Question Set No. : 111

Instructions:

1. All the questions are to be answered and maximum time 60 minutes.

2. This question paper contains 45 questions.

3. Each question carries equal mark.

4. No negative marks

5. !vlaximummark 45.

6. Please do not write any marks on the question paper.

7. Ask for rough sheets if required.

8. Directions for answering the questions are given in the test questionpaper before each group of questions to which they apply. Read thesedirections carefully and answer the questions by darkening theappropriate ovals.

9. Follow the instructions of the invigilator. Candidates found violatingthe instructions will be disqualified.

fi.

G - -----

[ Question Set No. - 111

1. There are 27 students in a Chemistry class and 22 students in a physics class. Seven of thesestudents take physics and chemistry. What is the ratio of the number of students taking onlyphysics to those taking only chemistry.(a) 3 : 4 (b) 4 : 3 (c) 7 : 6 (d) 22 : 27

2. A trailer carries 3, 4, or 5 crates on a trip. Each crate weights no less than 125 pounds and nomore than 250 pounds. What is the minimum weight (in pounds) of the crates on a single trip?(a) 375 (b) 600 (c) 625 (d) 750

3. There are 200 questions on a 3-hour examination. Among these questions are 50 mathematicsproblems. It is suggested that twice as much time be allowed for each mathematics problem asfor each of the other questions. How many minutes should be spent on the mathematicsproblems?(a) 36 (b) 60 (c) 72 (d) 100

4. ~. If 13 =13w/1-w, then (2W)2=(a) % (b) % (c) 1 (d) 2

5. The first of a series of cog wheels working into each other in a straight line, has certain number ofteeth; the number of teeth in the second to that of the first is 6 : 7; of the third to the second is 5 :6 and of the fourth to the second is 2 : 3. Ifthe wheels are set in motion, then how many leastnumber of revolutions must each wheel make before they are simultaneously in their originalpositions?a. 420 each b. 70,60, 50,40 c.7,6,5,4 d.60, 70,84,105

6. In a certain city only two newspapers A and B are published. It is known that 25% of the citypopulation reads A and 20% reads B, while 8% read both A and B. It is also known that 30% ofthose who read A but not B, look into advertisements and 40% of those who read B but not A,look into advertisements while 50% of those who read both A and B look into advertisements.What percentage of the population reads an advertisement?a.13% b.13.9% c.14% d. None of these

7. If x, 1, z are in AP and x, 2, Z are in GP, then x, 4 , Z are ina. AP b. GP c. HP d. None of these

8. If 2x + 3y + 4z = 27 and 3x + 2y + z = 33, then what is the average of x, y and z?a.3 b.4 c.6 d. 12

9. If 'IMPOVERISH' is coded 'SVXVBJVLUI' in a certain coded language, then how will'LUBRICATED' be coded in the same language?a. VDJYOHEWFE b. WEKZPIFXHF c. VDJYOHFWGE d. VDJYOHEWGE

10. The sum to n terms of the series 1.3.5 + 3.5.7 + 5.7.9 + ... isa. 8n3 + 12n2- 2n - 3 b. n (8n3 + 11n2- n - 3) c. n (2n3 + 8n2 + 7n - 2) d. None of these

11. If f(x) = (x + 1) tan-1(e-2X),then f'(O) isa. nl2 b. nl4 - 1 c. nl6 + 5 d. None of these

12. A sum of Rs. 1,683 is divided between A, Band C so that for every rupee that A has, B has 50paise and for every rupee that B has, C has 40 paise. What is the share of B?a. Rs. 495 b. Rs. 990 c. Rs. 594 d. Rs. 198

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8J1D"__,,-"".I.13. If 20 pumps can raise 4,000 tonnes of water in 48 days, working for 8 hr a days. In how many

days will 30 pumps raise 5,600 tonnes of water, working 12 hr a day (approximately)?a. 36 days b. 42 days c. 30 days d. None of these

14. There are two women participating in a chess tournament. Each participant played two gameswith every other participants. The number of games played by the men among themselvesexceeded by 66 than the number of games played by men against women. How manyparticipants were there in the tournament?a.16 b.15 c.14 d.13

Direction Questions 15 and 16: Given below are based on letter series from which some ofthe lettersare missing. The missing letters are given in the proper sequence as one of the alternatives among fourgiven under each question. Find the correct alternative from answer choices marked a - d :

