Recent questions and answers in Others / GATE Overflow for GATE CSE

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1

TIFR CSE 2024 | Part A | Question: 15
Suppose Michelle gives Asna and Badri two different numbers from $\mathbb{N}=\{1,2,3, \ldots\}$. It is commonly known to both Asna and Badri that they each know only their own number and that it is different from the other one. The following conversation ensues ... was given $3$, Badri was given $4$. Asna was given $4$, Badri was given $3$. None of the above.

Suppose Michelle gives Asna and Badri two different numbers from $\mathbb{N}=\{1,2,3, \ldots\}$. It is commonly known to both Asna and Badri that they each know only thei...

꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂

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꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂ answered 3 days ago

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2

Graph Theory
A vertex colouring with three colours of a graph G = (V, E) is a mapping V → {R, G, B }. So that any two adjacent vertices does not same colour. Consider the below graphs:

A vertex colouring with three colours of a graph G = (V, E) is a mapping V → {R, G, B }. So that any two adjacent vertices does not same colour. Consider the below grap...

alexa16

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alexa16 asked Apr 11

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1 answer

3

UGCNET CSE December 2022: 64
Consider the following Learning algorithms. Logistic regression. Back propagation. Linear regression. Forward propagation. Which of the following options represents classification algorithm? Choose the correct answer from the options given below: $\mathrm{A}$ & $\mathrm{C}$ ... $3 [39555]) 3$ (Option $4 [39556]) 4$ Answer Given by Candidate: $2$

Consider the following Learning algorithms.Logistic regression.Back propagation.Linear regression.Forward propagation.Which of the following options represents classifica...

ajayraho

170 views

ajayraho answered Mar 12

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1 answer

4

UGCNET CSE December 2022: 88
An $\text{OS}$ follows round-robin scheduling with time quantum of $4 \mathrm{~ms}$. Assuming that the $\mathrm{CPU}$ is free now and there are $20$ ... $2[39650]) 2$ (Option $3[39651]) 3$ (Option $4[39652]) 4$ Answer Given by Candidate: $2$

An $\text{OS}$ follows round-robin scheduling with time quantum of $4 \mathrm{~ms}$. Assuming that the $\mathrm{CPU}$ is free now and there are $20$ processes waiting in ...

ajayraho

452 views

ajayraho answered Mar 12

0 votes

1 answer

5

UGCNET CSE December 2022: 62
The Solution to Silly Window Syndrome problem is/are: Nagle's Algorithm Clark's Algorithm Jacobson's Algorithm Piggy backing Algorithm Choose the correct answer from the options given below: $\mathrm{A}$ and $\mathrm{B}$ Only $\mathrm{A}$ and $\mathrm{C}$ Only ... $2[39546]) 2$ (Option $3 [39547]) 3$ (Option $4 [39548]) 4$ Answer Given by Candidate: $3$

The Solution to Silly Window Syndrome problem is/are:Nagle's AlgorithmClark's AlgorithmJacobson's AlgorithmPiggy backing AlgorithmChoose the correct answer from the optio...

ajayraho

216 views

ajayraho answered Mar 12

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1 answer

6

UGCNET CSE December 2022: 83
What is the safest order while simplifying Context Free Grammar? Elimination of $\varepsilon$-productions, Unit productions and then Useless symbols \& productions. Elimination of useless symbols \& productions, $\varepsilon$-productions and then Unit productions. Elimination of ... $3[39631]) 3$ (Option $4 [39632]) 4$ Answer Given by Candidate: $2$

What is the safest order while simplifying Context Free Grammar?Elimination of $\varepsilon$-productions, Unit productions and then Useless symbols \& productions.Elimina...

ajayraho

191 views

ajayraho answered Mar 12

0 votes

1 answer

7

UGCNET CSE December 2022: 80
Select the correct order of events after power is initialized on a system. A. Bootstrap loader is loaded from the disk B. Kernel is loaded onto the memory C. Firmware $\text{ROM}$ ... Option $2 [39618]) 2$ (Option $3 [39619]) 3$ (Option $4 [39620]) 4$ Answer Given by Candidate: $4$

Select the correct order of events after power is initialized on a system.A. Bootstrap loader is loaded from the diskB. Kernel is loaded onto the memoryC. Firmware $\text...

