How man Y different pairs(a,b) of positive integers are there such that $$a\geq b$$ and $$\frac{1}{a}+\frac{1}{b}=\frac{1}{9}$$? ?->(Show Answer!)

1. How man Y different pairs(a,b) of positive integers are there such that $$a\geq b$$ and $$\frac{1}{a}+\frac{1}{b}=\frac{1}{9}$$?

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MCQ-> Every age has its pet contradictions. A few decades back, we used to accept Marx and Freud together, and then wonder, like the chameleon on the turkey carpet, why life was so confusing. Today there is similar trouble over the question whether there is, or is not, something called Human Nature. On the one hand, there has been an explosion of animal behavior studies, and comparisons between animals and men have become immensely popular. People use evidence from animals to decide whether man is naturally aggressive, or naturally territorial; even whether he has an aggressive or territorial instinct. Moreover, we are still much influenced by Freudian psychology, which depends on the notion of instinct. On the other hand, many still hold what may be called the Blank Paper view, that man is a creature entirely without instincts. So do Existentialist philosophers. If man has no instincts, all comparison with animals must be irrelevant. (Both these simple party lines have been somewhat eroded over time, but both are still extremely influential.)According to the Blank Paper view, man is entirely the product of his culture. He starts off infinitely plastic, and is formed completely by the society in which he grows up. There is then no end to the possible variations among cultures; what we take to be human instincts are just the deep-dug prejudices of our own society. Forming families, fearing the dark, and jumping at the sight of a spider are just results of our conditioning. Existentialism at first appears a very different standpoint, because the Existentialist asserts man’s freedom and will not let him call himself a product of anything. But Existentialism too denies that man has a nature; if he had, his freedom would not be complete. Thus Sartre insisted that “there is no human nature …. Man first of all exists, encounters himself, surges up in the world, and defines himself afterwards. If man as the Existentialist sees him is not definable, it is because to begin with he is nothing. He will not be anything until later, and then he will be what he makes himself.” For Existentialism there is only the human condition, which is what happens to man and not what he is born like. If we are afraid of the dark, it is because we choose to be cowards; if we care more for our own children than for other people’s, it is because we choose to be partial. We must never talk about human nature or human instincts. This implicit moral notion is still very influential, not at all confined to those who use the metaphysic of essence and existence. So I shall sometimes speak of it, not as Existentialist, but as Libertarian ― meaning that those holding it do not just (like all of us) think liberty important, but think it supremely important and believe that our having a nature would infringe it.Philosophers have not yet made much use of informed comparison with other species as a help in the understanding of man. One reason they have not is undoubtedly the fear of fatalism. Another is the appalling way terms such as instinct and human nature have been misused in the past. A third is the absurdity of some ethological propaganda.A business school led by an existentialist director, wanted to decide on admission policy for its executive MBA program, which requires candidates to possess minimum five years of managerial experience.With respect to the selection process, which of the following statements will be closest to the director’s belief:
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MCQ-> Read the following passage carefully and answer the question given below it. Certain words are printed in bold to help you to locate them while answering some of the question.Once upon a time in a village, there lived six blind men. In spite of their blindness they had managed to educate themselves Seeking to expand their knowledge they decided to visit a zoo and try out their skills in recognizing animals by their touch. The first animal they came across, as soon as they entered the zoo was an elephant.As the first man approched the elephant, the elephant waved its trunk, and the man felt something brush past him. Managing to hold on to it, and found something long and moving. He jumped back in alarm, shouting "Move away ! This is a snake !" Meanwhile ,the second man had moved closer, and walked right near its legs. As the man touched the thick, cylindrical¬shaped legs, he called out "Do not worry. These are just four trees here. There is acertainly no snake !" The third man was curious hearing the other two, and moved forward. As he walked towards the elephant, he felt his hand touch one of the tusks. Feeling the smooth, sharp ivory tusk, the man cried out " Be careful ! There is a sharp spear here". The fourth man cautiously walked up behind the elephant and felt its swinging tail. "It's just a rope ! he said. The fifth man had meanwhile reached out and was touching the huge ears of the animal. "I think all of you have lost your sense of touch !" he said. "This is nothing but a huge fan!" The sixth man did not want to be left out. As he walked towards the elephant, he bumped into the massive body, and he exclaimed, "Hey ! This is just a huge mud wall ! There is no animal at all !" All six of them were convinced that they were right, and began arguing amongst themselves.The zoo keeper returned to the elephant and saw each of them shouting at the top of their voice ! "Quiet" he shouted out and when they had calmed down, he asked, "Why are all of you shouting and arguing in this manner ?" They replied, "sir, as you can see, we all are blind. We came here to expand our knowledge. We sensed an animal here and tried to get an idea of its appearance by feeling it. However, we are not able to arrive at a consensus over its appearance, and hence are arguing. Can you please help us and tell us which of us is right" ?The zoo keeper laughed before answering "My dear men, each of you has touched just one portion of the animal. The animal you see is neither a snake, nor any of other things you have mentioned. The animal in front on you is an elephant !" As the men, bowed their head ashamed of the scence they had created, the zoo keeper said, "My dear men, this is a huge animal and luckily, it is tame. It stood by calmly as each of you touched it. You are extremely lucky that it stayed calm even during your argument, for if it had got angry, it would have trampled all of you to death !" He continued further , "It is also important to learn to share and pool your knowledge .Instead of fighting amongst yourselves, if you had tried to put all your observations together, you might have had an idea of the animal as a whole ! Also, when you cannot see the entire truth, it is better to go to someone who does know the complete truth, rather than guess about small parts of it. Such half¬knowledge is not only useless, but also dangerous. If you had come directly to me, I would have helped you identify all the animals without putting you in danger !" The six men apologized to the zoo keeper, and assured him that they had learnt their lesson. From now on they would seek true knowledge from qualified people, and would seek true knowledge from qualified people, and would also try to work together as a team so that they could learn moreWhich part of the elephant resembled a big fan ?