15. __a a b_a_a_b_aa. b b a a b b b. a b a a b a c. b a b a b a d. a b a b a a

16. _b a m - am b - m - a_b aa. m a b b m b. m n b a b c. m b a b a d. m b a b m

17. A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side3 cm. What is the total number of smaller cubes having none of their faces painted?a.16 b.8 c.12 d.24

18. Manju and Anju solved a quadratic equation. While solving, Manju made a mistake in theconstant term and got the roots as 6 and 2, whereas Anju made a mistake in the coefficient of xonly and got the roots as -7 and -1. The correct roots of the equation area.6,-1 b. 7,1 c.-7,-2 d.-6,2

19. Find out total number of positive integral solution of 4x + 3y = 63.a.4 b.5 c.6 d. None of these

20. 16 men are divided equally into 4 groups, how many such grouping can be made?a.16C4x 12C4x 8C4X4C4 b. 1/4! X 16C4x 12C4XfiC4X4C4c. 1/4! X 16P4x 12p4X8P4X4P4 d. None of these

21. On a certain day, Rohit started with p newspapers.Frommorningto noon,hesold40% of thepapers, and betweeo noon and evening he sold 60% of the remaining. Then he realised that hadhe sold double the number of newspapers than he sold in the afternoon, he would have had toborrow 12 papers from another vendor. Find p.a.108 b.100 c.96 d.72

22. The wages received by A, Band C together amount to Rs. 144. If A works for 10 days, B for 12days and C for 15 days, then the amount received by A, when the proportion of their daily wagesis 1/2, 1/3, 1/5, isa. Rs. 60 b. Rs. 48 c. Rs. 90 d. None of these

23. I sold two watches for Rs. 300 each, one at the loss of 10% and the other at the profit of 10%.What is the percentage of loss(-) or profit(+) that resulted from the transaction?a. (+)10 b. (-)1 c. (+)1 d. (-)10

24. When all the students of standard IV of ABC school were made to stand in ascending order oftheir heights, Ajay was standing at the 7th position. When they were standing in decreasing orderof their height, Ajay was standing at the 35th position. How many students are there in the class?(No two students have equal height.)

a.42 b.40 c.41 d. Cannot be determined?

25. If 1st, 3rd, 5th, 6th and 8th letters of the word 'REGULATE' are used to form a new meaningfulword, then what will be the first letter of the word so formed? Mark 'X' as the answer if nomeaningful word is formed out of these letters and 'M' if more than two meaningful words can beformed.a. R b. L c. M d.X

26. In June a baseball team that played 60 games had won 30% of its game played. After aphenomenal winning streak this team raised its average to 50%. How many games must theteam have won in a row to attain this average?(a) 12 (b) 20 (c) 24 (d) 30

27. Two hours after a freight train leaves Cricleville a passenger train leaves the same stationtraveling in the same direction at an average speed of 60 miles per hour. After traveling fourhours, the passenger train overtakes the freight train. The average speed of the freight train wasOOM ~~ ~~ ~OO

28. Snowhite Paint Company contract to pain three houses. Mr. Brown can paint a house in 6 days.While Mr. Piter would take 8 days and Mr. Slocum would take 12 days. After 8 days Mr. Browngoes on vacation and Mr. Pinter begins to work for a period of 6 days. How many days will it takeMr. Slocum to complete the contract?(a) 7 (b) 8 (c) 11 (d) 12

29. The price of a garment is reduced by 20 percent. During an 'early-bird' special all garments aremarked "Take an additional 30 percent off the reduced price." The two reductions are equivalentto a single reduction of(a) 25% (b) 44% (c) 50% (d) 56%

30. One wheel rotates once every 7 minutes, and another rotates once every 5 minutes. How oftenwill both begin to rotate at the same time?(a) every 6 minutes (b) every 12 minutes (c) every 17.5 minutes (d) every 36 minutes

31. A rectangle 1inches long and w inches wide is made 3 inches longer. The area (in square inches)has increased by(a) 3w (b) 31 (c) 31w (d) 3(/+w)

32. City X is 200 miles east of City Y, and City 2 is 150 miles directly north of City Y. What is theshortest distance (in miles) between X and 2?(a) 50"7 (b) 175 (c) 200 (d) 250

