Directions for the next 2 questions:For a real number x, let$$f(x) = 1/(1+x),$$ if $$x$$ is non-negative $$f(x) = 1+x,$$ if $$x$$ is negative$$f^n(x) = f(f^{n-1}(x)), n = 2, 3.....$$What is the value of the product, $$f(2) f^2(2)f^3(2) f^4(2)f^5( ?->(Show Answer!)

1. Directions for the next 2 questions:For a real number x, let$$f(x) = 1/(1+x),$$ if $$x$$ is non-negative $$f(x) = 1+x,$$ if $$x$$ is negative$$f^n(x) = f(f^{n-1}(x)), n = 2, 3.....$$What is the value of the product, $$f(2) f^2(2)f^3(2) f^4(2)f^5(2)$$?

Write Comment

Comments

By: anil on 05 May 2019 02.30 am

f(2) = 1/3 $$f^2(2)$$ = f(1/3) = 3/4 $$f^3(2)$$ = f(3/4) = 4/7 $$f^4(2)$$ = f(4/7) = 7/11 $$f^5(2)$$ = f(7/11) = 11/18 So, product = 1/18

Tags

Show Similar Question And Answers

QA->What is the negative logarithmic value of hydrogen on called?....

QA->Which product is the export leading from India in the terms of value?....

QA->“Intensity of pressure at a point in a fluid at rest is same in all directions”, this law is :....

QA->Powers to issue directions for interception or monitoring or decryption of any information through any computer resource....

QA->Power to issue directions for blocking for public access of any information through any computer resource....

MCQ-> DI
rectI
ons: I
n the followI
ng passage there are blanks, each of whI
ch has been numbered. These numbers are prI
nted below the passage and agaI
nst each, fI
ve words/ phrases are suggested, one of whI
ch fI
ts the blank approprI
ately. FI
nd out the approprI
ate word/ phrase I
n each case.There I
s a consI
derable amount of research about the factors that make a company I
nnovate. So I
s I
t possI
ble to create an envI
ronment (I
) to I
nnovatI
on? ThI
s I
s a partI
cularly pertI
nent (I
I
) for I
ndI
a today. MassI
ve problems I
n health, educatI
on etc (I
I
I
) be solved usI
ng a conventI
onal Approach but (I
V) creatI
ve and I
nnovatI
ve solutI
ons that can ensure radI
cal change and (V). There are several factors I
n I
ndI
a's (VI
). Few countrI
es have the rI
ch dI
versI
ty that I
ndI
a or I
ts large, young populatI
on (VI
I
). WhI
le these (VI
I
I
) I
nnovatI
on polI
cy I
nterventI
ons certaI
n addI
tI
onal steps are also requI
red. These I
nclude (I
X) I
nvestment I
n research and development by (X) the government and the prI
vate sector, easy transfer of technology from the academI
c world etc. To fulfI
ll I
ts promI
se of beI
ng prosperous and to be at the forefront, I
ndI
a must be I
nnovatI
ve.I
....