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MCQ-> The current debate on intellectual property rights (IPRs) raises a number of important issues concerning the strategy and policies for building a more dynamic national agricultural research system, the relative roles of public and private sectors, and the role of agribusiness multinational corporations (MNCs). This debate has been stimulated by the international agreement on Trade Related Intellectual Property Rights (TRIPs), negotiated as part of the Uruguay Round. TRIPs, for the first time, seeks to bring innovations in agricultural technology under a new worldwide IPR regime. The agribusiness MNCs (along with pharmaceutical companies) played a leading part in lobbying for such a regime during the Uruguay Round negotiations. The argument was that incentives are necessary to stimulate innovations, and that this calls for a system of patents which gives innovators the sole right to use (or sell/lease the right to use) their innovations for a specified period and protects them against unauthorised copying or use. With strong support of their national governments, they were influential in shaping the agreement on TRIPs, which eventually emerged from the Uruguay Round. The current debate on TRIPs in India - as indeed elsewhere - echoes wider concerns about ‘privatisation’ of research and allowing a free field for MNCs in the sphere of biotechnology and agriculture. The agribusiness corporations, and those with unbounded faith in the power of science to overcome all likely problems, point to the vast potential that new technology holds for solving the problems of hunger, malnutrition and poverty in the world. The exploitation of this potential should be encouraged and this is best done by the private sector for which patents are essential. Some, who do not necessarily accept this optimism, argue that fears of MNC domination are exaggerated and that farmers will accept their products only if they decisively outperform the available alternatives. Those who argue against agreeing to introduce an IPR regime in agriculture and encouraging private sector research are apprehensive that this will work to the disadvantage of farmers by making them more and more dependent on monopolistic MNCs. A different, though related apprehension is that extensive use of hybrids and genetically engineered new varieties might increase the vulnerability of agriculture to outbreaks of pests and diseases. The larger, longer-term consequences of reduced biodiversity that may follow from the use of specially bred varieties are also another cause for concern. Moreover, corporations, driven by the profit motive, will necessarily tend to underplay, if not ignore, potential adverse consequences, especially those which are unknown and which may manifest themselves only over a relatively long period. On the other hand, high-pressure advertising and aggressive sales campaigns by private companies can seduce farmers into accepting varieties without being aware of potential adverse effects and the possibility of disastrous consequences for their livelihood if these varieties happen to fail. There is no provision under the laws, as they now exist, for compensating users against such eventualities. Excessive preoccupation with seeds and seed material has obscured other important issues involved in reviewing the research policy. We need to remind ourselves that improved varieties by themselves are not sufficient for sustained growth of yields. in our own experience, some of the early high yielding varieties (HYVs) of rice and wheat were found susceptible to widespread pest attacks; and some had problems of grain quality. Further research was necessary to solve these problems. This largely successful research was almost entirely done in public research institutions. Of course, it could in principle have been done by private companies, but whether they choose to do so depends crucially on the extent of the loss in market for their original introductions on account of the above factors and whether the companies are financially strong enough to absorb the ‘losses’, invest in research to correct the deficiencies and recover the lost market. Public research, which is not driven by profit, is better placed to take corrective action. Research for improving common pool resource management, maintaining ecological health and ensuring sustainability is both critical and also demanding in terms of technological challenge and resource requirements. As such research is crucial to the impact of new varieties, chemicals and equipment in the farmer’s field, private companies should be interested in such research. But their primary interest is in the sale of seed materials, chemicals, equipment and other inputs produced by them. Knowledge and techniques for resource management are not ‘marketable’ in the same way as those inputs. Their application to land, water and forests has a long gestation and their efficacy depends on resolving difficult problems such as designing institutions for proper and equitable management of common pool resources. Public or quasi-public research institutions informed by broader, long-term concerns can only do such work. The public sector must therefore continue to play a major role in the national research system. It is both wrong and misleading to pose the problem in terms of public sector versus private sector or of privatisation of research. We need to address problems likely to arise on account of the public-private sector complementarity, and ensure that the public research system performs efficiently. Complementarity between various elements of research raises several issues in implementing an IPR regime. Private companies do not produce new varieties and inputs entirely as a result of their own research. Almost all technological improvement is based on knowledge and experience accumulated from the past, and the results of basic and applied research in public and quasi-public institutions (universities, research organisations). Moreover, as is increasingly recognised, accumulated stock of knowledge does not reside only in the scientific community and its