IIM MOCK PAPER – II

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 scales

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MOCK PAPER 1I

1. If sinx 𝛼 + cosx 𝛼 1, 0 < 𝛼 <

2 , 𝑡𝑕𝑒𝑛

(a) x (2, ∞) (b) x (-∞, 2] (c) x [-1, 1] (d) None of these 2. If a, b, c are in AP then 10𝑎𝑥+10 , 10𝑏𝑥+10 , 10𝑐𝑥+10 (x 0) are in

(a) AP (b) GP only when x > 0 (c) GP for all x (d) GP only when x < 0

3. If 𝑥2𝑘 occurs in the expansion of 𝑥 +1

𝑥2 𝑛−3

, then

(a) n – 2k is a multiple of 2 (b) n – 2k is a multiple of 3 (c) k = 0 (d) None of the above

4. The equation of the bisector of the obtuse angle between the lines 3x – 4y + 7 = 0 and -12x – 5y + 2 = 0 is (a) 21x + 77y + 101 = 0 (b) 21x + 77y – 101 = 0 (c) 21x + 77y = 0 (d) None of these

5. A person was asked to state his age in years. His reply was, “Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am.” What was the age of the person? (a) 18 years (b) 20 years (c) 24 years (d) 32 years

Directions for (Questions 6 – 7): In each of these questions, there are two statements 1 and 2 followed by two conclusions numbered I and II. Decide which of the given conclusion logically follow from the two given statements, disregarding commonly known facts. Mark (a) if only conclusion I follow. Mark (b) if only conclusion II follow. Mark (c) if either I or II follows. Mark (d) if neither I nor II follows.

6. Statements: Some parrot are crows. No crow is green. Conclusions: I. No parrot is green. II. No crow is white.

7. Statements: All ants are hardworking. Some ants are lazy. Conclusions: I. All lazy ants are hardworking. II. All hardworking ants are lazy.

8. A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. what would have been the percentage of profit earned if no discount was offered? (a) 24.5 (b) 28.5 (c) 30 (d) Data inadequate

9. There are n distinct points on the circumference of a circle. The number of pentagons that can be formed with these points as vertices is equal to the number of possible triangles. Then, the value of n is (a) 7 (b) 8 (c) 15 (d) 30

10. Let A, B and C be n × n matrices. Which one of the following is a correct statement? (a) If AB = AC, then B = C (b) If 𝐴3 + 2𝐴2 + 3𝐴 + 5𝐼 = 0, then A is invertible (c) If 𝐴2 = 0 then A = 0 (d) None of the above

11. If f x dx = g x + c, then f−1 (x) dx is equal to

(a) 𝑥𝑓−1 𝑥 + 𝑐 (b) 𝑓 𝑔−1 𝑥 + 𝑐 (c) 𝑥𝑓−1 𝑥 − 𝑔 𝑓−1 𝑥 + 𝑐 (d) 𝑔−1 𝑥 + 𝑐

12. A and B are partners in a business. A contributes 1

4 of the capital for 15 months and B received

2

3 of the profit. For

how long B‟s money was used? (a) 6 months (b) 9 months (c) 10 months (d) 1 year

13. Two cards are drawn successively with replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is (a) 1/13 (b) 3/13 (c) 2/13 (d) None of these

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MOCK PAPER 1I

14. If the roots of equation 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 𝑎𝑟𝑒𝑘+1

𝑘 𝑎𝑛𝑑

𝑘+2

𝑘+1, then the value of (a + b + c)2 is

(a) 𝑏2 + 4𝑎𝑐 (b) – 𝑏2 + 4𝑎𝑐 (c) 𝑏2 − 4𝑎𝑐 (d) None of these 15. A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 litres a

minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold? (a) 7580 (b) 7960 (c) 8290 (d) 8640

16. Find the odd man out: 19, 28, 39, 52, 67, 84, 102 (a) 52 (b) 102 (c) 84 (d) 67

17. limx→∞ x+ 1

x+2

2x+1 is equal to

(a) 𝑒−2 (b) e (c) 𝑒2 (d) None of these 18. Let p be the proposition Mathematics is interesting and let q be the proposition that Mathematic is difficult, then the

symbol p ⋀ q means (a) Mathematics is interesting implies that Mathematics is difficult (b) Mathematics is interesting implies and is implied by Mathematics is difficult. (c) Mathematics is interesting and Mathematics is difficult. (d) Mathematics is interesting or Mathematics is difficult.

19. Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is: (a) 500 km (b) 630 km (c) 660 km (d) 900 km

20. A person invested in all Rs. 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is: (a) Rs. 200 (b) Rs. 600 (c) Rs. 800 (d) Rs. 1200

21. If 𝑓(𝑥) is differentiable and strictly increasing function, then the value of limx→0f x2 − f(x)

𝑓 𝑥 −𝑓(0) is

(a) 1 (b) 0 (c) – 1 (d) 2 Directions for (Questions 22 – 25): A school has four sections A, B, C, D of Class IX students. The results of half-yearly and annual examinations are shown in the table given below. Answer the questions based on this table.

Result Number of Students

Section A Section B Section C Section D

Students failed in both Exams 28 23 17 27

Students failed in half-yearly but passed in Annual Exams 14 12 8 13 Students passed in half-yearly but failed in Annual Exams 6 17 9 15

Students passed in both Exams 64 55 46 76

22. How many students are there in Class IX in the school?

(a) 336 (b) 189 (c) 286 (d) 430 23. Which section has the minimum failure rate in half-yearly examination?

(a) A (b) B (c) C (d) D 24. Which section has the maximum success rate in annual examination?

(a) A (b) B (c) C (d) D

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MOCK PAPER 1I

25. Which section has the maximum pass percentage in at least one of the two examinations? (a) A (b) B (c) C (d) D

26. In how many different ways can the letters of the word „DETAIL‟ be arranged in such a way that the vowels occupy only the odd positions? (a) 32 (b) 48 (c) 36 (d) 60

27. Of the two square fields, the area of one is 1 hectare while the other one is broader by 1%. The difference in their areas is: (a) 100 m2 (b) 101 m2 (c) 200 m2 (d) 201 m2

28. A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective, is:

(a) 4

19 (b)

7

19 (c)

12

19 (d)

21

95

29. If variable x and y are related by the equation 𝑥 = 1

1+9𝑢2

𝑦

0 𝑑𝑢, 𝑡𝑕𝑒𝑛

𝑑2𝑦

𝑑𝑥2 is equal to, (use formula I = f t dx,v

u

𝑑𝐼

𝑑𝑥= 𝑓 𝑣

𝑑𝑣

𝑑𝑥− 𝑓 𝑢

𝑑𝑢

𝑑𝑥)

(a) 1 + 9y2 (b) 1

1+9𝑦2 (c) 9y (d) 1

9 𝑦

30. A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 450 with the man‟s eye when at a distance of 60 metres from the tower. After 5 seconds, the angle of depression becomes 300. What is the approximate speed of the boat, assuming that it is running in still water? (a) 32 kmph (b) 36 kmph (c) 38 kmph (d) 40 kmph

31. Let A be a finite set. If f : A A is a one-one function, then (a) f is onto (b) f is many one (c) f is continuous (d) f is differentiable

32. Find the absolute maximum and minimum values of a function f given by 𝑓 𝑥 = (2𝑥)3 − 15𝑥2 + 36𝑥 +1 𝑜𝑛 𝑡𝑕𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 1, 5 (a) Absolute max. value = 52 at x = 5 Absolute Min. value = 29 at x = 1 (b) Absolute max. value = 62 at x = 5 Absolute Min. value = 41 at x = 1 (c) Absolute max. value = 56 at x = 5 Absolute Min. value = 24 at x = 1 (d) Absolute max. value = 52 at x = 5 Absolute Min. value = 60 at x = 1

