IIM MOCK PAPER - I

Instructions to Test Takers:

This test is of 90 minutes and is meant to be taken at one sitting without any break. Candidates are advised to be sure about the correct answer before they darken with HB Pencil. They should

also ensure that each oval is completely darkened with HP Pencil. Partially or faintly darkened ovals may be rejected by the optical scanner.

If a candidate darkens more than one oval, it may be deemed to be an incorrect answer. Check immediately that all the pages of the booklet are in order. In the rare event of the Test Booklet being

defective, bring it to the notice of the invigilator immediately who will arrange for the replacement of test booklet if required.

Each question carries 1 mark. 0.25 marks will be deducted for every incorrect answer. DO YOUR scratch work on the space available in the test booklet itself and not in the OMR sheet. DO NOT use any additional paper for rough work. You are not allowed to use any calculation devices or scale.

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MOCK PAPER 1

1. Let A = R – {3}, B = R – {1}. Let f: A B be defined by f x =x−2

x−3. Then

(a) f is bijective (b) f is one-one but not onto (c) f is onto but not one-one (d) None of the above

2. The inequality z − 4 < z − 2 represents the region given by (a) Re(z) > 0 (b) Re(z) < 0 (c) Re(z) > 3 (d) None of these

3. The graphs of the equation 3x + 2y = 5 and 2x – y = 11 are (a) Intersecting (b) Parallel (c) Concident (d) None

4. A father‘s age is equal to the ages of 5 children. In fifteen years, his age will be only half of their united age. Find his present age. (a) 40 years (b) 45 years (c) 42 years (d) None

5. What image from bottom row should replace the question mark?

(a) 4 (b) 6 (c) 1 (d) None of these

6. The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet? (a) 10 a.m. (b) 10.30 a.m. (c) 11 a.m. (d) 11.30 a.m.

7. A cone of height 7 cm and base radius 3 cm is carved from a rectangular block of wood 10 cm × 5 cm × 2 cm. the percentage of wood wasted is: (a) 34% (b) 46% (c) 54% (d) 66%

Directions for (Questions 8 – 10): Read the graph carefully and answer the questions that follow. One of the graph below represent the market share of five different brands of bikes sold in a particular city. The total number of bikes sold as 25000. The other one shows the unit sales price and the Tax the brand is subjected to. Tax is calculated on the sales price.

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MOCK PAPER 1

8. What is the difference in number of units sold by the most popular brand and the second most popular brand?

(a) 800 (b) 1000 (c) 1200 (d) 1400 9. Which brand earned the maximum revenue before tax?

(a) A (b) B (c) C (d) D 10. Which brand earned the maximum revenue after tax?

(a) A (b) B (c) C (d) D Directions for (Question 11): A statement is given and which is followed by two conclusion I and II, give the answer on the basis of given statement only. (a) if only conclusion I follows (b) if only conclusion II follows (c) if either I or II follows (d) if neither I nor II follows

11. Statement: A corporate general manager asked four managers to either submit their resignations by the next day

or face termination of services. Three of them submitted their resignation by that evening Conclusion I: The next day the remaining manager would also resign. Conclusion II: The General Manager would terminate his service the next day.

12. Debu walks towards East, then towards North and turning 450 right walks for a while and lastly turns towards left. In which direction is he walking now? (a) North (b) East (c) South – East (d) North – West

13. The condition for which 𝑎2 𝑥4 + 𝑏𝑥3 + 𝑐𝑥2 + 𝑑𝑥 + 𝑓2 may be a perfect square is (a) 4𝑎2 𝑐 − 𝑏2 = 8𝑎3 𝑓 (b) 4𝑎2𝑐 = 8𝑎3𝑓 (c) 2𝑎2𝑐 = 𝑎3𝑓 (d) None of these

14. The largest number among the following that will perfectly divide 101100 − 1 is (a) 100 (b) 10000 (c) 100100 (d) 100000

15. Let u = (log2 x)2 – 6 log 2 x + 12 where, x is a real number. Then the equation xu = 256, has (a) No solution for x (b) exactly one solution for x (c) exactly two distinct solutions for x (d) exactly three distinct solutions for x

16. How much does a watch lose per day, if its hands coincide every 64 min?

(a) 96 min (b) 90 min (c) 36 5

11 𝑚𝑖𝑛 (d) 32

8

11 𝑚𝑖𝑛

Direction for (Question 17): (1 + 𝑚)𝑥2 − 2 1 + 3𝑚 𝑥 + 1 + 8𝑚 = 0

Where, m ∈ R – {-1}. 17. The set of value of m such that the given quadratic equation has at least one root is negative, is

(a) 𝑚 𝜖 − ∞, −1 (b) m ϵ −1

8, ∞ (c) 𝑚 𝜖 −1 −

1

8 (d) m ϵ R

18. In a certain language, (A) ‗Sun shines brightly‘ is written as ‗ba lo sul‘ (B) ‗Houses are brightly lit‘ as ‗kado udo ari ba‘; and (C) ‗Light comes from sun‘ as ‗dapi kup lo nro‘. What words will be written for ‗sun‘ and ‗brightly‘? (a) lo, ba (b) ba, lo (c) snl, lo (d) ba, sul

19. Evaluate: ∫ 𝑥2+ 1[log 𝑥2+ 1 − 2 log 𝑥]

𝑥4 𝑑𝑥

(a) 𝐼 = − 1 +1

𝑥2 3/2

log 1 +1

𝑥2 −2

3 + 𝐶 (b) 𝐼 = −

1

3 1 +

1

𝑥2 3/2

log 1 +1

𝑥2 −2

3 + 𝐶

(c) 𝐼 = + 1 +1

𝑥2 3/2

log 1 +1

𝑥2 −2

3 + 𝐶 (d) 𝐼 =

1

3 1 +

1

𝑥2 3/2

log 1 +1

𝑥2 −2

3 + 𝐶

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MOCK PAPER 1

Directions for (Questions 20 – 22): Read the following instructions and answer. I. There is a rectangular wooden block of length 4 cm, height 3 cm and breadth 3 cm. II. The two opposite surfaces of 4 cm × 3 cm are painted yellow on the outside. III. The other two opposite surfaces of 4 cm × 3 cm are painted red on the outside. IV. The remaining two surfaces of 3 cm × 3 cm are painted green on the outside. V. Now the block is cut in such a way that cubes of 1cm × 1 cm × 1 cm are created.