academic publications, but is also widely diffused in traditions and folk knowledge of local communities all over. The deciphering of the structure and functioning of DNA forms the basis of much of modern biotechnology. But this fundamental breakthrough is a ‘public good’ freely accessible in the public domain and usable free of any charge. Various techniques developed using that knowledge can however be, and are, patented for private profit. Similarly, private corporations draw extensively, and without any charge, on germplasm available in varieties of plants species (neem and turmeric are by now famous examples). Publicly funded gene banks as well as new varieties bred by public sector research stations can also be used freely by private enterprises for developing their own varieties and seek patent protection for them. Should private breeders be allowed free use of basic scientific discoveries? Should the repositories of traditional knowledge and germplasm be collected which are maintained and improved by publicly funded organisations? Or should users be made to pay for such use? If they are to pay, what should be the basis of compensation? Should the compensation be for individuals or (or communities/institutions to which they belong? Should individual institutions be given the right of patenting their innovations? These are some of the important issues that deserve more attention than they now get and need serious detailed study to evolve reasonably satisfactory, fair and workable solutions. Finally, the tendency to equate the public sector with the government is wrong. The public space is much wider than government departments and includes co- operatives, universities, public trusts and a variety of non-governmental organisations (NGOs). Giving greater autonomy to research organisations from government control and giving non- government public institutions the space and resources to play a larger, more effective role in research, is therefore an issue of direct relevance in restructuring the public research system.Which one of the following statements describes an important issue, or important issues, not being raised in the context of the current debate on IPRs?
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MCQ-> The conceptions of life and the world which we call ‘philosophical’ are a product of two factors: one inherited religious and ethical conceptions; the other, the sort of investigation which may be called ‘scientific’, using this word in its broadest sense. Individual philosophers have differed widely in regard to the proportions in which these two factors entered into their systems, but it is the presence of both, in some degree, that characterizes philosophy.‘Philosophy’ is a word which has been used in many ways, some wider, some narrower. I propose to use it in a very wide sense, which I will now try to explain.Philosophy, as I shall understand the word, is something intermediate between theology and science. Like theology, it consists of speculations on matters as to which definite knowledge has, so far, been unascertainable; but like science, it appeals to human reason rather than to authority, whether that of tradition or that of revelation. All definite knowledge so I should contend belongs to science; all dogma as to what surpasses definite knowledge belongs to thelogy. But between theology and science there is a ‘No man’s Land’, exposed to attack from both sides; this ‘No Man’s Land’ is philosophy. Almost all the questions of most interest to speculative minds are such as science cannot answer, and the confident answers of theologians no longer seem so convincing as they did in former centuries. Is the world divided into mind and matter, and if so, what is mind and what is matter? Is mind subject to matter, or is it possessed of independent powers? Has the universe any unity or purpose? It is evolving towards some goal? Are there really laws of nature, or do we believe in them only because of our innate love of order? Is man what he seems to the astronomer, a tiny lump of carbon and water impotently crawling on a small and unimportant planet? Or is he what he appears to Hamlet? Is he perhaps both at once? Is there a way of living that is noble and another that is base, or are all ways of living merely futile? If there is a way of living that is noble, in what does it consist, and how shall we achieve it? Must the good be eternal in order to deserve to be valued, or is it worth seeking even if the universe is inexorably moving towards death? Is there such a thing as wisdom, or is what seems such merely the ultimate refinement of folly? To such questions no answer can be found in the laboratory. Theologies have professed to give answers, all too definite; but their definiteness causes modern minds to view them with suspicion. The studying of these questions, if not the answering of them, is the business of philosophy.Why, then, you may ask, waste time on such insoluble problems? To this one may answer as a historian, or as an individual facing the terror of cosmic loneliness.The answer of the historian, in so far as I am capable of giving it, will appear in the course of this work. Ever since men became capable of free speculation, their actions in innumerable important respects, have depended upon their theories as to the world and human life, as to what is good and what is evil. This is as true in the present day as at any former time. To understand an age or a nation, we must understand its philosophy, and to understand its philosophy we must ourselves be in some degree philosophers. There is here a reciprocal causation: the circumstances of men’s lives do much to determine their philosophy, but, conversely, their philosophy does much to determine their circumstances.There is also, however, a more personal answer. Science tells us what we can know, but what we can know is little, and if we forget how much we cannot know we may become insensitive to many things of very great importance. Theology, on the other hand, induces a dogmatic belief that we have knowledge, where in fact we have ignorance, and by doing so generates a kind of impertinent insolence towards the universe. Uncertainty, in the presence of vivid hopes and fears, is painful, but must be endured if we wish to live without the support of comforting fairy tales. It is good either to forget the questions that philosophy asks, or to persuade ourselves that we have found indubitable answers to them. To teach how to live without certainty, and yet without being paralyzed by hesitation, is perhaps the chief thing that philosophy, in our age, can still do for those who study it.The purpose of philosophy is to