33. ex cos

4+

𝑥

2 𝑑𝑥

2

0

(a) 2 3

5 𝑒2 + 1 (b) -

3 2

5 𝑒2 + 1 (c) -

3 2

5 𝑒2 + 2 (d) None

34. If (a + b + c) = 0 the value of 𝑎2+ 𝑏2+ 𝑐2

𝑎2− 𝑏𝑐 is

(a) 0 (b) 1 (c) 2 (d) None

35. Which figure belongs in neither groups?

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MOCK PAPER 1I

36. The area bounded by the curves |x| + |y| 1 and 𝑥2 + 𝑦2 1 is

(a) 2 sq unit (b) sq unit (c) ( - 2) sq unit (d) ( + 2) sq unit 37. If the number of students passing an examination be considered a criteria for comparison of difficulty level of two

examinations, which of the following statements is true in this context? (a) Half-yearly examinations were more difficult (b) Annual examinations were more difficult. (c) Both the examinations had almost the same difficulty level. (d) The two examinations cannot be compared for difficulty level.

38. x 1 − x 5 𝑑𝑥1

0

(a) 2

42 (b)

1

44 (c)

1

42 (d) None

39. In a hospital, there are 20 kidney dialysis machines and that the change of any one of them to be out of service during a day is 0.02. Determine the probability that exactly 3 machines will be out of service of the same day. (a) 0.0071 (b) 0.1144 (c) 1.450 (d) None

40. The differential equation of all straight lines passing through origin is

(a) y = 𝑥𝑑𝑦

𝑑𝑥 (b)

𝑑𝑦

𝑑𝑥= 𝑦 + 𝑥 (c)

𝑑𝑦

𝑑𝑥= 𝑦 − 𝑥 (d) None of these

Directions for (Questions 41-44) Choose the word which is closest in the meaning to the given word. 41. Decry

(a) deviate (b) despoil (c) demure (d) disparage 42. Brash

(a) invective (b) rude (c) abusive (d) superficial 43. Superannuated

(a) accepted (b) senile (c) retired (d) experienced 44. Indict

(a) accuse (b) condemn (c) allege (d) reprimand Directions for (Questions 45-48) Choose the word which is farthest in the meaning to the given word.

45. Monologue

(a) dialogue (b) prologue (c) epilogue (d) catalogue 46. Frugal

(a) gaudy (b) generous (c) extravagant (d) charitable 47. Pastel

(a) urban (b) delicate (c) bright (d) sweet 48. Terse

(a) concise (b) detailed (c) expressive (d) descriptive

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MOCK PAPER 1I

Directions for (Question 49-52): In the question below, the first and the sixth sentence are given in the beginning. The middle four sentences in each have been jumbled up. These are labeled A, B, C and D. you are required to find out the proper sequence of the four sentences from the given alternatives. 49. S1: Biological evolution has not fitted man to any specific environment.

S6: That brilliant sequence of cultural peaks can most appropriately be termed the ascent of Man. A. It is by means a biological evolution, but it is a cultural one. B. His imagination, his reason, his emotional subtlety and toughness, make it possible for him not to accept the

environment but. to change it. C. And that series of inventions by which man from age to age has reshaped his environment is a different kind of

evolution. D. Among the multitude of animals which scamper, fly, burrow and swim around us, he is the only one who is not

locked into his own environment. (a) BCDA (b) BACD (c) DBCA (d) DCBA

50. S1: Since the sixties there has been an increasing interest in human neurophysiology, which deals with the neural bases of mental activity and behaviour. S6: So far the journal has published a mixture of articles including reports and investigations. A. It has format which is very similar to that of Brain and Language, a sister journal. B. Since then, a number of journals devoted entirely to this area of research have appeared. C. Before the 1960s when this field was the concern of a small number of investigators, research articles were

scattered in various neurological journals. D. Brain and Cognition is one such journal, (a) BCDA (b) BDAC (c) CBDA (d) CDAB