ajayraho

278 views

ajayraho answered Mar 12

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1 answer

8

UGCNET CSE December 2022: 29
The transition function ' $\delta$ ' in multi-tape Turing machine is defined as: $\delta: 2 \mathrm{Q} \times \Gamma^{\mathrm{k}} \rightarrow 2^{\mathrm{Q}} \times \Gamma^{\mathrm{k}} \times\{\mathrm{L}, \mathrm{R}, \mathrm{S}\}^{\mathrm{k}}$ ... $2[39414]) 2$ (Option $3[39415]) 3$ (Option $4 [39416]) 4$ Answer Given by Candidate : $3$

The transition function ' $\delta$ ' in multi-tape Turing machine is defined as:$\delta: 2 \mathrm{Q} \times \Gamma^{\mathrm{k}} \rightarrow 2^{\mathrm{Q}} \times \Gamma^...

ajayraho

263 views

ajayraho answered Mar 12

0 votes

1 answer

9

UGCNET CSE December 2022: 27
Given the $\text{FFT}$ we can have time procedure for multiplying two polynomials $\mathrm{A}(\mathrm{x})$ and $\mathrm{B}(\mathrm{x})$ of degree bound $\mathrm{n}$ where input and output representations are in coefficient form, assuming $\mathrm{n}$ is a power of ... $2 [39406]) 2$ (Option $3 [39407]) 3$ (Option $4 [39408]) 4$ Answer Given by Candidate : $3$

Given the $\text{FFT}$ we can have time procedure for multiplying two polynomials $\mathrm{A}(\mathrm{x})$ and $\mathrm{B}(\mathrm{x})$ of degree bound $\mathrm{n}$ where...

ajayraho

209 views

ajayraho answered Mar 12

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1 answer

10

UGCNET CSE December 2022: 95
An organization is granted the block $130.56 .0 .0 / 16$. The administrator wants to create $1024$ subnets. Find subnet mask. $130.255 .255 .255$ $130.56 .255 .255$ $130.56 .0 .255$ $130.56 .155 .192$ (Option $1 [39677]) 1$ (Option $2 [39678]) 2$ (Option $3 [39679]) 3$ (Option $4 [39680]) 4$ Answer Given by Candidate: $2$

An organization is granted the block $130.56 .0 .0 / 16$. The administrator wants to create $1024$ subnets.Find subnet mask.$130.255 .255 .255$$130.56 .255 .255$$130.56 ....

ajayraho

142 views

ajayraho answered Mar 12

0 votes

1 answer

11

UGCNET CSE December 2022: 91
An organization is granted the block $130.56.0.0/16$. The administrator wants to create $1024$ subnets. Find the number of addresses in each subnet $32$ $64$ $128$ $16$ (Option $1 [39661]) 1$ (Option $2[39662]) 2$ (Option $3[39663]) 3$ (Option $4[39664]) 4$ Answer Given by Candidate: $2$

An organization is granted the block $130.56.0.0/16$. The administrator wants to create $1024$ subnets. Find the number of addresses in each subnet$32$$64$$128$$16$(Optio...

ajayraho

298 views

ajayraho answered Mar 12

0 votes

1 answer

12

UGCNET CSE December 2022: 14
Identify the incorrect statement(s). A candidate key is minimal set of one or more attributes that, taken collectively, allows us to uniquely identify any entity in the entity set. A candidate key for which no proper subset is also a candidate key is called a super key. A ... $2[39354]) 2$ (Option $3[39355]) 3$ (Option $4 [39356]) 4$ Answer Given by Candidate : $3$

Identify the incorrect statement(s).A candidate key is minimal set of one or more attributes that, taken collectively, allows us to uniquely identify any entity in the en...

ajayraho

563 views

ajayraho answered Mar 12

0 votes

1 answer

13

UGCNET CSE December 2022: 22
$\text{COCOMO}$ stands for Consumed cost model Constructive cost model Common control model Composition cost model (Option $1[39385]) 1$ (Option $2 [39386]) 2$ (Option $3[39387]) 3$ (Option $4 [39388]) 4$ Answer Given by Candidate : $2$

$\text{COCOMO}$ stands forConsumed cost modelConstructive cost modelCommon control modelComposition cost model(Option $1[39385]) 1$(Option $2 [39386]) 2$(Option $3[39387]...

rajesh1

150 views

rajesh1 answered Mar 7

5 votes

0 answers

14

IIIT Delhi Coding questions
Can somebody please tell what kind of coding question should I prepare for IIIT Delhi PGCAT Coding round? Also please share memory based questions for PGCAT Technical exam.

