For two positive integers a and b define the function h(a,b):as the greatest common factor (G.C.F) of a, b. Let A be a set of n positive integers. G(A), the GCF of the elements of set A is computed by repeatedly using the function h. The minimum n ?->(Show Answer!)

1. For two positive integers a and b define the function h(a,b):as the greatest common factor (G.C.F) of a, b. Let A be a set of n positive integers. G(A), the GCF of the elements of set A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is:

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By: anil on 05 May 2019 02.31 am

Let p and q be any two elements of the set A.
For the computation of the GCF of elements of the set A, we can replace both p and q by just the GCF(p,q) and the result is unchanged. So, for every application of the function h, we are reducing the number of elements of the set A by 1. (In this case two numbers p and q are replaced by one number GCF(p,q)).
Expanding this concept further, the minimum number of times the function h should be called is n-1

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MCQ->For two positive integers a and b define the function h(a,b):as the greatest common factor (G.C.F) of a, b. Let A be a set of n positive integers. G(A), the GCF of the elements of set A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is:....

MCQ-> In a modern computer, electronic and magnetic storage technologies play complementary roles. Electronic memory chips are fast but volatile (their contents are lost when the computer is unplugged). Magnetic tapes and hard disks are slower, but have the advantage that they are non-volatile, so that they can be used to store software and documents even when the power is off.In laboratories around the world, however, researchers are hoping to achieve the best of both worlds. They are trying to build magnetic memory chips that could be used in place of today’s electronics. These magnetic memories would be nonvolatile; but they would also he faster, would consume less power, and would be able to stand up to hazardous environments more easily. 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). Since 1997, the exploitation of GMR has made cheap multi-gigabyte hard disks commonplace. The magnetic orientations of the magnetised spots on the surface of a spinning disk are detected by measuring the changes they induce in the resistance of a tiny sensor. This technique is so sensitive that it means the spots can be made smaller and packed closer together than was previously possible, thus increasing the capacity and reducing the size and cost of a disk drive. Dr. Prinz and his colleagues are now exploiting the same phenomenon on the surface of memory chips, rather spinning disks. In a conventional memory chip, each binary digit (bit) of data is represented using a capacitor-reservoir of electrical charge that is either empty or fill -to represent a zero or a one. In the NRL’s magnetic design, by contrast, each bit is stored in a magnetic element in the form of a vertical pillar of magnetisable material. A matrix of wires passing above and below the elements allows each to be magnetised, either clockwise or anti-clockwise, to represent zero or one. Another set of wires allows current to pass through any particular element. By measuring an element’s resistance you can determine its magnetic orientation, and hence whether it is storing a zero or a one. Since the elements retain their magnetic orientation even when the power is off, the result is non-volatile memory. Unlike the elements of an electronic memory, a magnetic memory’s elements are not easily disrupted by radiation. And compared with electronic memories, whose capacitors need constant topping up, magnetic memories are simpler and consume less power. The NRL researchers plan to commercialise their device through a company called Non-V olatile Electronics, which recently began work on the necessary processing and fabrication techniques. But it will be some years before the first chips roll off the production line.Most attention in the field in focused on an alternative approach based on magnetic tunnel-junctions (MTJs), which are being investigated by researchers at chipmakers such as IBM, Motorola, Siemens and Hewlett-Packard. IBM’s research team, led by Stuart Parkin, has already created a 500-element working prototype that operates at 20 times the speed of conventional memory chips and consumes 1% of the power. Each element consists of a sandwich of two layers of magnetisable material separated by a barrier of aluminium oxide just four or five atoms thick. The polarisation of lower magnetisable layer is fixed in one direction, but that of the upper layer can be set (again, by passing a current through a matrix of control wires) either to the left or to the right, to store a zero or a one. The polarisations of the two layers are then either the same or opposite directions.Although the aluminum-oxide barrier is an electrical insulator, it is so thin that electrons are able to jump across it via a quantum-mechanical effect called tunnelling. It turns out that such tunnelling is easier when the two magnetic layers are polarised in the same direction than when they are polarised in opposite directions. So, by measuring the current that flows through the sandwich, it is possible to determine the alignment of the topmost layer, and hence whether it is storing a zero or a one.To build a full-scale memory chip based on MTJs is, however, no easy matter. According to Paulo Freitas, an expert on chip manufacturing at the Technical University of Lisbon, magnetic memory elements will have to become far smaller and more reliable than current prototypes if they are to compete with electronic memory. At the same time, they will have to be sensitive enough to respond when the appropriate wires in the control matrix are switched on, but not so sensitive that they respond when a neighbouring elements is changed. Despite these difficulties, the