51. S1: For decades, American society has been called a melting pot. S6: In recent years, such differences - accentuated by the arrival of immigrants from Asia and other parts of the world in the United States - have become something to celebrate and to nurture. A. Differences remained - in appearance, mannerisms, customs, speech, religion and more. B. The term has long been a cliche, and a half truth. C. But homogenization was never achieved. D. Yes, immigrants from diverse cultures and traditions did cast off vestiges of their native lands and become almost

imperceptibly woven into the American fabric, (a) BCDA (b) BDCA (c) DBAC (d) DBCA

52. S1: The cooperative system of doing business a good way of encouraging ordinary workers to work hard. S6: The main object is to maintain the interest of every member of the society and to ensure that the members participate actively in the projects of the society. A. If the society is to be well run, it is necessary to prevent insincere officials being elected to the committee which

is solely responsible for the running of the business. B. To that end, an elected body is formed based on consensus. C. To a large extent, many cooperative societies need advice and guidance. D. The capital necessary to start a business venture is obtained by the workers contributions, (a) DBAC (b) DCBA (c) ADCB (d) ABDC

Directions for (Questions 53 – 54): In each question, there are four sentences. Each sentence has pairs of words/phrases that are highlighted. From the highlighted word(s) /phrase(s), select the most appropriate word(s)/phrase(s) to form correct sentences. Then, from the options given, choose the best one.

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MOCK PAPER 1I

53. The cricket council that was (a)/ were (b) elected last March is (a)/ are (b) at sixes and seven over new rules.

The critics censored (a)/ censured (b) the new movie because of its social unacceptability. Amit‟s explanation for missing the meeting was credulous (a)/ credible (b). She coughed discreetly (a)/ discretely (b) to announce here presence. (a) AABBA (b) AAABA (c) BBBBA (d) BBAAA

54. The further (a)/ farther (b) he pushed himself, the more disillusioned he grew. For the crowds it was more of a historical (a)/ historic (b) event; from their leader, it was just another day. The old man has a healthy distrust (a)/ mistrust (b) for all new technology. This film is based on a real (a)/ true (b) story. One suspects that the compliment (a)/ complement (b) was backhanded. (a) BABAB (b) ABBBA (c) BAABA (d) ABABA

Directions for (Questions 55 – 58): From the given alternatives, select the one in which the pairs of words have a relationship similar to the one in capital words. 55. SHALE : GEOLOGIST : :

(a) Aster : Botanist (b) Obelisk : Fireman (c) Love : Philologist (d) Reef : Astrologer

56. APOSTATE : RELIGION : : (a) Potentate : Kingdom (b) Jailer : Law (c) Traitor : Country (d) Teacher : Education

57. MISDEMEANOR : FELONY : : (a) Police : Prison (b) Thief : Burglar (c) Crime : Degree (d) Mishap : Education

58. PUSILLANIMOUS : DASTARD : : (a) Impecunious : Mendicant (b) Plebeian : Entrepreneur (c) Magnanimous : Misanthrope (d) Optimistic : Pessimist

Direction for (Question 59 - 62): Find which of the following option fits in the blank space(s) of the sentence to make it meaningfully complete. 59. If misery is the effect of ill fortune, it ought to be pitied, if of …………to be …………

(a) virtue, criticized (b) calamity, reverenced (c) virtue, protected (d) virtue, reverenced

60. ……… of different categories of problems often leads to design of improper solutions that fail to address the complexities of the problem. (a) confabulation (b) conflation (c) conflict (d) confession

61. Kagan maintains that an infant‟s reactions to its first stressful experiences are part of a natural process of development, not harbingers of childhood unhappiness or ………… signs of adolescent anxiety. (a) prophetic (b) normal (c) typical (d) virtual