20. How many cubes will have only one colour?

(a) 10 (b) 12 (c) 14 (d) 18 21. How many cubes will have no colours?

(a) 1 (b) 2 (c) 4 (d) 8 22. How many cubes will have any two colours?

(a) 32 (b) 24 (c) 16 (d) 12

23. Two pipes A and B can fill a cistern in 371

2 minutes and 45 minutes respectively. Both pipes are opened. The cistern

will be filled in just half an hour, if the pipe B is turned off after: (a) 5 min (b) 9 min (c) 10 min (d) 15 min

24. A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is: (a) 3 : 2 (b) 4 : 1 (c) 4 : 3 (d) 7 : 4

25. Which figure is the odd one out?

26. The positive value of m for 6𝑥2 = 𝑚𝑥 + 5 = 0 𝑕𝑎𝑣𝑒 𝑟𝑜𝑜𝑡𝑠 𝑖𝑛 𝑡𝑕𝑒 𝑟𝑎𝑡𝑖𝑜 1 ∶ 2 𝑖𝑠

(a) 15 3 (b) 3 15 (c) 15 (d) None

Direction for (Question 27): Find the point of local maxima or local minima.

27. 𝑓 𝑥 = 2 sin𝑥 − 𝑥, −

2 𝑥

2

(a) x =

3 point of local. Maximum, x =

−

3 points of local minimum,

(b) x =

4 point of local. Maximum, x =

−

4 points of local minimum,

(c) x =

6 point of local. Maximum, x =

−

6 points of local minimum,

(d) x =

5 point of local. Maximum, x =

−

5 points of local minimum,

28. If x > 0. y > 0, z > 0, are in G. P. then log x, log y, log z, are in (a) A. P. (b) G. P. (c) H. P. (d) A. G. P.

29. In how many ways 7 boys be seated at a round table so that 2 particular boys are together (a) 240 (b) 120 (c) 480 (d) None

30. The greatest common divisor of 123456789 and 987654321 is (a) 1 (b) 3 (c) 9 (d) greater than 9

31. If 5% of the electric bulbs manufactured by a company are defective then what is the probability that in a sample of 100 bulbs none is defective? (a) 𝑒−3 (b) 𝑒−5 (c) 𝑒5 (d) e

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MOCK PAPER 1

32. The central pole of a conical tent is 3/2m high. The pole is supported by ropes tied to its top and nails on the ground. If, on the ground from the foot of the pole, the distances of the surface of the tent and the nail(s) are in the ratio of 1:3 and if the angles of depression from the top of the pole of the nails and the surface of the tent are in the ratio of 1: 2, then the length of one such rope is

(a) 2m (b) 6 m (c) 3 2 m (d) 3m 33. The angle of elevation of an artificial satellite as measured from two earth station are 300 and 600 if two distance

between two earth station is 2000 k. m. find for height of satellite (a) 5760 m (b) 3460 m (c) 2730 m (d) None

34. Suppose the English alphabet letters A, B, C, ….., Z are denoted by the remainders obtained on dividing the numbers 20, 21, 22, …………… 225, respectively, by 29, then the letter ‗K‘ would be denoted by (a) 6 (b) 7 (c) 8 (d) 9

35. ∫ 1

log 𝑥 −

1

(log 𝑥)2 𝑑𝑥

e2

3

(a) 𝑒2

2− 𝑒 (b)

𝑒2

2+ 2 (c)

–𝑒2

2− 𝑒 (d)

–𝑒2

2+ 𝑒

Direction (Question 36): Find the odd man out: 36. 385, 462, 572, 396, 427, 671, 264

(a) 385 (b) 427 (c) 671 (d) 264

37. If 𝑓 𝑥 = sin𝑥 cos𝑥 tan𝑥𝑥3 𝑥2 𝑥2𝑥 1 1

𝑡𝑕𝑒𝑛 lim𝑥→0𝑓(𝑥)

𝑥2 𝑖𝑠

(a) 3 (b) – 1 (c) 0 (d) 1 38. If the vertices of a triangle have integral coordinates, the triangle cannot be

(a) an equilateral triangle (b) a right angled triangle (c) an isosceles triangle (d) None of the above

39. In order that the function 𝑓 𝑥 = 𝑥 + 1 cot 𝑥 is continuous at x = 0, 𝑓 0 𝑚𝑢𝑠𝑡 𝑏𝑒 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑎𝑠

(a) 𝑓 0 =1

𝑒 (b) 𝑓 0 = 0 (c) 𝑓 0 = 𝑒 (d) None of these

40. If an angle of a triangle remain unchanged but each of its two including sides is doubled, then by what factor does the area get multiplied? (a) 2 (b) 3 (c) 4 (d) 6

Directions for (Questions 41 – 44): Answer the questions on the basis of reading the passage below Pick up a glossy magazine or newspaper supplement and there will almost certainly be at least one double page spread that looks like a regular editorial page but is headed up either 'promotion' or 'advertisement'. These hybrid - unattractively but aptly called advertorials — are being used with increasing frequency by a growing number of companies. Traditionally the preserve of high-technology clients with a complicated message to get across to potential customers, the use of this technique has now spread to sectors like financial services, alcohol and automobiles. One major reason why marketing departments are becoming more receptive to ideas for advertorials is that publishers are pursuing them more aggressively at a time of shrinking ad budgets, while they are being treated far more professionally in a bid to persuade clients that this is a creative opportunity to spread their message to their target audiences. Pouring more imagination into them allied with raising production standards has also been a means whereby the commercial executives of magazines and newspapers can try- to convince skeptical editors who strongly disapprove of blurring the advertising / editorial line of their worth.