general consensus is that MTJs are the more promising ideas. Dr. Parkin says his group evaluated the GMR approach and decided not to pursue it, despite the fact that IBM pioneered GMR in hard disks. Dr. Prinz, however, contends that his plan will eventually offer higher storage densities and lower production costs.Not content with shaking up the multi-billion-dollar market for computer memory, some researchers have even more ambitious plans for magnetic computing. In a paper published last month in Science, Russell Cowburn and Mark Well and of Cambridge University outlined research that could form the basis of a magnetic microprocessor — a chip capable of manipulating (rather than merely storing) information magnetically. In place of conducting wires, a magnetic processor would have rows of magnetic dots, each of which could be polarised in one of two directions. Individual bits of information would travel down the rows as magnetic pulses, changing the orientation of the dots as they went. Dr. Cowbum and Dr. Welland have demonstrated how a logic gate (the basic element of a microprocessor) could work in such a scheme. In their experiment, they fed a signal in at one end of the chain of dots and used a second signal to control whether it propagated along the chain.It is, admittedly, a long way from a single logic gate to a full microprocessor, but this was true also when the transistor was first invented. Dr. Cowburn, who is now searching for backers to help commercialise the technology, says he believes it will be at least ten years before the first magnetic microprocessor is constructed. But other researchers in the field agree that such a chip, is the next logical step. Dr. Prinz says that once magnetic memory is sorted out “the target is to go after the logic circuits.” Whether all-magnetic computers will ever be able to compete with other contenders that are jostling to knock electronics off its perch — such as optical, biological and quantum computing — remains to be seen. Dr. Cowburn suggests that the future lies with hybrid machines that use different technologies. But computing with magnetism evidently has an attraction all its own.In developing magnetic memory chips to replace the electronic ones, two alternative research paths are being pursued. These are approaches based on:
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MCQ-> The broad scientific understanding today is that our planet is experiencing a warming trend over and above natural and normal variations that is almost certainly due to human activities associated with large-scale manufacturing. The process began in the late 1700s with the Industrial Revolution, when manual labor, horsepower, and water power began to be replaced by or enhanced by machines. This revolution, over time, shifted Britain, Europe, and eventually North America from largely agricultural and trading societies to manufacturing ones, relying on machinery and engines rather than tools and animals.The Industrial Revolution was at heart a revolution in the use of energy and power. Its beginning is usually dated to the advent of the steam engine, which was based on the conversion of chemical energy in wood or coal to thermal energy and then to mechanical work primarily the powering of industrial machinery and steam locomotives. Coal eventually supplanted wood because, pound for pound, coal contains twice as much energy as wood (measured in BTUs, or British thermal units, per pound) and because its use helped to save what was left of the world's temperate forests. Coal was used to produce heat that went directly into industrial processes, including metallurgy, and to warm buildings, as well as to power steam engines. When crude oil came along in the mid- 1800s, still a couple of decades before electricity, it was burned, in the form of kerosene, in lamps to make light replacing whale oil. It was also used to provide heat for buildings and in manufacturing processes, and as a fuel for engines used in industry and propulsion.In short, one can say that the main forms in which humans need and use energy are for light, heat, mechanical work and motive power, and electricity which can be used to provide any of the other three, as well as to do things that none of those three can do, such as electronic communications and information processing. Since the Industrial Revolution, all these energy functions have been powered primarily, but not exclusively, by fossil fuels that emit carbon dioxide (CO2), To put it another way, the Industrial Revolution gave a whole new prominence to what Rochelle Lefkowitz, president of Pro-Media Communications and an energy buff, calls "fuels from hell" - coal, oil, and natural gas. All these fuels from hell come from underground, are exhaustible, and emit CO2 and other pollutants when they are burned for transportation, heating, and industrial use. These fuels are in contrast to what Lefkowitz calls "fuels from heaven" -wind, hydroelectric, tidal, biomass, and solar power. These all come from above ground, are endlessly renewable, and produce no harmful emissions.Meanwhile, industrialization promoted urbanization, and urbanization eventually gave birth to suburbanization. This trend, which was repeated across America, nurtured the development of the American car culture, the building of a national highway system, and a mushrooming of suburbs around American cities, which rewove the fabric of American life. Many other developed and developing countries followed the American model, with all its upsides and downsides. The result is that today we have suburbs and ribbons of highways that run in, out, and around not only America s major cities, but China's, India's, and South America's as well. And as these urban areas attract more people, the sprawl extends in every direction.All the coal, oil, and natural gas inputs for this new economic model seemed relatively cheap, relatively inexhaustible, and relatively harmless-or at least relatively easy