Recent questions without answers / GATE Overflow for GATE CSE

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211

TIFR CSE 2024 | Part B | Question: 10
Arun has a non-empty subset $\text{S}$ of the numbers $\{1,2,3, \ldots, 1000\}$. Bela wants to find any number $\text{x}$ in Arun's set $\text{S}$. To do this, Arun and Bela decide to play a game which proceeds in rounds. In each round, Bela ... rounds will Bela need to find out some $\text{x}$ in Arun's set $\text{S}$? $9$ $10$ $11$ $1023$ $1024$

Arun has a non-empty subset $\text{S}$ of the numbers $\{1,2,3, \ldots, 1000\}$. Bela wants to find any number $\text{x}$ in Arun's set $\text{S}$.To do this, Arun and Be...

admin

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admin asked Jan 13

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212

TIFR CSE 2024 | Part B | Question: 11
Let $\mathbb{C}$ denote the set of complex numbers and let $k$ be a positive integer. Given a non-zero univariate polynomial $f(x)$ with coefficients in $\mathbb{C}$ and an $a \in \mathbb{C}$, we say that $a$ is a zero of $f$ ... larger than $d$ as well. The number of distinct zeroes in $\mathbb{C}$ of $f$ of multiplicity $k$ is equal to $d$.

Let $\mathbb{C}$ denote the set of complex numbers and let $k$ be a positive integer. Given a non-zero univariate polynomial $f(x)$ with coefficients in $\mathbb{C}$ and ...

admin

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admin asked Jan 13

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213

TIFR CSE 2024 | Part B | Question: 12
In the $n$-queens completion problem, the input is an $n \times n$ chess board with queens on some squares, and the goal is to determine if there is a way to place more queens so that the total number of queens is $n$ and no two queens attack each other (two queens are ... $\text{(iii),(iv) and (v)}$. Only $\text{(i), (iii) and (iv)}$.

In the $n$-queens completion problem, the input is an $n \times n$ chess board with queens on some squares, and the goal is to determine if there is a way to place more q...

admin

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admin asked Jan 13

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214

TIFR CSE 2024 | Part B | Question: 13
Suppose we are given a graph $\text{G=(V, E)}$ with non-negative edge weights $\left\{w_{e}\right\}_{e \in E}$. Consider the following problems: P1: Finding a minimum spanning tree of $\text{G}$. P2: Finding a maximum spanning tree of $\text{G}$. P3: Finding a ... $\text{P1 but not P2,P3, P4}$. $\text{P1,P2,P3 but not P4}$. $\text{P1, P4 but not P2, P3}$.

Suppose we are given a graph $\text{G=(V, E)}$ with non-negative edge weights $\left\{w_{e}\right\}_{e \in E}$.Consider the following problems:P1: Finding a minimum spann...

admin

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admin asked Jan 13

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215

TIFR CSE 2024 | Part B | Question: 14
For an undirected graph $G$, let $\bar{G}$ refer to the complement (a graph on the same vertex set as $G$, with $(i, j)$ as an edge in $\bar{G}$ if and only if it is not an edge in $G$ ). Consider the following statements. $G$ has ... (i) is equivalent to (ii) and (iv). (i) is equivalent to (ii) and (v) None of the five statements are equivalent to each other.

For an undirected graph $G$, let $\bar{G}$ refer to the complement (a graph on the same vertex set as $G$, with $(i, j)$ as an edge in $\bar{G}$ if and only if it is not ...

admin

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admin asked Jan 13

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216

What will be the time complexity of recurrence relation T(n)? T(n) = T(n-1) + T(n-2) + n if n >2 , Otherwise -3

Taaps8116

113 views

Taaps8116 asked Jan 13

3 votes

0 answers

217

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 13
Given the portion of an ER diagram shown above (with a thickened arrow from $R$ to $A),$ which of the following statements are true? $R$ connects each entity in $A$ to at least one entity in $B$ $R$ connects each entity in $A$ to at ... in $B$ to at most one entity in $A$ only I and II only II and III only I and IV only III and IV

Given the portion of an ER diagram shown above (with a thickened arrow from $R$ to $A),$ which of the following statements are true?$R$ connects each entity in $A$ to at ...

