1. Mistakes on the stencil paper can be corrected by





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MCQ-> Mathematicians are assigned a number called Erdos number (named after the famous mathematician, Paul Erdos). Only Paul Erdos himself has an Erdos number of zero. Any mathematician who has written a research paper with Erdos has an Erdos number of 1.For other mathematicians, the calculation of his/her Erdos number is illustrated below:Suppose that a mathematician X has co-authored papers with several other mathematicians. 'From among them, mathematician Y has the smallest Erdos number. Let the Erdos number of Y be y. Then X has an Erdos number of y+1. Hence any mathematician with no co-authorship chain connected to Erdos has an Erdos number of infinity. :In a seven day long mini-conference organized in memory of Paul Erdos, a close group of eight mathematicians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the conference, A was the only participant who had an infinite Erdos number. Nobody had an Erdos number less than that of F.On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdos number of the group of eight mathematicians to 3. The Erdos numbers of B, D, E, G and H remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdos number of the group of eight to as low as 3.• At the end of the third day, five members of this group had identical Erdos numbers while the other three had Erdos numbers distinct from each other.• On the fifth day, E co-authored a paper with F which reduced the group's average Erdos number by 0.5. The Erdos numbers of the remaining six were unchanged with the writing of this paper.• No other paper was written during the conference.The person having the largest Erdos number at the end of the conference must have had Erdos number (at that time):
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MCQ-> Read the following passage carefully and answer the questions given below it. Certain words/phrases have been printed in bold to help you locate them while answering some of the questions. The wisdom of learning from failure is incontrovertible. Yet organisations that do it well are extraordinarily rare. This gap is not due to a lack of commitment to learning. Managers in the vast majority of enterprises that I have studied over the past 20 years —pharmaceutical. financial services, product design, telecommunications, and construction companies: hospitals; and NASA’s space shuttle program, among others— genuinely wanted to help their organisations learn from failures to improve future performance. In some cases they and their teams had devoted many hours to afteraction reviews, postmortems, and the like. But time after time I saw that these painstaking efforts led to no real change. The reason: Those managers were thinking about failure the wrong way. Most executives I’ve talked to believe that failure is bad (of course!). They also believe that learning from it is pretty straightforward: Ask people to reflect on what they did wrong and exhort them to avoid similar mistakes in the future—or, better yet, assign a team to review and write a report on what happened and then distribute it throughout the organisation. These widely held beliefs are misguided. First, failure is not always bad. In organisational life it is sometimes bad, sometimes inevitable, and sometimes even good. Second, learning from organisational failures is anything but straightforward. The attitudes and activities required to effectively detect and analyze failures are in short supply in most companies, and the need for context-specific learning strategies is underappreciated. Or – ganisations need new and better ways to go beyond lessons that are superficial (“Procedures weren’t followed”) or self-serving (“The market just wasn’t ready for our great new product”). That means jettisoning old cultural beliefs and stereotypical notions of success and embracing failure’s lessons. Leaders can begin by understanding how the blame game gets in the way. The Blame Game Failure and fault are virtually inseparable in most households. organisations, and cultures. Every child learns at some point that admitting failure means taking the blame. That is why so few organisations have shifted to a culture of psychological safety in which the rewards of learning from failure can be fully realised. Executives I’ve interviewed in organisations as different as hospitals and investment banks admit to being torn: How can they respond constructively to failures without giving rise to an anything-goes attitude? If people aren’t blamed for failures, what will ensure that they try as hard as possible to do their best work? This concern is based on a false dichotomy. In actuality, a culture that makes it safe to admit and report on failure can—and in some organisational contexts must–coexist with high standards for performance. To understand why, look at the exhibit “A Spectrum of Reasons for Failure,” which lists causes ranging from deliberate deviation to thoughtful experimentation. Which of these causes involve blameworthy actions? Deliberate deviance, first on the list, obviously warrants blame. But inattention might not. If it results from a lack of effort, perhaps it’s blameworthy. But if it results from fatigue near the end of an overly long shift, the manager who assigned the shift is more at fault than the employee. As we go down the list, it gets more and more difficult to find blameworthy acts. In fact, a failure resulting from thoughtful experimentation that generates valuable information may actually be praiseworthy. When I ask executives to consider this spectrum and then to estimate how many of the failures in their organisations are truly blameworthy, their answers are usually in single digits—perhaps 2% to 5%. But when I ask how many are treated as blameworthy, they say (after a pause or a laugh) 70% to 90%. The unfortunate consequence is that many failures go unreported and their lessons are lost. Question : sophisticated understanding of failure’s causes and contexts will help to avoid the blame game and institute an effective strategy for learning from failure. Although an infinite number of things can go wrong in organisations, mistakes fall into three broad categories: preventable, complexity-related, and intelligent.Which of the following statement (s) is/are true in the context of the given passage ? I. Most executives believe that failure is bad and learning from it is pretty straightforward. II. The wisdom of learning from failure is disputable. III. Deliberate deviance, first on the list of the exhibit, “A Spectrum of Reasons for Failure” obviously warrants blame.....
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