to clean up afterward. So there wasn't much to stop the juggernaut of more people and more development and more concrete and more buildings and more cars and more coal, oil, and gas needed to build and power them. Summing it all up, Andy Karsner, the Department of Energy's assistant secretary for energy efficiency and renewable energy, once said to me: "We built a really inefficient environment with the greatest efficiency ever known to man."Beginning in the second half of the twentieth century, a scientific understanding began to emerge that an excessive accumulation of largely invisible pollutants-called greenhouse gases - was affecting the climate. The buildup of these greenhouse gases had been under way since the start of the Industrial Revolution in a place we could not see and in a form we could not touch or smell. These greenhouse gases, primarily carbon dioxide emitted from human industrial, residential, and transportation sources, were not piling up along roadsides or in rivers, in cans or empty bottles, but, rather, above our heads, in the earth's atmosphere. If the earth's atmosphere was like a blanket that helped to regulate the planet's temperature, the CO2 buildup was having the effect of thickening that blanket and making the globe warmer.Those bags of CO2 from our cars float up and stay in the atmosphere, along with bags of CO2 from power plants burning coal, oil, and gas, and bags of CO2 released from the burning and clearing of forests, which releases all the carbon stored in trees, plants, and soil. In fact, many people don't realize that deforestation in places like Indonesia and Brazil is responsible for more CO2 than all the world's cars, trucks, planes, ships, and trains combined - that is, about 20 percent of all global emissions. And when we're not tossing bags of carbon dioxide into the atmosphere, we're throwing up other greenhouse gases, like methane (CH4) released from rice farming, petroleum drilling, coal mining, animal defecation, solid waste landfill sites, and yes, even from cattle belching. Cattle belching? That's right-the striking thing about greenhouse gases is the diversity of sources that emit them. A herd of cattle belching can be worse than a highway full of Hummers. Livestock gas is very high in methane, which, like CO2, is colorless and odorless. And like CO2, methane is one of those greenhouse gases that, once released into the atmosphere, also absorb heat radiating from the earth's surface. "Molecule for molecule, methane's heat-trapping power in the atmosphere is twenty-one times stronger than carbon dioxide, the most abundant greenhouse gas.." reported Science World (January 21, 2002). “With 1.3 billion cows belching almost constantly around the world (100 million in the United States alone), it's no surprise that methane released by livestock is one of the chief global sources of the gas, according to the U.S. Environmental Protection Agency ... 'It's part of their normal digestion process,' says Tom Wirth of the EPA. 'When they chew their cud, they regurgitate [spit up] some food to rechew it, and all this gas comes out.' The average cow expels 600 liters of methane a day, climate researchers report." What is the precise scientific relationship between these expanded greenhouse gas emissions and global warming? Experts at the Pew Center on Climate Change offer a handy summary in their report "Climate Change 101. " Global average temperatures, notes the Pew study, "have experienced natural shifts throughout human history. For example; the climate of the Northern Hemisphere varied from a relatively warm period between the eleventh and fifteenth centuries to a period of cooler temperatures between the seventeenth century and the middle of the nineteenth century. However, scientists studying the rapid rise in global temperatures during the late twentieth century say that natural variability cannot account for what is happening now." The new factor is the human factor-our vastly increased emissions of carbon dioxide and other greenhouse gases from the burning of fossil fuels such as coal and oil as well as from deforestation, large-scale cattle-grazing, agriculture, and industrialization.“Scientists refer to what has been happening in the earth’s atmosphere over the past century as the ‘enhanced greenhouse effect’”, notes the Pew study. By pumping man- made greenhouse gases into the atmosphere, humans are altering the process by which naturally occurring greenhouse gases, because of their unique molecular structure, trap the sun’s heat near the earth’s surface before that heat radiates back into space."The greenhouse effect keeps the earth warm and habitable; without it, the earth's surface would be about 60 degrees Fahrenheit colder on average. Since the average temperature of the earth is about 45 degrees Fahrenheit, the natural greenhouse effect is clearly a good thing. But the enhanced greenhouse effect means even more of the sun's heat is trapped, causing global temperatures to rise. Among the many scientific studies providing clear evidence that an enhanced greenhouse effect is under way was a 2005 report from NASA's Goddard Institute for Space Studies. Using satellites, data from buoys, and computer models to study the earth's oceans, scientists concluded that more energy is being absorbed from the sun than is emitted back to space, throwing the earth's energy out of balance and warming the globe."Which of the following statements is correct? (I) Greenhouse gases are responsible for global warming. They should be eliminated to save the planet (II) CO2 is the most dangerous of the greenhouse gases. Reduction in the release of CO2 would surely bring down the temperature (III) The greenhouse effect could be traced back to the industrial revolution. But the current development and the patterns of life have enhanced their emissions (IV) Deforestation has been one of the biggest factors contributing to the emission of greenhouse gases Choose the correct option:....