Can somebody please tell what kind of coding question should I prepare for IIIT Delhi PGCAT Coding round? Also please share memory based questions for PGCAT Technical exa...

Starprince07

446 views

Starprince07 asked Mar 5

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1 answer

15

TIFR CSE 2024 | Part A | Question: 5
Let $p(x)$ be a polynomial with real coefficients which satisfies $p(r)=p(-r)$ for every real number $r$. Let $n \geq 5$ be a positive integer. Suppose that $p(i)=i$ for all $1 \leq i \leq n$. What is the maximum possible value of the absolute value of the coefficient of ${x^{5}}$ in $p(x)$ ? $0$ $5$ $10$ $n$ $n+1$

Let $p(x)$ be a polynomial with real coefficients which satisfies $p(r)=p(-r)$ for every real number $r$. Let $n \geq 5$ be a positive integer. Suppose that $p(i)=i$ for ...

Ishan Banerjee

153 views

Ishan Banerjee answered Mar 2

0 votes

1 answer

16

TIFR CSE 2024 | Part A | Question: 4
Let $z_{1}, z_{2}, z_{3}, \ldots, z_{2023}$ be a permutation of the numbers $1,2,3, \ldots, 2023$. Which of the following is true about the product $\prod_{i=1}^{2023}\left(z_{i}-i\right)$ ? Note: The parity of an ... such that swapping their values does not change the parity of the above product. None of the above statements is true.

Let $z_{1}, z_{2}, z_{3}, \ldots, z_{2023}$ be a permutation of the numbers $1,2,3, \ldots, 2023$. Which of the following is true about the product $\prod_{i=1}^{2023}\le...

Ishan Banerjee

126 views

Ishan Banerjee answered Mar 2

0 votes

1 answer

17

UGCNET CSE December 2022: 131
The hardware address of a computer network device consists of $48$ bits. Which of the following is a valid address in hexadecimal numbers? $00 \mathrm{E} 0071944 \mathrm{~A} 0$ $0 \mathrm{~A} 23 \mathrm{~B} 5$ $1 \mathrm{E} 07 \mathrm{FG} 124372$ ... $1 [39821]) 1$ (Option $2 [39822]) 2$ (Option $3 [39823]) 3$ (Option $4 [39824]) 4$

The hardware address of a computer network device consists of $48$ bits. Which of the following is a valid address in hexadecimal numbers?$00 \mathrm{E} 0071944 \mathrm{~...

ajayraho

395 views

ajayraho answered Mar 1

0 votes

1 answer

18

UGCNET CSE December 2022: 132
The computer uses a bootstrap. Which of the following shows the part of a computer of which the bootstrap is an example? application software firmware hard disk drive IP address (Option $1 [39825]) 1$ (Option $2 [39826]) 2$ (Option $3 [39827]) 3$ (Option $4 [39828]) 4$

The computer uses a bootstrap. Which of the following shows the part of a computer of which the bootstrap is an example?application softwarefirmwarehard disk driveIP addr...

ajayraho

125 views

ajayraho answered Mar 1

0 votes

1 answer

19

UGCNET CSE December 2022: 133
Given below are two statements: Statement I: One always uses $\text{CD-ROMs}$ to save data. Statement II: A computer has $2048$ MB of $\text{RAM}$. That means computer has $1.2$ GB of $\text{RAM}$. In the light of the above statements, choose the correct answer from ... $1[39829]) 1$ (Option $2[39830]) 2$ (Option $3[39831]) 3$ (Option $4 [39832]) 4$

Given below are two statements:Statement I: One always uses $\text{CD-ROMs}$ to save data.Statement II: A computer has $2048$ MB of $\text{RAM}$. That means computer has ...

ajayraho

94 views

ajayraho answered Mar 1

0 votes

1 answer

20

UGCNET CSE December 2022: 134
Which file formats are used to store music files? $\mathrm{bmp}$ $\text{wav}$ $\operatorname{mp} 3$ $\text{htm}$ $\text{wma}$ Choose the correct answer from the options given below : $\text{A, B}$ and $\text{D}$ only $\text{A, D}$ and $\mathrm{E}$ ... and $\mathrm{E}$ only (Option $1[39833]) 1$ (Option $2 [39834]) 2$ (Option $3[39835]) 3$ (Option $4[39836]) 4$

Which file formats are used to store music files?$\mathrm{bmp}$$\text{wav}$$\operatorname{mp} 3$$\text{htm}$$\text{wma}$Choose the correct answer from the options given b...