GO Classes

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GO Classes asked Jan 13

4 votes

0 answers

218

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 45
Consider the scenario where $\text{L}$ is a shared variable which is a pointer to the head of a linked list originally containing three nodes with keys $3, 4,$ and $5.$ Consider the function List_Insert() which is being used by two concurrent threads $\text{T}1$ ... are separated by commas. $6,3,4,5$ $6,2,3,4,5$ $2,6,3,4,5$ $2,3,4,5$

Consider the scenario where $\text{L}$ is a shared variable which is a pointer to the head of a linked list originally containing three nodes with keys $3, 4,$ and $5.$ C...

GO Classes

358 views

GO Classes asked Jan 13

6 votes

0 answers

219

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 52
Consider the following binary heap – Suppose the last operation you performed in the binary heap above was inserting the key $x$. What are the possible values of $x?$ $20$ $8$ $13$ $11$

Consider the following binary heap –Suppose the last operation you performed in the binary heap above was inserting the key $x$.What are the possible values of $x?$$20$...

GO Classes

526 views

GO Classes asked Jan 13

4 votes

0 answers

220

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 59
Which of the following statements is/are false? In a cascade-less schedule if a transaction $T_j$ read a data item written by transaction $T_i$ then the commit of $T_i$ has to be before this read operation of $T_j$ A ... $2 \mathrm{PL}$ (could have been produced using the $2 \mathrm{PL}$ locking protocol) is conflict-serializable.

Which of the following statements is/are false?In a cascade-less schedule if a transaction $T_j$ read a data item written by transaction $T_i$ then the commit of $T_i$ ha...

GO Classes

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GO Classes asked Jan 13

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221

UPENN | ML | DA Practice
Using the same data as above $ \mathbf{X} = [-3, 5, 4] $ and $ \mathbf{Y} = [-10, 20, 20] $, assuming a ridge penalty $ \lambda = 50 $, what ratio versus the MLE estimate $ \hat{\mathbf{w}}_{\text{MLE}} $ do you think the ridge regression $ L_2 $ estimate $ \hat{\mathbf{w}}_{\text{ridge}} $ will be? (a)] 2 b)] 1 (c)] 0.666 (d)] 0.5

Using the same data as above $ \mathbf{X} = [-3, 5, 4] $ and $ \mathbf{Y} = [-10, 20, 20] $, assuming a ridge penalty $ \lambda = 50 $, what ratio versus the MLE es...

rajveer43

137 views

rajveer43 asked Jan 13

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0 answers

222

Madeeasy 2024 full length test 3
Can anyone please help me solve this question or explain the formula used in the solution part of the same?

Can anyone please help me solve this question or explain the formula used in the solution part of the same?

VinayBhojwani

162 views

VinayBhojwani asked Jan 12

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0 answers

223

TIFR CSE 2024 | Part A | Question: 3
There is a $100 \mathrm{~cm}$ long ruler that has 11 ants on positions $0 \mathrm{~cm}, 10 \mathrm{~cm}, 20 \mathrm{~cm}, 30 \mathrm{~cm}$, ..., $100 \mathrm{~cm}$. The ant at the $0 \mathrm{~cm}$ mark ... without knowing the directions of all ants. $100$ seconds. More than $100$ seconds, but cannot be determined without knowing the directions of all ants.

There is a $100 \mathrm{~cm}$ long ruler that has 11 ants on positions $0 \mathrm{~cm}, 10 \mathrm{~cm}, 20 \mathrm{~cm}, 30 \mathrm{~cm}$, ..., $100 \mathrm{~cm}$. The a...

admin

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admin asked Jan 12

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224

TIFR CSE 2024 | Part A | Question: 6
For each month in the year (i.e., January, February, March,...), let us assume the probability that a person's birthday falls in that particular month is exactly $1 / 12$, and let us assume that this is independent for different persons. What is the smallest value of ... is a pair of them born in the same month is at least $1 / 2$? $3$ $4$ $5$ $6$ $7$

For each month in the year (i.e., January, February, March,...), let us assume the probability that a person's birthday falls in that particular month is exactly $1 / 12$...

admin

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admin asked Jan 12

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225

TIFR CSE 2024 | Part A | Question: 7
Let $S:=\{(a, b) \mid 0 \leq a \leq 1,0 \leq b \leq 1\}$, a unit square, in $\mathbb{R}^{2}$. Let $B:=$ $\left\{(x, y) \mid x^{2}+y^{2} \leq 1\right\}$, a unit disk, in $\mathbb{R}^{2}$. Define the set $S+B$ as follows: \[ S+B:=\{(u, v) \ ... \text { such that } u=a+x, v=b+y\} . \] What is the area of $S+B$ ? $\pi+4$ $\pi+5$ $\pi+3$ $\pi+2$ None of the above.

