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Answers by ankitgupta.1729
4
votes
41
Construct a grammar which generates all odd integers up to 999
275
views
answered
Aug 11, 2022
Theory of Computation
context-free-grammar
+
–
3
votes
42
Self Doubt
$L=\{wa^nw^Rb^n\mid w\in \left \{ a,b \right \}^\ast ,n\geqslant 0\}$ Can anyone give me step by step solution that shows this is not CFL by pumping Lemma?
$L=\{wa^nw^Rb^n\mid w\in \left \{ a,b \right \}^\ast ,n\geqslant 0\}$Can anyone give me step by step solution that shows this is not CFL by pumping Lemma?
497
views
answered
Jul 30, 2022
Theory of Computation
self-doubt
theory-of-computation
pumping-lemma
+
–
8
votes
43
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...
13.7k
views
answered
Jul 19, 2022
Graph Theory
gatecse-2020
numerical-answers
graph-theory
graph-coloring
2-marks
+
–
7
votes
44
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....
7.6k
views
answered
Jul 15, 2022
Graph Theory
gatecse-2022
graph-theory
graph-isomorphism
multiple-selects
2-marks
+
–
4
votes
45
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 11
How many squares are there in a chess board? $64$ $204$ $1296$ $4096$
How many squares are there in a chess board?$64$$204$$1296$$4096$
865
views
answered
Jun 20, 2022
Combinatory
goclasses_wq13
goclasses
combinatory
counting
2-marks
+
–
3
votes
46
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below?$$ a_{n} = \left\{\begin{matrix} n + 1, &...
9.6k
views
answered
May 19, 2022
Combinatory
gatecse-2022
combinatory
generating-functions
2-marks
+
–
1
votes
47
No of solution of the given equation
The Number of Points $x \in \Re$ for which $\sin ^{2} x-3x=5$ is , 0 1 more than one but finite $\infty$
The Number of Points $x \in \Re$ for which $\sin ^{2} x-3x=5$ is ,01more than one but finite$\infty$
296
views
answered
May 16, 2022
Mathematical Logic
nptel-quiz
calculus
+
–
2
votes
48
GATE-2014 EC
Which one of the following statements is NOT true for a square matrix A? If A is real symmetric, the eigen values of A are the diagonal elements of it. If all the principal minors of A are positive, all the eigen values of A are also positive. My question is what is “principal minors of A” ?
Which one of the following statements is NOT true for a square matrix A?If A is real symmetric, the eigen values of A are the diagonal elements of it.If all the principal...
1.0k
views
answered
May 10, 2022
Linear Algebra
linear-algebra
gate2014-ec-1
eigen-value
+
–
6
votes
49
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?$$ a_{n} = \left\{\begin{matrix} n + 1, &...
9.6k
views
answered
May 7, 2022
Combinatory
gatecse-2022
combinatory
generating-functions
2-marks
+
–
2
votes
50
Calculus by Spivak 4th edition Chapter 10 problem 9
361
views
answered
May 3, 2022
0
votes
51
ISI2004-MIII: 13
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then $X< 1$ $X>\frac{3}{2}$ $1< X< \frac{3}{2}$ none of the above
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then$X< 1$$X>\frac{3}{2}$$1< X< \frac{3}{2}$none of the above
2.7k
views
answered
May 3, 2022
Calculus
isi2004
engineering-mathematics
integration
+
–
2
votes
52
GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$
Consider the following recurrence:$$\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) – 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text...
7.8k
views
answered
Apr 14, 2022
Combinatory
gatecse-2022
combinatory
recurrence-relation
multiple-selects
2-marks
+
–
8
votes
53
GO Classes 2023 | Weekly Quiz 3 | Question: 13
Consider the following proposition : $A_n=\underbrace{(p\rightarrow (q\rightarrow (p\rightarrow (q\rightarrow (\dots )))))}_{\text{number of p's+ number of q's = n}}$ Which of the following is true for $A_n$ : For every $n \geq 2$, ... $n \geq 2$, $A_n$ is a contingency. For every $n \geq 2$, $A_n$ is either a tautology or a contingency.
Consider the following proposition :$A_n=\underbrace{(p\rightarrow (q\rightarrow (p\rightarrow (q\rightarrow (\dots )))))}_{\text{number of p's+ number of q's = n}}$Which...
650
views
answered
Mar 25, 2022
Mathematical Logic
goclasses
goclasses_wq3
mathematical-logic
propositional-logic
1-mark
+
–
2
votes
54
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 ________________.$$\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$$
6.5k
views
answered
Feb 23, 2022
Calculus
gatecse-2022
numerical-answers
calculus
limits
1-mark
+
–
29
votes
55
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.$$x_{1} + x_{2} – 2x_{3} = 4$$$$x_{1} + 3x_{2} – x_{3} = 7$$$$2x_{1} +...
11.5k
views
answered
Feb 17, 2022
Linear Algebra
gatecse-2022
linear-algebra
matrix
system-of-equations
2-marks
+
–
22
votes
56
GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$
Consider the following recurrence:$$\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) – 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text...
