1. If the arcs of a same length in two circles subtend angles of $$60°$$ and $$75°$$ at their centres, the ratio of their radii is





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MCQ->If the arcs of a same length in two circles subtend angles of $$60°$$ and $$75°$$ at their centres, the ratio of their radii is....
MCQ->Two equal arcs of two circles subtend angle of 60° and 75° at the centre. The ratio of the radii of the two circles is....
MCQ-> The story begins as the European pioneers crossed the Alleghenies and started to settle in the Midwest. The land they found was covered with forests. With incredible efforts they felled the trees, pulled the stumps and planted their crops in the rich, loamy soil. When they finally reached the western edge of the place we now call Indiana, the forest stopped and ahead lay a thousand miles of the great grass prairie. The Europeans were puzzled by this new environment. Some even called it the “Great Desert”. It seemed untillable. The earth was often very wet and it was covered with centuries of tangled and matted grasses. With their cast iron plows, the settlers found that the prairie sod could not be cut and the wet earth stuck to their plowshares. Even a team of the best oxen bogged down after a few years of tugging. The iron plow was a useless tool to farm the prairie soil. The pioneers were stymied for nearly two decades. Their western march was hefted and they filled in the eastern regions of the Midwest.In 1837, a blacksmith in the town of Grand Detour, Illinois, invented a new tool. His name was John Deere and the tool was a plow made of steel. It was sharp enough to cut through matted grasses and smooth enough to cast off the mud. It was a simple too, the “sod buster” that opened the great prairies to agricultural development.Sauk Country, Wisconsin is the part of that prairie where I have a home. It is named after the Sauk Indians. In i673 Father Marquette was the first European to lay his eyes upon their land. He found a village laid out in regular patterns on a plain beside the Wisconsin River. He called the place Prairie du Sac) The village was surrounded by fields that had provided maize, beans and squash for the Sauk people for generations reaching back into the unrecorded time.When the European settlers arrived at the Sauk prairie in 1837, the government forced the native Sank people west of the Mississippi River. The settlers came with John Deere’s new invention and used the tool to open the area to a new kind of agriculture. They ignored the traditional ways of the Sank Indians and used their sod-busting tool for planting wheat. Initially, the soil was generous and the nurturing thrived. However each year the soil lost more of its nurturing power. It was only thirty years after the Europeans arrived with their new technology that the land was depleted, Wheat farming became uneconomic and tens of thousands of farmers left Wisconsin seeking new land with sod to bust.It took the Europeans and their new technology just one generation to make their homeland into a desert. The Sank Indians who knew how to sustain themselves on the Sauk prairie land were banished to another kind of desert called a reservation. And they even forgot about the techniques and tools that had sustained them on the prairie for generations unrecorded. And that is how it was that three deserts were created — Wisconsin, the reservation and the memories of a people. A century later, the land of the Sauks is now populated by the children of a second wave of European tanners who learned to replenish the soil through the regenerative powers of dairying, ground cover crops and animal manures. These third and fourth generation farmers and townspeople do not realise, however, that a new settler is coming soon with an invention as powerful as John Deere’s plow.The new technology is called ‘bereavement counselling’. It is a tool forged at the great state university, an innovative technique to meet the needs of those experiencing the death of a loved one, tool that an “process” the grief of the people who now live on the Prairie of the Sauk. As one can imagine the final days of the village of the Sauk Indians before the arrival of the settlers with John Deere’s plow, one can also imagine these final days before the arrival of the first bereavement counsellor at Prairie du Sac) In these final days, the farmers arid the townspeople mourn at the death of a mother, brother, son or friend. The bereaved is joined by neighbours and kin. They meet grief together in lamentation, prayer and song. They call upon the words of the clergy and surround themselves in community.It is in these ways that they grieve and then go on with life. Through their mourning they are assured of the bonds between them and renewed in the knowledge that this death is a part of the Prairie of the Sauk. Their grief is common property, an anguish from which the community draws strength and gives the bereaved the courage to move ahead.It is into this prairie community that the bereavement counsellor arrives with the new grief technology. The counsellor calls the invention a service and assures the prairie folk of its effectiveness and superiority by invoking the name of the great university while displaying a diploma and certificate. At first, we can imagine that the local people will be puzzled by the bereavement counsellor’s claim, However, the counsellor will tell a few of them that the new technique is merely o assist the bereaved’s community at the time of death. To some other prairie folk who are isolated or forgotten, the counsellor will approach the Country Board and advocate the right to treatment for these unfortunate souls. This right will be guaranteed by the Board’s decision to reimburse those too poor tc pay for counselling services. There will be others, schooled to believe in the innovative new tools certified by universities and medical centres, who will seek out the bereavement counsellor by force of habit. And one of these people will tell a bereaved neighbour who is unschooled that unless his grief is processed by a counsellor, he will probably have major psychological problems in later life. Several people will begin to use the bereavement counsellor because, since the Country Board now taxes them to insure access to the technology, they will feel that to fail to be counselled is to waste their money, and to be denied a benefit, or even a right.Finally, one day, the aged father of a Sauk woman will die. And the next door neighbour will not drop by because he doesn’t want to interrupt the bereavement counsellor. The woman’s kin will stay home because they will have learned that only the bereavement counsellor knows how to process grief the proper way. The local clergy will seek technical assistance from the bereavement counsellor to learn the connect form of service to deal with guilt and grief. And the grieving daughter will know that it is the bereavement counsellor who really cares for her because only the bereavement counsellor comes when death visits this family on the Prairie of the Sauk.It will be only one generation between the bereavement counsellor arrives and the community of mourners disappears. The counsellor’s new tool will cut through the social fabric, throwing aside kinship, care, neighbourly obligations and communality ways cc coming together and going on. Like John Deere’s plow, the tools of bereavement counselling will create a desert we a community once flourished, And finally, even the bereavement counsellor will see the impossibility of restoring hope in clients once they are genuinely alone with nothing but a service for consolation. In the inevitable failure of the service, the bereavement counsellor will find the deserts even in herself.Which one of the following best describes the approach of the author?
