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On a straight road XY, 100 m long, five heavy stones are placed 2 m apart beginning at the end X. A worker, starting at X, has to transport all the stones to Y, by carrying only one stone at a time. The minimum distance he has to travel is
The longest side of a triangle is 40 cm. Another side of the triangle is 20 cm. The area of the triangle is 320 cm2. Find the length of the third side.
The central park of the city is 40 metres wide. The mayor wants to construct two roads of equal width in the park such that the roads intersect each other at right angles and the diagonals of the park are also the diagonals of the small rectangle formed at the intersection of the two roads. Further, the mayor wants that the area of the two roads to be equal to the remaining area of the park. What should be the width of the roads?
no. of non negative integral solutions for x+2y+3z=8
Circle C, has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X axis. P and Q are points on curves given by the equations y−ax and y−2a respectively, where a<1. The value of a is:
Find the smallest four digit number which leaves a remainder of 4 and 6 when divided by 7 and 9 respectively?
225 students in a class take an exam and no set of four students got the same marks. Suppose all the students got marks from 0 to 100 (integers only), what is the maximum number of students who got unique marks?
Directions for questions 1 to 4: The passage given below is followed by a set of four questions. Choose the most appropriate answer to each question. Today's campaigners against action on climate change are in many cases backed by the same lobbies, individuals, and organisations that sided with the tobacco industry to discredit the science linking smoking and lung cancer. Later, they fought the scientific evidence that sulphur oxides from coal-fired power plants were causing "acid rain." Then, when it was discovered that certain chemicals called chlorofluorocarbons (CFCs) were causing the depletion of ozone in the atmosphere, the same groups launched a nasty campaign to discredit that science, too. Later still, the group defended the tobacco giants against charges that second-hand smoke causes cancer and other diseases. And then, starting mainly in the 1980s, this same group took on the battle against climate change. What is amazing is that, although these attacks on science have been wrong for 30 years, they still sow doubts about established facts. The truth is that there is big money backing the climate-change deniers, whether it is companies that don't want to pay the extra costs of regulation, or free-market ideologues opposed to any government controls. The latest round of attacks involves two episodes. The first was the hacking of a climate-change research centre in England. The emails that were stolen suggested a lack of forthrightness in the presentation of some climate data. Whatever the details of this specific case, the studies in question represent a tiny fraction of the overwhelming scientific evidence that points to the reality and urgency of man-made climate change. The second issue was a blatant error concerning glaciers that appeared in a major IPCC report. Here it should be understood that the IPCC issues thousands of pages of text. There are, no doubt, errors in those pages. But errors in the midst of a vast and complex report by the IPCC point to the inevitability of human shortcomings, not to any fundamental flaws in climate science. When the emails and the IPCC error were brought to light, editorial writers at The Wall Street Journal launched a vicious campaign describing climate science as a hoax and a conspiracy. They claimed that scientists were fabricating evidence in order to obtain government research grants — a ludicrous accusation, I thought at the time, given that the scientists under attack have devoted their lives to finding the truth, and have certainly not become rich relative to their peers in finance and business. But then I recalled that this line of attack — charging a scientific conspiracy to drum up "business" for science — was almost identical to that used by The Wall Street Journal and others in the past, when they fought controls on tobacco, acid rain, ozone depletion, second-hand smoke, and other dangerous pollutants. In other words, their arguments were systematic and contrived, not at all original to the circumstances. We are witnessing a predictable process by ideologues and right-wing think tanks and publications to discredit the scientific process. Their arguments have been repeatedly disproved for 30 years — time after time — but their aggressive methods of public propaganda succeed in causing delay and confusion.
Q.1 Which of the following best reflects the authorÂ’s primary intent in the passage?
a To show that the same group of people has consistently tried to confuse the public and discredit the scientists whose insights are helping to save the world from environmental harm.
b To show that the same group of people has consistently tried to confuse the public by drawing support from people with big money and people in big publications.
c To show that the effort by the same group of people to confuse the public and discredit the scientists is not unjustified and deserves some attention.
d To show that the process adopted by the same group of people to confuse the public and discredit the scientists whose insights are helping to save the world from environmental harm, has become predictable and needs an overhaul.
If the integers m and n are chosen at random out of integers 1 to 100, with replacement, then the probability that a number of the form (7m + 7n) is divisible by 5 equals.....
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