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Previous GATE Questions in Engineering Mathematics
12
votes
4
answers
41
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
6.7k
views
Arjun
asked
Feb 15, 2022
Calculus
gatecse-2022
numerical-answers
calculus
limits
1-mark
+
–
26
votes
6
answers
42
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?$$ a_{n} = \left\{\begin{matrix} n + 1, &...
Arjun
9.8k
views
Arjun
asked
Feb 15, 2022
Combinatory
gatecse-2022
combinatory
generating-functions
2-marks
+
–
14
votes
3
answers
43
GATE CSE 2022 | Question: 27
Consider a simple undirected unweighted graph with at least three vertices. If $\textit{A}$ is the adjacency matrix of the graph, then the number of $3–$cycles in the graph is given by the trace of $\textit{A}^{3}$ $\textit{A}^{3}$ divided by $2$ $\textit{A}^{3}$ divided by $3$ $\textit{A}^{3}$ divided by $6$
Consider a simple undirected unweighted graph with at least three vertices. If $\textit{A}$ is the adjacency matrix of the graph, then the number of $3–$cycles in the g...
Arjun
7.7k
views
Arjun
asked
Feb 15, 2022
Graph Theory
gatecse-2022
graph-theory
graph-connectivity
2-marks
+
–
22
votes
5
answers
44
GATE CSE 2022 | Question: 35
Consider solving the following system of simultaneous equations using $\text{LU}$ decomposition. $x_{1} + x_{2} - 2x_{3} = 4$ $x_{1} + 3x_{2} - x_{3} = 7$ $2x_{1} + x_{2} - 5x_{3} = 7$ where $\textit{L}$ and $\textit{U}$ ... $\textit{L}_{32}= - \frac{1}{2}, \textit{U}_{33}= - \frac{1}{2}, x_{1}= 0$
Consider solving the following system of simultaneous equations using $\text{LU}$ decomposition.$$x_{1} + x_{2} – 2x_{3} = 4$$$$x_{1} + 3x_{2} – x_{3} = 7$$$$2x_{1} +...
Arjun
11.8k
views
Arjun
asked
Feb 15, 2022
Linear Algebra
gatecse-2022
linear-algebra
matrix
system-of-equations
2-marks
+
–
14
votes
2
answers
45
GATE CSE 2022 | Question: 40
The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are $\text{TRUE}?$ The chromatic number of the graph is $3.$ The graph has a Hamiltonian path. The following graph is isomorphic to the Peterson ... $3.$ (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
The following simple undirected graph is referred to as the Peterson graph.Which of the following statements is/are $\text{TRUE}?$The chromatic number of the graph is $3....
Arjun
7.7k
views
Arjun
asked
Feb 15, 2022
Graph Theory
gatecse-2022
graph-theory
graph-isomorphism
multiple-selects
2-marks
+
–
15
votes
6
answers
46
GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$
Consider the following recurrence:$$\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) – 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text...
Arjun
8.0k
views
Arjun
asked
Feb 15, 2022
Combinatory
gatecse-2022
combinatory
recurrence-relation
multiple-selects
2-marks
+
–
17
votes
4
answers
47
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
7.6k
views
Arjun
asked
Feb 15, 2022
Graph Theory
gatecse-2022
graph-theory
graph-connectivity
multiple-selects
2-marks
+
–
26
votes
1
answer
48
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?$$\begin{pmatrix} – 9 & – 6 & – 2 & – 4 \\ – 8 & – 6 & – 3 & – ...
Arjun
10.7k
views
Arjun
asked
Feb 15, 2022
Linear Algebra
gatecse-2022
linear-algebra
eigen-value
multiple-selects
2-marks
+
–
4
votes
1
answer
49
GATE CSE 1995 | Question: 7(B)
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
admin
1.5k
views
admin
asked
Apr 25, 2021
Calculus
gate1995
calculus
limits
numerical-answers
+
–
26
votes
3
answers
50
GATE CSE 2021 Set 2 | Question: 11
Consider the following sets, where $n \geq 2$: $S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$ $S_2$: Set of all functions from the set $\{0,1,2, \dots, n^2-1\}$ ... There exists a surjection from $S_1$ to $S_2$ There exists a bijection from $S_1$ to $S_2$ There does not exist an injection from $S_1$ to $S_2$
Consider the following sets, where $n \geq 2$:$S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$$S_2$: Set of all functions from the set $\{...
Arjun
6.6k
views
Arjun
asked
Feb 18, 2021
Set Theory & Algebra
gatecse-2021-set2
multiple-selects
set-theory&algebra
functions
1-mark
+
–
30
votes
9
answers
51
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
9.3k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
+
–
14
votes
1
answer
52
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
6.3k
views
Arjun
asked
Feb 18, 2021
Probability
gatecse-2021-set2
numerical-answers
probability
random-variable
1-mark
statistics
+
–
48
votes
14
answers
53
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 __________
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...
Arjun
19.3k
views
Arjun
asked
Feb 18, 2021
Linear Algebra
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
+
–
17
votes
3
answers
54
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 __________
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 fo...
Arjun
6.4k
views
Arjun
asked
Feb 18, 2021
Calculus
gatecse-2021-set2
numerical-answers
calculus
continuity
1-mark
+
–
27
votes
4
answers
55
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$.
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...
Arjun
7.7k
views
Arjun
asked
Feb 18, 2021
Probability
gatecse-2021-set2
probability
expectation
2-marks
+
–
36
votes
4
answers
56
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 ...
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 ...
Arjun
11.1k
views
Arjun
asked
Feb 18, 2021
Probability
gatecse-2021-set2
probability
normal
2-marks
+
–
23
votes
1
answer
57
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$
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])$$Let $\mathcal{L}$ ...
Arjun
7.3k
views
Arjun
asked
Feb 18, 2021
Set Theory & Algebra
gatecse-2021-set2
set-theory&algebra
set-theory
2-marks
+
–
27
votes
6
answers
58
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Arjun
12.3k
views
Arjun
asked
Feb 18, 2021
Combinatory
gatecse-2021-set2
combinatory
counting
numerical-answers
2-marks
+
–
14
votes
8
answers
59
GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic.$S_1: (\neg p\wedge(p\vee q))\rightarrow q$$S_2: q\rightarrow(\neg p\wedge...
Arjun
8.6k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
+
–
13
votes
5
answers
60
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 _________.
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.
Arjun
8.3k
views
Arjun
asked
Feb 18, 2021
Graph Theory
gatecse-2021-set1
graph-theory
graph-planarity
numerical-answers
easy
1-mark
+
–
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