MCQ-> Read the passage carefully and answer the questions given at the end of each passage:Turning the business involved more than segmenting and pulling out of retail. It also meant maximizing every strength we had in order to boost our profit margins. In re-examining the direct model, we realized that inventory management was not just core strength; it could be an incredible opportunity for us, and one that had not yet been discovered by any of our competitors. In Version 1.0 the direct model, we eliminated the reseller, thereby eliminating the mark-up and the cost of maintaining a store. In Version 1.1, we went one step further to reduce inventory inefficiencies. Traditionally, a long chain of partners was involved in getting a product to the customer. Let’s say you have a factory building a PC we’ll call model #4000. The system is then sent to the distributor, which sends it to the warehouse, which sends it to the dealer, who eventually pushes it on to the consumer by advertising, “I’ve got model #4000. Come and buy it.” If the consumer says, “But I want model #8000,” the dealer replies, “Sorry, I only have model #4000.” Meanwhile, the factory keeps building model #4000s and pushing the inventory into the channel. The result is a glut of model #4000s that nobody wants. Inevitably, someone ends up with too much inventory, and you see big price corrections. The retailer can’t sell it at the suggested retail price, so the manufacturer loses money on price protection (a practice common in our industry of compensating dealers for reductions in suggested selling price). Companies with long, multi-step distribution systems will often fill their distribution channels with products in an attempt to clear out older targets. This dangerous and inefficient practice is called “channel stuffing”. Worst of all, the customer ends up paying for it by purchasing systems that are already out of date Because we were building directly to fill our customers’ orders, we didn’t have finished goods inventory devaluing on a daily basis. Because we aligned our suppliers to deliver components as we used them, we were able to minimize raw material inventory. Reductions in component costs could be passed on to our customers quickly, which made them happier and improved our competitive advantage. It also allowed us to deliver the latest technology to our customers faster than our competitors. The direct model turns conventional manufacturing inside out. Conventional manufacturing, because your plant can’t keep going. But if you don’t know what you need to build because of dramatic changes in demand, you run the risk of ending up with terrific amounts of excess and obsolete inventory. That is not the goal. The concept behind the direct model has nothing to do with stockpiling and everything to do with information. The quality of your information is inversely proportional to the amount of assets required, in this case excess inventory. With less information about customer needs, you need massive amounts of inventory. So, if you have great information – that is, you know exactly what people want and how much - you need that much less inventory. Less inventory, of course, corresponds to less inventory depreciation. In the computer industry, component prices are always falling as suppliers introduce faster chips, bigger disk drives and modems with ever-greater bandwidth. Let’s say that Dell has six days of inventory. Compare that to an indirect competitor who has twenty-five days of inventory with another thirty in their distribution channel. That’s a difference of forty-nine days, and in forty-nine days, the cost of materials will decline about 6 percent. Then there’s the threat of getting stuck with obsolete inventory if you’re caught in a transition to a next- generation product, as we were with those memory chip in 1989. As the product approaches the end of its life, the manufacturer has to worry about whether it has too much in the channel and whether a competitor will dump products, destroying profit margins for everyone. This is a perpetual problem in the computer industry, but with the direct model, we have virtually eliminated it. We know when our customers are ready to move on technologically, and we can get out of the market before its most precarious time. We don’t have to subsidize our losses by charging higher prices for other products. And ultimately, our customer wins. Optimal inventory management really starts with the design process. You want to design the product so that the entire product supply chain, as well as the manufacturing process, is oriented not just for speed but for what we call velocity. Speed means being fast in the first place. Velocity means squeezing time out of every step in the process. Inventory velocity has become a passion for us. To achieve maximum velocity, you have to design your products in a way that covers the largest part of the market with the fewest number of parts. For example, you don’t need nine different disk drives when you can serve 98 percent of the market with only four. We also learned to take into account the variability of the lost cost and high cost components. Systems were reconfigured to allow for a greater variety of low-cost parts and a limited variety of expensive parts. The goal was to decrease the number of components to manage, which increased the velocity, which decreased the risk of inventory depreciation, which increased the overall health of our business system. We were also able to reduce inventory well below the levels anyone thought possible by constantly challenging and surprising ourselves with the result. We had our internal skeptics when we first started pushing for ever-lower levels of inventory. I remember the head of our procurement group telling me that this was like “flying low to the ground 300 knots.” He was worried that we wouldn’t see the trees.In 1993, we had $2.9 billion in sales and $220 million in inventory. Four years later, we posted $12.3 billion in sales and had inventory of $33 million. We’re now down to six days of inventory and we’re starting to measure it in hours instead of days. Once you reduce your inventory while maintaining your growth rate, a significant amount of risk comes from the transition from one generation of product to the next. Without traditional stockpiles of inventory, it is critical to precisely time the discontinuance of the older product line with the ramp-up in customer demand for the newer one. Since we were introducing new products all the time, it became imperative to avoid the huge drag effect from mistakes made during transitions. E&O; – short for “excess and obsolete” - became taboo at Dell. We would debate about whether our E&O; was 30 or 50 cent per PC. Since anything less than $20 per PC is not bad, when you’re down in the cents range, you’re approaching stellar performance.Find out the TRUE statement:
....

MCQ-> The English alphabet is divided into five groups. Each group starts with the vowel and the consonants immediately following that vowel and the consonants immediately following that vowel are included in that group. Thus, the letters A, B, C, D will be in the first group, the letters E, F, G, H will be in the second group and so on. The value of the first group is fixed as 10, the second group as 20 and so on. The value of the last group is fixed as 50. In a group, the value of each letter will be the value of that group. To calculate the value of a word, you should give the same value of each of the letters as the value of the group to which a particular letter belongs and then add all the letters of the word: If all the letters in the word belong to one group only, then the value of that word will be equal to the product of the number of letters in the word and the value of the group to which the letters belong. However, if the letters of the words belong to different groups, then first write the value of all the letters. The value of the word would be equal to the sum of the value of the first letter and double the sum of the values of the remaining letters.For Example : The value of word ‘CAB’ will be equal to 10 + 10 + 10 = 30, because all the three letters (the first letter and the remaining two) belong to the first group and so the value of each letter is 10. The value of letter BUT = $$10 + 2 \times 40 + 2 \times 50 = 190$$ because the value of first letter B is 10, the value of T = 2 $$\times$$ 40 (T belongs to the fourth group) and the value of U = 2 $$\times$$ 50 (U belongs to the fifth group). Now calculate the value of each word given in questions 161 to 165 :AGE
....