7.8k
views
answered
Feb 16, 2022
Combinatory
gatecse-2022
combinatory
recurrence-relation
multiple-selects
2-marks
+
–
2
votes
57
gate book test series output waveform
Please post The solution.
Please post The solution.
579
views
answered
Dec 26, 2021
Digital Logic
digital-logic
+
–
2
votes
58
GATE IT 2006 | Question: 28
The following definite integral evaluates to $\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$
The following definite integral evaluates to$$\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$$$\frac{1}{2}$$\pi \sqrt{10}$$\sqrt{10}$$\pi$
5.1k
views
answered
Sep 14, 2021
Numerical Methods
gateit-2006
numerical-methods
normal
non-gate
+
–
1
votes
59
TIFR CSE 2021 | Part A | Question: 9
Fix $n\geq 6$. Consider the set $\mathcal{C}$ of binary strings $x_{1}, x_{2} \dots x_{n}$ of length $n$ such that the bits satisfy the following set of equalities, all modulo $2$: $x_{i}+x_{i+1}+x_{i+2}=0$ ... $3$ $\left | \mathcal{C} \right |=4$. If $n\geq 6$ is not divisible by $3$ then $\left | \mathcal{C} \right |=1$.
Fix $n\geq 6$. Consider the set $\mathcal{C}$ of binary strings $x_{1}, x_{2} \dots x_{n}$ of length $n$ such that the bits satisfy the following set of equalities, all m...
500
views
answered
Apr 4, 2021
Set Theory & Algebra
tifr2021
set-theory&algebra
set-theory
+
–
1
votes
60
TIFR CSE 2016 | Part A | Question: 3
Consider the following set of $3n$ linear equations in $3n$ ... $\mathbb{R}^{3n}$ of dimension n $S$ is a subspace of $\mathbb{R}^{3n}$ of dimension $n-1$ $S$ has exactly $n$ elements
Consider the following set of $3n$ linear equations in $3n$ variables:$\begin{matrix} x_1-x_2=0 & x_4-x_5 =0 & \dots & x_{3n-2}-x_{3n-1}=0 \\ x_2-x_3=0 & x_5-x_6=0 & & x_...
557
views
answered
Feb 20, 2021
Linear Algebra
tifr2016
linear-algebra
vector-space
non-gate
+
–
46
votes
61
GATE CSE 2021 Set 1 | Question: 30
Consider the following recurrence relation. $T\left ( n \right )=\left\{\begin{array} {lcl} T(n ∕ 2)+T(2n∕5)+7n & \text{if} \; n>0\\1 & \text{if}\; n=0 \end{array}\right.$ Which one of the following options is correct? $T(n)=\Theta (n^{5/2})$ $T(n)=\Theta (n\log n)$ $T(n)=\Theta (n)$ $T(n)=\Theta ((\log n)^{5/2})$
Consider the following recurrence relation.$$T\left ( n \right )=\left\{\begin{array} {lcl} T(n ∕ 2)+T(2n∕5)+7n & \text{if} \; n>0\\1 & \text{if}\; n=0 \end{array}\r...
23.9k
views
answered
Feb 19, 2021
Algorithms
gatecse-2021-set1
algorithms
recurrence-relation
time-complexity
2-marks
+
–
1
votes
62
TIFR CSE 2013 | Part A | Question: 7
For any complex number $z$, $arg$ $z$ defines its phase, chosen to be in the interval $0\leq arg z < 360^{∘}$. If $z_{1}, z_{2}$ and $z_{3}$ ... $\frac{1}{3}$ 1 3 $\frac{1}{2}$
For any complex number $z$, $arg$ $z$ defines its phase, chosen to be in the interval $0\leq arg z < 360^{∘}$. If $z_{1}, z_{2}$ and $z_{3}$ are three complex numbers w...
632
views
answered
Feb 9, 2021
Quantitative Aptitude
tifr2013
quantitative-aptitude
complex-number
non-gate
+
–
3
votes
63
TIFR CSE 2012 | Part A | Question: 11
Let $N$ be the sum of all numbers from $1$ to $1023$ except the five primes numbers: $2, 3, 11, 17, 31.$ Suppose all numbers are represented using two bytes (sixteen bits). What is the value of the least significant byte (the least significant eight bits) of $N$? $00000000$ $10101110$ $01000000$ $10000000$ $11000000$
Let $N$ be the sum of all numbers from $1$ to $1023$ except the five primes numbers: $2, 3, 11, 17, 31.$ Suppose all numbers are represented using two bytes (sixteen bits...
1.8k
views
answered
Feb 8, 2021
Digital Logic
tifr2012
digital-logic
number-representation
+
–
2
votes
64
TIFR CSE 2011 | Part A | Question: 5
Three distinct points $x, y, z$ lie on a unit circle of the complex plane and satisfy $x+y+z=0$. Then $x, y, z$ form the vertices of . An isosceles but not equilateral triangle. An equilateral triangle. A triangle of any shape. A triangle whose shape can't be determined. None of the above.
