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MCQ-> Mathematicians are assigned a number called Erdos number (named after the famous mathematician, Paul Erdos). Only Paul Erdos himself has an Erdos number of zero. Any mathematician who has written a research paper with Erdos has an Erdos number of 1.For other mathematicians, the calculation of his/her Erdos number is illustrated below:Suppose that a mathematician X has co-authored papers with several other mathematicians. 'From among them, mathematician Y has the smallest Erdos number. Let the Erdos number of Y be y. Then X has an Erdos number of y+1. Hence any mathematician with no co-authorship chain connected to Erdos has an Erdos number of infinity. :In a seven day long mini-conference organized in memory of Paul Erdos, a close group of eight mathematicians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the conference, A was the only participant who had an infinite Erdos number. Nobody had an Erdos number less than that of F.On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdos number of the group of eight mathematicians to 3. The Erdos numbers of B, D, E, G and H remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdos number of the group of eight to as low as 3.• At the end of the third day, five members of this group had identical Erdos numbers while the other three had Erdos numbers distinct from each other.• On the fifth day, E co-authored a paper with F which reduced the group's average Erdos number by 0.5. The Erdos numbers of the remaining six were unchanged with the writing of this paper.• No other paper was written during the conference.The person having the largest Erdos number at the end of the conference must have had Erdos number (at that time):
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MCQ-> Answer questions on the basis of information given in the following case. Bright Engineering College (BEC) has listed 20 elective courses for the next term and students have to choose any 7 of them. Simran, a student of BEC, notices that there are three categories of electives: Job - oriented (J), Quantitative - oriented (Q) and Grade - oriented (G). Among these 20 electives, some electives are both Job and Grade - oriented but are not Quantitative - oriented (JG type). QJ type electives are both job and Quantitative - oriented but are not Grade - oriented and QG type electives are both Quantitative and Grade - oriented but are not Job - oriented. Simran also notes that the total number of QJ type electives is 2 less than QG type electives. Similarly, the total number of QG type electives is 2 less than JG type and there is only 1 common elective (JQG) across three categories. Furthermore, the number of only Quantitative - oriented electives is same as only Job - oriented electives, but less than the number of only Grade - oriented electives. Each elective has at least one registration and there is at least one elective in each category, or combinations of categories.On her way back Simran met her friend Raj and shared the above information. Raj is preparing for XAT and is only interested in Grade - oriented (G) electives. He wanted to know the number of G - type electives being offered. Simran replied, “You have all the information. Calculate the number of G - type electives yourself. It would help your XAT preparation”. Raj calculates correctly and says that there can be _______ possible answers. Which of the following options would b est fit the blank above?
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MCQ-> Read the following passage and answer the questions. Passage: A new paper published by Rochman and her colleagues in February, in the journal Ecology, sifts through past research on marine debris to assess the true extent of the environmental threat. Plenty of studies have sounded alarm bells about the state of marine debris: Rochman and her colleagues set out to determine how many of those perceived risks are real Often. Rochman says, scientists will wrap up a paper by speculating about the broader impacts of what they've found. Maybe their study has shown that certain seabirds eat plastic bags, for example, and the paper goes on to warn that whole bird populations are at risk of dying out. "But the truth was that nobody had yet tested those perceived threats." Rochman says. "There wasn't a lot of information." Rochman and her colleagues examined more than a hundred papers on the impacts of marine debris that were published through 2013. Within each paper. they asked what threats scientists had studied-366 perceived threats in all and what they'd actually found. In 83 percent of cases, the perceived dangers of ocean trash were proven true. In most of the remaining cases. the working group found the studies too shoddy to draw conclusions from—they lacked a control group, for example. or used faulty statistics. Strikingly. Rochman says, only one well-designed study failed to find the effect it was looking for, an investigation of mussels ingesting microscopic plastic bits. The plastic moved from the mussels' stomachs to their bloodstreams. scientists found. and stayed there for weeks—but didn't seem to stress out the shellfish. A lot of ocean debris is "microplastic," or pieces smaller than five millimetres. These may be the beads from a facial scrub. fibres shed by synthetic clothing in the wash. or eroded remnants of larger debris. Compared to the number of studies investigating large-scale debris. Roclunan's group found little research on the effects of these tiny bits. There are also, she adds, a lot of open questions about the ways that ocean debris can lead to sea-creature death. Many studies have looked at how plastic affects an individual animal or that animal's tissues or cells, rather than whole populations. And in the lab, scientists often use higher concentrations of plastic than what's really in the ocean. None of that tells us how many birds or fish or sea turtles could die form plastic pollution or how deaths in one species could affect that animal's predators, or the rest of the ecosystem. "We need to be asking more ecologically relevant questions." Rothman says. Usually, scientists don't know how disasters like oil spills or nuclear meltdowns will affect the environment until after they've happened. she says. "We don't ask the right questions early enough." But if ecologists can understand how the slow-moving disaster of ocean garbage is affecting ecosystems. they might be able to prevent things from getting worse.Which ONE of the following conclusions based on the examination of the hundred-odd papers on marine debris and its ecological impact by Rachman and her colleagues is NOT CORRECT?
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