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1

GATE CSE 2005 | Question: 39
Suppose there are $\lceil \log n \rceil$ sorted lists of $\lfloor n /\log n \rfloor$ elements each. The time complexity of producing a sorted list of all these elements is: (Hint:Use a heap data structure) $O(n \log \log n)$ $\Theta(n \log n)$ $\Omega(n \log n)$ $\Omega\left(n^{3/2}\right)$

madhes23 commented in Algorithms 23 minutes ago

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2

GATE CSE 2004 | Question: 40
Suppose each set is represented as a linked list with elements in arbitrary order. Which of the operations among $\text{union, intersection, membership, cardinality}$ will be the slowest? $\text{union}$ only $\text{intersection, membership}$ $\text{membership, cardinality}$ $\text{union, intersection}$

ayush3298 commented in DS 1 hour ago

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3

TIFR2021-Maths-A: 20
How many subgroups does $(\mathbb{Z}/13\mathbb{Z})\times (\mathbb{Z}/13\mathbb{Z})$ have? $13$ $16$ $4$ $25$

jothee edited in Others 2 hours ago

by jothee

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4

TIFR2021-Maths-A: 19
Let $G$ be any finite group of order $2021$. For which of the following positive integers $m$ is the map $G\rightarrow G$, given by $g\mapsto g^m$, a bijection? $43$ $45$ $47$ none of the other three options

jothee edited in Others 2 hours ago

by jothee

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5

TIFR2021-Maths-A: 18
Consider the following two subgroups $A,B$ of the group $\mathbb{Q}[x]$ of one variable rational polynomials under addition: $A=\{p(x)\in \mathbb{Z}[x]|p \text{ has degree at most } 2\}, \text{ and} $ ... $[B:A]$ of $A$ in $B$ equals $1$ $2$ $4$ none of the other three options

jothee edited in Others 2 hours ago

by jothee

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6

TIFR2021-Maths-A: 17
Which of the following is a necessary and sufficient condition for two real $3\times 3$ matrices $A$ and $B$ to be similar $($i.e., $PAP^{-1}=B$ for an invertible real $3\times 3$ matrix $P)$? They have the same characteristic polynomial They have the same minimal polynomial They have the same minimal and characteristic polynomials None of the other three conditions

jothee edited in Others 2 hours ago

by jothee

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7

TIFR2021-Maths-A: 16
The matrix $\begin{pmatrix} 4 & -3 & -3\\3 & -2 & -3\\ -1 & 1& 2 \end{pmatrix}$ is diagonalizable nilpotent idempotent none of the other three options

jothee edited in Others 2 hours ago

by jothee

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8

TIFR2021-Maths-A: 15
Which one of the following statements is correct? There Exists a $\mathbb{C}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$ There exists no $\mathbb{C}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$ ... there exists a $\mathbb{Q}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$ None of the other three statements is correct

jothee edited in Others 2 hours ago

by jothee

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9

TIFR2021-Maths-A: 14
Let $\mathbb{R}^{\mathbb{N}}$ denote the real vector space of sequences $(x_0,x_1,x_2,\dots)$ of real numbers. Define a linear transformation $T:\mathbb{R}^{\mathbb{N}}\rightarrow\mathbb{R}^{\mathbb{N}}$ ... space $\mathbb{R}^{\mathbb{N}}/T(\mathbb{R}^{\mathbb{N}})$ is infinite dimensional None of the other three statements is correct

jothee edited in Others 2 hours ago

by jothee

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10

TIFR2021-Maths-A: 13
$T:\mathbb{C}[x]\rightarrow\mathbb{C}[x]$ be the $\mathbb{C}-$linear transformation defined on the complex vector space $\mathbb{C}[x]$ of one variable complex polynomials by $Tf(x)=f(x+1)$. How many eigenvalues does $T$ have? $1$ finite but more than $1$ countably infinite uncountable

jothee edited in Others 2 hours ago

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11

TIFR2021-Maths-A: 12
Let $V$ be a vector space over a field $F$. Consider the following assertions: $V$ is finite dimensional For every linear transformation $T:V\rightarrow V$, there exists a nonzero polynomial $p(x)\in F[x]$ such that $p(T):V\rightarrow V$ is the zero map. Which one of the ... $(\text{I})$ does not imply $(\text{II})$, and $(\text{II})$ does not imply $(\text{I})$

jothee edited in Others 2 hours ago

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12

TIFR2021-Maths-A: 11
What is the number of surjective maps from the set $\{1,\dots,10\}$ to the set $\{1,2\}$? $90$ $1022$ $98$ $1024$

jothee edited in Others 2 hours ago

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13

TIFR2021-Maths-A: 10
Let $\mathcal{C}$ denote the set of colorings of an $8\times 8$ chessboard, where each square is colored either black or white. Let $\thicksim$ denote the equivalence relation on $\mathcal{C}$ defined as follows: two colorings are equivalent if and only if one of them can be obtained from the other by a ... $2^{62}+2^{30}+2^{15}$ $2^{64}-2^{32}+2^{16}$ $2^{63}-2^{31}+2^{15}$

jothee edited in Others 3 hours ago

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14

GATE CSE 2017 Set 1 | Question: 11
Consider the $C$ struct defined below: struct data { int marks [100]; char grade; int cnumber; }; struct data student; The base address of student is available in register $R1$. The field student.grade can be accessed efficiently using: Post-increment ... mode, $X(R1)$, where $X$ is an offset represented in $2's$ complement $16\text{-bit}$ representation

