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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

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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

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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

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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

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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

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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

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7

doubt
where can I find all barc’s PYQ

someshawasthi asked in BARC 6 days ago

by someshawasthi

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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1 vote

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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

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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

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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

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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

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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

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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

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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

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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

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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

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