MCQ-> 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. Once upon a time there was a King of Benaras who was very rich. He had many servants and a beautiful palace with wonderful gardens; he had chariots and a stable full of horses. But his most prized possession was a magnificent elephant called Mahaghiri. She was as tall as two men, and her skin was of the colour of thunder clouds. She had large flapping ears and small, bright eyes and she was very clever. Mahaghiri lived in her own special elephant house and had her own keeper, Rajinder. The King would often visit Mahaghiri to take her some special tit-bit to eat and check that Rajinder was looking after her properly. But Rajinder needed no reminding, for he also loved the elephant dearly, and trusted her completely. Every morning, he would take her down to the river for her bath. Then he would bring her freshly cut grass, leaves and the finest fruits he could find in the market for her breakfast. During the day, he would talk to her and, in the evening, he would play his flute to send her to sleep. One morning, Rajinder arrived as usual with fruit for Mahaghiri’s breakfast. Suddenly, before he knew what was happening, she picked him up with her trunk and threw him out of the stall, breaking his arm. She began to stamp on the ground and trumpet so loudly that it took several strong men all morning to bind her with ropes and chains, When the king heard about what had happened, he was very upset and sent for the doctor to help Rajinder. Then he called for his chief minister. “You must go and see Mahaghiri at once,” he said. “She used to be so kind and gentle, but this morning she threw her keeper out of her stall. I can’t understand it. She must be ill or in pain. Spare no expense in finding a cure.” So the chief minister went to see Mahaghiri. who was still bound firmly with ropes. First he looked at her eyes – they were as clear and bright as usual. Then he felt behind her ears – her temperature was normal. Next he listened to her heart that was fine too – and checked all over for cuts or sores. He could find nothing wrong with her. “Strange,” he thought. “I can find no explanation for her bad behaviour.”But then his eye was caught by something gleaming in the straw. It was a sharp, curved knife, like the ones used by robbers. Could there be a connection? That night, when everyone else had gone to bed, the chief minister returned to the elephant house. There, in the stall next to Mahaghiri’s, sat a band of robbers. “Tonight we’ll burgle the palace,” said the chief. “First, we’ll make a hole in the wall, then we’ll steal the treasure. “But what about the guards?” someone asked. “Don’t tell me you’re still afraid to kill! When will you learn to be a real robber?” From the shadows, the minister could see the elephant, her ears pinned back, listening to every hateful and violent word.”Just as I suspected,” thought the minister. Then he slipped out, bolted the door on the outside so the robbers could not escape, and went immediately to the king.”Your majesty,” he said, “I think I have found the cause of your elephant’s bad behaviour.” As soon as the king heard what the minister had to say, he sent for his guards and had the robbers arrested. “But what about the elephant? How can she be cured?’ he asked. “Well, your majesty, if Mahaghiri became dangerous through being.in the company of those wicked robbers, perhaps she could be cured by being in the company of good people.” “What a brilliant idea!” exclaimed the king. “Let us invite the friendliest, happiest and kindest people in the city to meet in the stall next to the elephant.” “Mahaghiri, the king’s most prized elephant, has been in bad company and has become violent and dangerous,” the minister told his friends. “Will you help her to become her old self again?””Of course,” they replied. “What do you want us to do?” “Just meet in the elephant house every day for the next week. Let her hear how kindly and thoughtfully you speak to each other, and how helpful you are.” So the minister’s friends met in the elephant house as planned. They talked together and enjoyed each other’s company. Sometimes they brought cakes and sweets to share; sometimes their children came and played happily in the straw. All the while, Mahaghiri watched and listened. Gradually, she became calmer. “I think it’s working,” said the minister. “Soon we’ll be able to remove the ropes.” Everyone felt a bit nervous when the day came for Mahaghiri to be untied. The king ordered everyone to wait outside as, very carefully, brave Rajinder began to undo the ropes around her ears and trunk. Next he removed the ropes holding her head. Finally, he loosened the thick chains holding her great feet. Everyone held their breath. What if she was still wild?Mahaghiri looked round shuffling her feet to stretch them. Then she slowly curled her trunk around her keeper’s waist and lifted him high into the air before placing him gently on her back. A great cheer went up. The king was delighted. “Let’s have a picnic to celebrate,” he announced. “Mahaghiri can come too.” What a great afternoon they all had! Mahaghiri bathed in the lake and gave the children rides. It seemed as though she had now become kinder, gentler and even more trustworthy than ever. But Rajinder never forgot what had happened and was always careful to set Mahaghiri a good example by being kind and friendly himself.As per the context of passage, what was the most prized possession of the king of Benaras ?
....

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
....