Past Paper Set 01 - PDF

SET 01 8. How many colors are necessary for the squares 1. Stations A and B are 120 miles apart on a single- of a chessboard in order to assure that a bishop track railroad. At the same time that a train leaves cannot move...

SET 01 8. How many colors are necessary for the squares 1. Stations A and B are 120 miles apart on a single- of a chessboard in order to assure that a bishop track railroad. At the same time that a train leaves cannot move from one square to another of the A for B at 25 mph, a train leaves B for A at 15 mph. same color? Just as the first train leaves A, a South American a. 4 c. 8 botfly flies from the front of the engine straight b. 6 d. 10 toward the other train at 100 mph. On meeting the second train it immediately turns back and flies 9. A neat computer programmer wears a clean shirt straight for the first train. It continues to fly back every day. If he drops off his laundry and picks up and forth with undiminished speed until it is the previous week's load every Monday night, crushed in the eventual collision. How far had the how many shirts must he own to keep him going? fly flown? a. 14 c. 16 a. 200 miles c. 400 miles b. 13 d. 15 b. 300 miles d. 500 miles 10. Very few people are aware of the growth pattern 2. A man walks one mile south, one mile west, then of Jack's beanstalk. On the first day it increased one mile north, ending where he began. From its height by 1/2, on the second day by 1/3, on the how many points on the surface of the earth can third day by 1/4, and so on. How long did it take such a journey be made? (There are more than to achieve its maximum height (100 times its 1). original height)? a. Infinite c. 1000 a. 198 c. 199 b. 100 d. 10 b. 189 d. 188 3. Maynard's Grandfather Clock is driven by two 11. Six boys on a hockey team pick a captain by weights, one for the striking mechanism which forming a circle and counting out until only one strikes the hours only, the other for the time remains. Joe is given the option of deciding what mechanism. When he hears the clock strike his number to count by. If he is second in the original bedtime, he immediately winds the clock and counting order what number should he choose? retires. After winding, the weights are exactly a. 9 c. 10 opposite each other. The weights are again b. 12 d. 11 opposite every six hours thereafter. What is Maynard's bedtime? 12. A jig-saw puzzle contains 100 pieces. A "move" a. 8PM or 2PM c. 9PM or 3AM consists of connecting two clusters (including b. 10PM or 4AM d. 11PM or 1AM "clusters" of just one piece.) What is the minimum number of moves required to complete the 4. Assuming the sun rises at 6:00 a.m., sets at 6:00 puzzle? p.m., and moves at a uniform rate, how can a lost a. 66 c. 88 boy scout determine south by means of a watch b. 77 d. 99 on a cloudless day? a. Align the hour hand with the sun's azimuth, 13. A novice librarian shelved a twelve-volume set of and north will be midway between the hour encyclopedias in the following order from left to hand and 10. right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and b. Align the hour hand with the sun's azimuth, 2. Using her system, where will the annual- and south will be midway between the hour supplement, Volume 13, go? hand and 10. a. Between volumes 9 and 1 c. Align the hour hand with the sun's b. Between volumes 10 and 3 azimuth, and south will be midway c. Between volumes 12 and 2 between the hour hand and 12. d. Between volumes 11 and 5 d. Align the hour hand with the sun's azimuth, and north will be midway between the hour 14. A lighthouse shows successive one- second hand and 12. flashes of red, white, green, green, white, red. A second lighthouse does the same only with two- 5. In a fast Major League baseball game, pitcher Hi second flashes. The six-second sequence of the N. Outside managed to get by with the minimum first lighthouse is repeated steadily, as is the number of pitches possible. He played the entire twelve-second sequence of the other lighthouse. game, which was not called prior to completion. What fraction of the time do the two lights show How many pitches did he make? the same color if the given sequences start at the a. 22 c. 28 same time? b. 25 d. 31 a. 1/6 c. 1/3 b. 1/4 d. 1/5 6. What is the least number of links that must be disengaged from a 23- link chain so that any 15. Four boys, Alan, Brian, Charles and Donald, and number of links from 1 to 23 can be obtained by four girls, Eve, Fay, Gwen and Helen are each in taking one or more of the pieces? love with one of the others, and, sad to say, in no a. 3 c. 5 case is their love requited. Alan loves the girl who b. 4 d. 2 loves the man who loves Eve. Fay is loved by the man who is loved by the girl loved by Brian. 7. State University won their first football game of Charles loves the girl who loves Donald. If Brian the season 17 to 0. Though they scored no is not loved by Gwen, and the boy who is loved safeties, they managed to score more points each by Helen does not love Gwen, who loves Alan? quarter than they had scored in the previous a. Helen c. Gwen quarter. What were State's quarter scores? b. Eve d. Fay a. 0, 3, 6, 8 c. 0, 6, 3, 8 b. 0, 3, 8, 6 d. 6, 0, 3, 8 16. Six grocers in a town each sell a different brand of tea in four-ounce packets at 25 cents per packet. One of the grocers gives short weight,  each packet of his brand weighing only 33/4 23. On a certain day, our parking lot contains 999 ounces. If I can use a balance for only one cars, no two of which have the same 3-digit weighing, what is the minimum amount I must license number. After 5:00 PM, what is the spend to be sure of finding the grocer who gives probability that the license numbers of the first 4 short weight? cars to leave the parking lot are in increasing a. $7.3 c. $7.7 order of magnitude? b. $3.3 d. $3.7 a. 1/6 c. 1/18 b. 1/24 d. 1/12 17. Between Kroflite and Beeline are five other towns. The seven towns are an integral number of miles 24. Three marksmen simultaneously shoot at and hit from each other along a straight road. The towns a rapidly spinning spherical target. What is the are so spaced that if one knows the number of probability that the three points of impact are on miles a person has traveled between any two the same hemisphere? towns, he can determine the particular towns a. 0 c. 0.50 uniquely. What is the minimum distance between b. 0.25 d. 1.0 Kroflite and Beeline to make this possible? a. 30 miles c. 25 miles 25. Assume that a single depth charge has a b. 20 miles d. 15 miles probability of 1/2 of sinking a submarine, 1/4 of damage and 1/4 of missing. Assume also that two 18. A man has red, gray and black flagstones for damaging explosions sink the sub. What is the making a walk. He wants no two consecutive probability that 4 depth charges will sink the sub? stones to be the same color, no consecutive pair a. 215/256 c. 251/265 of stones to have the same two colors in the same b. 152/265 d. 251/256 order, no repetition of three consecutive colors, etc. He starts out laying first a red stone, then a 26. Three dart players threw simultaneously at a tic- gray, and continues until he finishes laying the tac-toe board, each