Dark Mode

Recent questions and answers in Others

1 vote

1 answer

1

TIFR CSE 2023 | Part B | Question: 2
Which of the following is true about the set of regular languages and the set of recursively enumerable languages over a finite alphabet $\Sigma$ ? The set of regular languages is countable while the set of recursively enumerable languages ... whether the set of recursively enumerable languages is countable or not is not known and is a longstanding open problem.

Kabir5454 answered in Others Mar 14

30 views

0 votes

1 answer

2

NIELIT 2022 April Scientist B | Section A | Question: 21
Choose the word which is least like the other words in the group : Shimmer Simmer Glimmer Glint

Sagnick p answered in Others Mar 14

70 views

0 votes

1 answer

3

NIELIT 2022 April Scientist B | Section A | Question: 27
The first republic day of India was celebrated on January $26, 1950.$ What day of the week was it ? Wednesday Friday Thursday Tuesday

Sagnick p answered in Others Mar 14

57 views

1 vote

0 answers

4

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 Mar 14

by admin

21 views

1 vote

0 answers

5

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 Mar 14

by admin

22 views

1 vote

0 answers

6

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 Mar 14

by admin

16 views

1 vote

0 answers

7

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 Mar 14

by admin

25 views

1 vote

0 answers

8

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 Mar 14

by admin

11 views

1 vote

0 answers

9

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 Mar 14

by admin

11 views

1 vote

0 answers

10

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 Mar 14

by admin

9 views

1 vote

0 answers

11

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 Mar 14

by admin

14 views

1 vote

0 answers

12

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 Mar 14

by admin

18 views

1 vote

0 answers

13

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 Mar 14

by admin

15 views

1 vote

0 answers

14

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 Mar 14

by admin

16 views

1 vote

0 answers

15

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 Mar 14

by admin

14 views

1 vote

0 answers

16

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 Mar 14

by admin

11 views

1 vote

0 answers

17

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 Mar 14

by admin

12 views

1 vote

0 answers

18

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 Mar 14

by admin

13 views

1 vote

0 answers

19

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 Mar 14

by admin

15 views

1 vote

0 answers

20

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 Mar 14

by admin

10 views

1 vote

0 answers

21

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 Mar 14

by admin

7 views

1 vote

0 answers

22

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 Mar 14

by admin

10 views

1 vote

0 answers

23

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 Mar 14

by admin

8 views

1 vote

0 answers

24

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 Mar 14

by admin

16 views

1 vote

0 answers

25

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 Mar 14

by admin

9 views

1 vote

0 answers

26

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 Mar 14

by admin

10 views

1 vote

0 answers

27

TIFR Mathematics 2023 | Part A | Question: 4
Consider the function $f:(0, \infty) \rightarrow(0, \infty)$ given by $f(x)=x e^{x}$. Let $L:(0, \infty) \rightarrow(0, \infty)$ ... $\lim _{x \rightarrow \infty} \frac{L(x)}{\sqrt{\log x}}=1$. None of the remaining three options is correct.

admin asked in Others Mar 14

by admin

15 views

1 vote

0 answers

28

TIFR Mathematics 2023 | Part A | Question: 5
Let $\left\{b_{n}\right\}_{n}$ be a monotonically increasing sequence of positive real numbers such that $\lim _{n \rightarrow \infty} b_{n}=$ $\infty$. Which of the following statements is true about \[ \lim _{n \rightarrow \ ... $0$. The limit exists for all such sequences, and its value is always $1$. None of the remaining three options is correct.

admin asked in Others Mar 14

by admin

7 views

1 vote

0 answers

29

TIFR Mathematics 2023 | Part A | Question: 6
For every positive integer $n$, define $f_{n}:[0,1] \rightarrow \mathbb{R}$ by $f_{n}(x)=\frac{\sin \left(n^{2} x\right)+\cos \left(e^{n} x\right)}{1+n^{2} x^{2}}$. Then \[ \lim _{n \rightarrow \infty} \int_{0}^{1-\sin (1 / n)} f_{n}(x) d x \] equals $1$. $0.$ $\infty$. $1 / 2$.

admin asked in Others Mar 14

by admin

12 views

1 vote

0 answers

30

TIFR Mathematics 2023 | Part A | Question: 7
Consider the functions $f_{1}, f_{2}:(0, \infty) \rightarrow \mathbb{R}$ defined by \[ f_{1}(x)=\sqrt{x}, \quad \text { and } \quad f_{2}(x)=\sqrt{x} \sin x . \] Which of the following statements is correct? $f_{1}$ and $f_{2}$ ... $f_{2}$ is not. $f_{2}$ is uniformly continuous, but $f_{1}$ is not. Neither $f_{1}$ nor $f_{2}$ is uniformly continuous.

