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JEST 2020
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that F is one-one For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.

asked 2 days ago in Set Theory & Algebra by vivek_mishra Junior (577 points) | 34 views

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2

TIFR2020-B-14

asked Feb 11 in Others by Lakshman Patel RJIT Veteran (60.6k points) | 98 views

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3

TIFR2020-B-15

asked Feb 11 in Others by Lakshman Patel RJIT Veteran (60.6k points) | 43 views

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4

TIFR2020-B-13

asked Feb 11 in Others by Lakshman Patel RJIT Veteran (60.6k points) | 41 views

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5

TIFR2020-B-7

asked Feb 11 in Others by Lakshman Patel RJIT Veteran (60.6k points) | 23 views

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6

TIFR2020-B-5

asked Feb 11 in Others by Lakshman Patel RJIT Veteran (60.6k points) | 16 views

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7

TIFR2020-B-4

asked Feb 11 in Others by Lakshman Patel RJIT Veteran (60.6k points) | 23 views

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8

TIFR2020-B-1

asked Feb 11 in Digital Logic by Lakshman Patel RJIT Veteran (60.6k points) | 24 views

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9

TIFR2020-A-11
Suppose we toss $m=3$ labelled balls into $n=3$ numbered bins. Let $A$ be the event that the first bin is empty while $B$ be the event that the second bin is empty. $P(A)$ and $P(B)$ denote their respective probabilities. Which of the following is true? $P(A)>P(B)$ $P(A) = \dfrac{1}{27}$ $P(A)>P(A\mid B)$ $P(A)<P(A\mid B)$ None of the above

asked Feb 11 in Probability by Lakshman Patel RJIT Veteran (60.6k points) | 17 views

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TIFR2020-A-8
Consider a function $f:[0,1]\rightarrow [0,1]$ which is twice differentiable in $(0,1).$ Suppose it has exactly one global maximum and exactly global minimum inside $(0,1).$ What can you say about the behaviour of the first derivative $f'$ and and second derivative $f''$ on ... is zero at at-least one point $f'$ is zero at at-least two points, $f''$ is zero at at-least two points

asked Feb 10 in Calculus by Lakshman Patel RJIT Veteran (60.6k points) | 17 views

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11

TIFR2020-A-7
A lottery chooses four random winners. What is the probability that at least three of them are born on the same day of the week? Assume that the pool of candidates is so large that each winner is equally likely to be born on any of the seven days of the week independent of the other ... . $\dfrac{17}{2401}$ $\dfrac{48}{2401}$ $\dfrac{105}{2401}$ $\dfrac{175}{2401}$ $\dfrac{294}{2401}$

asked Feb 10 in Probability by Lakshman Patel RJIT Veteran (60.6k points) | 10 views

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TIFR2020-A-4
Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of the particle be denoted by $\overrightarrow{\pi}.$ In the first step, if the particle is at position $i,$ it ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$

asked Feb 10 in Probability by Lakshman Patel RJIT Veteran (60.6k points) | 18 views

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TIFR2020-A-3
Let $d\geq 4$ and fix $w\in \mathbb{R}.$ Let $S = \{a = (a_{0},a_{1},\dots ,a_{d})\in \mathbb{R}^{d+1}\mid f_{a}(w) = 0\: \text{and}\: f'_{a}(w) = 0\},$ where the polynomial function $f_{a}(x)$ ... is a $d$-dimensional vector subspace of $\mathbb{R}^{d+1}$ $S$ is a $(d-1)$-dimensional vector subspace of $\mathbb{R}^{d+1}$ None of the other options

asked Feb 10 in Linear Algebra by Lakshman Patel RJIT Veteran (60.6k points) | 15 views

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14

TIFR2020-A-2
Let $M$ be a real $n\times n$ matrix such that for every non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above

asked Feb 10 in Linear Algebra by Lakshman Patel RJIT Veteran (60.6k points) | 25 views

+2 votes

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15

ISRO2020-78
In the following procedure Integer procedure P(X,Y); Integer X,Y; value x; begin K=5; L=8; P=x+y; end $X$ is called by value and $Y$ is called by name. If the procedure were invoked by the following program fragment K=0; L=0; Z=P(K,L); then the value of $Z$ will be set equal to $5$ $8$ $13$ $0$

asked Jan 13 in Programming by Satbir Boss (25.1k points) | 216 views

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16

NTA NET DEC 2019 (microprocessor)

asked Dec 30, 2019 in CO and Architecture by Sanjay Sharma Boss (49.4k points) | 88 views

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17

NTA NET DEC 2019 (sequence diagram)
In a system for a restaurant the main scenario for placing order is given below: Customer reads menu Customer places order Order is sent to kitchen for preparation Order items are served Customer request for a bill for the order Bill is prepared for this order Customer ... at least how many objects among whom the messages will be exchanged) 1) 3 (2) 4 (3) 5 (4) 6

asked Dec 29, 2019 in Object Oriented Programming by Sanjay Sharma Boss (49.4k points) | 66 views