hitting a different square. seventh stone. He then finds himself stymied and What is the probability that the three hits unable to use any stone for the eighth without constituted a win at tic-tac-toe? repetition of some color pattern. What were the a. 2/11 c. 1/21 colors of the first seven stones? b. 1/12 d. 2/21 a. R G R B R G R b. R G B R G B B 27. There are three families, each with two sons and c. G R R B R G R two daughters. In how many ways can all these d. B R G B R B G young people be married? a. 60 c. 70 19. A game proceeds as follows: Smith starts with a b. 80 d. 90 10-link chain and removes any single link, presenting Jones either with a 9-link chain or two 28. How many three-digit telephone area codes are chains having a total of 9 links. Jones removes possible given that: (a) the first digit must not be any one link from each of the chains. Smith zero or one; (b) the second digit must be zero or removes any one link from each of the remaining one; (c) the third digit must not be zero; (d) the chains and so on, until the winner removes the third digit may be one only if the second digit is last link or links. What should Smith do first? zero. a. Smith should leave two chains of 1 and 8 a. 163 c. 152 links b. 136 d. 125 b. Smith should leave two chains of 7 and 2 links 29. There are four volumes of an encyclopedia on a c. Smith should leave two chains of 4 and 5 shelf, each volume containing 300 pages, (that is, links numbered 1 to 600), but these have been placed d. Smith should leave two chains of 6 and 3 on the shelf in random order. A bookworm starts links at the first page of Vol. 1 and eats his way through to the last page of Vol. 4. What is the expected 20. In Bristol 90% of the citizens drink tea; 80% drink number of pages (excluding covers) he has eaten coffee; 70% drink whiskey; and 60% drink gin. No through? one drinks all four beverages. What percent of a. 450 c. 400 Bristol's citizens drink liquor? b. 500 d. 550 a. 100% c. 95% b. 90% d. 85% 30. The local weather forecaster says "no rain" and 21. You and a friend spot a loose $20 bill his record is 2/3 accuracy of prediction. But the simultaneously and agree to an auction in which Federal Meteorological Service predicts rain and you write down your bids and compare them. their record is 3/4. With no other data available, High bidder gets the $20 and pays the other the what is the chance of rain? amount of the higher bid. Tie bidders split the $20. a. 4/5 c. 2/5 How much do you bid? b. 3/5 d. 1/5 a. $10 c. $10.99 b. $9.99 d. $11 22. Smith and Jones, both 50% marksmen, decide to fight a duel in which they exchange alternate shots until one is hit. What are the odds in favor of the man who shoots first? a. 2/3 c. 2/5 b. 3/2 d. 5/2 SET 2 8. Dad and his son have the same birthday. On the 1. A, B and C participate in a track meet, consisting last one, dad was twice as old as junior. Uncle of at least three events. A certain number of points Observed that this was the ninth occasion on are given for first place, a smaller number of which Dad’s birthday age had been an integer second place, and a still smaller number for third multiple of Junior’s. How old is junior? place. A won the meet with a total score of 14 a. Junior is 36 and Dad is 72 points; B and C are tied for second with 7 points b. Junior is 18 and Dad is 54 apiece. B won first place in the high jump. Who c. Junior is 12 and Dad is 48 won the pole vault assuming no ties occurred in d. Junior is 9 and Dad is 45 any event? a. A won the pole vault 9. The undergraduates of a School. Of Engineering b. B won the pole vault wished to form ranks for a parade. In ranks of 3 c. C won the pole vault abreast, 2 men were left over; in ranks of 5, 4 d. Cannot be determined over; and 11’s 10 over. What is the least number of marchers there must have been? 2. Maynard the Census Taker visited a house and a. 1451 c. 1154 was told, “Three people live there. The product of b. 1145 d. 1514 their ages is 1296, and the sum of their ages is our house number.” After an hour of cogitation, 10. What is the remainder upon dividing 5^(999,999) Maynard returned for more information. The by 7? house owner said, “I forgot to tell you that my son a. 5 c. 7 and grandson live here with me.” How old were b. 6 d. 8 the occupants and what was their street number? a. the ages must be 1, 18 and 72 11. My house is on a road where the number run b. the ages must be 1, 17 and 82 1,2,3,4, … consecutively. My number is a three c. the ages must be 2, 17 and 81 digit one and, by a curious coincidence, the sum d. the ages must be 2, 18 and 71 of all house numbers less than mine is the same as the sum of all house number greater than 3. Three farmers, Adams, Brown and Clark all have mine. What is my number and how many houses farms containing the same number of acres. are there on my road? Adams’ farm is most nearly square, the length a. house number is 204 and there are 288 being only 8 miles longer than the width. Clark houses has the most oblong farm, the length being 34 b. houses number is 240 and there are 288 miles longer than the width. Brown’s farm is houses intermediate between these two, the length being c. houses number 244 and there are 288 28 miles longer than the width. If all the houses dimensions are in exact miles, what is the size of d. houses number is 200 and there are 288 each farm? houses a. 40x48, 32x60, 30x64 b. 40x84, 23x60, 30x46 12. On what days of the week can the first day of c. 40x46, 30x60, 32x64 century fall? (The first day of the twentieth century d. 40x64, 32x46, 30x60 was Jan. 1 1901) a. Monday c. Thursday 4. There are 100 coins in a piggy bank totaling $5.00 b. Tuesday d. Saturday in value, the coins consisting of pennies dimes and half dollars. How many of each are there? 13. The sultan arranged his wives in order of a. H =60, D + 39, P=1 increasing seniority and presented each with a b. H=1, D= 60, P= 39 golden ring. Next, every 3rd wife, staring with the c. H= 39, D= 1, P=60 2nd, was given a 2nd ring; of every 3rd one staring d. H= 1, D= 39, P= 60 with the 2nd received a 3rd ring, etc. His first and most cherished wife was the only one to receive 5. Every year an engineering consultant pays a 10 rings. How many wives had the Sultan? bonus of $300 to his most industrious assistant, a. 9284 c. 9842 and $75 each to the rest of his staff, After how b. 9248 d. 9824 many Years would his outlay be exactly $6,000 if all but two of his staff had merited the $300 bonus, 14. A ball is dripped from a height of 10 feet. It but none of them more than twice? rebounds one – half the distance on each bounce. a. 8 years c. 9 years What is the total distance it travels? b. 7 years d. 6 years a. 25 ft c. 35 ft b. 30 ft d. 40 ft 6. Two wheels in the same plane are mounted on shafts 13 in. apart. A belt goes around both 15. Obviously the smaller the compounding period, wheels to transmit power from one to the other. the greater the interest. How much does one The radii of the two wheels and the length of the dollar amount to after one year at 100% per belt not in contact with the wheels at any moment annum interest, compounded continuously, i.e., are all integers. How much larger is one wheel instantaneously? than the other? a. $1.72 c. $2.71 a. 3 in. c. 8 in. b. $2.17 d. $1.27 b. 5 in. d. 11 in. 16. A rectangular box without a top is to be made from 7. Five points are located in or on the perimeter of a sheet in the manner familiar to all calculus an equilateral triangle with 9 – inch sides. If d is students, i.e., by cutting out squares from the the distance between the closest pair of points, corners and bending the sides. The finished what is the maximum possible value of d? product is to have maximum volume, and its a. 2.5 inches c. 3.5 inches dimensions are to be all integers. How will these b. 5.5 inches d. 4.5 inches dimensions compare if the metal cutout amounts to 10% of the original sheet?  