In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other? ?->(Show Answer!)

1. In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?

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By: anil on 05 May 2019 02.37 am

Total number of houses = 10 If first house is robbed, then II is not and if II house is robbed, then III is not and so on. Thus 2 adjacent houses can never be chosen So, number of ways in which three houses can be robbed such that no two of them are next to each other. = $$C^{10 - 2}_3 = C^8_3$$ = $$frac{8 imes 7 imes 6}{1 imes 2 imes 3}$$ = $$56$$

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MCQ-> I want to stress this personal helplessness we are all stricken with in the face of a system that has passed beyond our knowledge and control. To bring it nearer home, I propose that we switch off from the big things like empires and their wars to more familiar little things. Take pins for example! I do not know why it is that I so seldom use a pin when my wife cannot get on without boxes of them at hand; but it is so; and I will therefore take pins as being for some reason specially important to women.There was a time when pinmakers would buy the material; shape it; make the head and the point; ornament it; and take it to the market, and sell it and the making required skill in several operations. They not only knew how the thing was done from beginning to end, but could do it all by themselves. But they could not afford to sell you a paper of pins for the farthing. Pins cost so much that a woman's dress allowance was calling pin money.By the end of the 18th century Adam Smith boasted that it took 18 men to make a pin, each man doing a little bit of the job and passing the pin on to the next, and none of them being able to make a whole pin or to buy the materials or to sell it when it was made. The most you could say for them was that at least they had some idea of how it was made, though they could not make it. Now as this meant that they were clearly less capable and knowledgeable men than the old pin-makers, you may ask why Adam Smith boasted of it as a triumph of civilisation when its effect had so clearly a degrading effect. The reason was that by setting each man to do just one little bit of the work and nothing but that, over and over again, he became very quick at it. The men, it is said, could turn out nearly 5000 pins a day each; and thus pins became plentiful and cheap. The country was supposed to be richer because it had more pins, though it had turned capable men into mere machines doing their work without intelligence and being fed by the spare food of the capitalist just as an engine is fed with coals and oil. That was why the poet Goldsmith, who was a farsighted economist as well as a poet, complained that 'wealth accumulates, and men decay'.Nowadays Adam Smith's 18 men are as extinct as the diplodocus. The 18 flesh-and-blood men have been replaced by machines of steel which spout out pins by the hundred million. Even sticking them into pink papers is done by machinery. The result is that with the exception of a few people who design the machines, nobody knows how to make a pin or how a pin is made: that is to say, the modern worker in pin manufacture need not be one-tenth so intelligent, skilful and accomplished as the old pinmaker; and the only compensation we have for this deterioration is that pins are so cheap that a single pin has no expressible value at all. Even with a big profit stuck on to the cost-price you can buy dozens for a farthing; and pins are so recklessly thrown away and wasted that verses have to be written to persuade children (without success) that it is a sin to steal, if even it’s a pin.Many serious thinkers, like John Ruskin and William Morris, have been greatly troubled by this, just as Goldsmith was, and have asked whether we really believe that it is an advance in wealth to lose our skill and degrade our workers for the sake of being able to waste pins by the ton. We shall see later on, when we come to consider the Distribution of Leisure, that the cure for this is not to go back to the old free for higher work than pin-making or the like. But in the meantime the fact remains that the workers are now not able to make anything themselves even in little bits. They are ignorant and helpless, and cannot lift their finger to begin their day's work until it has all been arranged for them by their employer's who themselves do not understand the machines they buy, and simply pay other people to set them going by carrying out the machine maker's directions.The same is true for clothes. Earlier the whole work of making clothes, from the shearing of the sheep to the turning out of the finished and washed garment ready to put on, had to be done in the country by the men and women of the household, especially the women; so that to this day an unmarried woman is called a spinster. Nowadays nothing is left of all this but the sheep shearing; and even that, like the milking of cows, is being done by machinery, as the sewing is. Give a woman a sheep today and ask her to produce a woollen dress for you; and not only will she be quite unable to do it, but you are likely to find that she is not even aware of any connection between sheep and clothes. When she gets her clothes, which she does by buying them at the shop, she knows that there is a difference between wool and cotton and silk, between flannel and merino, perhaps even between stockinet and other wefts; but as to how they are made, or what they are made of, or how they came to be in the shop ready for her to buy, she knows hardly anything. And the shop assistant from whom she buys is no wiser. The people engaged in the making of them know even less; for many of them are too poor to have much choice of materials when they buy their own clothes.Thus the capitalist system has produced an almost universal ignorance of how things are made and done, whilst at the same time it has caused them to be made and done on a gigantic scale. We have to buy books and encyclopaedias to find out what it is we are doing all day; and as the books are written by people who are not doing it, and who get their information from other books, what they tell us is twenty to fifty years out of date knowledge and almost impractical