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

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1

TIFR Mathematics 2024 | Part B | Question: 16
Let $R$ be the ring $\mathbb{C}[x] /\left(x^{2}\right)$ obtained as the quotient of the polynomial ring $\mathbb{C}[x]$ by its ideal generated by $x^{2}$. Let $R^{\times}$be the multiplicative group of units of this ring. Then there is an injective group homomorphism from $(\mathbb{Z} / 2 \mathbb{Z}) \times(\mathbb{Z} / 2 \mathbb{Z})$ into $R^{\times}$.

Let $R$ be the ring $\mathbb{C}[x] /\left(x^{2}\right)$ obtained as the quotient of the polynomial ring $\mathbb{C}[x]$ by its ideal generated by $x^{2}$. Let $R^{\times}...

Mukul.iitb

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Mukul.iitb answered Apr 16

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2

ISI2020-MMA: 8
The particular solution of $\log_{e}\left ( \frac{dy}{dx} \right ) = 5x + 7y, \;y(0)= 0$ is. $e^{5x}+5e^{-7y}=7$ $7e^{5x}-5e^{-7y}=5$ $5e^{5x}+7e^{7y}=12$ $7e^{5x}+5e^{-7y}=12$

The particular solution of$$\log_{e}\left ( \frac{dy}{dx} \right ) = 5x + 7y, \;y(0)= 0$$is.$e^{5x}+5e^{-7y}=7$$7e^{5x}-5e^{-7y}=5$$5e^{5x}+7e^{7y}=12$$7e^{5x}+5e^{-7y}=1...

Pragya Goel

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Pragya Goel answered Apr 12

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1 answer

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ISI2020-MMA: 5
The set of all solutions of the inequality $\frac{1}{2^{x} - 1} > \frac{1}{1 - 2^{x - 1}}$ is. $\left(1, \infty \right)$ $\left(0, \log_{2} \left ( \frac{4}{3} \right )\right)$ $\left(0, \log_{2} \left ( \frac{4}{3} \right )\right) \cup \left(1, \infty \right)$ $\left(-1, \infty \right)$

The set of all solutions of the inequality $\frac{1}{2^{x} - 1} \frac{1}{1 - 2^{x - 1}}$is.$\left(1, \infty \right)$$\left(0, \log...

Pragya Goel

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Pragya Goel answered Apr 12

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#Doubt #GO+Gateoverflow test series
Anyone have taken two consecutive years of combine (GO+Go classes )Test series ? I wanted to know if question are repeated or all new question will be in 2025 test series of go classes ? Actually I purchased combine test series of go ... I will get All repeated question then my money will be lost ..So please help me in this regard @DeepakPoonia @SachinMittal 1

Anyone have taken two consecutive years of combine (GO+Go classes )Test series ? I wanted to know if question are repeated or all new question will be in 2025 test series...

ENTJ007

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ENTJ007 asked Apr 2

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5

Test series
Is there any test series for pgee ece available

Is there any test series for pgee ece available

Soymya

35 views

Soymya asked Apr 1

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6

when the gate overflow test series for 2025 will avalilabe ?

jenilS7

40 views

jenilS7 asked Apr 1

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1 answer

7

ISI 2019 | PCB CS | Question: 10
Let $R$ be a relation with functional dependencies $\mathcal{F}$. For any subset of attributes $X \subseteq R$, the closure of $X$ is defined as the set $ X^{+}=\{A \in R \mid X \rightarrow A \text { holds with respect to } \mathcal{F}\} . $ For two non-empty ... each of the following statements: $\left(Y^{+} Z\right)^{+}=(Y Z)^{+}$ $(Y Z)^{+}=Y^{+} Z^{+}$

Let $R$ be a relation with functional dependencies $\mathcal{F}$. For any subset of attributes $X \subseteq R$, the closure of $X$ is defined as the set$$ X^{+}=\{A \in R...

Abhay123

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Abhay123 answered Mar 31

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1 answer

8

Discrete Mathematics | Relations | Equivalence relation |
The relation R on the set {(a, b) |a, b € Z} where (a, b)R(c, d) means a = c or b = d. Is R a equivalence relation or not ?

The relation R on the set {(a, b) |a, b € Z} where (a, b)R(c, d) means a = c or b = d. Is R a equivalence relation or not ?