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MOCK PAPER 1

What advertorials are about is control - controlling the message in an editorial format. Positive editorial coverage of a company and / or its products in credible publications is the best publicity any company can hope for, but often proves elusive. A successful advertorial can pinpoint the way the company delivers its message to the heart of its target audience. High technology was one of the main sources of early advertorials - unsurprisingly, the products are complex and need to be explained with some technical detail to get the story across. That is not so easy with traditional advertising. Advertorials can also to some degree circumvent journalistic indifference to what a company is doing because editorial coverage has already been so extensive. For example, in the case of a company like Compaq, whose swift growth in the computer market attracted many inches of editorial space that very success can lead to journalists wondering how they can write something different about Compaq. There can be diminishing returns from an editorial point of view. So advertorials let the company present things editorially but with bought space. While they should be strongly labelled, information is being given to readers in a format that looks familiar.

41. In the light of your reading of the passage above, identify the option that contains the set of words CLOSEST in

meaning to the set of words in CAPITALS : SCEPTICAL: CIRCUMVENT: ELUSIVE (a) incredulous: surround : baffling (b) doubtful: avoid : evasive (c) thoughtful: deceit: illustrative (d) philosophical: revolve : deceptive

42. In the above passage, the phrase "blurring the advertising / editorial line of their worth" implies (a) diluting the perceived quality of their editorials (b) hiding the actual value of the paper (c) obscuring the actual facts in the paper (d) devaluing the advertising potential of the editorials

43. The passage DOES NOT discuss (a) attitude of journalists towards advertising (b) advertorials and the publishing industry (c) use of advertorials in industries (d) impact of new technologies on advertorials

44. According to the passage (a) high technology does not support traditional advertising. (b) traditional journalists are indifferent to advertorials. (c) advertorials facilitate advertising of complex products in a professional manner (d) advertorials occupy double-page spreads in magazines

Directions for (Questions 45 – 48): Answer the questions on the basis of reading the passage below. "Popular art" has a number of meanings, impossible to define with any precision, which range from folklore to junk. The poles are clear enough, but the middle tends to blur. The Hollywood Western of the 1930's, for example, has elements of folklore, but is closer to junk than to high art or folk art. There can be great trash, just as there is bad high art. The musicals of George Gershwin are great popular art, never aspiring to high art. Schubert and Brahms, however, used elements of popular music - folk themes - in works clearly intended as high art. The case of Verdi is a different one: he took a popular genre - bourgeois melodrama set to music (an accurate definition of nineteenth-century opera) – and, without altering its fundamental nature, transmuted it into high art. This remains one of the greatest achievements in music, and one that cannot be fully appreciated without recognizing the essential trashiness of the genre. As an example of such a transmutation, consider what Verdi made of the typical political elements of nineteenth-century opera. Generally in the plots of these operas, a hero or heroine - usually portrayed only as an individual, unfettered by class - is caught between the immoral corruption of the aristocracy and the doctrinaire

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MOCK PAPER 1

rigidity or secret greed of the leaders of the proletariat. Verdi transforms this naive and unlike formulation with music of extraordinary energy and rhythmic vitality, music more subtle than it seems at first hearing. There are scenes and arias that still sound like calls to arms and were clearly understood as such when they were first performed. Such pieces lend an immediacy to the otherwise veiled political message of these operas and call up feelings beyond those of the opera itself. Or consider Verdi's treatment of character. Before Verdi, there were rarely any characters at all in musical drama, only a series of situations which allowed the singers to express a series of emotional states. Any attempt to find coherent psychological portrayal in these operas is misplaced ingenuity. The only coherence was the singer's vocal technique: when the cast changed, new arias were almost always substituted, generally adapted from other operas. Verdi's characters, on the other hand, have genuine consistency and integrity, even if, in many cases, the consistency is that of pasteboard melodrama. The integrity of the character is achieved through the music: once he had become established, Verdi did not rewrite his music for different singers or countenance alterations or substitutions of somebody else's arias in one of his operas, as every eighteenth-century composer had done. When he revised an opera, it was only for dramatic economy and effectiveness.

45. It can be inferred that the author regards Verdi's revisions to his operas with

(a) regret that the original music and texts were altered. (b) concern that many of the revisions altered the plots of the original work. (c) approval for the intentions that motivated the revisions. (d) puzzlement, since the revisions seem largely insignificant.

46. According to the passage, one of Verdi's achievements within the framework of nineteenth-century opera and its conventions was to (a) limit the extent to which singers influenced the musical compositions and performance of his operas (b) use his operas primarily as forums to protest both the moral corruption and dogmatic rigidity of the political

leaders of his time (c) portray psychologically complex characters shaped by the political environment surrounding them (d) incorporate elements of folklore into both the music and plots of his operas

47. Which of the following best describes the relationship of the first paragraph of the passage to the passage as a whole? (a) It provides a group of specific examples from which generalizations are drawn later in the passage. (b) It leads to an assertion that is supported by examples later in the passage. (c) It defines terms and relationships that are challenged in an argument later in the passage. (d) It briefly compares and contrasts several achievements that are examined in detail later in the passage.