ajayraho

205 views

ajayraho answered Mar 1

0 votes

1 answer

21

UGCNET CSE December 2022: 135
Match $\text{List I}$ with $\text{List II}$ $\text{List I (Internet Term)}$ $\text{List II (Description)}$ $\text{A}$. Spyware $\text{List I}$. Malicious software installed on a user's hard drive or a web server; the software re-directs the user to a fake website ... $1[39837]) 1$ (Option $2[39838]) 2$ (Option $3[39839]) 3$ (Option $4 [39840]) 4$

Match $\text{List I}$ with $\text{List II}$$\text{List I (Internet Term)}$$\text{List II (Description)}$$\text{A}$. Spyware$\text{List I}$. Malicious software installed ...

ajayraho

126 views

ajayraho answered Mar 1

0 votes

1 answer

22

UGCNET CSE December 2022: 25
How many different trees are possible with ' $n$ ' nodes? $\mathrm{n}_{-1}$ $2^{\mathrm{n}}-1$ $2^{\mathrm{n}}$ $2^{\mathrm{n}}-\mathrm{n}$ (Option $1 [39397]) 1$ (Option $2 [39398]) 2$ (Option $3[39399]) 3$ (Option $4 [39400]) 4$ Answer Given by Candidate : $2$

How many different trees are possible with ' $n$ ' nodes?$\mathrm{n}_{-1}$$2^{\mathrm{n}}-1$$2^{\mathrm{n}}$$2^{\mathrm{n}}-\mathrm{n}$(Option $1 [39397]) 1$(Option $2 [3...

꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂

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꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂ answered Feb 29

0 votes

2 answers

23

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 20
The Pearson's correlation coefficient between $\mathrm{x}$ and $\mathrm{y}$ rounded to the first decimal point for the given data in below table is: $\mathbf{x}$ $\mathbf{y}$ $-6$ $6.4$ $2$ $4.7$ $0.2$ $8$ $7$ $2$ $-4$ $3.4$ $-0.5$ $0.5$ $0.3$ $-0.3$

The Pearson's correlation coefficient between $\mathrm{x}$ and $\mathrm{y}$ rounded to the first decimal point for the given data in below table is:$\mathbf{x}$$\mathbf{y...

rajveer43

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rajveer43 answered Feb 2

2 votes

4 answers

24

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 13
A decision tree classifier learned from a fixed training set achieves $100 \%$ accuracy. Which of the following models trained using the same training set will also achieve $100 \%$ accuracy? i) Logistic regressor. ii) A ... Naïve Bayes classifier. $\text{i}$ $\text{i and ii}$ all of the above none of the above

A decision tree classifier learned from a fixed training set achieves $100 \%$ accuracy. Which of the following models trained using the same training set will also achie...

squirrel69

3.8k views

squirrel69 answered Feb 1

1 votes

2 answers

25

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 30
For perfectly spherical $2\text{D}$ data centered at the origin, which of the following the pairs of vectors are possible pairs of principal components? $(1,0)$ and $(0,1)$ $(0,-1)$ and $(-1,0)$ $(1,1)$ and $(1,-1)$ $(-1,1)$ and $(-1,-1)$ $\text{i}$ $\text{i and iii}$ $\text{i, ii, and iii}$ $\text{i, ii, iii and iv}$

For perfectly spherical $2\text{D}$ data centered at the origin, which of the following the pairs of vectors are possible pairs of principal components?$(1,0)$ and $(0,1)...

rajveer43

2.0k views

rajveer43 answered Feb 1

0 votes

6 answers

26

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 6
Which among the following may help to reduce overfitting demonstrated by a model Change the loss function. Reduce model complexity. Increase the training data. Increase the number of optimization routine steps. $\text{ii and i}$ $\text{ii and iii}$ $\text{i, ii, and iii}$ $\text{i, ii, iii, and iv}$

Which among the following may help to reduce overfitting demonstrated by a modelChange the loss function. Reduce model complexity.Increase the training data.Increase the ...

rajveer43

3.2k views

rajveer43 answered Feb 1

0 votes

1 answer

27

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 29
$K\left(x, x^{\prime}\right)=f(x) g\left(x^{\prime}\right)+f\left(x^{\prime}\right) g(x)$, where $f$ and $g$ are real-valued functions $\left(\mathcal{R}^{D} \rightarrow \mathcal{R}\right)$ is not a valid kernel ... $f\left(x^{\prime}\right)+g\left(x^{\prime}\right)$