Let $S:=\{(a, b) \mid 0 \leq a \leq 1,0 \leq b \leq 1\}$, a unit square, in $\mathbb{R}^{2}$. Let $B:=$ $\left\{(x, y) \mid x^{2}+y^{2} \leq 1\right\}$, a unit disk, in $...

admin

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admin asked Jan 12

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226

TIFR CSE 2024 | Part A | Question: 9
Compute $\int_{16}^{\infty} \frac{1}{x} \cdot \frac{1}{\sqrt{\sqrt{x}-1}} d x$. $0$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\frac{2 \pi}{3}$ $2 \pi$

Compute $\int_{16}^{\infty} \frac{1}{x} \cdot \frac{1}{\sqrt{\sqrt{x}-1}} d x$.$0$$\frac{\pi}{3}$$\frac{\pi}{2}$$\frac{2 \pi}{3}$$2 \pi$

admin

86 views

admin asked Jan 12

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227

TIFR CSE 2024 | Part A | Question: 10
Let $\text{M}$ be a $3 \times 3$ matrix over the real numbers such that $\text{M}^{\text{T}} \text{M}=\mathbf{I}$. Consider the following statements. There exists a non-zero vector $x \in \mathbb{R}^{3}$ such that $M x=\mathbf{0}$. There ... /are true? Only $\text{(i)}$ Only $\text{(ii)}$. Only $\text{(iii)}$. All three statements. None of the three statements.

Let $\text{M}$ be a $3 \times 3$ matrix over the real numbers such that $\text{M}^{\text{T}} \text{M}=\mathbf{I}$. Consider the following statements.There exists a non-ze...

admin

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admin asked Jan 12

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0 answers

228

TIFR CSE 2024 | Part A | Question: 11
Consider the following sequence of polynomials with real coefficients. \[ \begin{aligned} P_{0}(x) & =1 \\ P_{1}(x) & =2 x \\ P_{n+1}(x) & =2 x P_{n}(x)-P_{n-1}(x), \text { for all natural numbers } n \geq 1 . \end{aligned} \] ... }(x), P_{4}(x)\right\} \] in the vector space of polynomials in variable $x$ with real coefficients? $1$ $2$ $3$ $4$ $5$

Consider the following sequence of polynomials with real coefficients.\[\begin{aligned}P_{0}(x) & =1 \\P_{1}(x) & =2 x \\P_{n+1}(x) & =2 x P_{n}(x)-P_{n-1}(x), \text { fo...

admin

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admin asked Jan 12

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0 answers

229

TIFR CSE 2024 | Part A | Question: 12
A subset $\text{S}$ of the rational numbers is said to be "nice" if for every infinite sequence of $x_1, x_2, \ldots$ of elements from $\text{S}$, there is always two indices $i<j$ such that $x_i \leq x_j$. Consider the following ... $\text{(i)}$ and $\text{(iii)}$. All three statements are true. None of the three statements is true.

A subset $\text{S}$ of the rational numbers is said to be "nice" if for every infinite sequence of $x_1, x_2, \ldots$ of elements from $\text{S}$, there is always two ind...

admin

83 views

admin asked Jan 12

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230

TIFR CSE 2024 | Part A | Question: 13
Let $n \geq 100$ be a positive integer. Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent random variables, each taking values in the set $\{0,1\}$ such that $\operatorname{Pr}\left[X_{i}=1\right]=\frac{2}{3}$ for each $1 \leq i \leq n$ ... with respect to $x$. $0$ $n$ $\frac{2 n}{3}$ $\frac{4 n^{2}+2 n}{9}$ $\frac{4 n^{2}-4 n}{9}$

Let $n \geq 100$ be a positive integer. Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent random variables, each taking values in the set $\{0,1\}$ such that $\operatornam...

admin

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admin asked Jan 12

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231

TIFR CSE 2024 | Part A | Question: 14
Let $\text{A}$ and $\text{B}$ be two $n \times n$ invertible matrices with real entries such that every row in $\text{A}$ sums to $1$ and every row in $\text{B}$ sums to $2$ ... $\text{(iii)}$. Statements $\text{(i)}$ and $\text{(iii)}$ are true but not necessarily statement $\text{(ii)}$.