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MCQ-> Since World War II, the nation-state has been regarded with approval by every political system and every ideology. In the name of modernisation in the West, of socialism in the Eastern bloc, and of development in the Third World, it was expected to guarantee the happiness of individuals as citizens and of peoples as societies. However, the state today appears to have broken down in many parts of the world. It has failed to guarantee either security or social justice, and has been unable to prevent either international wars or civil wars. Disturbed by the claims of communities within it, the nation-state tries to repress their demands and to proclaim itself as the only guarantor of security of all. In the name of national unity, territorial integrity, equality of all its citizens and non-partisan secularism, the state can use its powerful resources to reject the demands of the communities; it may even go so far as genocide to ensure that order prevails.As one observes the awakening of communities in different parts of the world, one cannot ignore the context in which identity issues arise. It is no longer a context of sealed frontiers and isolated regions but is one of integrated global systems. In a reaction to this trend towards globalisation, individuals and communities everywhere are voicing their desire to exist, to use their power of creation and to play an active part in national and international life.There are two ways in which the current upsurge in demands for the recognition of identities can be looked at. On the positive side, the efforts by certain population groups to assert their identity can be regarded as "liberation movements", challenging oppression and injustice. What these groups are doing - proclaiming that they are different, rediscovering the roots of their culture or strengthening group solidarity - may accordingly be seen as legitimate attempts to escape from their state of subjugation and enjoy a certain measure of dignity. On the downside, however, militant action for recognition tends to make such groups more deeply entrenched in their attitude and to make their cultural compartments even more watertight. The assertion of identity then starts turning into self-absorption and isolation, and is liable to slide into intolerance of others and towards ideas of "ethnic cleansing", xenophobia and violence.Whereas continuous variations among peoples prevent drawing of clear dividing lines between the groups, those militating for recognition of their group's identity arbitrarily choose a limited number of criteria such as religion, language, skin colour, and place of origin so that their members recognise themselves primarily in terms of the labels attached to the group whose existence is being asserted. This distinction between the group in question and other groups is established by simplifying the feature selected. Simplification also works by transforming groups into essences, abstractions endowed with the capacity to remain unchanged through time. In some cases, people actually act as though the group has remained unchanged and talk, for example, about the history of nations and communities as if these entities survived for centuries without changing, with the same ways of acting and thinking, the same desires, anxieties, and aspirations. Paradoxically, precisely because identity represents a simplifying fiction, creating uniform groups out of disparate people, that identity performs a cognitive function. It enables us to put names to ourselves and others, form some idea of who we are and who others are, and ascertain the place we occupy along with the others in the world and society. The current upsurge to assert the identity of groups can thus be partly explained by the cognitive function performed by identity. However, that said, people would not go along as they do, often in large numbers, with the propositions put to them, in spite of the sacrifices they entail, if there was not a very strong feeling of need for identity, a need to take stock of things and know "who we are", "where we come from", and "where we are going".Identity is thus a necessity in a constantly changing world, but it can also be a potent source of' violence and disruption. How can these two contradictory aspects of identity be reconciled? First, we must bear the arbitrary nature of identity categories in mind, not with a view to eliminating all forms of identification—which would be unrealistic since identity is a cognitive necessity—but simply to remind ourselves that each of us has several identities at the same time. Second, since tears of nostalgia are being shed over the past, we recognise that culture is constantly being recreated by cobbling together fresh and original elements and counter-cultures. There are in our own country a large number of syncretic cults wherein modern elements are blended with traditional values or people of different communities venerate saints or divinities of particular faiths. Such cults and movements are characterised by a continual inflow and outflow of members which prevent them from taking on a self-perpetuating existence of their own and hold out hope for the future, indeed, perhaps for the only possible future. Finally, the nation-state must respond to the identity urges of its constituent communities and to their legitimate quest for security and social justice. It must do so by inventing what the French philosopher and sociologist, Raymond Aron, called "peace through law". That would guarantee justice both to the state as a whole and its parts, and respect the claims of both reason and emotions. The problem is one of reconciling nationalist demands with the exercise of democracy.According to the author, happiness of individuals was expected to be guaranteed in the name of:
