Let A be a 3 x 3 matrix with characteristic polynomial p(A) = - 1)(J - 2). Which of thefollowing statement is wrong: ?->(Show Answer!)

1. Let A be a 3 x 3 matrix with characteristic polynomial p(A) = - 1)(J - 2). Which of thefollowing statement is wrong:

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MCQ->Let A be a 3 x 3 matrix with characteristic polynomial p(A) = - 1)(J - 2). Which of thefollowing statement is wrong:....

MCQ-> Analyse the following transcript (from the movie Matrix) and provide an appropriate answer for the questions that follow: Neo: Morpheus, what's happened to me? What is this place? Morpheus: More important than what is when. Neo: When? Morpheus: You believe it's the year 1999 when in fact it's closer to 2199. I can't tell you exactly what year it is because we honestly don't know.There's nothing I can say that will explain it for you, Neo. Come with me. See for yourself. This is my ship, the Nebuchadnezzar. It's a hovercraft. This is the main deck. This is the core where we broadcast our pirate signal and hack into the Matrix. Most of my crew you already know. (Next Scene: Construct) Morpheus: This is the construct. It's our loading programme. We can load anything from clothing, to equipment, weapons, training simulations, anything we need. Neo: Right now we're inside a computer programme? Morpheus: Is it really so hard to believe? Your clothes are different. The plugs in your arms and head are gone. Your hair is changed. Your appearance now is what we call residual self image. It is the mental projection of your digital self. Neo: This...this isn't real? Morpheus: What is real? How do you define real? If you're talking about what you can feel, what you can smell, what you can taste and see, then real is simply electrical signals interpreted by your brain. ...This is the world that you know. The world as it was at the end of the twentieth century. It exists now only as part of a neural-interactive simulation that we call the Matrix. You've been living in a dream world, Neo. .. .This is the world as it exists today. Welcome to the Desert of the Real. We have only bits and pieces of information but what we know for certain is that at some point in the early twenty-first century all of mankind was united in celebration. We marvelled at our own magnificence as we gave birth to AI. Neo: AI? You mean artificial intelligence? Morpheus: A singular consciousness that spawned an entire race of machines. We don't know who struck first, us or them. But we know that it was us that scorched the sky. At the time they were dependent on solar power and it was believed that they would be unable to survive without an energy source as abundant as the sun. Throughout human history, we have been dependent on machines to survive. Fate it seems is not without a sense of irony. The human body generates more bio-electricity than a 120-volt battery and over 25,000 BTU's of body heat. Combined with a form of fusion the machines have found all the energy they would ever need. There are fields, endless fields, where human beings are no longer born, we are grown. For the longest time I wouldn't believe it, and then I saw the fields with my own eyes. Watch them liquefy the dead so they could be fed intravenously to the living. And standing there, facing the pure horrifying precision, I came to realize the obviousness of the truth. What is the Matrix? Control. The Matrix is a computer generated dream world built to keep us under control in order to change a human being into this. Neo: No. I don't believe it. It's not possible. Morpheus: I didn't say it would be easy, Neo. I just said it would be the truth. Neo: Stop. Let me out. Let me out. I want out.The innate factor responsible for the status of human beings in later part of 22nd century is
....

MCQ->Let A be a 3 x 3 matrix with characteristic polynomial p(X) = X(X - 1)(A - 2). Which of the following statement is wrong:....

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?
....

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
....