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MCQ-> Read passage carefully. Answer the questions by selecting the most appropriate option (with reference to the passage). PASSAGE 1We use the word culture quite casually when referring to a variety of thoughts and actions. I would like to begin my attempt to define cultures by a focus on three of its dictionary meanings that I think are significant to our understanding of the general term-culture. We often forget that it's more essential usage is as a verb rather than as a noun, since the noun follows froth the activities involved in the verb. Thus the verb, to culture, means to cultivate. This can include at least three activities: to artificially grow microscopic organisms; to improve and refine the customs, manners and activities of one's life; to give attention to the mind as part of what goes into the making of what we call civilization, or what was thought to be the highest culture. In short, one might argue that culture is the intervention of human effort in refining and redefining that which is natural, but that it gradually takes on other dimensions in the life of the individual, and even more in the interface between the individual and society. When speaking of society, this word also requires defining. Society, it has been said, is what emerges from a network of interactions between people that follow certain agreed upon and perceptible patterns. These arc determined by ideas of status, hierarchy and a sense of community governing the network. They are often, but not invariably, given a direction by those who control the essentials in how a society functions, as for instance, its economic resources, its technology and its value systems. The explanation and justification for who controls these aspects of a society introduces the question of its ideology and often its form. The resulting patterns that can be differentiated from segment to segment of the society are frequently called its cultures. Most early societies register inequalities, The access of their members to wealth and status varies. The idea of equality therefore has many dimensions. All men and women may be said to be equal in the eyes of god, but may at the same time be extremely differentiated in terms of income and social standing, and therefore differentiated in the eyes of men and women. This would not apply to the entire society. There may be times when societies conform to a greater degree of equality, but such times may be temporary. It has been argued that on a pilgrimage, the status of every pilgrim is relatively similar but at the end returns to inequalities. Societies are not static and change their forms and their rules of functioning. Cultures are reflections of these social patterns, so they also change. My attempt in this introduction is to explain how the meaning of a concept such as culture has changed in recent times and has come to include many more facets than it did earlier. What we understand as the markers of culture have gone way beyond what we took them to be a century or two ago. Apart from items of culture, which is the way in which culture as heritage was popularly viewed, there is also the question of the institutions and social codes that determine the pattern of living, and upon which pattern a culture is constructed. Finally, there is the process of socialization into society and culture through education. There is a historical dimension to each of these as culture and history are deeply intertwined. There is also an implicit dialogue between the present and the past reflected in the way in which the readings of the past changed over historical periods. Every. society has its cultures, namely, the patterns of how the people of that society live. In varying degrees this would refer to broad categories that shape life, such as the environment that determines the relationship with the natural world, technology that enables a control over the natural world, political-economy that organizes the larger vision of a society as a community or even as a state, structures of social relations that ensure its networks of functioning, religion that appeals to aspirations and belief, mythology that may get transmuted into literature and philosophy that teases the mind and the imagination with questions. The process of growth is never static therefore there are mutations and changes within the society. There is communication and interaction with other societies through which cultures evolve and mutate. There is also the emergence of subcultures that sometimes take the form of independent and dominant cultures or amoeba-like breakaway to form new cultures. Although cultures coincide with history and historical change, the consciousness of a category such as culture, in the emphatic sense in which the term is popularly used these days, emerges in the eighteenth century in Europe. The ideal was the culture of elite groups, therefore sometimes a distinction is made between what carne to be called 'high culture' that of the elite, and low culture' that of those regarded as not being of the elite, and sometimes described as 'popular'. Historical records of elite cultures in forms such as texts and monuments for instance, received larger patronage and symbolized the patterns of life of dominant groups. They were and are more readily available as heritage than the objects of the socially lower groups in society whose less durable cultural manifestations often do not survive. This also predisposed people to associate culture as essentially that of the elite.What is the central idea of the passage?
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