a. the complete box has dimensions in the 23. If 2 Marbles are removed at random from a bag ratio 6:3:1 containing black and white marbles, the chance b. the complete box has dimensions in the ratio that they are both white is 1/3. If 3 are removed at 6:4:3 random, the chance that they all are white is 1/6. c. the complete box has dimensions in the ratio How many marbles are there of each color? 6:5:2 a. w =6; b=4 c. w=4; b=6 d. the complete box has dimensions in the ratio b. w=6; b=6 d. w=4; b=4 6:4:1 24. A coin is so unbalanced that you are likely to get 17. A boat owner agrees to take a group on an outing two heads in two successive throws as you are to at $4:50 apiece if the number of passengers is get tails in one. What is the probability of getting equal to or less than his break -even point. For heads in a single throw? each person above this he reduces the fare for all a. 0.816 c. 0.861 passengers 3 cents per person. If he has on b. 0.681 d. 0.618 board now the number of passengers that maximizes the total collected, what is the boat 25. Six men decide to play Russian roulette with a six- owner’s profit? gun loaded with one cartridge. They draw for a. 0 c. $5.00 position, and afterwards, the sixth man casually b. $2.50 d. $7.50 suggests that instead of letting the chamber rotate in sequence, each man spin the chamber 18. A student studying series starts with the familiar 1 before shooting. How would this improve his +1/2 + 1/4 +1/8 +… and inserts terms midway chances? between these, obtaining 1 + ¾ + ½ +3/8 +1/4 a. his survival probability is enhanced about.2 +…. He divides as many terms as before. “He by spinning repeats the process, interpolating terms between b. his survival probability is enhanced about.4 those already placed, again dividing by 2. If he by spinning continues this indefinitely, what limit will the c. his survival probability is enhanced series approach? about.1 by spinning a. 4/3 c. 3/2 d. his survival probability is enhanced about.3 b. 3/4 d. 2/3 by spinning 19. Mr. X veers to the right when he walks. The 26. To stimulate his son in the pursuit of partial curvature of his path is proportional to his latitude. differential equations, a math professor offered to He start walking North from point A on the pay him $8 for every equation correctly solved equator, in the area of a large level plain, and and to fine him $5 for every incorrect solution. At finds he is proceeding East when he is one mile the end of 26 problems, neither owed any money north of the equator, He continues walking and to the other. How many did the boy solve arrives back at the equator at point B. What is the correctly? straight-line distance from A to B? a. 16 c. 10 a. 2.3 miles c. 3.2 miles b. 12 d. 14 b. 1.2 miles d. 2.1 miles 27. An expert on transformer design relaxed on 20. The teacher marked the quiz on the following Saturday by going to the races. At the end of the basis: one point for each correct answer, one first race, he had doubled his money. He bet $30 point off for each question left blank and two on the second race and tripled his money. He bet points off for each question answered incorrectly. $54 on the third race and quadrupled his money. Pat made four times as many errors as Mike, but He bet $72 on the fourth race and lost it, but still Mike left nine more questions blanks. If they both had $48 left. With how much money did he start? got the same score, how many errors did each a. 25 c. 21 make? b. 29 d. 33 a. Pat made 8 errors and Mike made 2 errors 28. The passengers on an excursion bus consisted of b. Pat made 2 errors and Mike made 8 errors 14 married couples, 8 of whom brought no c. Pat made 6 errors and Mike made 4 errors children, and 6 of whom brought 3 children d. Pat made 4 errors and Mike made 6 errors apiece. Counting the driver, the bus had 31 occupants. How is this possible? 21. A teenager wants to go out 2 consecutive nights a. Included among the 18 children were 8 out of a 3- day weekend. Permission for each married couples night is obtained (or denied) by asking either b. Included among the 18 children were 6 Father or mother. Father is known to be more married couples likely to grant permission. However, if the same c. Included among the 18 children were 5 parent is asked on 2 consecutuve days, the married couples answer are never the same 2 days running. d. Included among the 18 children were 7 Whom should he ask first? married couples a. Father c. Do not attempt b. Mother d. Father and Mother 29. A pupil wrote on the black board a series of fractions having positive integral terms and 22. Hard Knox College is a member of a six- school connected by signs which were either all + or all basketball League in which Every pair of schools X, although they ere so carelessly written it was plays each other twice. The other five schools impossible to tell which they were. It still wasn’t ended the season with respective league records clear even though he announced the result of the of.200,.300,.500,.600, and.800. How did Hard operation at every step. The third fraction had Knox make out? denominator 19. What was the numerator? a..300 c..800 a. 34 c. 25 b..600 d..500 b. 52 d. 43 30. Near the town of Lunch, Nebraska There is a large triangular plot of land bounded by three straight roads which are 855, 870, and 975 yards long respectively. The owner of the land, a friend of mine. Told me that he had decided to sell half the plot to a neighbor, but that the buyer had stipulated that the seller of the land should erect the fence which was to be a straight one. The cost of fences being high my friend naturally wanted the fence to be as short as possible. What is the minimum length the fence can be? a. 500 yd c. 600 yd b. 550 yd d. 650 yd SET 3: a. 18 c. 14 1. An expert on transformer design relaxed one b. 16 d. 12 Saturday by going to the races. At the end of the first race, he had doubled his money. He bet $30 10. Two snails start from the same point in opposite on the second race and tripled his money. He bet direction toward two bits of food. Each reaches $54 on the third race and quadrupled his money. his destination in one hour. If each snail had gone He bet $72 on the fourth race and lost it, but still in the direction the other took, the first snail would had $48 left. With how much money did he start? have reached his food 35 minutes after the a. 25 c. 21 second. How do their speeds compare? b. 29 d. 33 a. the first snail traveled at 4/3 the speed of the second 