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Basic computer instructor
Which one is measure of software complexity? Ans:- number of lines of code (LOC) I want to proof this quest answer, please

LRU answered in Others Sep 20

by LRU

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2

PhD Admissions Written Test (Basic)
Let A be an array containing n integers. It is required to find 3 indices i, j, k such that i < j < k and either A[i] ≤ A[j] ≤ A[k] or A[i] ≥ A[j] ≥ A[k], if such indices exist. The asymptotic time complexity of the fastest algorithm for this problem, assuming the array is already available, is Θ(_____________).

Joey answered in Others Sep 20

by Joey

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3

IITB Practice Set: 22
Suppose the stop and wait protocol is employed over an asymmetric link $A$ to $B$. The $A$ to $B$ link bandwidth is $8\text{ Mbps}$ with a propagation delay of $20\;ms$, however the $B$ to $A$ link bandwidth is $800\;\text{Kbps}$ ... other delays. Express answer in kbps. ($1\text{ Mbps} = 10^6 \text {bps and } 1\text{ Kbps} = 10^3 \text{bps})$

Debanjan_2000 answered in Others Sep 16

by Debanjan_2000

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4

How to prepare for GATE 2023 CSE along with a job and only self-study?
I am a past student of Made Easy and got AIR 7500 in GATE 2022. I would like to get suggestions.

sanju s answered in Others Sep 16

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5

UGC NET CSE | December 2005 | Part 2 | Question: 37
If you want to execute more than one program at a time, the systems software that are used must be capable of : word processing virtual memory compiling multitasking

amder111 answered in Others Sep 14

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6

Go Class Test Series + GO Test series
sir i am subscribed the go test series + go classes test series both but July 19, Aug 22, Aug 25 tests are not unlocked why ? and sir after Aug 29 tests are not unlocked why ? please reply fast, I pay full amount bu the tests are not unlocked

ashishk205 asked in Study Resources Sep 12

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7

PhD Admissions Written Test (Basic)
Let A be a sorted array of distinct integers of length n. Design an algorithm to find an index i such that A[i] = i if such an index exists. If there are more than one such indices, you may output any one ... −1. The asymptotic time complexity of the fastest algorithm for this problem, assuming the array is already available, is Θ ______________________________

rsansiya111 asked in Others Sep 10

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8

PhD Admissions Written Test (Basic)
Consider all permutations of the 16 numbers from 1 to 16 which satisfy the property that every number is placed such that it is either bigger than ALL numbers preceding it or it is smaller than ALL numbers preceding it. The number of such permutations is ________________________

rsansiya111 asked in Others Sep 10

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9

TIFR Mathematics 2022 | Part B | Question: 19
Answer whether the following statements are True or False. There are $N$ balls in a box, out of which $n$ are blue $(1 < n < N)$ and the rest are red. Balls are drawn from the box one by one at random, and discarded. Then the ... in the first $n$ drawn is the same as the probability of picking all the red balls in the first $(N - n)$ draws.

afroze answered in Others Sep 10

by afroze

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10

ISI2020-PCB-CS: 3
You are given two sorted arrays $X[\;]$ and $Y[\;]$ of positive integers. The array sizes are not given. Accessing any index beyond the last element of the arrays returns $-1$. The elements in each array are distinct but the two arrays may have common ... marks will be awarded if the time complexity of your algorithm is linear (or higher) in the maximum size of $X$ and $Y.$

shishir__roy answered in Others Sep 10

by shishir__roy

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11

TIFR Mathematics 2022 | Part B | Question: 1
Answer whether the following statements are True or False. $\mathbb{R}^{2} \backslash \mathbb{Q}^{2}$ is connected but not path-connected.

admin asked in Others Sep 9

by admin

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12

TIFR Mathematics 2022 | Part B | Question: 2
Answer whether the following statements are True or False. If $X$ is a connected metric space, and $F$ is a subring of $C(X, \mathbb{R})$ that is a field, then every element of $C(X, \mathbb{R})$ that belongs to $F$ is a constant function.

admin asked in Others Sep 9

by admin

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13

TIFR Mathematics 2022 | Part B | Question: 3
Answer whether the following statements are True or False. Let $K \subseteq[0,1]$ be the Cantor set. Then there exists no injective ring homomorphism $C([0,1], \mathbb{R}) \rightarrow C(K, \mathbb{R})$.

admin asked in Others Sep 9

by admin

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14

TIFR Mathematics 2022 | Part B | Question: 4
Answer whether the following statements are True or False. There exists a metric space $(X, d)$ such that the group of isometries of $X$ is isomorphic to $\mathbb{Z}$.

admin asked in Others Sep 9

by admin

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15

TIFR Mathematics 2022 | Part B | Question: 5
Answer whether the following statements are True or False. Let $A \subset \mathbb{R}^{2}$ be a nonempty subset such that any continuous function $f: A \rightarrow \mathbb{R}$ is constant. Then $A$ is a singleton set.