admin asked in Others Mar 14

by admin

7 views

1 vote

0 answers

31

TIFR Mathematics 2023 | Part A | Question: 8
Let $x_{1} \in \mathbb{R}^{2} \backslash\{0\}$ be fixed, and inductively define $x_{n+1}=A x_{n}$ for $n \geq 1$, where $A$ is the $2 \times 2$ real matrix given by \[ A:=\left(\begin{array}{cc} \frac{\sqrt{3}}{ ... , but it has a convergent subsequence. $\lim _{n \rightarrow \infty}\left\|x_{n}\right\|=0$. None of the remaining three options is correct.

admin asked in Others Mar 14

by admin

15 views

1 vote

0 answers

32

TIFR Mathematics 2023 | Part A | Question: 9
Let $T: \mathrm{M}_{3}(\mathbb{R}) \rightarrow \mathbb{R}^{3}$ be the linear map defined by $T(A)=A\left(\begin{array}{c}1 \\ 0 \\ -1\end{array}\right)$. Then the dimension of the kernel of $T$ equals $2$. $8$. $1$. None of the remaining three options.

admin asked in Others Mar 14

by admin

8 views

1 vote

0 answers

33

TIFR Mathematics 2023 | Part A | Question: 10
Let $V=\{f(x) \in \mathbb{R}[x] \mid f(0)=0\}$, viewed as a real vector space. Consider the following assertions: $\text{(I)}$ $V$ contains three linearly independent polynomials of degree $2$ . $\text{(II)}$ $V$ contains two linearly independent ... $\text{(II)}$ is true. Neither $\text{(I)}$ nor $\text{(II)}$ is true.

admin asked in Others Mar 14

by admin

6 views

0 votes

1 answer

34

NIELIT 2022 April Scientist B | Section B | Question: 119
In a binary data transmission $\text{DPSK}$ is preferred to $\text{PSK}$ because : a coherent carrier is not required to be generated at the receiver for a given energy per bit, the probability of error is less the $1800$ phase shifts of the carrier are unimportant more protection is provided against impulse noise

Sagnick p answered in Others Mar 14

63 views

1 vote

1 answer

35

TIFR Mathematics 2022 | Part B | Question: 17
Answer whether the following statements are True or False. There exists a differentiable function $f: \mathbb{R} \rightarrow \mathbb{R}$ such that \[ \lim _{x \rightarrow \infty} f(x)=2 \quad \text { and } \quad \lim _{x \rightarrow \infty} f^{\prime}(x)=1 .\]

KG answered in Others Mar 12

by KG

64 views

0 votes

1 answer

36

NIELIT 2022 April Scientist B | Section A | Question: 6
The following question is based on the information given below: Data of $450$ candidates, who took part in an examination in social sciences, Mathematics and Science is given as below : Number of Students who : passed in all subjects are $167$ ... in Social sciences only $= 62.$ How many failed in two subjects only? $162$ $152$ $100$ $52$

abhisham62 answered in Others Mar 7

83 views

0 votes

2 answers

37

NIELIT 2021 Dec Scientist A - Section B: 93
Which of the following step is not a part of the requirement engineering process? Feasibility Study Programming Language Requirement Specification Software Requirement Specification Requirement Gathering & Validation

Bharat Bhushan answered in Others Mar 5

by Bharat Bhushan

67 views

0 votes

1 answer

38

NIELIT 2021 Dec Scientist A - Section B: 87
The postfix equivalent of the infix expression $(a+b)^{*}(c^{*}d-e)^{*}f/g$ is : $ab + cd^{*}e – fg^{*}/^{*}$ $ab + cd^{*}e - fg/^{**}$ $ab + cde^{*} – fg/^{**}$ $abcd + e^{*} fg – /^{**}$

khushbook answered in Others Mar 4

68 views

0 votes

1 answer

39

NIELIT 2022 April Scientist B | Section A | Question: 31
In a family of six persons $\text{A, B, C, D, E}$ and $\text{F},$ there are two married couples. The family has equal number of male and female. $\text{D}$ is the grandmother of $\text{A}$ and mother of $\text{B}$ $\text{C}$ is ... $ $\text{A}$ is the sister of $\text{F}.$ $\text{D}$ has two grandsons$ None of these

DMeher answered in Others Feb 15

by DMeher

66 views

0 votes

1 answer

40

NIELIT 2022 April Scientist B | Section A | Question: 12
Read following information and answer the question. There is a group of five persons, $\text{P, Q, R, S}$ and $\text{T.}$ One of them is a Horticulturist, one is Physicist, one is Journalist, one is Industrialist and one is an Advocate. Three of the ... $\text{R's}$ brother. Who is industrialist ? $\text{P}$ $\text{Q}$ $\text{R}$ $\text{S}$

DMeher answered in Others Feb 15

by DMeher

84 views

To see more, click for all the questions in this category.

Recent questions and answers in Others