33. If a roast that requires 1 hour and 40minutes of roasting time has been in the oven for 55 minuteshow many more minutes of roasting time are required?(a) 15 (b) 20 (c) 30 (d) 45

34. A watch was running 14 minutes late at 6 am on a Saturday. Exactly one week later, it wasrunning 28 minutes fast. If the clock gained time uniformly, then what was the actual time whenthe clock showed 6.07 pm on Tuesday?(a) 5:58pm b) 6:00 pm c) 6:01pm d) 6:02 pm

35. If 15thAugust, 2018 will be Wednesday, then what was the day on 26thJanuary, 1977?(a) Tuesday (b) Wednesday (c) Thursday (d) None of these

Directions for questions 3640: Eachquestionhas a sentencewith one word underlined.Identifythemeaningof the underlinedword, as used in the sentence,from amongthe four alternativesand mark itsnumberas the answer.

36. The cosmetic preparations that are used for beautifying purposes have deleterious effects.(a) harmful (b) unpredictable (c) tremendous (d) beneficial

3

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37. Rachna would often reminisce the days when she had not yet been married.(a) forget (b) recall the past (c) reexamine (d) remark

38. The hero is known for his liking for foot-tapping tunes and sonorous music.(a) lingering (b) melliflous (c) imposing (d) throbbing

39. The apparently infalliable Americans have forever been the epitome of efficiency.(a) source (b) perfect example (c) culmination (d) peak

40. Many scientific discoveries are serendipitous rather than the result of planned research(a) development of events by chance in a beneficial way (b) miraculous (c) sudden(d) the result of perseverance

Directions for questions 41 to 45: Fill in the blanks in the given sentence so as to make sense. Selectthe correct word from the answer choices and mark its number as the answer.

41. This Indian Experience Programme is inearly this year.(a) reciprocation (b) relation

to a batch of students who went to Japan

(c) exchange (d) response

42. Without opening your mouth, you - a lot about your personalitythroughyour handwriting.(a) show (b) visualize (c) hide (d) reveal

43. In India there are as many New Year days as regions and communities but January 1 has - allas the one secular New Year Day.(a) beaten (b) outgrown (c) overtaken (d) undertaken

44. Internet cafe owners fear that a police crackdown may cause - damage to their business.(a) irreparable (b) eternal (c) untold (d) reparable

45. There is needto - modernchildren'sliteratureand teachingaids for the mentalgrowthofchildren.(a) invent (b) generate (c) discover (d) multiply

Name:

/45 ]

Question Answer

No. a bed

1 0000

2 0000

3 0000

4 0000

5 0000

6 0000

7 0000

8 0000

9 0000

10 0000

11 0000

12 0000

13 0000

14 0000

15 0000

16 0000

17 0000

18 0000

19 0000

20 0000

21 0000

22 0000

23 0000

24 0000

25 0000

t 11 p~(0 Roll No:

ANSWER CODING SHEET I Question Set No.111 I

Question

No.

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

Answer

a bed

00000000

0000

000000000000

00000000

0000

000000000000

0000

000000000000

00000000

0000

0000

BR£~JDR~5

t,

Name:

/45 I

Question Answer

No. a bed

1 8000

2 8000

3 0080

4 0080

5 0008

6 0800

7 0080

8 0800

9 0008

10 0080

11 0800

12 8000

13 0080

14 0008

15 0008

16 0008

17 0800

18 0800

19 0800

20 0800

21 0800

22 8000

23 0800

24 0080

25 0080

, , f p~ G) Roll No:

ANSWER CODING SHEET I Question Set No.111 I

Question

No.

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

Answer

a bed

00800800

0080

080000088000

00080008

0800

08008000

0800

0080

08008000

0008

00080080

8000

0800

E3R~~JDR~5

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'" r~@BR.R~DR~5

ANSWER KEY FOR QUESTION SET NO - 111

1. (a) Note that 7 students take both subjects. 20 students take chemistry only and 15 students take physics only. The ratio ofthose taking physics only to those taking chemistry only is 15/20 or % or 3 : 4

2. (a) Minimum crates = 3, Minimum weight = 125 pounds3 x 125 = 375 pounds

3. (c) Let x = number of minutes allowed for each of the questions other than the mathematics problems. Then 2x = number ofminutes allowed for each mathematics problem. (50)(2x) or 100x = number of minutes allowed for all mathematics problems.(150)(x) or 150x = number of minutes allowed for all other questions.100x + 150x = total time = 3 hours

= 180 minutes= 180= 180= 180/250= (180/250 (100» = 72 minutes.