admin asked in Others Sep 9

by admin

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16

TIFR Mathematics 2022 | Part B | Question: 6
Answer whether the following statements are True or False. For a nilpotent matrix $A \in \mathrm{M}_{n}(\mathbb{R})$, let \[ \exp (A):=\sum_{n=0}^{\infty} \frac{A^{n}}{n !}=\mathrm{Id}+\frac{A}{1 !}+\frac{A^{2}}{2 !}+\cdots \in \mathrm{M}_{n}(\mathbb{R}) \] If $A$ is a nilpotent matrix such that $\exp (A)=\mathrm{Id}$, then $A$ is the zero matrix.

admin asked in Others Sep 9

by admin

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17

TIFR Mathematics 2022 | Part B | Question: 7
Answer whether the following statements are True or False. There exists $A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \in \mathrm{M}_{2}(\mathbb{R})$, with $A^{2}=A \neq 0$, such that $|a|+|b|<1 \quad \text{and} \quad|c|+|d|<1.$

admin asked in Others Sep 9

by admin

21 views

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18

TIFR Mathematics 2022 | Part B | Question: 8
Answer whether the following statements are True or False. If $A \in \mathrm{M}_{3}(\mathbb{C})$ is such that $A^{i}$ has trace zero for all positive integers $i$, then $A$ is nilpotent.

admin asked in Others Sep 9

by admin

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19

TIFR Mathematics 2022 | Part B | Question: 9
Answer whether the following statements are True or False. For any finite cyclic group $G$, there exists a prime power $q$ such that $G$ is a subgroup of $\mathbb{F}_{q}^{\times}.$

admin asked in Others Sep 9

by admin

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20

TIFR Mathematics 2022 | Part B | Question: 10
Answer whether the following statements are True or False. There are only finitely many isomorphism classes of finite nonabelian groups, all of whose proper subgroups are abelian.

admin asked in Others Sep 9

by admin

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21

TIFR Mathematics 2022 | Part B | Question: 11
Answer whether the following statements are True or False. Every subring of a unique factorization domain is a unique factorization domain.

admin asked in Others Sep 9

by admin

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22

TIFR Mathematics 2022 | Part B | Question: 12
Answer whether the following statements are True or False. Let $f_{1}, f_{2}, f_{3}, f_{4} \in \mathbb{R}[x]$ be monic polynomials each of degree exactly two. Then there exist a real polynomial $p \in \mathbb{R}[x]$ and a subset $\{i, j\} \subset\{1,2,3,4\}$ with $i \neq j$, such that $f_{i} \circ p=c f_{j}$ for some $c \in \mathbb{R}$.

admin asked in Others Sep 9

by admin

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23

TIFR Mathematics 2022 | Part B | Question: 13
Answer whether the following statements are True or False. There exists a finite abelian group $G$ such that the group Aut$(G)$ of automorphisms of $G$ is isomorphic to $\mathbb{Z} / 7 \mathbb{Z}$.

admin asked in Others Sep 9

by admin

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24

TIFR Mathematics 2022 | Part B | Question: 14
Answer whether the following statements are True or False. There exists an integral domain $R$ and a surjective homomorphism $R \rightarrow R$ of rings that is not injective.

admin asked in Others Sep 9

by admin

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25

TIFR Mathematics 2022 | Part B | Question: 15
Answer whether the following statements are True or False. There exists $f \in C([0,1], \mathbb{R})$ satisfying the following two conditions: $\int_{0}^{1} f(x) d x=1$; and $\lim _{n \rightarrow \infty} \int_{0}^{1} f(x)^{n} d x=0$.

admin asked in Others Sep 9

by admin

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26

TIFR Mathematics 2022 | Part B | Question: 16
Answer whether the following statements are True or False. Let $a_{n} \geq 0$ for each positive integer $n$. If the series $\sum_{n=1}^{\infty} \sqrt{a_{n}}$ converges, then so does the series $\sum_{n=1}^{\infty} \frac{a_{n}}{n^{1 / 4}}$.

admin asked in Others Sep 9

by admin

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27

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 \[ \lim _{x \rightarrow \infty} f(x)=2 \quad \text { and } \quad \lim _{x \rightarrow \infty} f^{\prime}(x)=1 .\]

admin asked in Others Sep 9

by admin

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28

TIFR Mathematics 2022 | Part B | Question: 18
Answer whether the following statements are True or False. Let $f:[0,1] \rightarrow[0, \infty)$ be continuous on $[0,1]$ and twice differentiable in $(0,1)$. If $f^{\prime \prime}(x)=7 f(x)$ for all $x \in(0,1)$, then $f(x) \leq \max \{f(0), f(1)\}$ for all $x \in[0,1]$.

admin asked in Others Sep 9

by admin

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29

TIFR Mathematics 2022 | Part B | Question: 20
Answer whether the following statements are True or False. The set $\{f(x) \in \mathbb{R}[x] \mid f(n) \in \mathbb{Z}$ for all $n \in \mathbb{Z}\}$ is uncountable.