48. It can be inferred that the author regards the independence from social class of the heroes and heroines of nineteenth-century opera as (a) an idealized but fundamentally accurate portrayal of bourgeois life (b) a plot convention with no real connection to political reality (c) a plot refinement unique to Verdi (d) a symbolic representation of the position of the bourgeoisie relative to the aristocracy and the proletariat

Direction for (Questions 49 – 56): In the following questions, some of the sentences have errors and some have none. Find out which part of the sentence has error. If there is no error mark (d) 49. Were 1 you /1 should have not / allowed him to stay in a hotel / No error

(a) (b) (c) (d) 50. With a liberalized duty structure/ and the governments stand at allowing multinationals to set up shop directly /

(a) (b)

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MOCK PAPER 1

imported parts are now freely available / No error (c) (d)

51. Many of the authors/ of this book are members of a national support group and have / participated in several (a) (b) (c) conferences / No error (d)

52. It is not feasible but / in many ways desirable that an organization should run its / own courses for developing (a) (b) (c) employees / No error

(d) 53. Having said this / let us hasten to add that we are / not against social mixing / No error

(a) (b) (c) (d) 54. What makes most technology / profitable for remarketers is / the support and service opportunities that are built

into it / (a) (b) (c) No error (d)

55. The chief has instructed the manager to / appraise the Governor of/ the activities of our institute / No error (a) (b) (c) (d)

56. He is an idealist / and when it comes to principles, does not/ budge an inch/No error (a) (b) (c) (d)

Directions for (Questions 57 – 63): In the following questions, the first and the last part of the sentence are numbered 1 and 6. The rest of the sequence is split up into four parts and named A, B, C, D. These four parts are not given in their proper order. Find out the correct sequence. 57. 1. Religion has been used

A. both as a weapon of isolation B. to dull awareness C. about real problems D. and as morphia 6. like, education, health and environment. (a) ABCD (b) ADBC (c) BADC (d) CABD

58. 1. When all the members were seated A. during the previous year B. the secretary came to the dais C. and read out the report D. detailing the activities of the organisation 6. and plans for the coming year, (a) A BCD (b) DABC (c) CDAB (d) BCDA

59. 1. In spite of the unprecedented boom in the market A. and had to remain content B. the paper dealer could not C. push up his sales D. with volume of sales lower than 6. what he had sold the previous year. (a) BCAD (b) DACB (c) ACBD (d) CADB

60. 1.1 was not sure A. to hear his voice B. in my heart of hearts C. through that window once more D. that I really wished 6. or never to see him there again, (a) BACD (b) DBAC (c) ACDB (d) CDBA

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MOCK PAPER 1

61. 1. Yet so few of us have A. walls of daily routine B. the time or the means C. that enclose our lives D. to break through the narrow 6. to get to know this. (a) DCBA (b) CADB (c) BDAC (d) ABCD

62. 1.1 realized that I could have A. into the sea with nothing to cling to B. by a mere second, I would have drowned C. had a life line around me D. for if my hand had filled 6. and that would have been the end. (a) DCAB (b) ABDC (c) CDBA (d) BACD

63. 1. One of the outstanding feature of the present century A. more health and leisure B. and better facilities for health C. has been the importance of living conditions D. of the working men-great political power 6. security and education. (a) ABDC (b) DCBA (c) BACD (d)CDAB

Direction for (Question 64): In each of the following questions the two words given on one side of double colon i.e., :: bear a certain relationship. The other side shows as incomplete pair marked by a missing word which bears a similar relationship with the given word. Find the missing word out of the given options (a) (b) (c) or (d). 64. Axis : Earth : : ? : Wheel

(a) Equinox (b) Tyre (c) Hub (d) Gear Directions for (Questions 65 – 66): Fill in the blanks. 65. The doctor gave him an injection to ……………..the temperature.

(a) put down (b) get dowry (c) bring down (d) take down 66. He filled the glass with water to the ……………..

(a) margin (b) edge (c) brim (d) rin Directions for (Questions 67 – 68): Answer the question based on the following information. Each question is a logical sequence of statements with a missing link, the location of which is shown parenthetically. From the four choices available you are required to choose the one which best fits the sequence logically. 67. (………..) the more they remain the same.

(a) The more the merrier (b) The less the dynamism (c) The more things change (d) The more pronounced the transformation

68. The safest general characterization of the European philosophical tradition as it has developed up to now with all its diverse proponents, is that it consists of a (………..) Plato. (a) series of footnotes to (b) set of prologues to (c) collection of chapters (d) string of commentaries to

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MOCK PAPER 1

Directions for (Questions 69 – 70): In each of the following sentences, a part of the sentence is left unfinished. Below each sentence. Four/five different words to complete the sentence are given. Choose the best alternative among them. 69. Though the programme was originally …………. for seven days, it was later ………….to four days.