2. Dr. Reed, arriving late at the lab one morning, b. the first snail traveled at 3/4 the speed of pulled out his watch and said, “I must have it seen the second to. I have noticed that the minute and the hour c. the first snail traveled at 2/3 the speed of the hand are exactly together every sixty-five second minutes.” Does Dr. Reed’s watch gain or lose, and d. the first snail traveled at 3/2 the speed of the how much per hour? second a. loses 60/143 minutes b. loses 40/163 minutes 11. A necklace consists of pearls which increase c. gains 60/143 minutes uniformly form a weight of 1 carat for the end d. gains 40/163 minutes pearls to a weight of 100 carats for the middle pearl. If the necklace weighs altogether 1650 3. At this moment, the hands of a clock in the course carats and the clasp and string together weigh as of normal operation describe a time somewhere much (in carats) as the total number of pearls, between 4:00 and 5:00 on a standard clock face. how many pearls does the necklace contain? Within one hour or less, the hands will have a. 33 c. 44 exactly exchanged positions; what time is it now? b. 22 d. 55 a. 4:25:86 c. 4:26:85 b. 4:28:65 d. 4:25:68 12. Jai Alai balls come in boxes of 8 and 15; so that 38 balls (one small box and two large) can be 4. Two men are walking towards each other at the bought without having to break open a box, but side of a railway. A freight train overtakes one of not 39. What is the maximum number of balls them in 20 seconds and exactly ten minutes later which cannot be bought without breaking boxes? meets the other man coming in the opposite a. 86 c. 97 direction. The train passes this man in 18 b. 79 d. 68 seconds. How long after the train has passed the second man will the two men meet? (Constant 13. Mr. Field, a speeder, travels on a busy highway speed are to be assumed throughout.) having the same rate of traffic flow in each a. 6255 s c. 6525 s direction. Except for Mr. Field, the traffic is moving b. 5265 s d. 5562 s at the legal speed limit. Mr. Field passes one car for every nine which he meets form the opposite 5. Using the French tricolor as a model, much many direction. By what percentage is he exceeding the flags are possible with five available colors if two speed limit? adjacent rows must not be colored the same? a. 5/4 c. 5/6 a. 40 c. 60 b. 4/5 d. 6/5 b. 50 d. 70 14. A pencil, eraser and notebook together cost 6. A cubic box with sides ‘a’ feet long is placed flat $1.00. A notebook costs more than two pencils, against a wall. A ladder ‘p’ foot long is placed in and three pencils cost more than four erasers. If such a way that it touches the wall as well as the three erasers cost more than a notebook, how free horizontal edge of the box. If a= 1 and p √15, much does each cost? calculate at what height the ladder touches the a. P= 19, E = 24, N=54 wall, using quadratics only. b. P= 24, E = 19, N =54 a. 2.63 or 1.83 ft c. 3.62 or 1.38 ft c. P = 19, E = 26, N=55 b. 2.36 or 1.38ft d. 3.26 or 1.83 ft d. P = 26, E = 19, N = 55 7. Dr. Irving Weiman, who is always in a hurry, walks 15. There are four towns at the corners of a square. up an upgoing escalator at the rate of one step Four motorists set out, each man but the fourth per second, reaching the top in 32 steps. How going 8 mi./hr. faster than the car ahead-thus the many steps are there in the escalator? first car travels 24 mi./hr. faster than the fourth. At a. 70 c. 60 the end of one hour the first and third cars are b. 80 d. 90 204, and the second and fourth 212 (beeline) miles apart. How fast is the first car traveling and 8. Citizens of Franistan pay as much income tax how far apart are the towns? (percentage- wise) as they make rupees per a. The first car traveled 50 mi/hr, and the week. What is the optimal salary in Franistan? distance is 180 mi a. 45 rupees c. 55 rupees b. The first car raveled 50 mi/hr, and the b. 50 rupees d. 60 rupees distance is 150 mi c. The first car traveled 80 mi/hr, and the 9. There are nine cities which are served by two distance is 180 mi competing airlines. One or the other airline (but d. The first car traveled 80 mi/hr, and the not both) has a flight between every pair of cities. distance is 150 mi What is the minimum number of triangular flights (i.e, trips from A to B to C ad back to A on the 16. A new kind of atom smasher is to be same airline)? composed of two tangents and a circular arc which is concave towards the point of intersection of the two tangents. Each tangent  and the arc of the circle is 1 mile long. What the oasis, If the Azouli can cover 18 miles a is the radius of the circle? day, how long will it take them to reach the a. 1744.53 ft c. 1375.44 ft railroad? b. 1544.73 ft d. 1437.45 ft a. 4 days c. 3 days b. 5 days d. 2 days 17. The faces of a solid figure are all triangles. The figure has nine vertices. At each of six of 24. A cross section through the center of a football these vertices, four faces meet, and at each is a circle x inches in circumference. The of the other three vertices, six faces meet. football is x – 8 inches long from top to top and How many faces does the figure have? each seam is an arc of a circle 3/4 x inches in a. 21 c. 28 diameter. Find x. b. 14 d. 7 a. 29.06 c. 20.69 b. 26.90 d. 29.60 18. A spider and a fly are located at opposite vertices o a room of dimensions 1,2, and 3 25. A yang, ying, and Yung is constructed by units. Assuming that the fly is too terrified to dividing a diameter of a circle, AB, into three move, find the minimum distance the spider parts by points C and D, then describing on must crawl to reach the fly. one side of AB semicircles having AC and AD a. √26 c. √20 as diameters and on the other side of AB b. √24 d. √18 semicircles having BD and BC as diameters. Which is larger, the central portion or one of 19. In a room 40 feet long, 20 feet wide, and 20 the outside pieces? feet high a bug sits on an end wall at a point a. Yang one foot from the floor, midway between the b. Yung sidewalls. He decides to go on a journey to a c. Ying point on the other end wall which is one foot d. All three have the same size from the ceiling midway between the sidewalls. Having no wings, the bug must 26. A diaper is in the shape of a triangle with make this trip by sticking to the surfaces of the sides, 24, 20 and 20 inches. The long side is room, what is the shortest route that the bug wrapped around the baby’s waist and can take? overlapped two inches. The third point is a. 69 ft c. 58 ft brought up to the center of the overlap and b. 85 ft d. 96 ft pinned in place. The pin is to go through three thicknesses of material. What is the area in 20. A circle of radius 1 inch is inscribed in an which the pin may be placed? equilateral triangle. A smaller circle is a. 1-1/4 in2 c. 2-1/2 in2 inscribed at each vertex, tangent to the circle b. 2-1/4 in2 d. 1-1/2 in2 and two sides of the triangle. The process is continued with progressively smaller circles. 