Sahil5635

74 views

Sahil5635 answered Mar 30

1 votes

1 answer

9

ISI 2019 | PCB CS | Question: 1
Let $A$ be a sorted array containing $n$ distinct integers, such that, for all $1 \leq i<j \leq n$, we have $A[i]<A[j]$. Note that the integers stored in the array $A$ ... time of the algorithm should be asymptotically better than $O(n)$. Prove the correctness of your algorithm and state its asymptotic time complexity.

Let $A$ be a sorted array containing $n$ distinct integers, such that, for all $1 \leq i<j \leq n$, we have $A[i]<A[j]$. Note that the integers stored in the array $A$ ar...

vaibhav_mani

168 views

vaibhav_mani answered Mar 28

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1 answer

10

ISI 2019 | PCB CS | Question: 18
Consider a $5$-stage instruction pipeline. The stages and the corresponding stage delays are given below. Instruction Stage delay Fetch instruction (FI) 3 ns Decode instruction (DI) 4 ns Fetch operand (FO) 7 ns Execute instruction (EI) 10 ns Write ... flow through the pipeline stages in this processor. Calculate the time (in ns) needed to execute the program.

Consider a $5$-stage instruction pipeline. The stages and the corresponding stage delays are given below. InstructionStage delayFetch instruction (FI)3 nsDecode instruct...

sanjeet24

217 views

sanjeet24 answered Mar 6

1 votes

1 answer

11

ISI 2021 | PCB Mathematics | Question: 4
In the figure below, there are three circles touching each other externally and also touching the line below. Let $r_{1}, r_{2}$ and $r_{3}$ be the radii of the three circles as shown in the figure. If $r_{1}=25$ and $r_{3}=9$, then find $r_{2}$.

In the figure below, there are three circles touching each other externally and also touching the line below. Let $r_{1}, r_{2}$ and $r_{3}$ be the radii of the three cir...

sanjeet24

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sanjeet24 answered Mar 3

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1 answer

12

UGC NET CSE | December 2005 | Part 2 | Question: 43
The Reliability of the software is directly dependent upon : Quality of the design Programmer's experience Number of error Set of user requirements

The Reliability of the software is directly dependent upon :Quality of the designProgrammer's experienceNumber of errorSet of user requirements

ajayraho

205 views

ajayraho answered Mar 1

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1 answer

13

UGC NET CSE | June 2005 | Part 2 | Question: 47
The frequency reuse plan is divided into cell grouping using how many cells, where the number of cells equals $N$ ? $3$ $10$ $7$ $21$

The frequency reuse plan is divided into cell grouping using how many cells, where the number of cells equals $N$ ?$3$$10$$7$$21$

ajayraho

416 views

ajayraho answered Mar 1

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1 answer

14

UGC NET CSE | June 2005 | Part 2 | Question: 45
Which type of coupling is least preferred ? Content coupling Data coupling Control coupling Common coupling

Which type of coupling is least preferred ? Content couplingData couplingControl couplingCommon coupling

ajayraho

309 views

ajayraho answered Mar 1

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1 answer

15

UGC NET CSE | June 2005 | Part 2 | Question: 44
Which one is measure of software complexity ? Number of lines of code $(LOC)$ Number of man years Number of function points $(FP)$ All of the above

Which one is measure of software complexity ?Number of lines of code $(LOC)$Number of man yearsNumber of function points $(FP)$All of the above

ajayraho

298 views

ajayraho answered Mar 1

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1 answer

16

UGC NET CSE | June 2005 | Part 2 | Question: 43
System Development Life-cycle has following stages : Requirement analysis Coding Design Testing Which option describes the correct sequence of stages ? III, I, IV, II II, III, I, IV I, III, IV, II None of the above

System Development Life-cycle has following stages : Requirement analysisCodingDesignTestingWhich option describes the correct sequence of stages ?III, I, IV, IIII, III, ...

ajayraho

418 views

ajayraho answered Mar 1

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1 answer

17

UGC NET CSE | June 2005 | Part 2 | Question: 41
The capability maturity model $(err)$ defines $5$ ...