62. This cruise gives you a taste of ………….. living. (a) fine (b) high (c) gracious (d) cool

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MOCK PAPER 1I

Directions for (Questions 63 – 70): Answer the questions that follow the passage. The concept of paradigm, because it emphasizes the importance of social agreement among scientists, had the effect of turning attention to the human side of science. It resonated with a great wave of interest in sociology of science. It seems particularly appropriate for psychologists to pay some attention to the human aspect of their own discipline, its psychology as well as its sociology. It is in the end of social fact that psychology has become a powerful institution and profession that makes its scientific approach something to be reckoned with. But were the scientific clothes necessary? Granted psychology, like the physical science, had to break away organizationally from philosophy, but why is its subject matter - mind - not sufficient distinction? While these doubts remain the imposition of a scientific approach is bound to seem totalitarian - may be historically it was. The scientific part of psychology came to dominate the whole but this particular dialectic of part and whole may be beginning to unwind - though the rapid rise of Artificial Intelligence underlines the continuing appeal of science. Artificial Intelligence is a field based on the new metaphor that the programme of a computer is its 'mind', so truly a 'ghost' in the machine - Narhari Rao's derisive phrase to dismiss dualistic mentalism. It is disturbing to note that a mantle of science seems to call for attempts to launder away human debating tactics and other influences from the received or canonical account of what happens. The imaginary picture portrayed, of reason in action, is possible because the outside world accepts the version agreed upon by a core-set of scientists. Outside the core-set distance lends enchantment. The idealized version succeeds in compelling acceptance and even certainty about the knowledge involved. 63. A totalitarian regime would most likely be a

(a) autarchy (b) pantisocracy (c) meritocracy (d) gerontocracy 64. Why is the idea of „reason in action' accepted by most people?

(a) It is put forward by scientists. (b) It is an idealized version. (c) It compels acceptance. (d) People are awed by scientists and easily believe what they say.

65. The antonym of „canonical' is (a) accepted (b) authorized (c) standard (d) unorthodox

66. When Narhari Rao coined the phrase 'ghost in the machine', he was (a) complimenting the ingenuity of Artificial Intelligence (b) being scornful about endowing inert objects with the quality of a soul (c) heralding the arrival of a new age in science (d) being immune to the scientific onslaught on psychology

67. The word 'dialectic' in this context means (a) dialogue (b) comment (c) dispute (d) inquisition

68. We can infer from the passage that (a) psychologists eagerly adopted the scientific approach. (b) physics dissociated itself from philosophy. (c) the scientific approach remained marginal in psychology. (d) the subject matter of psychology is human feelings.

69. The closest substitute to 'paradigm' in this context would be (a) Pattern (b) Paragon (c) Parallel (d) Positioning

70. What makes the scientific approach of psychology so significant? (a) The social agreement between scientists (b) The attention paid by the scientific community to the human side of science (c) The concept of paradigm

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MOCK PAPER 1I

(d) The emergence of psychology as a powerful institution 71. The coin rupia was first issued by

(a) Sher Shah (b) Alauddin Khilji (c) Akbar (d) Muhammad – bin – tughlaq 72. Who levied the tax known by the name of „Chauth‟?

(a) Chandellas (b) Cholas (c) Marathas (d) Mughals 73. Who was the ruler of medieval India who is credited with the building of the Grand Trunk Road?

(a) Babur (b) Sher Shah Suri (c) Jahangir (d) Krishnadeva Raya 74. Artillery was used for the first time in India by

(a) Ala-ud-din Khilji (b) Timur (c) Sher Shah Suri (d) Babar 75. The first Muslim ruler in India was

(a) Bairam Khan (b) Sher Shah (c) Muhammad Shab (d) Ahmad Shah 76. East India Company was promoted by the merchants of

(a) Manchester (b) London (c) Liverpool (d) Amsterdam 77. Who was the founder of Qutab Shahi dynasty?

(a) Adil Shah (b) Ibrahim Adil Shah II (c) Ibrahim Qutb Shah (d) Quli Qutb Shah 78. Which one is the place of origin of Narmada river?