Let $\text{A}$ and $\text{B}$ be two $n \times n$ invertible matrices with real entries such that every row in $\text{A}$ sums to $1$ and every row in $\text{B}$ sums to ...

admin

111 views

admin asked Jan 12

1 votes

0 answers

232

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...

admin

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admin asked Jan 12

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0 answers

233

OIL IT Senior officer
From where to get syllabus for OIL senior officer IT.

From where to get syllabus for OIL senior officer IT.

mk_007

43 views

mk_007 asked Jan 12

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0 answers

234

Linear Transformation of Matrix

Debargha Mitra Roy

68 views

Debargha Mitra Roy asked Jan 12

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235

Objects First with Java™: A Practical Introduction Using BlueJ
Write a program in BlueJ Q4. Draw Class Diagram and Object Diagram from the below given Details. public class University { private Student stdob; private Faculty fctob; }

Write a program in BlueJQ4. Draw Class Diagram and Object Diagram from the below given Details. public class University{ private Student stdob; private Faculty ...

Ebrahim

80 views

Ebrahim asked Jan 12

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0 answers

236

Consider a weighted undirected graph with positive edge weights and let (u, v) be an [2] edge in the graph. It is known that the shortest path from source vertex r to u has weight 53 and shortest path from r to v has weight 65. Which statement is always true?

Consider a weighted undirected graph with positive edge weights and let (u, v) be an edge in the graph. It is known that the shortest path from source vertex r to u hasw...

Malusi

108 views

Malusi asked Jan 12

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0 answers

237

GFG CSE Mock 2018 | Sequential Circuits
Consider following counters: Counter-1: Counter-2: Which of the following option is correct? Counter-1 is a three-bit "counter" which counts $0, 1, 2, 4, 5, 7, 0, ... . $ ... $0, 1, 2, 3, 5, 6, 0, ... $.

Consider following counters:Counter-1: Counter-2: Which of the following option is correct? Counter-1 is a three-bit "counter" which counts $0, 1, 2, 4, 5, 7, 0, ... . $ ...

rajveer43

101 views

rajveer43 asked Jan 12

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0 answers

238

GATE 2016 | MATHS | QUESTION-47
Let $ A = \begin{bmatrix} a & b & c \\ b& d & e\\ c& e& f\end{bmatrix} $ be a real matrix with eigenvalues 1, 0, and 3. If the eigenvectors corresponding to 1 and 0 are $\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}$ and $\begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix}$ respectively, then the value of $3f$ is equal to ________________________

Let $ A = \begin{bmatrix} a & b & c \\ b& d & e\\ c& e& f\end{bmatrix} $ be a real matrix with eigenvalues 1, 0, and 3. If the eigenvectors corresponding to 1 and 0 are...

rajveer43

167 views

rajveer43 asked Jan 11

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0 answers

239

GATE 2016 | MATHS | Q-12
Consider the following statements P and Q: (P) : If $ M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix} $, then M is singular. (Q) : Let S be a diagonalizable matrix. If T is a matrix such that \( ... ), then T is diagonalizable. Which of the above statements hold TRUE? (A) both P and Q (B) only P (C) only Q (D) Neither P nor Q

Consider the following statements P and Q:(P) : If $ M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix} $, then M is singular.(Q) : Let S be a diagon...

rajveer43

97 views

rajveer43 asked Jan 11

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0 answers

240

GATE 2016 | MATHS | Q-14
Consider a real vector space $ V $ of dimension $ n $ and a non-zero linear transformation $ T: \mathbb{V} \rightarrow \mathbb{V} $. If $ \text{dim}(T) < n $ and $T^2 = \lambda T$, for some $ \lambda \in \mathbb{R} \backslash \{0\} $, then which ... 0 \) for all $ X \in \mathbb{W} $ (C) $ T $ is invertible (D) $ \lambda$ is the only eigenvalue of $ T $

Consider a real vector space $ V $ of dimension $ n $ and a non-zero linear transformation $ T: \mathbb{V} \rightarrow \mathbb{V} $. If $ \text{dim}(T) < n $ and ...

rajveer43

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rajveer43 asked Jan 11

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