1. In Bode plot, A.R. vs. w is plotted on a/an __________ graph paper.





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MCQ-> Read the following information, graph and table and answer the questions that follow. Ellen Inc. is a Mumbai based company which sells five products branded as A, B, C, D and E in India. Anita looks after entire sales of North India working from regional office in Delhi. She was preparing for annual review meeting scheduled next day in Mumbai. She was attempting to analyse sales in North India for the seven year period from 2009 to 2015. She first calculated average sales in rupees of all the five brands and constructed a table exhibiting the difference between average sales of each pair of brands as shown in the following table:                     Average Sales of Product A minus Average Sales of Product B After taking a print out of the above table, she attempted to look at the trend of sales and plotted a graph in MS Excel. Later she took a print out of the graph and left for a meeting. While on her way she figured out that due to some printer cartridge problem sales of Product A in 2013, Product C in 2010, and Product D in 2012 were not visible in the graph as reproduced below. Anita had to make some quick calculations to arrive at the information outlined in the following question. What are the sales of Product A in 2013, Product C in 2010 and Product D in 2012?
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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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