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1
Context Free Language
The complement of the languages: i) {ww | w in (0+1)*} ii) {$a^n b^nc^n$ | n>1} are a) Context Free b) Not Context Free c)are DCFL’s d)None
practicalmetal
asked
in
Theory of Computation
2 hours
ago
by
practicalmetal
6
views
context-free-language
theory-of-computation
ace-test-series
0
votes
0
answers
2
Context Free Languages
Is the following language CFL : { ww | w in (a+b)* and |w| <1000 }
practicalmetal
asked
in
Theory of Computation
2 hours
ago
by
practicalmetal
6
views
context-free-language
theory-of-computation
context-free-grammar
pushdown-automata
0
votes
0
answers
3
Fork() system call.
main(){ int i,n; for(int i=0;i<n;i++){ fork(); printf("*"); } } How many times ‘*’ will be printed? The answer is not 2^n ? why?
vikranty2j
asked
in
Operating System
9 hours
ago
by
vikranty2j
26
views
programming-in-c
operating-system
0
votes
0
answers
4
GATE CS 2023
Got 262 Rank,Score 746 and 67.67 marks in Gen Category in GATE CS 2023., Which IITs can offer direct admission and in which courses.
rajdkaur
asked
in
Written Exam
12 hours
ago
by
rajdkaur
37
views
admissions
query
0
votes
0
answers
5
Float representation using normalised mantissa
while representing an exponent in floating point number why do we add a biased term? What is the benifit of adding this??
Sk Jamil Ahemad
asked
in
Digital Logic
1 day
ago
by
Sk Jamil Ahemad
16
views
digital-logic
number-system
0
votes
0
answers
6
Self doubt
For barc cse exam, what subjects do i have to prepare other than gate syllabus?
gaddalakonda_ganesh
asked
in
GATE
5 days
ago
by
gaddalakonda_ganesh
44
views
self-doubt
0
votes
0
answers
7
doubt
where can I find all barc’s PYQ
someshawasthi
asked
in
BARC
6 days
ago
by
someshawasthi
36
views
self-doubt
1
vote
0
answers
8
TIFR Mathematics 2023 | Part B | Question: 1
Answer whether the following statements are True or False. Let $\alpha$ be a positive real number, and let $f:(0,1) \rightarrow \mathbb{R}$ be a function such that $|f(x)-f(y)| \leq$ $|x-y|^{\alpha}$ for all $x, y \in(0,1)$. Then $f$ can be extended to a continuous function $[0,1] \rightarrow \mathbb{R}$.
admin
asked
in
Others
6 days
ago
by
admin
17
views
tifrmaths2023
true-false
1
vote
0
answers
9
TIFR Mathematics 2023 | Part B | Question: 2
Answer whether the following statements are True or False. Suppose $f, g: \mathbb{R} \rightarrow \mathbb{R}$ are continuous functions such that $f^{2}+g^{2}$ is uniformly continuous. Then at least one of the two functions $f$ and $g$ is uniformly continuous.
admin
asked
in
Others
6 days
ago
by
admin
17
views
tifrmaths2023
true-false
1
vote
0
answers
10
TIFR Mathematics 2023 | Part B | Question: 3
Answer whether the following statements are True or False. Let $\left\{f_{n}\right\}_{n}$ be a sequence of (not necessarily continuous) functions from $[0,1]$ to $\mathbb{R}$. Let $f:[0,1] \rightarrow \mathbb{R}$ be such that for any $x \in[0,1]$ ... $\lim _{n \rightarrow \infty} f_{n}\left(x_{n}\right)=f(x)$. Then $f$ is continuous.
admin
asked
in
Others
6 days
ago
by
admin
13
views
tifrmaths2023
true-false
1
vote
0
answers
11
TIFR Mathematics 2023 | Part B | Question: 4
Answer whether the following statements are True or False. Let $A, B \in \mathrm{M}_{2}(\mathbb{Z} / 2 \mathbb{Z})$ be such that $\operatorname{tr}(A)=\operatorname{tr}(B)$ and $\operatorname{tr}\left(A^{2}\right)=\operatorname{tr}\left(B^{2}\right)$. Then $A$ and $B$ have the same eigenvalues.