27. A coffee pot with a circular bottom taper What is the sum of the circumference of all uniformly to a circular top with radius half that circles? of the base. A mark halfway up the side says a. 3π c. 7π “2 cups.” Where should the “3 cups” mark go? b. 5π d. 9π a. about 2% of the way up from the bottom of the pot 21. A farmer owned a square field measuring b. about 3% of the way up from the bottom exactly 2261 yards on each side. 1898 yards of the pot from one corner and 1009 yards from an c. about 2% of the way down from the adjacent corner stood a beech tree. A top of the pot neighbor offered to purchase a triangular d. about 3% of the way down from the top portion of the field stipulating that a fence of the pot should be erected in a straight line from one side of the field to an adjacent side so that that 28. An icicle forming from a dripping gutter is in beech tree was part of the fence. The farmer the shape of a cone five times as long as it is accepted the offer but made sure that the wide (at the top). A few hours later it has triangular portion was a minimum area. What doubled in length and the generating angle was the area of the field the neighbor has also double. How does it present weight received, and how long was the fence? compare with its previous weight? a. area=939,120 yd2; length = 2018 yd a. 28 times c. 23 times b. area=932,910 yd2; length = 2017 yd b. 38 times d. 33 times c. area=912,093 yd2; length = 2019 yd d. area=930,219 yd2; length = 2020 yd 29. An Origami expert started making Nani-des- ka by folding the top left corner of a sheet of 22. A one- acre field in the shape of a right triangle paper until it touched the right edge and the has a post at the midpoint of each side. A crease passed through the bottom left corner. sheep is tethered to each of the side posts He then did the same with the lower right and a goat to the post on the hypotenuse. The corner, thus making two slanting parallel lines. ropes are just long enough to let each animal The paper was 25 inched long and the reach the two adjacent vertices. What is the distance between the parallel lines was total area the two sheep have to themselves, exactly 7/40 of the width. How wide was the i.e., the area the goat cannot reach? sheet of paper? a. 1.5 acre c. 0.5 acre a. 28 in. c. 24 in. b. 1 acre d. 2 acre b. 20 in. d. 32 in. 23. The Ben Azouli are camped at an oasis 45 30. The isosceles right triangle shown above has miles west of Taqaba. They decide to a vertex at the center of the square. What is dynamite the Trans- Hadramaut railroad the area of the common quadrilateral? joining Taqabato Maqaba, 60 miles north of a. 12.52 c. 15.22 b. 12.25 d. 15.25  SET 4 Find the swell of a soil that weighs 1661 kg/m3 in Find the volume (bank measure) of excavation its natural state and 1186 kg/m3 after excavation. required for a trench 0.92 m wide, 1.83m deep Mark the correct answer from the selection below. and 152m long, Assume that the trench sides will a. 10% c. 30% be approximately vertical. a. 255 BCM c. 355 BCM b. 20% d. 40% b. 252 BCM d. 352 BCM Find the shrinkage of a soil that weighs 1661 kg/m in its natural state and 2077 kg/m3 after Estimate the actual bucket load in bank cubic compaction. meters for a loader bucket whose heaped a. 10% c. 30% capacity is 3.82 m3. The soil's bucket fill factor is 0.90 and its load factor is 0.80. b. 20% d. 40% a. 2.75 BCM c. 3.75 BCM A soil weighs 1163 kg/LCM, 1661 kg/BCM, and b. 2.57 BCM d. 3.57 BCM 2077 kg/CCM. Find the load factor and shrinkage factor for the soil Find the expected production in loose cubic meters (LCM) per hour of a small hydraulic excavator. Heaped a. Load factor = 0.70; Shrinkage factor = 0.80 bucket capacity is 0.57 m3. The material is sand and gravel with a bucket fill factor of 0.95. Job efficiency is b. Load factor = 0.80; Shrinkage factor = 0.80 50 min/h. Average depth of cut is 4.3 m. Maximum depth of cut is 6.1 m and average swing is 90. Hint: c. Load factor = 0.80; Shrinkage factor = 0.70 Cycle output = 250 cycles/ 60 min Swing-depth factor d. Load factor = 0.70; Shrinkage factor = 0.70 = 1.00 a. 131 LCM/h c. 121 LCM/h A soil weighs 1163 kg/LCM, 1661 kg/BCM, and b. 113 LCM/h d. 112 LCM/h 2077 kg/CCM. How many bank cubic meters (BCM) and compacted cubic meters (CCM) are contained in 593, 300 LCM of this soil? Find the expected production in loose cubic meters (LCM) per hour of a 2.3-m3 hydraulic shovel equipped a. bank vol. = 310,415 BCM; compacted vol. = 332,248 CCM with a front-dump bucket. The material is common earth with a bucket fill factor of 1.0. The average angle b. bank vol. = 415,310 BCM; compacted vol. = 332,248 CCM of swing is 75° and job efficiency Hint: Standard cycles = 150/60 min Swing factor = 1.05 c. bank vol. = 332,248 BCM; compacted vol. = 415,310 CCM a. 190 LCM/h c. 290 LCM/h d. bank vol. = 415,310 BCM; compacted vol. = 248,332 CCM b. 240 LCM/h d. 340 LCM/h Find the base diameter and height of a triangular spoil bank containing 76.5 BCM if the pile length Determine the expected dragline production in loose is 9.14m, the soil's angle of repose is 37° and its cubic meters (LCM) per hour based on the following information: swell is 25%. Job efficiency = 50 min/h a. B=7.45m; H=2.08 m c. B=7.54m; H=2.80m Dragline size = 1.53 m3 Soil swell op = 25% Swing angle = 120° b. B=7.45m; H=2.80 m d. B=7.54m; H=2.08m Hint: Ideal output = 176 BCM/h Average depth of cut = 2.4 m Find the base diameter and height of a conical Swing-depth factor = 0.90 spoil pile that will contain 76.5 BCM of excavation Material = common earth if the soil's angle of repose is 32° and its swell is a. 165 LCM/h c. 185 LCM/h 12%. b. 175 LCM/h d. 195 LCM/h a. D=11.06 m; H= 3.71 m c. D=10.61m; H=3.71m Estimate the production in loose cubic meters per hour for a medium-weight clamshell excavating loose earth. b. D=11.60 m; H= 3.17 m d. D=10.16m; H=3.17m Heaped bucket capacity is 0.75 m3. The soil is common earth with a bucket fill factor of 0.95. Estimated cycle time is 40 s. Job efficiency is estimated at 50 min/h. a. 53 LCM/h c. 55 LCM/h b. 35 LCM/h d. 33 LCM/h  A wheel tractor-scraper weighing 91 t is being A power-shift crawler tractor has a rated blade operated on a haul road with a tire penetration of capacity of 7.65 LCM. The dozer is excavating 5 cm. What is the total resistance (kg) and loose common earth and pushing it a distance of effective grade when the scraper is ascending a 61 m. Maximum reverse speed in third range is 8 slope of 5%? Hint: RRF = 20 + (6 x cm km/h. Estimate the production of the dozer if job penetration) GRF = 10 x grade (%) Effective efficiency is 50 min/h. Hint: Fixed time = 0.05 min grade = Grade (%) + RRF/10 Dozing speed = 4.0 km/h a. Total Resistance = 9100kg; Effective Grade = 10% a. 127 LCM/h c. 172 LCM/h b. Total Resistance = 4550kg; Effective Grade = 10% b. 217 LCM/h d. 271 LCM/h c. Total Resistance = 9100kg; Effective Grade = 0% Estimate the hourly production in loose volume d. Total Resistance = 4550kg; Effective Grade = 0% (LCM) of a 2.68-m3 wheel loader excavating sand and gravel (average material) from a pit and A wheel tractor-scraper weighing 91 t is being moving it to a stockpile. The average haul operated on a haul road with a tire penetration of distance is 61 m, the effective grade is 6%, the 5 cm. What is the total resistance (kg) and bucket fill factor is 1.00, and job efficiency is 50 effective grade when the scraper is descending a min/h. Hint: Basic cycle time = 0.50 min Travel slope of 5%? Hint: RRF = 20 + (6 x cm time = 0.30 min penetration) GRF = 10 x grade (%) Effective a. 168 LCM/h c. 186 LCM/h grade = Grade (%) + RRF/10 b. 157 LCM/h d. 175 LCM/h a. Total Resistance = 9100kg; Effective Grade = 10% b. Total Resistance = 0kg; Effective Grade = 10% The estimated cycle time for a wheel scraper is 6.5 min. Calculate the number of pushers c. Total Resistance = 9100kg; Effective Grade = 0% required to serve a fleet of nine scrapers using single pushers. Determine the result for both d. Total Resistance = 0kg; Effective Grade = 0% backtrack and chain-loading methods. Hint: Typical pusher cycle time (min) Back-track (single A crawler tractor weighing 36 t is towing a rubber- pusher) = 1.5 Chain or shuttle (single pusher) = tired scraper weighing 45.5 t up a grade of 4%. 