Subbu. commented in CO and Architecture 3 hours ago

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15

TIFR2021-Maths-A: 9
Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be an aritary function. Consider the following assertions: $f$ is continuous The set $ \text{Graph}(f)=\{(x,f(x))\in \mathbb{R}^2|x\in \mathbb{R}\}$ is a connected subset of $\mathbb{R}^2.$ Which one of the following statements is ... $(\text{I})$ $(\text{I})$ does not imply $(\text{II})$, and $(\text{II})$ does not imply $(\text{I})$

jothee edited in Others 3 hours ago

by jothee

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16

TIFR2021-Maths-A: 8
Let $X\subseteq \mathbb{R}$ be a subset. Let $\{f_n\}^{\infty}_{n=1}$ be a sequence of functions $f_n:X\rightarrow \mathbb{R}$, that converges uniformly to a function $f:X\rightarrow\mathbb{R}$. For each positive integer $n$ ... then $D$ has at most $7$ elements If each $D_n$ is uncountable, then $D$ is uncountable None of the other three statements is correct

jothee edited in Others 3 hours ago

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17

TIFR2021-Maths-A: 7
Let $A$ be the set of all real numbers $\lambda \in [0,1]$ such that $\displaystyle\lim_{p\rightarrow 0}\frac{\log(\lambda2^p+(1-\lambda)3^p)}{p}=\lambda \log2+(1-\lambda)\log3$ Then $A=\{0,1\}$ $A=\{0,\frac{1}{2},1\}$ $A=\{0,\frac{1}{3},\frac{1}{2},\frac{2}{3},1\}$ $A=[0,1]$

jothee edited in Others 3 hours ago

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18

TIFR2021-Maths-A: 6
For a positive integer $n$, let $a_n$ denote the unique positive real root of $x^n+x^{n-1}+\dots+x-1=0.$ Then the sequence $\{a_n\}^{\infty}_{n=1}$ is unbounded $\displaystyle \lim_{n\rightarrow \infty} a_n=0$ $\displaystyle \lim_{n\rightarrow \infty} a_n=1/2$ $\displaystyle \lim_{n\rightarrow \infty} a_n$ does not exist

jothee edited in Others 3 hours ago

by jothee

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19

TIFR2021-Maths-A: 5
The dimension of the real vector space $V=\{f:(-1,1)\rightarrow\mathbb{R}|f$ is infinitely differentiable on $(-1,1)$ and $f^{(n)}(0)=0$ for all $n\geq 0\}$ is $0$ $1$ greater than one, but finite infinite

jothee edited in Others 3 hours ago

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20

TIFR2021-Maths-A: 4
The set $S=\{x\in \mathbb{R}|x>0\text{ and } (1+x^2) \tan(2x)=x\}$ is empty nonempty but finite countably infinite uncountable

jothee edited in Others 3 hours ago

by jothee

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21

TIFR2021-Maths-A: 3
The value of $\displaystyle\lim_{n\rightarrow\infty}\prod_{k=2}^{n}\left(1-\frac{1}{k^2}\right)$ is $1/2$ $1$ $1/4$ $0$

jothee edited in Others 3 hours ago

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22

TIFR2021-Maths-A: 2
The number of bijective maps $g:\mathbb{N}\rightarrow\mathbb{N}$ such that $\sum_{n=1}^\infty\frac{g(n)}{n^2}<\infty$ is $0$ $1$ $2$ $\infty$

jothee edited in Others 3 hours ago

by jothee

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23

TIFR2021-Maths-A: 1
For each positive integer $n$, let $s_n=\frac{1}{\sqrt{4n^2-1^2}}+\frac{1}{\sqrt{4n^2-2^2}}+\dots+\frac{1}{\sqrt{4n^2-n^2}}$ Then the $\displaystyle \lim_{n\rightarrow \infty}s_n$ equals $\pi/2$ $\pi/6$ $1/2$ $\infty$

jothee edited in Others 3 hours ago

by jothee

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23 votes

2 answers

24

GATE CSE 1989 | Question: 2-ii
Match the pairs in the following questions: ...

Subbu. commented in CO and Architecture 4 hours ago

by Subbu.

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25

GATE CSE 2003 | Question: 31
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\implies\) P(y) for all $x, y \in S$ satisfying $x \leq y$ ... for all x \(\in\) S such that b ≤ x and x ≠ c P(x) = False for all x \(\in\) S such that a ≤ x and b ≤ x

KartikGawande commented in Set Theory & Algebra 6 hours ago

by KartikGawande

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23 votes

2 answers

26

GATE CSE 1999 | Question: 11b
Write a constant time algorithm to insert a node with data $D$ just before the node with address $p$ of a singly linked list.

ayush3298 commented in DS 7 hours ago

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27

Applied Test Series
The solution for process synchronization is given below : Which of the following is correct about the above given solution? (A) Satisfies Mutual Exclusion (B) Satisfies Progress (C) Satisfies Bounded wait (D) Suffers from deadlock

Vishal_kumar98 commented in Operating System 8 hours ago

by Vishal_kumar98

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28

Applied Test Series
In a system which has only 3 processes, there are 2 copies of R1 resource, 3 copies of R2 resource. Say, in the current snapshot of the system, Process P1 holds 2 copies of resource R1 and needs 1 copy of R2 to complete its execution. P2 holds 2 copies ... at a much later point in time. The probability that the system will be in a deadlock again is ____ (up to 2 decimal places).

Vishal_kumar98 answered in Operating System 8 hours ago

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29

Applied Test Series
What will be the output ?

Vishal_kumar98 answered in Digital Logic 8 hours ago

by Vishal_kumar98

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30

Closure Properties of Languages
let L = “CFL but not REGULAR”, Can we get complement of L as CFL? Unlike in the case of Recursively Enumerable(RE) language where if L = “RE but not RECURSIVE”, its complement can never be RE.

UltraRadiantX commented in Theory of Computation 12 hours ago

by UltraRadiantX

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