The capability maturity model $(err)$ defines $5$ levels :$\begin{array}{ll}\text{(a) Level 1} & \text{(i) Managed} \\ \text{(b) Level 2} & \text{(ii) Defined} \\ \text{(...

ajayraho

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ajayraho answered Mar 1

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1 answer

18

UGC NET CSE | June 2005 | Part 2 | Question: 28
Which type of links are used for a connection between two $DTE$ devices ? $X.21$ Frame Relay $ATM$ Modem

Which type of links are used for a connection between two $DTE$ devices ?$X.21$Frame Relay$ATM$Modem

ajayraho

295 views

ajayraho answered Mar 1

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1 answer

19

UGC NET CSE | June 2005 | Part 2 | Question: 18
A black hole in a $DFD$ is a : A data store with no in bound flows A data store with only in bound flows A data store with more than one in bound flow None of these

A black hole in a $DFD$ is a :A data store with no in bound flowsA data store with only in bound flowsA data store with more than one in bound flowNone of these

ajayraho

279 views

ajayraho answered Mar 1

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1 answer

20

UGC NET CSE | June 2005 | Part 2 | Question: 8
Which of the following logic has the maximum fan out ? $RTL$ $ECL$ $N MOS$ $C MOS$

Which of the following logic has the maximum fan out ?$RTL$$ECL$$N MOS$$C MOS$

ajayraho

204 views

ajayraho answered Mar 1

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0 answers

21

Chose the correct big- Θ expression to describe: T(N) = 8 T(N / 2) + 10 N Log(N/10) ;T(1) = c

MennaTullah

70 views

MennaTullah asked Mar 1

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1 answer

22

UGC NET CSE | December 2004 | Part 2 | Question: 39
Non modifiable procedures are called Serially useable procedures Concurrent procedures Reentrant procedures Topdown procedures

Non modifiable procedures are calledSerially useable proceduresConcurrent proceduresReentrant proceduresTopdown procedures

ajayraho

559 views

ajayraho answered Feb 29

0 votes

2 answers

23

GATE DS&AI 2024 | Question: 42
Let $H, I, L$, and $N$ represent height, number of internal nodes, number of leaf nodes, and the total number of nodes respectively in a rooted binary tree. Which of the following statements is/are always TRUE? $L \leq I+1$ $H+1 \leq N \leq 2^{H+1}-1$ $H \leq I \leq 2^{H}-1$ $H \leq L \leq 2^{H-1}$

Let $H, I, L$, and $N$ represent height, number of internal nodes, number of leaf nodes, and the total number of nodes respectively in a rooted binary tree...

naveendewangan

872 views

naveendewangan answered Feb 29

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1 answer

24

I have completed my masters with a major in mathematics in 2020. I have appeared for GATE-DA 2024 but failed miserably. Should i go for GATE-DA 2025? Any help would be appreciated. Thank you.

simi2426

102 views

simi2426 answered Feb 28

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0 answers

25

I have purchased the IIIT Hyderabad 2024 test series but i can't find the test series anywhere can any one help me

Rohith Katkuri

184 views

Rohith Katkuri asked Feb 26

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0 answers

26

Hello everyone, I am doing Btech in CSE with specialization in Data science I wanted to ask is it a eligible degree for admission in mtech of IITs (Is it considered the same as CSE Core) while admission

Rahul Sharma0408

94 views

Rahul Sharma0408 asked Feb 20

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1 answer

27

GATE DS&AI 2024 | Question: 44
Let game(ball, rugby) be true if the ball is used in rugby and false otherwise. Let shape(ball, round) be true if the ball is round and false otherwise. Consider the following logical sentences: s1: $\forall$ ball $\neg$ game(ball, rugby) $\Rightarrow$ shape(ball, round) ... used in rugby"? $s 1 \wedge s 3$ $s 1 \wedge s 2$ $s 2 \wedge s 3$ $s 3 \wedge s 4$

Let game(ball, rugby) be true if the ball is used in rugby and false otherwise.Let shape(ball, round) be true if the ball is round and false otherwise.Cons...

gate.datascience_ai

926 views

gate.datascience_ai answered Feb 19

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2 answers

28

GATE DS&AI 2024 | Question: 54
Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables: \begin{array}{|c|c|} \hline & P(\cdot) \\ \hline U=0 & 0.5 \\ \hline U=1 & 0.5 \\ \hline \end{array} \begin{array}{|c|c|c|} \ ... The value of $P(U=1, V=1, W=1, Z=1)= \_\_\_\_\_\_\_$ (rounded off to three decimal places).

Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables:\begin{array}{|c|c|}\hline & P(\cdot)...

ankitgupta.1729

1.0k views

ankitgupta.1729 answered Feb 19

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2 answers

29

GATE DS&AI 2024 | Question: 14
Consider five random variables $U, V, W, X$, and $Y$ whose joint distribution satisfies: \[ P(U, V, W, X, Y)=P(U) P(V) P(W \mid U, V) P(X \mid W) P(Y \mid W) \] Which ONE of the following statements is FALSE? ... $U$ given $W$ $U$ and $V$ are conditionally independent given $W$ $Y$ and $X$ are conditionally independent given $W$

Consider five random variables $U, V, W, X$, and $Y$ whose joint distribution satisfies:\[P(U, V, W, X, Y)=P(U) P(V) P(W \mid U, V) P(X \mid W) P(Y \mid...

jpj12345

908 views

jpj12345 answered Feb 18

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2 answers

30

GATE DS&AI 2024 | Question: 9
Euclidean distance based $k$-means clustering algorithm was run on a dataset of $100$ points with $k=3$. If the points $\left[\begin{array}{l}1 \\ 1\end{array}\right]$ and $\left[\begin{array}{c}-1 \\ 1\end{array}\right]$ ... $\left[\begin{array}{l}2 \\ 0\end{array}\right]$ $\left[\begin{array}{l}0 \\ 1\end{array}\right]$

Euclidean distance based $k$-means clustering algorithm was run on a dataset of $100$ points with $k=3$. If the points $\left[\begin{array}{l}1 \\ 1\end...

jpj12345

815 views

jpj12345 answered Feb 18

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2 answers

31

GATE DS&AI 2024 | Question: 40
Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ where $\mathbb{R}$ is the set of all real numbers. \[ f(x)=\frac{x^{4}}{4}-\frac{2 x^{3}}{3}-\frac{3 x^{2}}{2}+1 \] Which of the following statements is/are TRUE? $x=0$ is a local maximum of $f$ $x=3$ is a local minimum of $f$ $x=-1$ is a local maximum of $f$ $x=0$ is a local minimum of $f$

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ where $\mathbb{R}$ is the set of all real numbers.\[f(x)=\frac{x^{4}}{4}-\frac{2 x^{3}}{3}-\fr...

Sachin Mittal 1

746 views

Sachin Mittal 1 answered Feb 18

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2 answers

32

GATE DS&AI 2024 | Question: 24
The sample average of $50$ data points is $40$. The updated sample average after including a new data point taking the value of $142$ is $\_\_\_\_\_\_\_\_$.

The sample average of $50$ data points is $40$. The updated sample average after including a new data point taking the value of $142$ is $\_\_\_\_\_\_\_\_$.

gaurav0to1

791 views

gaurav0to1 answered Feb 18

0 votes

2 answers

33

GATE DS&AI 2024 | Question: 32
Consider the table below, where the $(i, j)^{t h}$ element of the table is the distance between points $x_{i}$ and $x_{j}$. Single linkage clustering is performed on data points, $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$. \begin{array} ... & 3 & 5 & 1 & 0 \\ \hline \end{array} Which ONE of the following is the correct representation of the clusters produced?

Consider the table below, where the $(i, j)^{t h}$ element of the table is the distance between points $x_{i}$ and $x_{j}$. Single linkage clustering is performed on data...

ankitgupta.1729

704 views

ankitgupta.1729 answered Feb 17

0 votes

1 answer

34

GATE DS&AI 2024 | Question: 19
Let $x$ and $y$ be two propositions. Which of the following statements is a tautology /are tautologies? $(\neg x \wedge y) \Rightarrow(y \Rightarrow x)$ $(x \wedge \neg y) \Rightarrow(\neg x \Rightarrow y)$ $(\neg x \wedge y) \Rightarrow(\neg x \Rightarrow y)$ $(x \wedge \neg y) \Rightarrow(y \Rightarrow x)$

Let $x$ and $y$ be two propositions. Which of the following statements is a tautology /are tautologies?$(\neg x \wedge y) \Rightarrow(y \Rightarrow x)$$...

himanshud2611

803 views

himanshud2611 answered Feb 17

0 votes

1 answer

35

GATE DS&AI 2024 | Question: 25
Consider the $3 \times 3$ matrix $\boldsymbol{M}=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6\end{array}\right]$. The determinant of $\left(\boldsymbol{M}^{2}+12 \boldsymbol{M}\right)$ is $\_\_\_\_\_\_\_\_\_$.