(a) Amarkantak (b) Panchmadhi (c) Mandu (d) Satpura 79. What is the “Flame”, which was recently in news?

(a) A satellite (b) A computer virus (c) A spacecraft (d) A submarine 80. Which country is known as 'Land of Thunder Dragon'?

(a) Nepal (b) Tibet (c) Bhutan (d) Afghanistan 81. In which continent does the Nile River flow?

(a) South America (b) Africa (c) Australia (d) North America 82. What was the old name of Ethiopia?

(a) Abyssinia (b) Mesopotamia (c) Misr (d) Armenia 83. On which river-bank is Ujjain situated?

(a) Tapti (b) Narmada (c) Chambal (d) Kshipra 84. What is called as Dakshin Ganga?.

(a) Narmada (b) Godavari (c) Tapti (d) Indian Research Station on the Antarctica 85. Which of the following are features of economic planning in India?

1. Indicative Planning 2. Limited centralization 3. Democratic Socialism 4. Development Orientation (a)3 only (b) 2 and 3 (c) 2, 3, and 4 (d) 1, 2, 3 and 4

86. Economic Planning refers to (a) The planning of manpower (b) The mobilization of taxes (c) The allocation of resources (d) None of these

87. „Interest Rate Policy‟ is a component of (a) Fiscal Policy (b) Monetary Policy (c) Trade Policy (d) Direct Control

88. The Winter Olympics came into being in (a) 1912 (b) 1916 (c) 1920 (d) 1924

89. The headquarters of International Olympic Committee is at (a) Lausanne (Switzerland) (b) Moscow (c) Los Angles (d) New York

90. Who won the Sultan Azlan Shah Cup hockey tournament 2012?

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MOCK PAPER 1I

(a) Malaysia (b) New Zealand (c) Argentina (d) South Korea 91. Beighton Cup and Agha Khan Cup are associated with which of the following games?

(a) Cricket (b) Football (c) Hockey (d) Volleyball 92. National Film Development Corporation of India (NFDC) is the central agency established in 1975. Who is the

current chairman of NFDC? (a) Manmohan Shetty (b) Ramesh Sippy (c) Om Puri (d) D. V Suryanarayana Raju

93. After WWE wrestler Great Khali who is the second sportsperson keen to open cricket academy in Himachal Pradesh? (a) Suresh Raina (b) Yuvraj Singh (c) Mahendra Singh Dhoni (d) Harbhajan Singh

94. Which of the following IT companies has finally launched 'MyEdu tablet' in India? (a) HCL (b) Wipro (c) Dell (d) Samsung

95. Who is the current Chief Information commissioner of India? (a) Wajahat Habibullah (b) Satyananda Mishra (c) A. N. Tiwari (d) Rajiv Mathur

96. Who among the following is the China's first female astronaut? (a) Yi So-yeon (b) Liu Yang (c) Yang Ju Liu (d) Chiaki Mukai

97. 3M is a name of a company. What is the full name? (a) Material, Mineral and Manufacturing Company (b) Mineral, Manufacturing and Mining Company (c) Minnesota Mining and Manufacturing Company (d) Minnesota Mineral and Mining Company

98. Subhash Ghai is the chairman of (a) Balaji Telefilms Ltd (b) Mukta Arts Ltd (c) F.T.I.I. (d) National School of Drama

99. BMW belongs to which of the following countries (a) U.K. (b) France (c) Austria (d) Germany

100. Who among the following won Indonesian Super Series Premier title 2012 in Jakarta. (a) Li Xuerui (b) Saina Nehwal (c) Wang Yihan (d) Zhang Ning