(a) planned, decided (b) announced, ended (c) scheduled, curtailed (d) recommended, concluded

70. When rain is …………. the meteorological department issues a ………….well in advance to that effect. (a) sufficient, letter (b) inadequate, circular (c) torrential, memorandum (d) imminent, warning

71. Which of the following rulers died while playing ‗Chougan‘? (a) Balban (b) Sher Shah (c) Jalal-ud-din-Khulj (d)Qutab-ud-din Aibak

72. Rudradaman was one of the greatest (a) Pallava rulers (b) Saka rulers (c) Kushan rulers (d) Maurya rulers

73. Bernier visited India during the reign of (a) Akbar (b) Jahangir (c) Shah jahan (d) Aurangzeb

74. The Hijri era is counted from (a) 622 A. D. (b) 632 A. D. (c) 712 A. D. (d) 1562 A. D.

75. The first Indian ruler to organize Haj pilgrimage at the expense of the state was (a) Alauddin Khilji (b) Feroz Tughlaq (c) Akbar (d) Aurangzeb

76. Pushyabhuti dynasty ruled over (a) Patliputra (b) Ujjain (c) Thaneshwar (d) Sakal

77. Sanchi is famous for (a) Rock-cut temples (b) Cave paintings (c) The rock edicts of Ashoka (d)The largest Buddhist Stupa

78. Which State is the 'Sugar Bowl' of India? (a) Uttar Pradesh (b) Himachal Pradesh (c) Tamil Nadu (d) Andhra Pradesh

79. Which State has the longest coastline in India? (a) Gujarat (b) Maharashtra (c) Tamil Nadu (d) Andhra Pradesh

80. Lakshmi Bai National College of Physical Education is located at: (a) Bhopal (b) Gwalior (c) Karnal (d) Patiala

81. Recently, which of the following High Courts has set aside the office memoranda issued by the Central government, carving out a sub-quota for minorities, from within the quota for the Other Backward Classes (OBC), in the fields of public employment and education? (a) Andhra Pradesh High Court (b) Allahabad High Court (c) Jabalpur High Court (d) Calcutta High Court

82. What is the average time taken by sun rays to reach the earth? (a) 400 seconds (b) 450 seconds (c) 500 seconds (d) 600 seconds

83. India ranks in terms of world production of coal. (a) First (b) Second (c) Third (d) Fourth

84. Which river form 'bird foot delta'? (a)Mississippi (b) Nile (c) Amazon (d) Brahamputra

85. The term ‗paper Gold‘ is associated with (a) Deficit budgeting (b) Currencies still in gold standard (c) Special drawing rights of the IMF (d) Special facility of the World Bank

86. Who among the following is the current President of France?

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MOCK PAPER 1

(a) Francois Hollande (b) Nicolas Sarkozy (c) Jacques Chirac (d) François Mitterrand 87. Which of the following states have achieved all most 100% rural electrification in India?

A. Haryana B. Kerala C. Uttar Pradesh D. Punjab (a) A, B and C (b) A, B and D (c) B, C and D (d) A and D

88. With which game is the Agha Khan Cup associated ? (a) Football (b) Cricket (c) Basketball (d) Hockey

89. Which of the following countries is not member of Shanghai Cooperation Organization (SCO)? (a) Mongolia (b) Kyrgyzstan (c) Tajikistan (d) Russia

90. The term 'Steeplechase' is associated with (a) Horse Racing (b) Boxing (c) Polo (d) Rowing

91. Rovers Cup is associated with? (a) Tennis (b) Volleyball (c) Football (d) Basketball

92. Who among the following is the current Governor of Goa? (a) K. Sankaranarayanan (b) Bharat Vir Wanchoo (c) Shivinder Singh Sidhu (d) S. C. Jamir

93. Steel tower structure in the form of five rings, for the London Olympic, has been designed by: (a) Shekhar Kapoor (b) Sukhdev Malhotra (c) Vikash Kumar Jha (d) Anish Kapoor

94. The first ‗zero waste toilet system' (ZWTS) in India was inaugurated at which of the following villages? (a) Evoor, Kerala (b) Tundlam, Tamil Nadu (c) Mattur, Karnatka (d) Kunkalamarru Andhra Pradesh

95. Who is the current Chief Managing Director (CMD) of Coal India Limited? (a) Sutirtha Bhattacharya (b) S. Narsing Rao (c) Ms. Chanda Kochhar (d) Sudip Bandyopadhyay

96. Who among the following won the women's 48kg gold medal in the Commonwealth weightlifting championships at Apia, Samoa? (a) Tikina Gopal (b) K. Sanjita Chanu (c) N. Sumanbala Devi (d) K. Venkata Lakshmi

97. What is Goldman Sachs and Co.? (a) An international securities firm (b) An international merchant banking firm (c) An international credit rating agency (d) An international financial derivatives firm

98. Who among the following has been recently re-appointed as Deputy Governor of Reserve Bank of India by the Central Government for a further period of three months beyond June 14, 2012, or until further orders? (a) V.K.Sharma (b) K. C. Chakrabarty (c) Usha Thorat (d) Anand Sinha

99. Which of the following companies own the IPL Team “Chennai Super Kings” ? (a) ACC (b) Ultratech (c) India Cements (d) Aircel

100. Zee (currently Zee Telefilms Ltd), was promoted by which group of companies in 1982? (a) The Essel Group (b) The Welcom Group

(c) The Tatas Group (d) Dr. Reddy‘s Group

12

MOCK PAPER 1

ANSWERS KEYS

1.(a) 2.(c) 3.(a) 4.(b) 5.(b) 6.(c) 7.(a) 8.(b) 9.(d) 10. (d) 11. (c) 12. (d) 13. (a) 14. (b) 15. (b) 16. (d) 17. (c) 18. (a) 19. (b) 20. (a) 21. (b) 22. (d) 23. (b) 24. (b) 25. (a) 26. (b) 27. (a) 28. (a) 29. (a) 30. (c)