admin asked in Others Sep 9

by admin

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30

TIFR Mathematics 2022 | Part A | Question: 1
Consider the following properties of a metric space $(X, d)$ : $(X, d)$ is complete as a metric space. For any sequence $\left\{Z_{n}\right\}_{n \in \mathbb{N}}$ of closed nonempty subsets of $X$, such that $Z_{1} \supseteq Z_{2} \supseteq$ ... (I). (I) does not imply (II) but (II) implies (I). (I) does not imply (II) and (II) does not imply (I).

admin asked in Others Sep 9

by admin

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31

TIFR Mathematics 2022 | Part A | Question: 2
Consider the following assertions: $\left\{(x, y) \in \mathbb{R}^{2} \mid x y=1\right\}$ is connected. $\left\{(x, y) \in \mathbb{C}^{2} \mid x y=1\right\}$ is connected. Which of the following sentences is true? Both (I) and (II) are true. (I) is true but (II) is false. (I) is false but (II) is true. Both (I) and (II) are false.

admin asked in Others Sep 9

by admin

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32

TIFR Mathematics 2022 | Part A | Question: 3
What is the number of solutions of: \[ x=\frac{x^{2}}{50}-\cos \frac{x}{2}+2 \] in $[0,10]$ ? $0$ $1$ $2$ $\infty$

admin asked in Others Sep 9

by admin

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33

TIFR Mathematics 2022 | Part A | Question: 4
Let $A$ be an element of $\mathrm{M}_{4}(\mathbb{R})$ with characteristic polynomial $t^{4}-t$. What is the characteristic polynomial of $A^{2}$ ? $t^{4}-t$ $t^{4}-2 t^{3}+t^{2}$ $t^{4}-t^{2}$ None of the other three options

admin asked in Others Sep 9

by admin

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34

TIFR Mathematics 2022 | Part A | Question: 5
Let $n$ be a positive integer, and let $V=\{f \in \mathbb{R}[x] \mid \operatorname{deg} f \leq n\}$ be the real vector space of real polynomials of degree at most $n$. Let $\operatorname{End}_{\mathbb{R}}(V)$ denote the real vector space of linear ... $1$ $n$ $n+1$ $n^{2}$

admin asked in Others Sep 9

by admin

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1 vote

1 answer

35

TIFR CSE 2022 | Part B | Question: 7
Consider the following grammar: $\text{P, Q, R}$ are non-terminals; $c, d$ are terminals; $\text{P}$ is the start symbol; and the production rules follow. $\mathrm{P}::=\mathrm{QR}$ $\text{Q ::= c}$ $\text{Q} ::=\text{RcR}$ ... has three consecutive $c\text{'s}$ Every string produced by the grammar has at least has many $d\text{'s}$ as $c\text{'s}$

afroze answered in Others Sep 9

by afroze

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2 answers

36

TIFR CSE 2022 | Part A | Question: 2
We would like to invite a minimum number $n$ of people (their birthdays are independent of each other) to a party such that the expected number of pairs of people that share the same birthday is at least $1.$ What should $n$ be? (Ignore leap years, so ... birthdays fall with equal probability on each of the $365$ days of the year.) $23$ $28$ $92$ $183$ $366$

shishir__roy answered in Others Sep 9

by shishir__roy

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1 answer

37

TIFR CSE 2022 | Part A | Question: 9
You are given the following properties of sets $A, B, X$, and $Y$. For notation, $|A|$ denotes the cardinality of set $A$ (i.e., the number of elements in $A$ ), and $A \backslash B$ denotes the set of elements that are in $A$ but not in $B$. $A \cup B=X \cup Y$ ... $|X|=5$ $|Y|=5$ $|A \cup X|=|B \cup Y|$ $|A \cap X|=|B \cap Y|$ $|A|=|B|$

shishir__roy answered in Others Sep 9

by shishir__roy

36 views

13 votes

1 answer

38

TIFR CSE 2022 | Part A | Question: 8
Let $A$ be the $(n+1) \times(n+1)$ matrix given below, where $n \geq 1$. For $i \leq n$, the $i$-th row of $A$ has every entry equal to $2i-1$ and the last row, i.e., the $(n+1)$-th row of $A$ has every entry equal to $-n^2$ ... $A$ has rank $n$ $A^2$ has rank $1$ All the eigenvalues of $A$ are distinct All the eigenvalues of $A$ are $0$ None of the above

shishir__roy answered in Others Sep 9

by shishir__roy

150 views

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1 answer

39

TIFR CSE 2022 | Part A | Question: 15
Fix $n \geq 4$. Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2, \ldots, n\}$. The initial probability distribution of the particle is $\pi$ i.e., the probability that particle is in location $i$ is given by $\pi(i)$. In the ... $\pi(1)=1$ and $\pi(i)=0$ for $i \neq 1$ $\pi(n)=1$ and $\pi(i)=0$ for $i \neq n$

shishir__roy answered in Others Sep 9

by shishir__roy

47 views

1 vote

1 answer

40

UGC NET CSE | January 2017 | Part 3 | Question: 73
Which of the following neural networks uses supervised learning? Multilayer perception Self organizing feature map Hopfield network (A) only (B) only (A) and (B) only (A) and (C) only

rsansiya111 answered in Others Sep 9

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