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MOCK PAPER 1I

ANSWERS KEY

1. (b) 2. (c) 3. (b) 4. (a) 5. (a) 6. (d) 7. (d) 8. (c) 9. (b) 10. (b) 11. (c) 12. (c) 13. (c) 14. (c) 15. (d) 16. (b) 17. (a) 18. (c) 19. (d) 20. (d) 21. (c) 22. (d) 23. (d) 24. (a) 25. (d) 26. (c) 27. (d) 28. (b) 29. (c) 30. (a) 31. (a) 32. (c) 33. (b) 34. (c) 35. (b) 36. (c) 37. (c) 38. (c) 39. (a) 40. (d) 41. (d) 42. (b) 43. (c) 44. (a) 45. (a) 46. (c) 47. (c) 48. (b) 49. (a) 50. (c)

51. (b) 52. (b) 53. (a) 54. (d) 55. (a) 56. (c) 57. (d) 58. (a) 59. (d) 60. (b) 61. (a) 62. (b) 63. (a) 64. (d) 65. (b) 66. (b) 67. (c) 68. (a) 69. (a) 70. (b) 71. (c) 72. (c) 73. (b) 74. (d) 75. (d) 76. (d) 77. (d) 78. (a) 79. (b) 80. (c) 81. (b) 82. (a) 83. (d) 84. (b) 85. (d) 86. (c) 87. (b) 88. (d) 89. (a) 90. (b) 91. (b) 92. (b) 93. (c) 94. (a) 95. (b) 96. (b) 97. (c) 98. (b) 99. (d) 100. (b)

SOLUTIONS

1. (b) 𝑐𝑜𝑠𝑥 𝛼 + 𝑠𝑖𝑛𝑥 𝑎 1 Equality holds when x = 2 If x < 2, both cos α and sin α are increasing. cosx sinx α > 1, 𝑖𝑓 𝑥 < 2 If x > 2, then cosx 𝑎 + sinx 𝑎 < 1 x (-∞, 2]

2. (c) Since a, b, c are in AP. 2b = a + c 2bx = (a + c) x for all x 2bx + 20 = (a + c)x + 20 for all x 2(bx + 10) = (ax + 10) + (cx + 10)

102(𝑏𝑥+10) = 10 𝑎𝑥+10 + (𝑐𝑥+10)

10𝑏𝑥+10 2

= 10𝑎𝑥 +10 . 10𝑐𝑥+10

10𝑎𝑥+10 , 10𝑏𝑥+10 , 10𝑐𝑥+10 are in GP for all x.

3. (b) the general term in the expansion of 𝑥 +1

𝑥2 𝑛−3

is given by

𝑇𝑟+1 = 𝑛 − 3𝐶𝑟 𝑥 𝑛−3−𝑟

1

𝑥2 𝑟

= 𝑛 − 3𝐶𝑟𝑥𝑛−3−3𝑟

As 𝑥2𝑘 𝑜𝑐𝑐𝑢𝑟𝑠 𝑖𝑛 𝑡𝑕𝑒 𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 𝑜𝑓 𝑥 +1

𝑥2 𝑛−3

, we must have n – 3 – 3r = 2k for some non-negative integer r.

3(1 + r) = n – 2k n – 2k is a multiple of 3.

4. (a) 𝑎1𝑎2 + 𝑏1𝑏2 = 3 × −12 −4 × −5 = - 36 + 20 = - 16 𝑎1𝑎2 + 𝑏1𝑏2 0

The equation of obtuse bisector is (3𝑥−4𝑦+7)

32+ −4 2= −

−12𝑥−5𝑦+2

−12 2+ −5 2

12

MOCK PAPER 1I

13(3x – 4y + 7) = - 5(-12x – 5y + 2) 21x + 77y – 101 = 0 is the obtuse angle bisector.

5. (a) Let the present age of the person be x years. Then, 3 (x + 3) – 3 (x – 3) = x (3x + 9) – (3x – 9) = x x = 18.

7. (d) The second premises is particular. If one premise is particular, the conclusion must also be particular. Here, both the conclusions are general or universal. Hence no conclusion follows.

8. (c) Let C.P. be Rs. 100. Then, S.P. = Rs. 123.50.

Let marked price be Rs. x. Then, 95

100𝑥 = 123.50 x = Rs.

12350

95 = 𝑅𝑠. 130.