1.0 Mark the correct answer from the selection What is the total resistance (kg) of the below. combination if the rolling resistance factor is 50 kg/t? Mark the correct answer from the selection a. back-track = 2; chain = 3 c. back-track = 3; chain = 3 below. b. back-track = 2; chain = 2 d. back-track = 3; chain = 2 a. 5335 kg c. 3535 kg b. 3355 kg d. 5535 kg Find the expected production of the scraper fleet of the previous problem if only one pusher is available and the chain-loading method is used. A four-wheel-drive tractor weighs 20,000 kg and Expected production of a single scraper produces a maximum rimpull of 18,160 kg at sea level. assuming adequate pusher support is 173 The tractor is being operated at an altitude of 3050 m on wet earth. A pull of 10,000 kg is required to move BCM/h. Hint: Number of pushers required to fully the tractor and its load. Can the tractor perform under serve fleet = 1.4 these conditions? Hint: Derating factor = [Altitude (m) - a. 1112 BCM/h c. 1221 BCM/h 915]/102 Coefficient of traction = 0.45 b. 2111 BCM/h d. 2211 BCM/h a. Because the maximum pull as limited by traction is greater than the required pull, the Given the following information on a shovel/truck tractor cannot perform under these conditions. operation, calculate the number of trucks b. Because the maximum pull as limited by theoretically required and the production of this traction is greater than the required pull, the combination. Shovel production at 100% tractor can perform under these conditions. efficiency = 283 BCM/h Job efficiency = 0.75 Truck capacity = 15.3 BM Truck cycle time, c. Because the maximum pull as limited by excluding loading = 0.5 h traction is less than the required pull, the a. No. of trucks required = 10; Expected production = 212 BCM/h tractor cannot perform under these b. No. of trucks required = 11; Expected production = 221 BCM/h conditions. c. No. of trucks required = 11; Expected production = 212 BCM/h d. Because the maximum pull as limited by traction is less than the required pull, the d. No. of trucks required = 10; Expected production = 221 BCM/h tractor can perform under these conditions. Given the following information on a shovel/truck Calculate the maximum hourly production of an operation, calculate the expected production if asphalt plant based on the data in the following two trucks are removed from the fleet. Shovel list. Mix composition: Asphalt = 6% Aggregate production at 100% efficiency = 283 BCM/h Job composition: Coarse A = 42% Coarse B = 35% efficiency = 0.75 Truck capacity = 15.3 BM Truck Sand = 18% Mineral filler = 5% Aggregate cycle time, excluding loading = 0.5 h moisture = 8% Dryer capacity at 8% moisture a. 268 BCM/h c. 186 BCM/h removal = 110 ton/h Hint: Plant capacity = [Dry capacity × 10^4]/[100 - asphalt%)(100 - fines%)] b. 286 BCM/h d. 168 BCM/h a. 213 ton/h c. 123 ton/h 24.1 km of gravel road require reshaping and leveling. You estimate that six passes of a motor b. 231 ton/h d. 132 ton/h grader will be required. Based on operator skill, machine characteristics, and job conditions, you Estimate the production of a single-engine two-axle estimate two passes at 6.4 km/h, two passes at tractor scraper based on the following information: 8.0 km/h, and two passes at 9.7 km/h. If job efficiency is 0.80, how many grader hours will be Maximum heaped volume = 24 LCM required for this job? Maximum payload = 34,020 kg a. 21.1 h c. 23.1 h Material: Sandy clay, 1898 kg/BCM, 1571 kg/LCM, b. 22.1 h d. 24.1 h rolling resistance 50 kg/t Job efficiency = 50 min/h Trial blasting indicates that a rectangular pattern of drilling using 7.6-cm holes spaced on 2.75-m Operating conditions = average Single pusher Haul centers and 6.1 m deep will produce a route: satisfactory rock break with a particular explosive loading. The effective hole depth resulting from Section 1. Level loading area the blast is 5.5 m. Determine the rock volume Section 2. Down a 4% grade, 610 m produced per meter of drilling. a. 5.7 m3/m c. 7.5 m3/m Section 3. Level dumping area b. 6.8 m3/m d. 8.6 m3/m Section 4. Up a 4% grade, 610 m Section 5. Level turnaround, 183 m A jaw crusher is producing 227 t/h of crushed Hint: Travel time: gravel and discharging it onto a three-screen deck. The top screen in the deck is a 38-mm Section 2 = 1.02 min screen. The gradation of crusher output shows 100% passing 76 mm, 92% passing 38 mm, and Section 5 = 0.45 min 80% passing 19 mm. Material weight is 1842 Section 4 = 1.60min kg/m3. Find the minimum size of the 38-mm screen to be used. Check both total screen load Fixed cycle: and screen passing capacity. Hint: Basic Load spot = 0.3 min capacity: Total feed = 62/t/h/m2 Passing screen = 34 t/h/m2 Deck position factor (top) = 1.0 Maneuver and dump = 0.7 min Halfsize factor (80%) = 1.8 Oversize factor (8%): Total feed = 0.96 Passing screen = 1.04 Weight Load = 0.6min factor = 1.15 a. 129 LCM/h c. 219 LCM/h a. 2.4 m2 c. 2.9 m2 b. 192 LCM/h d. 291 LCM/h b. 3.4 m2 d. 3.9 m2 [NOV 2022] Calculate the volume of plastic concrete that will be produced by the mix design given in the table: Component Specific Quantity Gravity (kg) Cement 3.15 154 Sand (SSD) 2.65 426 Gravel (SSD) 2.66 549 Water 1.00 95 a. 0.41 m3 c. 0.51 m3 b. 0.46 m3 d. 0.56 m3 Determine the actual weight of each component to be added if the sand contains 5% excess moisture and the gravel contains 2% excess moisture. Component Specific Quantity Gravity (kg) Cement 3.15 154 Sand (SSD) 2.65 426 Gravel (SSD) 2.66 549 Water 1.00 95 a. Water = 63kg; Sand = 447kg; Gravel=560kg b. Water = 63kg; Sand = 405kg; Gravel=538kg c. Water = 127kg; Sand = 447kg; Gravel=560kg d. Water = 127kg; Sand = 405kg; Gravel=538kg Refer to the previous problem. Determine the weight of each component required to make a three-bag mix and mix volume Component Specific Quantity Gravity (kg) Cement 3.15 154 Sand (SSD) 2.65 426 Gravel (SSD) 2.66 549 Water 1.00 95 a. Cement = 127.8kg; Sand = 370 kg; Gravel = 464kg; Water 52kg; Mix Volume = 0.42m3 b. Cement = 127.8kg; Sand = 370 kg; Gravel = 446kg; Water 52kg; Mix Volume = 0.42m3 c. Cement = 127.8kg; Sand = 370 kg; Gravel = 464kg; Water 42kg; Mix Volume = 0.52m3 d. Cement = 127.8kg; Sand = 370 kg; Gravel = 464kg; Water 42kg; Mix Volume = 0.52m3  a. 0.35 m3 b. 0.46 m3 c. 0.53 m3 d. 0.64 m3 a. 115.6 b. 135.6 c. 125.6 d. 145.6 a. 1.7 m b. 1.8 m c. 1.9 m d. 2.0 m a. $7000 b. $8000 c. $9000 d. $10,000 a. 