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MCQ-> India is rushing headlong toward economic success and modernisation, counting on high- tech industries such as information technology and biotechnology to propel the nation toprosperity. India’s recent announcement that it would no longer produce unlicensed inexpensive generic pharmaceuticals bowed to the realities of the World TradeOrganisation while at the same time challenging the domestic drug industry to compete with the multinational firms. Unfortunately, its weak higher education sector constitutes the Achilles’ Heel of this strategy. Its systematic disinvestment in higher education inrecent years has yielded neither world-class research nor very many highly trained scholars, scientists, or managers to sustain high-tech development. India’s main competitors especially China but also Singapore, Taiwan, and South Korea — are investing in large and differentiated higher education systems. They are providingaccess to large number of students at the bottom of the academic system while at the same time building some research-based universities that are able to compete with theworld’s best institutions. The recent London Times Higher Education Supplement ranking of the world’s top 200 universities included three in China, three in Hong Kong,three in South Korea, one in Taiwan, and one in India (an Indian Institute of Technology at number 41.— the specific campus was not specified). These countries are positioningthemselves for leadership in the knowledge-based economies of the coming era. There was a time when countries could achieve economic success with cheap labour andlow-tech manufacturing. Low wages still help, but contemporary large-scale development requires a sophisticated and at least partly knowledge-based economy.India has chosen that path, but will find a major stumbling block in its university system. India has significant advantages in the 21st century knowledge race. It has a large high ereducation sector — the third largest in the world in student numbers, after China andthe United States. It uses English as a primary language of higher education and research. It has a long academic tradition. Academic freedom is respected. There are asmall number of high quality institutions, departments, and centres that can form the basis of quality sector in higher education. The fact that the States, rather than the Central Government, exercise major responsibility for higher education creates a rather cumbersome structure, but the system allows for a variety of policies and approaches. Yet the weaknesses far outweigh the strengths. India educates approximately 10 per cent of its young people in higher education compared with more than half in the major industrialised countries and 15 per cent in China. Almost all of the world’s academic systems resemble a pyramid, with a small high quality tier at the top and a massive sector at the bottom. India has a tiny top tier. None of its universities occupies a solid position at the top. A few of the best universities have some excellent departments and centres, and there is a small number of outstanding undergraduate colleges. The University Grants Commission’s recent major support of five universities to build on their recognised strength is a step toward recognising a differentiated academic system and fostering excellence. At present, the world-class institutions are mainly limited to the Indian Institutes of Technology (IITs), the Indian Institutes of Management (IIMs) and perhaps a few others such as the All India Institute of Medical Sciences and the Tata Institute of Fundamental Research. These institutions, combined, enroll well under 1 percent of the student population. India’s colleges and universities, with just a few exceptions, have become large, under-funded, ungovernable institutions. At many of them, politics has intruded into campus life, influencing academic appointments and decisions across levels. Under-investment in libraries, information technology, laboratories, and classrooms makes it very difficult to provide top-quality instruction or engage in cutting-edge research.The rise in the number of part-time teachers and the freeze on new full-time appointments in many places have affected morale in the academic profession. The lackof accountability means that teaching and research performance is seldom measured. The system provides few incentives to perform. Bureaucratic inertia hampers change.Student unrest and occasional faculty agitation disrupt operations. Nevertheless, with a semblance of normality, faculty administrators are. able to provide teaching, coordinate examinations, and award degrees. Even the small top tier of higher education faces serious problems. Many IIT graduates,well trained in technology, have chosen not to contribute their skills to the burgeoning technology sector in India. Perhaps half leave the country immediately upon graduation to pursue advanced study abroad — and most do not return. A stunning 86 per cent of students in science and technology fields from India who obtain degrees in the United States do not return home immediately following their study. Another significant group, of about 30 per cent, decides to earn MBAs in India because local salaries are higher.—and are lost to science and technology.A corps of dedicated and able teachers work at the IlTs and IIMs, but the lure of jobs abroad and in the private sector make it increasingly difficult to lure the best and brightest to the academic profession.Few in India are thinking creatively about higher education. There is no field of higher education research. Those in government as well as academic leaders seem content to do the “same old thing.” Academic institutions and systems have become large and complex. They need good data, careful analysis, and creative ideas. In China, more than two-dozen higher education research centers, and several government agencies are involved in higher education policy.India has survived with an increasingly mediocre higher education system for decades.Now as India strives to compete in a globalized economy in areas that require highly trained professionals, the quality of higher education becomes increasingly important.India cannot build internationally recognized research-oriented universities overnight,but the country has the key elements in place to begin and sustain the process. India will need to create a dozen or more universities that can compete internationally to fully participate in the new world economy. Without these universities, India is destined to remain a scientific backwater.Which of the following ‘statement(s) is/are correct in the context of the given passage ? I. India has the third largest higher education sector in the world in student numbers. II. India is moving rapidly toward economic success and modernisation through high tech industries such as information technology and bitechonology to make the nation to prosperity. III. India’s systematic disinvestment in higher education in recent years has yielded world class research and many world class trained scholars, scientists to sustain high-tech development.....
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