admin
asked
in
Others
6 days
ago
by
admin
20
views
tifrmaths2023
true-false
1
vote
0
answers
12
TIFR Mathematics 2023 | Part B | Question: 5
Answer whether the following statements are True or False. Let $v_{1}, v_{2}, w_{1}, w_{2}$ be nonzero vectors in $\mathbb{R}^{2}$. Then there exists a $2 \times 2$ real matrix $A$ such that $A v_{1}=v_{2}$ and $A w_{1}=w_{2}$.
admin
asked
in
Others
6 days
ago
by
admin
8
views
tifrmaths2023
true-false
1
vote
0
answers
13
TIFR Mathematics 2023 | Part B | Question: 6
Answer whether the following statements are True or False. Let $A=\left(a_{i j}\right) \in \mathrm{M}_{n}(\mathbb{R})$ be such that $a_{i j} \geq 0$ for all $1 \leq i, j \leq n$. Assume that $\lim _{m \rightarrow \infty} A^{m}$ exists, and denote it by $B=\left(b_{i j}\right)$. Then, for all $1 \leq i, j \leq n$, we have $b_{i j} \in\{0,1\}$.
admin
asked
in
Others
6 days
ago
by
admin
7
views
tifrmaths2023
true-false
1
vote
0
answers
14
TIFR Mathematics 2023 | Part B | Question: 7
Answer whether the following statements are True or False. Given any monic polynomial $f(x) \in \mathbb{R}[x]$ of degree $n$, there exists a matrix $A \in \mathrm{M}_{n}(\mathbb{R})$ such that its characteristic polynomial equals $f$.
admin
asked
in
Others
6 days
ago
by
admin
7
views
tifrmaths2023
true-false
1
vote
0
answers
15
TIFR Mathematics 2023 | Part B | Question: 8
Answer whether the following statements are True or False. If $A \in \mathrm{M}_{4}(\mathbb{Q})$ is such that its characteristic polynomial equals $x^{4}+1$, then $A$ is diagonalizable in $\mathrm{M}_{4}(\mathbb{C})$.
admin
asked
in
Others
6 days
ago
by
admin
11
views
tifrmaths2023
true-false
1
vote
0
answers
16
TIFR Mathematics 2023 | Part B | Question: 9
Answer whether the following statements are True or False. If $A \in \mathrm{M}_{n}(\mathbb{R})$ is such that $A B=B A$ for all invertible matrices $B \in \mathrm{M}_{n}(\mathbb{R})$, then $A=\lambda \cdot$ Id for some $\lambda \in \mathbb{R}$.
admin
asked
in
Others
6 days
ago
by
admin
15
views
tifrmaths2023
true-false
1
vote
0
answers
17
TIFR Mathematics 2023 | Part B | Question: 10
Answer whether the following statements are True or False. There exists a homeomorphism $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(2 x)=3 f(x)$ for all $x \in \mathbb{R}$.
admin
asked
in
Others
6 days
ago
by
admin
12
views
tifrmaths2023
true-false
1
vote
0
answers
18
TIFR Mathematics 2023 | Part B | Question: 11
Answer whether the following statements are True or False. There exists a continuous bijection from $[0,1] \times[0,1]$ to $\left\{(x, y) \in \mathbb{R}^{2} \mid x^{2}+y^{2} \leq 1\right\}$, which is not a homeomorphism.
admin
asked
in
Others
6 days
ago
by
admin
13
views
tifrmaths2023
true-false
1
vote
0
answers
19
TIFR Mathematics 2023 | Part B | Question: 12
Answer whether the following statements are True or False. Let $f \in \mathbb{C}\left[z_{1}, \ldots, z_{n}\right]$ be a nonzero polynomial $(n \geq 1)$, and let \[ X=\left\{z \in \mathbb{C}^{n} \mid f(z)=0\right\} . \] Then $\mathbb{C}^{n} \backslash X$ is path connected.
admin
asked
in
Others
6 days
ago
by
admin
10
views
tifrmaths2023
true-false
1
vote
0
answers
20
TIFR Mathematics 2023 | Part B | Question: 13
Answer whether the following statements are True or False. A connected metric space with at least two points is uncountable.