52,896 lb b. 56,298 lb c. 58,269 lb d. 59,862 lb a. $4.08 b. $8.04 c. $4.80 d. $8.40 a. 144 t b. 166 t c. 164 t d. 146 t a. $93.47/h b. $94.73/h c. $97.34/h d. $97.43/h a. 1.46 kN/m b. 1.64 kN/m a. 9.7 kW or 11.3 hp b. 7.9 kW or 11.3 hp c. 2.46 kN/m d. 2.64 kN/m c. 9.7 kW or 13.1 hp d. 7.9 kW or 13.1 hp a. 819 b. 891 a. 7.46 kW b. 6.47 kW c. 918 d. 981 c. 7.64 kW d. 6.74 kW a. 0.64 bars b. 0.44 bars a. 438 mm b. 348 mm c. 0.46 bars d. 0.66 bars c. 384 mm d. 483 mm a. 6.70 b. 7.06 a. 1.0 m b. 1.5 m c. 7.60 d. 6.07 c. 2.0 m d. 2.5 m a. 55 kN/m2 b. 44 kN/m2 a. 25 wells b. 15 wells c. 66 kN/m2 d. 77 kN/m2 c. 35 wells d. 45 wells a. 33 m3/h b. 44 m3/h a. 115.2 b. 215.1 c. 55 m3/h d. 66 m3/h c. 112.5 d. 251.1 a. 1200 MPa b. 1250 MPa c. 1300 MPa d. 1350 MPa a. Four 4 m3 capacity b. Three 5 m3 capacity c. Five 2 m3 capacity d. Two 3 m3 capacity a. 174% b. 274% c. 247% d. 147% a. 17 °C b. 22 °C c. 12 °C d. 27 °C a. Waiting time of b. Waiting time of excavator = 12 min; of excavator = 16 min; of trucks = 12 min trucks = 16 min a. 1755 b. 1575 c. Waiting time of d. Waiting time of excavator = 12 min; excavator = 16 min; of c. 1557 d. 1775 of trucks = 16 min trucks = 12 min a. Open pores = 7.9% and b. Open pores = 5.9% and closed pores = 7.9% closed pores = 5.9% c. Open pores = 7.9% and d. Open pores = 5.9% and closed pores = 5.9% closed pores = 7.9% a. Bulk Density = 2.4 and b. Bulk Density = 2.62 and apparent density = 2.6 apparent density = 2.41 c. Bulk Density = 2.41 and d. Bulk Density = 2.26 and apparent density = 2.62 apparent density = 2.14 a. 9.99% b. 7.9% c. 7.7% d. 9.7% a. 71.1 unit mixes b. 75.1 unit mixes c. 71.5 unit mixes d. 75.5 unit mixes 1. Liquids 9. In an open tube, free surface mercury a. cannot be b. do not occupy remains compressed definite shape a. horizontal b. curved upwards c. are not affected d. none of these by change in c. curved downwards d. none of these pressure 10. If cohesion between the molecules of a 2. Specific Weight of liquid fluid is more than adhesion between the a. remains constant b. does not remain fluid and glass, the free level of fluid in a at every place constant at every place dipped glass tube will be c. varies from place to place on the d. does not vary on a. higher than the b. same as the surface earth any other planet surface of liquid of liquid 3. The specific weight of water is 1000 c. lower than the d. none of these kg/m3 surface of liquid a. at normal b. at 40 °C 11. A rise or fall of liquid in a glass tube of a pressure of 760 mm temperature very small diameter when dipped is c. at mean sea level d. all of the above a. directly proportional to b. directly proportional to 4. Specific weight of sea water is more than the force per unit length the sine of the angle of that of pure water because of of periphery contact a. dissolved air b. dissolved salts c. directly proportional d. inversely proportional to to the specific weight of the diameter of the glass c. suspended d. all of the above liquid tube matter 5. Water belongs to 12. Hydrostatic pressure on a dam depends a. Newtonian Fluids b. Non-Newtonian upon its Fluids c. Compressible a. length b. depth Fluids d. none of these c. shape d. both (b) and (c) 6. Fluids change the volume under external pressure due to 13. Barometers are used to measure a. pressure in water b. difference in a. plasticity b. viscosity channels, pipes, etc pressure at two points c. compressibility d. none of these c. atmospheric pressure d. very low pressure 7. Molecules of fluids get attracted due to a. capillarity action b. surface tension 14. Piezometers are used to measure c. adhesion d. cohesion a. pressure in water b. difference in channels, pipes, etc pressure at two points 8. Falling drops of water become spheres c. atmospheric d. very low pressure due to pressure a. adhesion b. cohesion c. surface tension d. viscosity 15. Manometers are used to measure a. pressure in water b. difference in channels, pipes, etc pressure at two points c. atmospheric d. very low pressure pressure 16. Differential Manometers are used to 23. When a body is totally or partially measure immersed in a fluid, it is buoyed up by a a. pressure in water b. difference in force equal to channels, pipes, etc pressure at two a. weight of the body b. weight of the fluid points c. atmospheric displaced by the body c. weight of the body pressure d. very low pressure and fluid displaced d. difference of weights by the body of the fluids displaced and that of the body 17. The pressure less than atmospheric pressure is known 24. A floating body attains stable equilibrium a. suction pressure b. vacuum pressure if its metacentre is c. negative gauge d. all the above a. at the centroid b. above the centroid pressure c. below the centroid d. anywhere 18. Atmospheric pressure varies with a. altitude b. temperature 25.Center of buoyancy is c. weather d. none of these a. Center of the floating b. centroid of the conditions body fluid displaced 19. Mercury is generally used in barometers c. Center of pressure of d. none of these because the displaced liquid a. its vapor b. the height of the pressure is barometer will be practically zero less c. it is a best liquid d. both (a) and (b) above 20. The total pressure force on a plane area is equal to the area multiplied by the intensity of pressure at its centroid, if a. area is horizontal b. area is vertical c. area is inclined d. all the above 21. The center of pressure of a vertical plane immersed in a liquid is at a. center of higher edge b. center of lower edge c. centroid of the area d. none of these 22. On an incline plane, center of pressure is located a. at the centroid b. above the centroid c. below the centroid d. anywhere  MEGALING 7 1. The rise of the liquid along the walls of a revolving cylinder above the initial level, is A. greater than the depression of the liquid at the axis of rotation B. lesser than the depression of the liquid at the axis of rotation C. the same as the depression of the liquid at the axis of rotation D. none of these 2. When a liquid rotates at constant angular velocity about a vertical axis of a rigid body, the pressure A. increases linearly to its radial distance B. varies inversely as the altitude along any vertical line C. varies as the square of the radial distance D. decreases as the square of the radial distance 3. The imaginary line drawn such that the tangents at its all points indicate the direction of the velocity of the fluid particles at each point, is called A. path line B. stream line C. potential line D. streak line 4. In fluids, steady flow occurs when A. conditions of flow change steadily with time B. conditions of flow do not change with time at a point C. conditions of flow remain the same at adjacent point D. velocity vector remains constant at a point 5. Uniform flow is said to occur when A. size and shape of the cross-section in a particular length remain constant B. size and shape of the cross-section change along a length C. frictional loss in the particular length of the channel will the more than the drop in its elevation D. frictional loss in the particular length of the channel, will be less than the drop in elevation 6. If velocities of fluid particles