Consider the $3 \times 3$ matrix $\boldsymbol{M}=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6\end{array}\right]$.The determinant of $\left(\boldsymbol{M}^{...

liontig37

649 views

liontig37 answered Feb 17

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1 answer

36

GATE DS&AI 2024 | Question: 27
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function. Note: $\mathbb{R}$ denotes the set of real numbers. \[ f(x)=\left\{\begin{array}{cl} -x, & \text { if } x<-2 \\ a x^{2}+b x+c, & \text { if } x \in[-2,2] \\ x, & \text { if } x>2 \end ... differentiable? $a=\frac{1}{4}, b=0, c=1$ $a=\frac{1}{2}, b=0, c=0$ $a=0, b=0, c=0$ $a=1, b=1, c=-4$

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function. Note: $\mathbb{R}$ denotes the set of real numbers.\[f(x)=\left\{\begin{array}{cl}-x, & \text { i...

liontig37

797 views

liontig37 answered Feb 17

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1 answer

37

GATE DS&AI 2024 | Question: 45
An OTT company is maintaining a large disk-based relational database of different movies with the following schema: \[ \begin{array}{l} \text { Movie (ID, CustomerRating) } \\ \text { Genre (ID, Name) } \\ \text { Movie_Genre ... attributes. Hash index on Movie.CustomerRating and $\mathrm{B}^{+}$tree on the remaining attributes. Hash index on all the attributes.

An OTT company is maintaining a large disk-based relational database of different movies with the following schema:\[\begin{array}{l}\text { Movie (ID, ...

liontig37

842 views

liontig37 answered Feb 17

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1 answer

38

GATE DS&AI 2024 | Question: 52
Details of ten international cricket games between two teams "Green" and "Blue" are given in Table $\mathrm{C}$. This table consists of matches played on different pitches, across formats along with their winners. The attribute Pitch can take one of two values: spin-friendly ( ... $S$ $O$ Green $8$ $F$ $T$ Blue $9$ $F$ $O$ Blue $10$ $S$ $O$ Green

Details of ten international cricket games between two teams "Green" and "Blue" are given in Table $\mathrm{C}$. This table consists of matches played on different pitche...

ankitgupta.1729

827 views

ankitgupta.1729 answered Feb 17

0 votes

2 answers

39

GATE DS&AI 2024 | Question: 29
Consider the function computes $(X)$ whose pseudocode is given below: computes $(X)$ $S[1] \leftarrow 1$ for $i \leftarrow 2$ to length $(X)$ $S[i] \leftarrow 1$ if $X[i-1] \leq X[i]$ $S[i] \leftarrow S[i]+S[i-1]$ end if end for return $S$ Which ONE of the following values is ... for $X=[6,3,5,4,10]$ ? $[1,1,2,3,4]$ $[1,1,2,3,3]$ $[1,1,2,1,2]$ $[1,1,2,1,5]$

Consider the function computes $(X)$ whose pseudocode is given below:computes $(X)$$S \leftarrow 1$for $i \leftarrow 2$ to length $(X)$$S[i] \leftarrow 1$...

ankitgupta.1729

663 views

ankitgupta.1729 answered Feb 17

0 votes

1 answer

40

GATE DS&AI 2024 | Question: 12
For any binary classification dataset, let $S_{B} \in \mathbb{R}^{d \times d}$ and $S_{W} \in \mathbb{R}^{d \times d}$ be the between-class and within-class scatter (covariance) matrices, respectively. The Fisher linear discriminant is defined by $u^{*} \in \mathbb{R}^{d}$, ... $S_{B} S_{W} u^{*}=\lambda u^{*}$ $u^{* T} u^{*}=\lambda^{2}$

For any binary classification dataset, let $S_{B} \in \mathbb{R}^{d \times d}$ and $S_{W} \in \mathbb{R}^{d \times d}$ be the between-class and within-c...

ankitgupta.1729

503 views

ankitgupta.1729 answered Feb 17

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