100x + 150x250x

x100x

4. (e) 13 = 13w/l-w13(I-w) = 13w13-13w = 13w13 = 26wY:,=w(2W)2= (2(1/2»2 = (1)2= 1

5. (d) The number of revolutions is inversely proportional to the number of teeth. The ratio of number of teeth of the wheels is 7 :6: 5 : 4. Thus the ratio of number of revolutions will be 1/7 : 1/6 : 1/5: 1/4, i.e. 60: 70: 84 : 105. When the wheels make 60,70,

84, 105 revolutions respectively they would come back to the original position.

6. (b) Let A and B denote the sets of people who read paper A and paper B respectively.Then n(A) = 25, n(B) = 20, n (A (1 B) = 8Hence, n(A- B) = n(A) - n(A (1 B) = 25 - 8 = 17n (B - A) = n(B) - n(A (1 B) = 20 - 8 = 12Now percentage of people reading an advertisement= [(30% of 17) + (40% of 12) + (50% of 8)]= 13.9%

7. (e) x, 1, z are in AP =} 2 = x + zx, 2, Z are in GP =} 4 = xz ...(i)(i) does not satisfy 8 = x + z and 16 = xz but itsatisfies 4 = 2xz / x+z :. x, 4, Z are in HP..

8. (b) 2x + 3y + 4z = 27... (i) and 3x + 2y + z = 33... (ii)Adding (i) and (ii), we get 5(x + y + z) = 60=} (x + y + z) = 12:. Average = (x+y+z) /3 = 12/3 = 4

9. (d) Letters are coded at an interval of +10, +9, +8 ..., +1 letters.

10. (e) The rth term of the series is given by tr = (2r - 1) (2r + 1) (2r + 3) = 8r3 + 12~ - 2r - 3

Therefore, S n, the sum to n terms of the series, is given by

= 2n2 <r + 1) 2+ 2n(n + 1) (2n + 1) - n(n + 1) - 3n= n(2n + 4n2 + 2n + 4n2 + 6n + 2 - n -1 - 3)= n(2n3 + 8n2 + 7n - 2)

11. (b) We have, f(x) = (x + 1) tan -j; -2~, therefore,f'(x) = tan-1 (e-2X) +((x+1)(-2) /1+e )e- x=} f'(O) = tan-1 (1) - 2/2 = ;c/4-1

12. (a) Ratio of shares = A : B : CA: B = 100 : 50B: C = 100: 40=} A : B : C = 200 : 100 : 40=10:5:2:.B's share = 5/17 x 1683 = Rs. 495

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111 p~@E3RR~DRI-"1S

13. (e) No. of pumps Tonnes of water Days Time(hr/day)

812

2030

40005600

48x

Number of days = 48 x 5600/4000 x 20 /30 x 8/12 = 29.8 = 30 days

14. (d) x men played 2 x 2x games with women and x(x - 1)games among themselves the difference being 66.So x(x - 1) = 4x + 66.~2x-5x-66=0~ x = 11, so x + 2 = 13

15. (d) the series is : aba, aba, aba, aba

16. (d) The series is : mba, mba, mba, mba, mba

17. (b) Since each side of the smaller cube is 3 em, it can be figured out that each face of the original cube is divided into 4 parts,or in other words, the original cube is divided into 64 smaller cubes. For a smaller cube to have none of its sides painted, itshould not be a part of the face of the original cube (i.e. none of its faces should be exposed).We can find at the centre of the original cube there are (2 x 2 x 2) = 8 such cubes.

Hint: Students please note that the answer can only be a cube of some integer. The only cube among the answerchoices is (2)3= 8.

18.(b)i+ax+b=0For Manju, i+ ax + b,= 0Sum of roots =-a6+2=-a~a=-8

For Anju, i + a1x + b = 0Multiplication of roots = b(-7) x (-1) = b ~ b = 7:. E(;!uationis i - 8x + 7 = 0~ i - 7x - x + 7 = 0or (x - 7) (x - 1) = 0~ x =7 or 1

19. (b) x and y both have to be integersy = 63/3 - 4x /3Y = 21 - (4/3)xwhen (3, 17); (6, 13); (9, 9); (12, 5); (15, 1) so number ofintegral solutions will be 5.