$K\left(x, x^{\prime}\right)=f(x) g\left(x^{\prime}\right)+f\left(x^{\prime}\right) g(x)$, where $f$ and $g$ are real-valued functions $\left(\mathcal{R}^{D} \rightarrow ...

rajveer43

1.2k views

rajveer43 answered Feb 1

3 votes

3 answers

28

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 50
Assume that $\text{S}$ is a stack and $\text{Q1}$ and $\text{Q2}$ are two Queues which support the Enqueue and Dequeue operations. Consider the following pseudo code for implementing the Pop and Push operation on $\text{S}$. Push(S, ... $\text{B, D}$- Enqueue $\text{A, D}$ - Enqueue $\text{B, C}$ - Dequeue

Assume that $\text{S}$ is a stack and $\text{Q1}$ and $\text{Q2}$ are two Queues which support the Enqueue and Dequeue operations. Consider the following pseudo code for ...

Arjunmaniya

1.2k views

Arjunmaniya answered Jan 28

0 votes

3 answers

29

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 35
Given a smooth sufficiently differentiable function, the following statements are given (P) A concave function can have a global minimum (Q) All convex functions have a global minimum $\text{P}$ and $\text{Q}$ are true $\text{P}$ is ... $\text{P}$ is false and $\text{Q}$ is true $\text{P}$ and $\text{Q}$ are false

Given a smooth sufficiently differentiable function, the following statements are given(P) A concave function can have a global minimum(Q) All convex functions have a glo...

Arjunmaniya

2.1k views

Arjunmaniya answered Jan 27

1 votes

3 answers

30

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 28
Given a discrete $\text{K}$-class dataset containing $\text{N}$ points, where sample points are described using $\text{D}$ features with each feature capable of taking $\text{V}$ values, how many parameters need to be estimated for Naïve Bayes Classifier? $V^{D} K$ $K^{V^{D}}$ $\text{VDK}$ $\text{K(V + D)}$

Given a discrete $\text{K}$-class dataset containing $\text{N}$ points, where sample points are described using $\text{D}$ features with each feature capable of taking $\...

squirrel69

2.4k views

squirrel69 answered Jan 26

0 votes

1 answer

31

TIFR CSE 2024 | Part A | Question: 1
If $\text{O}$ is the center of the circle, what is the area of the shaded portion in square cm? $4 \pi-4 \sqrt{2}$ $\frac{7}{2} \pi-4 \sqrt{2}$ $\frac{7}{2} \pi-4 \sqrt{3}$ $\frac{8}{3} \pi-4 \sqrt{3}$ $\frac{8}{3} \pi-4 \sqrt{2}$

If $\text{O}$ is the center of the circle, what is the area of the shaded portion in square cm?$4 \pi-4 \sqrt{2}$$\frac{7}{2} \pi-4 \sqrt{2}$$\frac{7}{2} \pi-4 \sqrt{3}$$...

USharma02

321 views

USharma02 answered Jan 25

1 votes

2 answers

32

GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 3
Which of the following first-order logic sentence matches closest with the sentence "All students are not equal"? ...

Which of the following first-order logic sentence matches closest with the sentence "All students are not equal"?$\forall x \exists y[\operatorname{student}(x) \wedge \op...

ankitagg

3.3k views

ankitagg answered Jan 23

0 votes

0 answers

33

TIFR Mathematics 2024 | Part A | Question: 1
What is the number of even positive integers $n$ such that every group of order $n$ is abelian? $1$ $2$ Greater than $2$, but finite Infinite

What is the number of even positive integers $n$ such that every group of order $n$ is abelian?$1$$2$Greater than $2$, but finiteInfinite

admin

170 views

admin asked Jan 19

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0 answers

34

TIFR Mathematics 2024 | Part A | Question: 2
Let $n$ be a positive integer, and let \[ S=\{g \in \mathbb{R}[x] \mid g \text { is a polynomial of degree at most } n\}. \] For $g \in S$, let $A_{g}=\left\{x \in \mathbb{R} \mid e^{x}=g(x)\right\} \subset \mathbb{R}$. Let \[ m=\min \left\{\# A_{g} \mid ... \left\{\# A_{g} \mid g \in S\right\} . \] Then $m=0, M=n$ $m=0, M=n+1$ $m=1, M=n$ $m=1, M=n+1$

Let $n$ be a positive integer, and let\[S=\{g \in \mathbb{R}[x] \mid g \text { is a polynomial of degree at most } n\}.\]For $g \in S$, let $A_{g}=\left\{x \in \mathbb{R}...