MCQ-> Directions : Choose the word/group of words which is most opposite in meaning to the word / group of words printed in bold as used in the passage.When times are hard, doomsayers are aplenty. The problem is that if you listen to them too carefully, you tend to overlook the most obvious signs of change. 2011 was a bad year. Can 2012 be any worse? Doomsday forecasts are the easiest to make these days. So let's try a contrarian's forecast instead. Let's start with the global economy. We have seen a steady flow of good news from the US. The employment situation seems to be improving rapidly and consumer sentiment, reflected in retail expenditures on discretionary items like electronics and clothes, has picked up. If these trends sustain, the US might post better growth numbers for 2012 than the 1.5 - 1.8 percent being forecast currently. Japan is likely to pull out of a recession in 2012 as post-earthquake reconstruction efforts gather momentum and the fiscal stimulus announced in 2011 begin to pay off. The consensus estimate for growth in Japan is a respectable 2 percent for 2012. The "hard landing' scenario for China remains and will remain a myth. Growth might decelerate further from the 9 percent that is expected to clock in 2011 but is unlikely to drop below 8 - 8.5 percent in 2012. Europe is certainly in a spot of trouble. It is perhaps already in recession and for 2012 it is likely to post mildly negative growth. The risk of implosion has dwindled over the last few months- peripheral economies like Greece, Italy and Spain have new governments in place and have made progress towards genuine economic reform. Even with some these positive factors in place, we have to accept the fact that global growth in 2012 will be tepid. But there is a flipside to this. Softer growth means lower demand for commodities, and this is likely to drive a correction in commodity prices. Lower commodity inflation will enable emerging market central banks to reverse their monetary stance. China, for instance, has already reversed its stance and have pared its reserve ratio twice. The RBI also seems poised for a reversal in its rate cycle as headline inflation seems well one its way to its target of 7 percent for March 2012. That said, oil might be an exception to the general trend in commodities. Rising geopolitical tensions, particularly the continuing face-off between Iran and the US, might lead to a spurt in prices. It might make sense for our oil companies to hedge this risk instead of buying oil in the spot market. As inflation fears abate, and emerging market central banks begin to cut rates, two things could happen. Lower commodity inflation would mean lower interest rates and better credit availability. This could set the floor to growth and slowly reverse the business cycle within these economies. Second, as the fear of untamed, runaway inflation in these economies abates, the global investor's comfort levels with their markets will increase. Which of the emerging markets will outperform and who will leave behind? In an environment in which global growth is likely to be weak, economies like India that have a powerful domestic consumption dynamic should lead; those dependent on exports should, prima facie, fall behind. Specifically for India, a fall in the exchange rate could not have come at a better time. It will help Indian exporters gain market share even if global trade remains depressed. More importantly, it could lead to massive import substitution that favours domestic producers.Let’s now focus on India and start with a caveat. It is important not to confuse a short run cyclical dip with a permanent derating of its long-term structural potential. The arithmetic is simple. Our growth rate can be in the range of 7-10 percent depending on policy action. Ten percent if we get everything right, 7 percent if we get it all wrong. Which policies and reforms are critical to taking us to our 10 percent potential? In judging this, let’s again be careful. Let’s not go by the laundry list of reforms that FIIs like to wave: The increase in foreign equity limits in foreign shareholding, greater voting rights for institutional shareholders in banks, FDI in retail, etc. These can have an impact only at the margin. We need not bend over backwards to appease the FIIs through these reforms they will invest in our markets when momentum picks up and will be the first to exit when the momentum flags, reforms or not. The reforms that we need are the ones that can actually raise our sustainable longterm growth rate. These have to come in areas like better targeting of subsidies, making projects in infrastructure viable so that they draw capital, raising the productivity of agriculture, improving healthcare and education, bringing the parallel economy under the tax net, implementing fundamental reforms in taxation like GST and the direct tax code and finally easing the MYRIAD
rules and regulations that make doing business in India such a nightmare. A number of these things do not require new legislation and can be done through executive order.MYRIAD
....

