The following graph is isomorphic to the Peterson ... $3.$ (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
The following simple undirected graph is referred to as the Peterson graph.Which of the following statements is/are $\text{TRUE}?$The chromatic number of the graph is $3....
Arjun
7.5k
views
Arjun
asked
Feb 15, 2022
Graph Theory
gatecse-2022
graph-theory
graph-isomorphism
multiple-selects
2-marks
+
–
15
votes
6
answers
44
GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$
Consider the following recurrence:$$\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) – 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text...
Arjun
7.8k
views
Arjun
asked
Feb 15, 2022
Combinatory
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.
Which of the properties hold for the adjacency matrix $A$ of a simple undirected unweighted graph having $n$ vertices?The diagonal entries of $A^{2}$ are the degrees of t...
Arjun
7.4k
views
Arjun
asked
Feb 15, 2022
Graph Theory
gatecse-2022
graph-theory
graph-connectivity
multiple-selects
2-marks
+
–
26
votes
1
answer
46
GATE CSE 2022 | Question: 43
Which of the following is/are the eigenvector(s) for the matrix given below? $\begin{pmatrix} - 9 & - 6 & - 2 & - 4 \\ - 8 & - 6 & - 3 & - 1 \\ 20 & 15 & 8 & 5 \\ 32 & 21 & 7 & 12 \end{pmatrix}$ ... $\begin{pmatrix} - 1 \\ 0 \\ 2 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 0 \\ 1 \\ - 3 \\ 0 \end{pmatrix}$
Which of the following is/are the eigenvector(s) for the matrix given below?$$\begin{pmatrix} – 9 & – 6 & – 2 & – 4 \\ – 8 & – 6 & – 3 & – ...
Arjun
10.4k
views
Arjun
asked
Feb 15, 2022
Linear Algebra
gatecse-2022
linear-algebra
eigen-value
multiple-selects
2-marks
+
–
4
votes
1
answer
47
GATE CSE 1995 | Question: 7(B)
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
admin
1.5k
views
admin
asked
Apr 25, 2021
Calculus
gate1995
calculus
limits
numerical-answers
+
–
24
votes
3
answers
48
GATE CSE 2021 Set 2 | Question: 11
Consider the following sets, where $n \geq 2$: $S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$ $S_2$: Set of all functions from the set $\{0,1,2, \dots, n^2-1\}$ ... There exists a surjection from $S_1$ to $S_2$ There exists a bijection from $S_1$ to $S_2$ There does not exist an injection from $S_1$ to $S_2$
Consider the following sets, where $n \geq 2$:$S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$$S_2$: Set of all functions from the set $\{...
Arjun
6.4k
views
Arjun
asked
Feb 18, 2021
Set Theory & Algebra
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 $S$
Choose the correct choice(s) regarding the following proportional logic assertion $S$:$$S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \righta...
Arjun
8.9k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
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 _________
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 ...
Arjun
6.1k
views
Arjun
asked
Feb 18, 2021
Probability
gatecse-2021-set2
numerical-answers
probability
random-variable
1-mark
+
–
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