Three distinct points $x, y, z$ lie on a unit circle of the complex plane and satisfy $x+y+z=0$. Then $x, y, z$ form the vertices of .An isosceles but not equilateral tri...
715
views
answered
Feb 6, 2021
Quantitative Aptitude
tifr2011
quantitative-aptitude
geometry
complex-number
non-gate
+
–
1
votes
65
TIFR CSE 2014 | Part A | Question: 9
Solve min $x^{2}+y^{2}$ subject to $\begin {align*} x + y &\geq 10,\\ 2x + 3y &\geq 20,\\ x &\geq 4,\\ y &\geq 4. \end{align*}$ $32$ $50$ $52$ $100$ None of the above
Solve min $x^{2}+y^{2}$ subject to$$\begin {align*} x + y &\geq 10,\\2x + 3y &\geq 20,\\x &\geq 4,\\y &\geq 4.\end{align*}$$$32$$50$$52$$100$None of the above
1.8k
views
answered
Oct 2, 2020
Calculus
tifr2014
calculus
maxima-minima
+
–
0
votes
66
TIFR CSE 2012 | Part B | Question: 6
Let $n$ be a large integer. Which of the following statements is TRUE? $2^{\sqrt{2\log n}}< \frac{n}{\log n}< n^{1/3}$ $\frac{n}{\log n}< n^{1/3}< 2^{\sqrt{2\log n}}$ $2^\sqrt{{2\log n}}< n^{1/3}< \frac{n}{\log n}$ $n^{1/3}< 2^\sqrt{{2\log n}}<\frac{n}{\log n}$ $\frac{n}{\log n}< 2^\sqrt{{2\log n}}<n^{1/3}$
Let $n$ be a large integer. Which of the following statements is TRUE?$2^{\sqrt{2\log n}}< \frac{n}{\log n}< n^{1/3}$$\frac{n}{\log n}< n^{1/3}< 2^{\sqrt{2\log n}}$$2^\sq...
4.3k
views
answered
Sep 24, 2020
Algorithms
tifr2012
algorithms
asymptotic-notation
+
–
1
votes
67
TIFR-2017-Maths-A: 30
True/False Question : The matrices $\begin{pmatrix} x &0 \\ 0 & y \end{pmatrix} and \begin{pmatrix} x &1 \\ 0 & y \end{pmatrix}, x\neq y,$ for any $x,y \in \mathbb{R}$ are conjugate in $M_{2}\left ( \mathbb{R} \right )$ .
True/False Question :The matrices $$\begin{pmatrix} x &0 \\ 0 & y \end{pmatrix} and \begin{pmatrix} x &1 \\ 0 & y \end{pmatrix}, x\neq y,$$for any $x,y \in \mathbb{R}$ ar...
305
views
answered
Sep 6, 2020
TIFR
tifrmaths2017
true-false
+
–
1
votes
68
TIFR-2017-Maths-A: 29
True/False Question : Let $y\left ( t \right )$ be a real valued function defined on the real line such that ${y}'=y \left ( 1-y \right )$, with $y\left ( 0\right ) \in \left [ 0,1 \right ]$. Then $\lim_{t\rightarrow \infty }y\left ( t \right )=1$ .
True/False Question :Let $y\left ( t \right )$ be a real valued function defined on the real line such that ${y}'=y \left ( 1-y \right )$, with $y\left ( 0\right ) \in \l...
275
views
answered
Sep 6, 2020
TIFR
tifrmaths2017
true-false
+
–
0
votes
69
TIFR-2018-Maths-A: 7
True/False Question : In the vector space $\left \{ f \mid f : \left [ 0,1 \right ] \rightarrow \mathbb{R}\right \}$ of real-valued functions on the closed interval $\left [ 0,1 \right ]$, the set $S=\left \{ sin\left ( x \right ) , cos\left ( x \right ),tan\left ( x \right )\right \}$ is linearly independent.
True/False Question :In the vector space $\left \{ f \mid f : \left [ 0,1 \right ] \rightarrow \mathbb{R}\right \}$ of real-valued functions on the closed interval $\lef...
336
views
answered
Sep 6, 2020
TIFR
tifrmaths2018
true-false
+
–
1
votes
70
TIFR-2019-Maths-A: 10
Let $S=\left \{ x \in\mathbb{R} \mid x=Trace\:(A) \:for\:some\:A \in M_{4} (\mathbb{R}) such\:that\:A^{2}=A \right\}.$ Then which of the following describes $S$? $S=\left \{ 0,2,4 \right \}$ $S=\left \{ 0,1/2,1,3/2,2,5/2,3,7/2,4 \right \}$ $S=\left \{ 0,1,2,3,4 \right \}$ $S=\left \{ 0,4 \right \}$
Let $$S=\left \{ x \in\mathbb{R} \mid x=Trace\:(A) \:for\:some\:A \in M_{4} (\mathbb{R}) such\:that\:A^{2}=A \right\}.$$Then which of the following describes $S$?$S=\left...
281
views
answered
Aug 31, 2020
TIFR
tifrmaths2019
+
–
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