31. (b) 32. (d) 33. (c) 34. (d) 35. (a) 36. (b) 37. (d) 38. (a) 39. (a) 40. (c) 41. (b) 42. (a) 43. (d) 44. (c) 45. (c) 46. (a) 47. (b) 48. (b) 49. (b) 50. (c) 51. (d) 52. (a) 53. (d) 54. (c) 55. (b) 56. (b) 57. (b) 58. (d) 59. (a) 60. (a)

61. (c) 62. (c) 63. (d) 64. (c) 65. (c) 66. (c) 67. (c) 68. (a) 69. (c) 70. (d) 71. (d) 72. (b) 73. (a) 74. (a) 75. (c) 76. (c) 77. (d) 78. (a) 79. (a) 80. (b)

81. (a) 82. (c) 83. (c) 84. (a) 85. (c) 86. (a) 87. (b) 88. (d) 89. (a) 90. (a)

91. (c) 92. (b) 93. (d) 94. (a) 95. (b) 96. (b) 97. (a) 98. (b) 99. (c) 100. (a)

SOLUTIONS

1. (a) Let x and y be two arbitrary elements is A. Then, 𝑓 𝑥 = 𝑓 𝑦

𝑥−2

𝑥−3=

𝑦−2

𝑦−3

𝑥𝑦 − 3𝑦 − 2𝑦 + 6 = 𝑥𝑦 − 3𝑦 − 2𝑥 + 6 x = y, ∀x, y ϵ A 𝑆𝑜, 𝑓 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑣𝑒 𝑚𝑎𝑝𝑝𝑖𝑛𝑔. 𝐴𝑔𝑎𝑖𝑛, 𝑙𝑒𝑡 𝑦 𝑏𝑒 𝑎𝑛 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑟𝑦 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑖𝑛 𝐵, 𝑡𝑕𝑒𝑛 𝑓 𝑥 = 𝑦

𝑥−2

𝑥−3= 𝑦

𝑥 = 3𝑦−2

𝑦−1

Clearly, ∀y ϵ B, x = 3𝑦−2

𝑦−1 𝜖 𝐴, 𝑡𝑕𝑢𝑠 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑦 𝜖 𝐵 𝑡𝑕𝑒𝑟𝑒 𝑒𝑥𝑖𝑠𝑡𝑠 𝑥 𝜖 𝐴 𝑠𝑢𝑐𝑕 𝑡𝑕𝑎𝑡

𝑓 𝑥 = 𝑓 3𝑦−2

𝑦−1 =

3𝑦−2

𝑦−1− 2

3𝑦−2

𝑦−1− 3

= 𝑦

Thus, every element in the codomain B has its preimage in A, so f is a surjection. Hence, f : A is bijective. 2. c ∵ 𝑧 − 4 < |𝑧 − 2| |𝑧 − 4 2 < 𝑧 − 2 2 𝑥 − 4 2 + 𝑦2 < 𝑥 − 2 2 + 𝑦2 (let z = x + iy) 𝑥2 − 8𝑥 + 16 < 𝑥2 − 4𝑥 + 4 x > 3 Re(z) > 3

3. (a) 3

2 ≠

2

−1

i.e., 𝑎1

𝑎2 ≠

𝑏1

𝑏2

unique solution hence graphs is intersecting 4. (b) let father‘s present age = x

13

MOCK PAPER 1

children‘s present age = x After fifteen years

Father‘s age = x + 15 And five children‘s age = x + 5 15 = x + 75 According to question

x + 15 = 1

2 𝑥 + 75

Or 2x + 30 = x + 75 2x – x = 45 Or x = 45 father‘s present age = 45 years

5. (b) The rectangle, triangle and the circle each moves one step to the left in every subsequent row. Thus, the rightmost figure in the third row is the triangle. The rectangle is labeled ―+‖, the triangle ―C‖ and the circle ―T‖. Thus, the black triangle in row three should also be labeled ―C‖. Hence, option (b)

6. (c) Suppose they meet x hrs after 8 a.m. then, (Distance moved by first in x hrs) + [Distance moved by second in (x – 1) hrs] = 330 60x + 75 (x – 1) = 330 x = 3. So, they meet at (8 + 3), i.e. 11 a.m.

7. (a) Volume of the block = (10 × 5 × 2) cm3 = 100 cm3.

Volume of the cone carved out = 1

3×

22

7× 3 × 3 × 7 𝑐𝑚3 = 66 𝑐𝑚3 .

Wood wasted = (100 – 66)% = 34%. 8. (b) Most popular brand is brand D and after that it is brand C as is clear from the pie-chart.

Brand D sold = 26% And Brand C sold = 22% So, the difference is 4% of total market

= 25000 × 4

100= 1000

9. (d) Revenue earned before tax = Number of units sold × Unit price

Revenue earned by brand A

= 18 ×25000

100 × 14500

= 65250000 Revenue earned by brand B

= 14 ×25000

100 × 16000 = 56000000

Similarly, the revenue earned by C = 66,000,000. Revenue earned by D

= 26 ×25000

100 × 13000

= 84500000 Revenue earned by E = 67500000 So, maximum revenue is earned by D. 10. (d) Revenue earned after tax

= Revenue earned before tax – Tax

14

MOCK PAPER 1

Sales tax % Revenue earned before tax

Tax paid Revenue earned after tax

Brand A 14 65250000 9135000 56115000 Brand B 11 56000000 6160000 49840000 Brand C 10 66000000 6600000 59400000 Brand D 9 84500000 7605000 76895000 Brand E 11 67500000 7425000 60075000

Total 339250000 36925000 302325000

So, brand D earned the maximum revenue after tax.