20. (b) Here the 4 teams been distinctly different the number of ways would have been

16C4x 12C4X 8C4x 4C4'but as the we arefindingthe groupingsthe numberof wayswill be 1/4! (16C4x 12C4X 8C4 x 4C4)

21. (b) In the morning-noon session, he sells 0.4p. So he is left with p - OAp = 0.6p. He sells 60% of it in the afternoonsession, i.e. 0.6p f.6 = 0.36p.Now, had he sold twice of 0.36p Le. O.72p, he would have to borrow 12 papers extra.:.p+12=0.4p+0.72p~12=1.12p-p=0.12p~p=100

22. (a) The ratio of their daily wages is %:1/3:1/5 So the ratio of their wages for the full work is 10/2:12/3:15/5.Le.5:4:3.Hence A's amount = 5/12 x 144 = Rs. 60

23. (b) In this case, we need not use the data that SP = Rs. 300 each. This has to be used only to figure out that the SP ofboth the articles is the same. Also since the profit percentage on one is equal to the loss percentage on the other, viz. 10%effectively, it will be a loss given by (10)2/100 = 1%. Hence, the correct answer is (-)1.

24. (e) Total number of students = 35 + 7 - 1=42-1 =41

25. (e) Letters at first, third, fifth, sixth and eighth positions are R, G, L, A and E. The words that calli'be formed usingthese letters are REGAL, GLARE, and LARGE. So we mark M as the answer.

", r~@ BRR~DRKS

26. (c) To have averaged 30% of 60 games, the team must have won 18 out of 60 games. Let x = number of games played andwon during winning streak.New average: 18 + x /60 + x = 50%

18+x/60+x=Yo36+2x=60+x

x=24

27. (b) The passenger train traveled 4 hours and covered 240 miles. When it overtook the freight train, the freight train had alsocovered 240 miles, but it traveled for 6 hours. The average rate of the freight train was 240/6 or 40 miles per hour.

28. (c) Mr. Brown completes a house and 1/3 of a second house in 8 days. Mr. Pinter does 6/8 or % of a house in 8 days.Together they have done 1(1/3)+3/4 or 25/12 or2 houses and 1/12 of the third house. Mr. Slocum must do 11/12 of the thirdhouse. In 1 day Mr. Slocum does 1/12 of a house. He will therefore need 11 days to do 11/12 of the house.

29. (b) After a reduction of 20%, the price of the garment is 80% of the original price. The additional reduction, 30% of the 80%,results in a price of 56% of the original price (note the incorrect Choice D). For the correct solution, consider that the price of 56%of the original is actually a 44% reduction of the original price.

30. (d)The first wheel rotates once every 7, 14,21,28,35, etc., minutesThe second wheel rotates once every 5,10,15,20,25,30,35, etc., minutesThey will both begin to rotate every 35 minutes.

31. (a) 3w

32. (d) 250

33. (d) 45

34. (b) The time gained by the watch in one week = 14+28=42 min.Let the actual time on Tuesday be 6 pm, which is 3 Yo days from 6 a.m. SaturdayHence, 7 days - 42 min gain

3 Yo-- 21 min gainOverall gain = 21 - 14 = 7mini.e. 6:07 pm, which is given in the question. Hence our initial assumption, i.e. 6 pm was correct.

35. (b) 1stAugust, 2018 -- Wednesday26th January, 1997 ?Working out backwards, the no. of years from 15th August 2008 to 15th August 1977 = 2018 - 1977 = 41 years.No. of leap years = 41/4 = 10No. of non-leap years = 41-10=31.Total No. of odd days in these 41 years = 1Ox2+3x1 =20+31=51=2 odd days.Now working out the no. of odd days backward from 15th August to 26th January of 1977.Aug Jul Jun May Apr Mar Feb Jan0 3 2 3 2 3 0 6

(14 days from 15th August to 1stAugust)(6 days from 31st January to 26th January)=10=5 odd days.Total odd days = 2+5=7=0Hence, 26th January, 1977 was Wednesday.

36. (a) harmful

37. (b) recall the past

38. (c) imposing

39. (b) perfect example

40. (a) development of events by chance in a beneficial way

41. (d) response

42. (d) reveal

43. (c) overtaken

44. (a) irreparable

45. (b) generate *,