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18

NTA NET DEC 2019 (Genetic algorithm)
Let the population of chromosomes in genetic algorithm is represented in terms of binary number. The strength of fitness of a chromosome in decimal form x, is given by S f(x) = f(x) where f(x) = x2 Σf(x) The population is given by P Where : P = ... 11000),(01000),(10011)} The strength of fitness of chromosomes (11000) is ___________ 1) 24 2) 576 3) 14.4 4) 49.2

asked Dec 22, 2019 in Others by Sanjay Sharma Boss (49.4k points) | 108 views

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19

NTA NET DEC 2019 (SQL_Query)
Given two tables EMPLOYEE (EID,ENAME,DEPTNO) DEPARTMENT(DEPTNO ,DEPTNAME) Find the most appropriate statement of the given query Select count(*) total from employee where DEPTNO IN (D1 ,D2) group by DEPTNO having count(*)>5 1)Total number of ... )Display total number of employees in both department D1 and D2 4)The output of the query must have at least two rows

asked Dec 20, 2019 in Databases by Sanjay Sharma Boss (49.4k points) | 94 views

+1 vote

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20

OS university exam

asked Dec 13, 2019 in Operating System by saurabh rai Boss (12.4k points) | 104 views

+1 vote

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21

Cormen Edition 3 Exercise 12.1 Question 5 (Page No. 289)
Argue that since sorting $n$ elements takes $\Omega (n\ lgn)$ time in the worst case in the comparison model, any comparison-based algorithm for constructing a $BST$ from an arbitrary list of n elements takes $\Omega (n\ lgn)$ time in the worst case.

asked Nov 20, 2019 in Algorithms by Kushagra गुप्ता Loyal (5.5k points) | 191 views

+1 vote

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22

Cormen Edition 3 Exercise 22.2 Question 7 (Page No. 539)
There are two types of professional wrestlers: babyfaces ( good guys ) and heels ( bad guys ). Between any pair of professional wrestlers, there may or may not be a rivalry. Suppose we have n professional wrestlers and we ... between a babyface and a heel. If it is possible to perform such a designation, your algorithm should produce it.

asked Nov 12, 2019 in Algorithms by Kushagra गुप्ता Loyal (5.5k points) | 59 views

+1 vote

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23

Cormen Edition 3 Exercise 22.2 Question 6 (Page No. 539)
Give an example of a directed graph $G=(V, E)$, a source vertex $s\ \epsilon\ V$ , and a set of tree edges $E_{\Pi}\subseteq E$ such that for each vertex $v\ \epsilon\ V$ ... set of edges $E_{\Pi}$ cannot be produced by running BFS on G, no matter how the vertices are ordered in each adjacency list.

asked Nov 12, 2019 in Algorithms by Kushagra गुप्ता Loyal (5.5k points) | 48 views

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24

Variation on Birthday Problem
So, I have read the birthday paradox problem, and now I came across below question: Assuming the following: there are no leap years, all years have $n = 365$ days and that people's birthdays are uniformly distributed across the $n$ days of the year. (i) How many ... $n=23$, this works out to be 0.53 and Yes it seems to me I am done. Please correct me If I am wrong.

asked Nov 12, 2019 in Probability by Ayush Upadhyaya Boss (30.6k points) | 185 views

+1 vote

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25

Data communication and networking by forouzan 12.7 Exercise
11. We have a pure ALOHA network with 100 stations. If $T_{fr} = 1 \mu s$, what is the number of frames each station can send to achieve the maximum efficiency. 12. Repeat Exercise 11 for slotted ALOHA.

asked Nov 7, 2019 in Computer Networks by Mk Utkarsh Boss (36.7k points) | 94 views

+3 votes

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26

The Interesting combination sum problems
Find the number of possible solutions for $x,y,z$ for each the following cases. $Case\ 1.$ Case of unlimited repetition. $x + y +z = 10$ and $x \geq 0\ , y \geq 0,\ z \geq 0 $ $Case\ 2 $ Case of unlimited repetition with variable lower bounds $x + y +z = 10$ and ... variable. $x + y +z = 10$ and $8 \geq x \geq 1\ , \ 20 \geq y \geq 2 \ , 12 \geq z \geq 3\ $

asked Nov 1, 2019 in Combinatory by Satbir Boss (25.1k points) | 224 views

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27

Andrew S. Tanenbaum (OS) Edition 4 Exercise 6 Question 43 (Page No. 470)
Write a program that detects if there is a deadlock in the system by using a resource allocation graph. Your program should read from a file the following inputs: the number of processes and the number of resources. ... system. In case there is, the program should print out the identities of all processes that are deadlocked.

asked Oct 30, 2019 in Operating System by Lakshman Patel RJIT Veteran (60.6k points) | 65 views

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28

Andrew S. Tanenbaum (OS) Edition 4 Exercise 6 Question 42 (Page No. 470)
Write a program to implement the deadlock detection algorithm with multiple resources of each type. Your program should read from a file the following inputs: the number of processes, the number of resource types, the ... . In case there is, the program should print out the identities of all processes that are deadlocked.

asked Oct 30, 2019 in Operating System by Lakshman Patel RJIT Veteran (60.6k points) | 30 views

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29

Andrew S. Tanenbaum (OS) Edition 4 Exercise 6 Question 41 (Page No. 470)
Program a simulation of the banker’s algorithm. Your program should cycle through each of the bank clients asking for a request and evaluating whether it is safe or unsafe. Output a log of requests and decisions to a file.

asked Oct 30, 2019 in Operating System by Lakshman Patel RJIT Veteran (60.6k points) | 29 views

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30

Andrew S. Tanenbaum (OS) Edition 4 Exercise 6 Question 40 (Page No. 469)
Repeat the previous problem, but now avoid starvation. When a baboon that wants to cross to the east arrives at the rope and finds baboons crossing to the west, he waits until the rope is empty, but no more westward-moving baboons are allowed to start until at least one baboon has crossed the other way.

asked Oct 30, 2019 in Operating System by Lakshman Patel RJIT Veteran (60.6k points) | 13 views

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