12. (d) North – West

13. (a) Given, 𝑎2 𝑥4 + 𝑏𝑥3 + 𝑐𝑥2 + 𝑑𝑥 + 𝑓2 = (𝑎𝑥2 + 𝑐𝑥 + 𝑓)2 a perfect square = 𝑎2 𝑥4 + 2𝑎𝑐𝑥3 + 2𝑎𝑓 + 𝑐2 𝑥2 + 2𝑐𝑓𝑥 + 𝑓2 b = 2ac, c = 2a𝑓 + 𝑐2 ,𝑑 = 3𝑐𝑓 Again, 4𝑎2𝑐 = 4𝑎2 2𝑎𝑓 + 𝑐2 = 8𝑎3𝑓 + 𝑏2 (∵ b = 2ac)

14. (b) The easiest way to solve such problems is trial and error or by back substituting answers is the choices given. 1012 = 10201 1012 − 1 = 10200 this is divisible by 100 Similarly try for 1013 - 1 = 1030301 – 1 = 1030300 So, you can safely conclude that (1011 − 1) to (1019 − 1) will be divisible by 100. 10110 − 1 𝑡𝑜 10199 − 1 will be divisible by 1000. 𝑡𝑕𝑒𝑟𝑒𝑓𝑜𝑟𝑒, (101100 − 1) will be divisible by 10000.

15. (b) 𝑥𝑢 = 256 Take log on base 2, u log2 x = 8 Lot log 2 x = p

Then 8

𝑝= 𝑝2 − 6𝑝 + 12

𝑝3 − 6𝑝2 + 12𝑝 − 8 = 0 𝑝2 𝑝 − 2 − 4𝑝 𝑝 − 2 + 4 𝑝 − 2

15

MOCK PAPER 1

𝑝2 − 4𝑝 + 4 𝑝 − 2 = 0 𝑝 − 2 3 = 0 p = 2

Hence, exactly one solution. Answer option is (b).

16. (d) 60 min are gained in 60

55× 60 = 65

5

11 min

But they are together after 64 min.

Gain in 64 min = 655

11− 64 = 1

5

11=

16

11 𝑚𝑖𝑛

Gain in 24 h = 16×24×60

11×64= 32

8

11 𝑚𝑖𝑛

17. (c) Since, at least one root is negative, then { 𝛼𝛽 < 0 ∪ { 𝛼 + 𝛽) < 0 ∩ (𝐷 0)

1+8𝑚

1+𝑚< 0 ∪

2(1+3𝑚

1+𝑚 < 0 ∩ 𝑚

ϵ (-∞, 0]∪ [3, ∞)

𝑚 𝜖 −1 −1

8 ∩ {𝑚 𝜖 − ∞, 0 ∪ 3, ∞

𝑚 𝜖 −1,−1

8

18. (a) From (A) and (B), the code for brightly is ‗ba‘ and from (B) and (C), the code for sun is ‗lo‘. 19. (b) Let

𝐼 = ∫ 𝑥2+ 1[log 𝑥2+ 1 − 2 log 𝑥]

𝑥4 𝑑𝑥

I ∫ x2+ 1

𝑥4 {log x2 + 1 − log x2} dx

𝐼 ∫ 1 +1

𝑥2 log 1 +1

𝑥2 1

𝑥3 𝑑𝑥

Let 1 + 1

𝑥2 = 𝑡 𝑇𝑕𝑒𝑛, 𝑑 1 +

1

𝑥2 = 𝑑𝑡 −2

𝑥3 𝑑𝑥 = 𝑑𝑡 1

𝑥3 𝑑𝑥 = −1

2 𝑑𝑡

𝐼 = −1

2 ∫ 𝑡

𝐼𝐼 𝑙𝑜𝑔𝐼

𝑡 𝑑𝑡

𝐼 = −1

2 {

2

3 𝑙𝑜𝑡 𝑡 𝑡

3

2 −2

3 ∫

1

𝑡× 𝑡3/2 𝑑𝑡}

𝐼 −1

2{

2

3 (log 𝑡)𝑡

3

2 −4

9 𝑡

3

2} + 𝐶

𝐼 = −1

3 𝑡3/2 {log 𝑡 −

2

3} + 𝐶

𝐼 = −1

3 1 +

1

𝑥2 3/2

log 1 +1

𝑥2 −2

3 + 𝐶

For (Questions 20 – 22):

Here, Front = Back = Yellow Top = Bottom = Red Left = Right = Green

16

MOCK PAPER 1

20. (a) The total number of cubes have only one colour

= (2 × 4) + (1 × 2) = 8 + 2 = 10 21. (b) The total number of cubes have no colour

= 2 × 1 = 2 22. (d) The total number of cubes have any two colour.

= (4 × 2) + (2 × 2) = (8 + 4) = 12

23. (b) Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 – x) min. = 1.

x 2

75+

1

45 + 30 − 𝑥 .

2

75= 1

11𝑥

225+

(60−2𝑥)

75= 1 11x + 180 – 6x = 225 x = 9.

24. (b) Volume of hemisphere = 2

3𝑟3 .

Volume of biggest sphere = Volume of sphere with diameter r = 4

3

𝑟

2

2=

1

6 𝑟3

Required ratio = 2

3 𝑟3

1

6 𝑟3

=4

1 i.e. 4 : 1.