vary from point to point in magnitude and direction, as well as from instant to instant, the flow is said to be A. turbulent flow B. laminar flow C. uniform flow D. non-uniform flow 7. A steady uniform flow is through A. an expanding tube at constant rate B. an expanding tube at increasing rate C. a long pipe at decreasing rate D. a long pipe at constant rate 8. A non-uniform steady flow is through  A. an expanding tube at constant rate B. a long pipe at increasing rate C. a long tube at a decreasing rate D. an expanding tube at increasing rate 9. The continuity equation A. requires that Newton's second law of motion be satisfied at every point in fluid B. relates mass rate of flow along a streamline C. expresses the relationship between work and energy D. relates the momentum per unit volume between two points on a streamline 10. Equation of continuity of fluids is applicable only if A. flow is one dimensional B. flow is compressive C. flow is steady D. all the above 11. The flow in which each liquid particle has a definite path, and the paths of adjacent particles do not cross each other, is called A. steady flow B. streamline flow C. turbulent flow D. uniform flow 12. Total head of a liquid particle in motion is the sum of A. potential head and kinetic head B. kinetic head and pressure head C. potential head and pressure head D. potential head, kinetic head and pressure head 13. The main assumption of Bernoulli's equation is: A. No external force except the gravity acts on the liquid B. The velocity of energy of liquid particle, across any cross-section of a pipe is uniform. C. There is no loss of energy of the liquid while flowing D. All the above 14. Reynold number is the ratio of initial force and A. elasticity B. surface tension C. gravitational force D. viscosity 15. The velocity of the fluid particle at the center of the pipe section, is A. equal throughout B. minimum C. maximum D. none of these 16. An independent mass of a fluid does not possess A. pressure energy  B. elevation energy C. kinetic energy D. none of these 17. Frictional loss of head includes the loss of energy due to A. viscosity B. turbulence C. both (a) and (b) D. none of these 18. Energy equation is usually applicable to A. steady flow B. laminar flow C. turbulent flow D. non-uniform flow 19. The line joining the points to which the liquid rises in vertical, piezometer tubes fitted at different cross-sections of a conduit, is known as A. hydraulic gradient B. piezometric line C. pressure grade line D. all the above 20. Hydraulic grade line A. may be above or below the center line of conduit B. remains parallel to the center line of conduit C. remains below the center line of conduit D. remains above the center line of conduit 21. A pitot tube is used to measure A. velocity of flow B. a difference in pressure C. pressure D. none of these 22. The ratio of the inertia and viscous forces acting in any flow, ignoring other forces, is called A. Weber number B. Reynold number C. Euler number D. Froude number 23. The ratio of the inertia and gravitational force acting in any flow, ignoring other forces, is called A. Weber number B. Euler number C. Reynold number D. Froude number 24. Mach number is the ratio of inertia force to A. surface tension B. elasticity  C. viscosity D. gravitational force 25. Weber number is the ratio of inertia force to A. gravitational force B. elasticity C. surface tension D. viscosity MEGALING 8 1. A piezometer opening in pipes measures A. velocity head B. static pressure C. total pressure D. negative static pressure 2. Manning's formula is used for A. head loss due to friction in pipes flowing full B. flow in pipes C. head loss due to friction in open channels D. flow in open channels 3. For a long pipe, the head loss A. at the entrance and outlet both are ignored B. at the outlet is ignored C. at the entrance is ignored D. due to friction 4. Hydraulic radius is equal to A. square root of the area B. area divided by the square of wetted perimeter C. area divided by wetted perimeter D. wetted perimeter divided by area 5. The magnitude of water hammer in a pipe depends upon A. elastic properties of the pipe material B. length of the pipeline C. speed at which value is closed D. all the above 6. For most economical rectangular section of a channel, the depth is kept A. half the width B. hydraulic mean depth C. three times the hydraulic radius D. one-fourth of the width 7. For the most economical trapezoidal section of a channel with regards to discharge, the required condition, is  A. perpendiculars drawn from the center of the top width on to the bottom sloping side, are all equal B. half of top width = sloping side C. hydraulic depth = half the depth D. all the above 8. Most economical section of a triangular channel, is A. equilateral triangle B. right angled triangle with equal sides C. isosceles triangle with 45 vertex angle D. right angled triangle 9. Most economical section of a circular channel for maximum discharge A. hydraulic mean depth = 0.286 diameter of circular section B. wetted perimeter = 2.6 diameter of circular section C. depth of water = 0.95 diameter of circular section D. all the above 10. The most efficient channel section, is A. rectangular B. semi-circular C. triangular D. half hexagon in the form of trapezoid 11. The phenomenon occurring in an open channel when a rapidly flowing stream abruptly changes to a slowly flowing stream causing a distinct rise of liquid surface, is A. water hammer B. hydraulic jump C. critical discharge D. none of these 12. An open container filled with water is moved vertically downward with a uniform linear acceleration. The pressure at its bottom will be A. equal to static pressure B. lesser than static pressure C. greater than static pressure D. none of these 13. The metacentric height of a body equals the distance between A. the metacenter and center of gravity B. the center of buoyancy and metacenter C. the center of gravity and center of buoyancy D. none of these 14. In steady flow, which one of the following changes with time A. pressure B. velocity C. density D. none of these 15. For a most economical rectangular channel, the width of the channel must be  A. twice the depth of flaw B. half the depth of flow C. equal to depth of flow D. none of these 16. For a most economical rectangular channel, the hydraulic mean depth, is equal to A. one-third depth of flow B. half the depth of flow C. the depth of flow D. none of these 17. For a most economical trapezoidal open channel, the half of the top width must be equal to A. the depth of flow B. one sloping side C. the bed width D. none of these 18. For the most economical: trapezoidal open channel, A. the semicircle drawn with top width as diameter must touch the three sides of the channel B. half of the top width must be equal to one of the sloping sides C. the hydraulic mean depth must be equal to half the depth of flow D. all of these 19. The best side slope for most economical trapezoidal section, is A. 45° B. 30° C. 60° D. None of these 20. For critical depth of flow of water in open channels, the specific energy must be A. maximum B. minimum C. average of maximum and minimum D. none of these