MCQ-> Directions: 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. When times are hard, doomsayers are aplenty. The problem is that if you listen to them too carefully, you tend to overlook the most obvious signs of change. 2011 was a bad year. Can 2012 be any worse? Doomsday forecasts are the easiest to make these days. So let's try a contrarian's forecast instead. Let's start with the global economy. We have seen a steady flow of good news from the US. The employment situation seems to be improving rapidly and consumer sentiment, reflected in retail expenditures on discretionary items like electronics and clothes, has picked up. If these trends sustain, the US might post better growth numbers for 2012 than the 1.5 - 1.8 percent being forecast currently. Japan is likely to pull out of a recession in 2012 as post-earthquake reconstruction efforts gather momentum and the fiscal stimulus announced in 2011 begin to pay off. The consensus estimate for growth in Japan is a respectable 2 percent for 2012. The "hard landing' scenario for China remains and will remain a myth. Growth might decelerate further from the 9 percent that is expected to clock in 2011 but is unlikely to drop below 8 - 8.5 percent in 2012. Europe is certainly in a spot of trouble. It is perhaps already in recession and for 2012 it is likely to post mildly negative growth. The risk of implosion has dwindled over the last few months- peripheral economies like Greece, Italy and Spain have new governments in place and have made progress towards genuine economic reform. Even with some these positive factors in place, we have to accept the fact that global growth in 2012 will be tepid. But there is a flipside to this. Softer growth means lower demand for commodities, and this is likely to drive a correction in commodity prices. Lower commodity inflation will enable emerging market central banks to reverse their monetary stance. China, for instance, has already reversed its stance and have pared its reserve ratio twice. The RBI also seems poised for a reversal in its rate cycle as headline inflation seems well one its way to its target of 7 percent for March 2012. That said, oil might be an exception to the general trend in commodities. Rising geopolitical tensions, particularly the continuing face-off between Iran and the US, might lead to a spurt in prices. It might make sense for our oil companies to hedge this risk instead of buying oil in the spot market. As inflation fears abate, and emerging market central banks begin to cut rates, two things could happen. Lower commodity inflation would mean lower interest rates and better credit availability. This could set the floor to growth and slowly reverse the business cycle within these economies. Second, as the fear of untamed, runaway inflation in these economies abates, the global investor's comfort levels with their markets will increase. Which of the emerging markets will outperform and who will leave behind? In an environment in which global growth is likely to be weak, economies like India that have a powerful domestic consumption dynamic should lead; those dependent on exports should, prima facie, fall behind. Specifically for India, a fall in the exchange rate could not have come at a better time. It will help Indian exporters gain market share even if global trade remains depressed. More importantly, it could lead to massive import substitution that favours domestic producers.Let’s now focus on India and start with a caveat. It is important not to confuse a short run cyclical dip with a permanent derating of its long-term structural potential. The arithmetic is simple. Our growth rate can be in the range of 7-10 percent depending on policy action. Ten percent if we get everything right, 7 percent if we get it all wrong. Which policies and reforms are critical to taking us to our 10 percent potential? In judging this, let’s again be careful. Let’s not go by the laundry list of reforms that FIIs like to wave: The increase in foreign equity limits in foreign shareholding, greater voting rights for institutional shareholders in banks, FDI in retail, etc. These can have an impact only at the margin. We need not bend over backwards to appease the FIIs through these reforms they will invest in our markets when momentum picks up and will be the first to exit when the momentum flags, reforms or not. The reforms that we need are the ones that can actually raise our sustainable longterm growth rate. These have to come in areas like better targeting of subsidies, making projects in infrastructure viable so that they draw capital, raising the productivity of agriculture, improving healthcare and education, bringing the parallel economy under the tax net, implementing fundamental reforms in taxation like GST and the direct tax code and finally easing the myriad rules and regulations that make doing business in India such a nightmare. A number of these things do not require new legislation and can be done through executive order.Which of the following is not true according to the passage?
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