26. (b) let Ist root = x

2nd

roots = 2x

Sum of roots = -𝑏

𝑎

i.e., x + 2x = 𝑚

6

3x = 𝑚

6

Or x = 𝑚

18 ................ (i)

Similarly products of roots = 𝑐

𝑎

x 2y = 5

6

𝑥2 =5

12

𝑜𝑟 𝑥 = 5

12 ....... (ii)

From (i) and (ii)

𝑚

18=

5

12

Or m = 18 5

12

Or m = 18 5

2 3

m = 9 5

3

Or m = 9 5

3

3

3

Or m = 9 15

3= 3 15

27. (a) x =

3 point of local. Maximum, x =

−

3 points of local minimum,

17

MOCK PAPER 1

28. (a) x, y, z are in GP

𝑦

𝑥=

𝑧

𝑦 ................ (i)

y2 = xz ............... (ii) taking log of the sides 2log y = log x + log z log x, log y, log z, are in A. P. [if a, b, c, is in A. P. then 2b + a + c]

29. (a) Let the 2 particular boys be taken together as one unit. Then the number of units will be 6. They can sit around the table is 5! Ways. For each of the arrangement, the 2 can be interchanged in 2! Ways.

The total number of arrangement = 5! 2! = 240 30. (c) We notice that 9 divides both numbers. Now,

𝟏𝟐𝟑𝟒𝟓𝟔𝟕𝟖𝟗)𝟗𝟖𝟕𝟔𝟓𝟒𝟑𝟐𝟏(𝟖

𝟗𝟖𝟕𝟔𝟓𝟒𝟑𝟏𝟐

𝟗

If x divides A and x divides B, x divided the Rem 𝐴

𝐵

Where (A > B) The GCD is 9.

31. (b) Since, the choices are in terms of e, let us apply the Poisson distribution. Since 5% of bulbs are defective.

Mean, λ = 5% of 100 = 5.

P(X = k) = λK

𝐾! .𝑒−1

P(X = 0) = 50

0!.𝑒−5 = 𝑒−5

32. (d)

The above figure gives the front view of the tent where OA is the pole (with O being the bottom), T and T1 are a pair of diametrically opposite points on the surface of the tent (on the base), N and N1 are the supporting nails which

are collinear with T, O, T1. Given that AO = 3

2 m and NO = 3 (TO). Let To be x m and let ANO = θ

ATO = 2θ

tan θ = 3

2

𝑥=

1

2𝑥 𝑎𝑛𝑑 2𝜃 =

3

2𝑥

2

2𝑥

1−1

4𝑥2

=3

2𝑥

4𝑥

4𝑥2− 1=

3

2𝑥 tan 2𝜃 =

2−𝑡𝑎𝑛𝜃

1 tan 2 𝜃

8𝑥2 = 12𝑥2 − 3 𝑥 = 3

2

18

MOCK PAPER 1

tan𝜃 =1

3 𝜃 = 300 .

AN = 𝐴𝑂

𝑠𝑖𝑛=

3

21

2

= 3

33. (c) Let satellite is at D ad two earth station are at A and B respectively and AB = 2000 mt, now is ∆DCB

h

x= tan 450

h = x ........................ (i)

now in ∆ DCA

𝑕

𝑥+2000= tan 300

h = x+2000

3

from (i) and (ii) h = x = 2730 m.

34. (d) A B C D E F G H I J K

20 21 22 23 24 25 26 27 28 29 210

Letter ‗K‘ is represented by = 210

29=

1024

29= 9 (Remainder)

35. (a) 𝑒2

2− 𝑒

36. (b) In each number except 427, the middle digit is the sum of the other two.

37. (d) Given that, 𝑓 𝑥 = sin𝑥 cos𝑥 tan 𝑥𝑥3 𝑥2 𝑥2𝑥 1 1

𝑓 𝑥 = 𝑥 𝑥 − 1 sin𝑥 − 𝑥3 − 2𝑥2 cos𝑥 − 𝑥3 tan𝑥 = 𝑥2 sin𝑥 − 𝑥3 cos 𝑥 − 𝑥3 tan𝑥 + 2𝑥2 cos𝑥 − 𝑥 sin𝑥

Hence, limx→0f(x)

𝑥2

= limx→0

sin𝑥 − 𝑥 cos𝑥 − 𝑥 tan𝑥 + 2 cos𝑥 −sin 𝑥

𝑥

= 0 – 0 – 0 + 2 – 1 = 1

38. (a) Area of triangle = 1

2

𝑥1 𝑦1 1𝑥2 𝑦2 1𝑥3 𝑥3 1

= A rational number if vertices have integral coordinates only. If triangle is equilateral, then area

= 3

4 𝑥1 − 𝑥2

2 𝑦1 − 𝑦2 2

= irrational quantity So, triangle cannot be equilateral.

39. (a) Since, the function at x = 0 is continuous, we must have 𝑓 0 = lim

x→0 f x

19

MOCK PAPER 1

= limx→0

x + 1 cot 𝑥 = limx→0

1 + x 1

𝑥 𝑥 cot 𝑥

= limx→0

1 + x 1

𝑥 limx→0

x

tan 𝑥

= 𝑒1 = 𝑒 [∵ limx→0

1 + x)1

x = e and limx→0

x

tan 𝑥= 1

40. (c) The area of the triangle will comes 4 times. 42. (a) Editors should be concerned with quality. 44. (c) Refer the fourth paragraph. 45. (c) Refer the last sentence of the passage. 46. (a) Explained in the sentence from ―Before Verdi, there were rarely….. ― 49. (b) ‗should‘ may be replace with ‗would‘, 50. (c) ‗parts‘ should be replaced with ‗goods‘, 52. (a) ‗feasible but‘ should be replaced with ‗only feasible but also‘. 54. (c) into should be replaced with ‗in‘. 55. (b) ‗appraise‘ should be replaced with ‗apprise‘. 56. (b) ‗does‘ should be replaced with ‗he does‘. 68. (a) ‗Prologue‘ to a drama, ‗chapter‘ of a book. ‗footnote‘ is better than ‗commentary‘.