admin

84 views

admin asked Jan 19

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0 answers

35

TIFR Mathematics 2024 | Part A | Question: 3
Let $V, W$ be nonzero finite dimensional vector spaces over $\mathbb{C}$. Let $m$ be the dimension of the space of $\mathbb{C}$-linear transformations $V \rightarrow W$, viewed as a real vector space. Let $n$ ... transformations $V \rightarrow W$, viewed as a real vector space. Then $n=m$ $2 n=m$ $n=2 m$ $4 n=m$

Let $V, W$ be nonzero finite dimensional vector spaces over $\mathbb{C}$. Let $m$ be the dimension of the space of $\mathbb{C}$-linear transformations $V \rightarrow W$, ...

admin

76 views

admin asked Jan 19

0 votes

0 answers

36

TIFR Mathematics 2024 | Part A | Question: 4
Consider the real vector space of infinite sequences of real numbers \[ S=\left\{\left(a_{0}, a_{1}, a_{2}, \ldots\right) \mid a_{k} \in \mathbb{R}, k=0,1,2, \ldots\right\} . \] Let $W$ be the subspace of $S$ ... 2}=2 a_{k+1}+a_{k}, \quad k=0,1,2, \ldots \] What is the dimension of $W$ ? $1$ $2$ $3$ $\infty$

Consider the real vector space of infinite sequences of real numbers\[S=\left\{\left(a_{0}, a_{1}, a_{2}, \ldots\right) \mid a_{k} \in \mathbb{R}, k=0,1,2, \ldots\right\}...

admin

75 views

admin asked Jan 19

0 votes

0 answers

37

TIFR Mathematics 2024 | Part A | Question: 5
Let $f:[0, \infty) \rightarrow \mathbb{R}$ be a continuous function. If \[ \lim _{n \rightarrow \infty} \int_{0}^{1} f(x+n) d x=2, \] then which of the following statements about the limit \[ \lim _{n \rightarrow \infty} ... equals $0$ The limit exists and equals $\frac{1}{2}$ The limit exists and equals $2$ None of the remaining three options is correct

Let $f:[0, \infty) \rightarrow \mathbb{R}$ be a continuous function. If\[\lim _{n \rightarrow \infty} \int_{0}^{1} f(x+n) d x=2,\]then which of the following statements a...

admin

51 views

admin asked Jan 19

0 votes

0 answers

38

TIFR Mathematics 2024 | Part A | Question: 6
Let $f: \mathbb{R} \rightarrow[0, \infty)$ be a function such that for any finite set $E \subset \mathbb{R}$ we have \[ \sum_{x \in E} f(x) \leq 1 . \] Let \[ C_{f}=\{x \in \mathbb{R} \mid f(x)>0\} \subset \mathbb{R} . \] Then $C_{f}$ is finite $C_{f}$ is a bounded subset of $\mathbb{R}$ $C_{f}$ has at most one limit point $C_{f}$ is a countable set

Let $f: \mathbb{R} \rightarrow[0, \infty)$ be a function such that for any finite set $E \subset \mathbb{R}$ we have\[\sum_{x \in E} f(x) \leq 1 .\]Let\[C_{f}=\{x \in \ma...

admin

59 views

admin asked Jan 19

0 votes

0 answers

39

TIFR Mathematics 2024 | Part A | Question: 7
Let $p$ be a prime. Which of the following statements is true? There exists a noncommutative ring with exactly $p$ elements There exists a noncommutative ring with exactly $p^{2}$ elements There exists a noncommutative ring with exactly $p^{3}$ elements None of the remaining three statements is correct

Let $p$ be a prime. Which of the following statements is true?There exists a noncommutative ring with exactly $p$ elementsThere exists a noncommutative ring with exactly ...

admin

61 views

admin asked Jan 19

0 votes

0 answers

40

TIFR Mathematics 2024 | Part A | Question: 8
Consider the sequence $\left\{a_{n}\right\}$ for $n \geq 1$ ... $\lim _{n \rightarrow \infty} n^{2} a_{n}$ exists and equals 1

Consider the sequence $\left\{a_{n}\right\}$ for $n \geq 1$ defined by\[a_{n}=\lim _{N \rightarrow \infty} \sum_{k=n}^{N} \frac{1}{k^{2}} .\]Which of the following statem...

admin

69 views

admin asked Jan 19

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