today. And of course most of us are too tired of our work when we come home to want to read about it; what we need is cinema to take our minds off it and feel our imagination.It is a funny place, this word of capitalism, with its astonishing spread of education and enlightenment. There stand the thousands of property owners and the millions of wage workers, none of them able to make anything, none of them knowing what to do until somebody tells them, none of them having the least notion of how it is made that they find people paying them money, and things in the shops to buy with it. And when they travel they are surprised to find that savages and Esquimaux and villagers who have to make everything for themselves are more intelligent and resourceful! The wonder would be if they were anything else. We should die of idiocy through disuse of our mental faculties if we did not fill our heads with romantic nonsense out of illustrated newspapers and novels and plays and films. Such stuff keeps us alive, but it falsifies everything for us so absurdly that it leaves us more or less dangerous lunatics in the real world.Excuse my going on like this; but as I am a writer of books and plays myself, I know the folly and peril of it better than you do. And when I see that this moment of our utmost ignorance and helplessness, delusion and folly, has been stumbled on by the blind forces of capitalism as the moment for giving votes to everybody, so that the few wise women are hopelessly overruled by the thousands whose political minds, as far as they can be said to have any political minds at all, have been formed in the cinema, I realise that I had better stop writing plays for a while to discuss political and social realities in this book with those who are intelligent enough to listen to me.A suitable title to the passage would be
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MCQ-> The second plan to have to examine is that of giving to each person what she deserves. Many people, especially those who are comfortably off, think this is what happens at present: that the industrious and sober and thrifty are never in want, and that poverty is due to idleness, improvidence, drinking, betting, dishonesty, and bad character generally. They can point to the fact that a labour whose character is bad finds it more difficult to get employment than one whose character is good; that a farmer or country gentleman who gambles and bets heavily, and mortgages his land to live wastefully and extravagantly, is soon reduced to poverty; and that a man of business who is lazy and does not attend to it becomes bankrupt. But this proves nothing that you cannot eat your cake and have it too; it does not prove that your share of the cake was a fair one. It shows that certain vices make us rich. People who are hard, grasping, selfish, cruel, and always ready to take advantage of their neighbours, become very rich if they are clever enough not to overreach themselves. On the other hand, people who are generous, public spirited, friendly, and not always thinking of the main chance, stay poor when they are born poor unless they have extraordinary talents. Also as things are today, some are born poor and others are born with silver spoons in their mouths: that is to say, they are divided into rich and poor before they are old enough to have any character at all. The notion that our present system distributes wealth according to merit, even roughly, may be dismissed at once as ridiculous. 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MCQ-> Read passage carefully. Answer the questions by selecting the most appropriate option (with reference to the passage). PASSAGE 4While majoring in computer science isn't a requirement to participate in the Second Machine Age, what skills do liberal arts graduates specifically possess to contribute to this brave new world? Another major oversight in the debate has been the failure to appreciate that a good liberal arts education teaches many skills that are not only valuable to the general world of business, but are in fact vital to innovating the next wave of breakthrough tech-driven products and services. Many defenses of the value of a liberal arts education have been launched, of course, with the emphasis being on the acquisition of fundamental thinking and communication skills, such as critical thinking, logical argumentation, and good communication skills. One aspect of liberal arts education that has been strangely neglected in the discussion is the fact that the humanities and social sciences are devoted to the study of human nature and the nature of our communities and larger societies. Students who pursue degrees in the liberal arts disciplines tend to be particularly motivated to investigate what makes us human: how we behave and why we behave as we do. They're driven to explore how our families and our public institutions-such as our schools and legal systems-operate, and could operate better, and how governments and economies work, or as is so often the case, are plagued by dysfunction. These students learn a great deal from their particular courses of study and apply that knowledge to today's issues, the leading problems to be tackled, and various approaches for analyzing and addressing those problems. 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Such chips would have obvious applications in storage cards for digital cameras and music- players; they would enable handheld and laptop computers to boot up more quickly and to operate for longer; they would allow desktop computers to run faster; they would doubtless have military and space-faring advantages too. But although the theory behind them looks solid, there are tricky practical problems and need to be overcome.Two different approaches, based on different magnetic phenomena, are being pursued. The first, being investigated by Gary Prinz and his colleagues at the Naval Research Laboratory (NRL) in Washington, D.c), exploits the fact that the electrical resistance of some materials changes in the presence of magnetic field— a phenomenon known as magneto- resistance. For some multi-layered materials this effect is particularly powerful and is, accordingly, called “giant” magneto-resistance (GMR). 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