admin
asked
in
Others
6 days
ago
by
admin
9
views
tifrmaths2023
true-false
1
vote
0
answers
21
TIFR Mathematics 2023 | Part B | Question: 14
Answer whether the following statements are True or False. If $A$ and $B$ are disjoint subsets of a metric space $(X, d)$, then \[ \inf \{d(x, y) \mid x \in A, y \in B\} \neq 0. \]
admin
asked
in
Others
6 days
ago
by
admin
11
views
tifrmaths2023
true-false
1
vote
0
answers
22
TIFR Mathematics 2023 | Part B | Question: 15
Answer whether the following statements are True or False. A countably infinite complete metric space has infinitely many isolated points (an element $x$ of a metric space $X$ is said to be an isolated point if $\{x\}$ is an open subset of $X$ ).
admin
asked
in
Others
6 days
ago
by
admin
10
views
tifrmaths2023
true-false
1
vote
0
answers
23
TIFR Mathematics 2023 | Part B | Question: 16
Answer whether the following statements are True or False. Suppose $G$ and $H$ are two countably infinite abelian groups such that every nontrivial element of $G \times H$ has order $7$ . Then $G$ is isomorphic to $H$.
admin
asked
in
Others
6 days
ago
by
admin
11
views
tifrmaths2023
true-false
1
vote
0
answers
24
TIFR Mathematics 2023 | Part B | Question: 17
Answer whether the following statements are True or False. There exists a nonabelian group $G$ of order $26$ such that every proper subgroup of $G$ is abelian.
admin
asked
in
Others
6 days
ago
by
admin
7
views
tifrmaths2023
true-false
1
vote
0
answers
25
TIFR Mathematics 2023 | Part B | Question: 18
Answer whether the following statements are True or False. Let $G$ be a group generated by two elements $x$ and $y$, each of order $2$ . Then $G$ is finite.
admin
asked
in
Others
6 days
ago
by
admin
6
views
tifrmaths2023
true-false
1
vote
0
answers
26
TIFR Mathematics 2023 | Part B | Question: 19
Answer whether the following statements are True or False. $\mathbb{R}[x] /\left(x^{4}+x^{2}+2023\right)$ is an integral domain.
admin
asked
in
Others
6 days
ago
by
admin
7
views
tifrmaths2023
true-false
1
vote
0
answers
27
TIFR Mathematics 2023 | Part B | Question: 20
Answer whether the following statements are True or False. Every finite group is isomorphic to a subgroup of a finite group generated by two elements.
admin
asked
in
Others
6 days
ago
by
admin
6
views
tifrmaths2023
true-false
1
vote
0
answers
28
TIFR Mathematics 2023 | Part A | Question: 1
Define $f: \mathbb{R} \rightarrow \mathbb{R}$ by $f(x)=\left(3 x^{2}+1\right) /\left(x^{2}+3\right)$. Let $f^{\circ 1}=f$, and let $f^{\circ n}=f^{\circ(n-1)} \circ f$ for all integers $n \geq 2$. Which of the following statements is ... $\lim _{n \rightarrow \infty} f^{\circ n}(1 / 2)$ nor $\lim _{n \rightarrow \infty} f^{\circ n}(2)$ exists.
admin
asked
in
Others
6 days
ago
by
admin
11
views
tifrmaths2023
1
vote
0
answers
29
TIFR Mathematics 2023 | Part A | Question: 2
Consider the following properties of a sequence $\left\{a_{n}\right\}_{n}$ of real numbers. $\text{(I)} \lim _{n \rightarrow \infty} a_{n}=0$. $\text{(II)}$ There exists a sequence $\left\{i_{n}\right\}_{n}$ ... $\text{(I)}$ does not imply $\text{(II)}$, and $\text{(II)}$ does not imply $\text{(I)}$.
admin
asked
in
Others
6 days
ago
by
admin
9
views
tifrmaths2023
1
vote
0
answers
30
TIFR Mathematics 2023 | Part A | Question: 3
Consider sequences $\left\{x_{n}\right\}_{n}$ of real numbers such that \[ \lim _{n \rightarrow \infty}\left(x_{2 n-1}+x_{2 n}\right)=2 \quad \text { and } \quad \lim _{n \rightarrow \infty}\left(x_{2 n}+x_{2 n+1}\right)=3 . \] Which of the ... $\left\{x_{n}\right\}_{n}$, for which $\lim _{n \rightarrow \infty} \frac{x_{2 n+1}}{x_{2 n}}$ does not exist.
admin
asked
in
Others
6 days
ago
by
admin
9
views
tifrmaths2023
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