Now, S.P. = Rs. 130, C.P. = Rs. 100. Profit % = 30%

9. (b) Since, there are n distinct points on a circle. For making a pentagon it requires a five points. According to given condition

nC5= nC3 n = 8 10. (b) Given, A, B, C are n × n matrices.

Since, A satisfies 𝑥3 + 2𝑥2 + 3𝑥 + 5 = 0 As 𝐴3 + 2𝐴2 + 3𝐴 + 5𝐼 = 0

A must be invertible

11. (c) Let 𝐼 = 𝑓−1 𝑥 𝑑𝑥 …………… (i) And 𝑓 𝑥 𝑑𝑥 = 𝑔 𝑥 + 𝑐 ……….. given (ii)

From Eq. (i) let 𝑓−1 𝑥 = 𝑢 x= 𝑓(𝑢) 𝑑𝑥 = 𝑓 ′ 𝑢 𝑑𝑢 𝐼 = 𝑢𝑓 ′ 𝑢 𝑑𝑢

= 𝑢𝑓 𝑢 − 𝑓 𝑢 𝑑𝑢 =𝑢𝑓 𝑢 − 𝑔 𝑢 + 𝑐 [from Eq. (ii)] On putting u = 𝑓−1 𝑥 , 𝑓 𝑢 = 𝑥

We putting u = 𝑓−1 𝑥 − 𝑔 𝑓−1 𝑥 + 𝑐

12. (c) Let the total profit be Rs. z, Then,

B‟s share = Rs. 2𝑧

3, 𝐴′𝑠𝑠𝑕𝑎𝑟𝑒 = 𝑅𝑠. 𝑧 −

2𝑧

3 = 𝑅𝑠.

𝑧

3.

A : B = 𝑧

3∶

2𝑧

3= 1: 2.

Let the total capital be Rs. x and suppose B‟s money was used for x months. Then, 1

4𝑥×15

3

4𝑥×𝑦

=1

2 y

15×2

3 = 10.

Thus, B‟s money was used for 10 months. 13. (c) Let x denote a random variable which is the number of aces.

Clearly, X takes values, 1, 2.

P= 4

52=

1

13, 𝑞 = 1 −

1

13=

12

13

𝑃 𝑋 = 1 = 2 × 1

13 ×

12

13 =

24

169

𝑃 𝑋 = 2 = 2 1

13

2 .

12

13

0=

2

169

13

MOCK PAPER 1I

𝑀𝑒𝑎𝑛 = 𝑃𝑖𝑋𝑖 =24

169+

2

169=

26

169=

2

13

14. (c) ∵ Sum of roots,

𝑘+1

𝑘+

𝑘+2

𝑘+1= −

𝑏

𝑎 …………… (i)

𝑎𝑛𝑑 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑟𝑜𝑜𝑡𝑠,

𝑘+1

𝑘×

𝑘+2

𝑘+1=

𝑐

𝑎

𝑘+2

𝑘=

𝑐

𝑎

2

𝑘=

𝑐

𝑎− 1 =

𝑐 −𝑎

𝑎

k = 2𝑎

𝑐−𝑎

On putting the value of k is Eq. (i), we get

𝑐+𝑎

2𝑎+

2𝑎

𝑐+𝑎= −

𝑏

𝑎

𝑐 + 𝑎 2 + 4𝑎𝑐 = −2𝑏 𝑎 + 𝑐 𝑎 + 𝑐 2 + 2𝑏 𝑎 + 𝑐 = −4𝑎𝑐 𝑎 + 𝑐 2 + 2𝑏 𝑎 + 𝑐 + 𝑏2 = 𝑏2 − 4𝑎𝑐 𝑎 + 𝑏 + 𝑐 2 = 𝑏2 − 4𝑎𝑐

15. (d) work done by the inlet in 1 hour = 1

8−

1

12 =

1

24 .

Work done by the inlet in 1 min. = 1

24×

1

60 =

1

1440.

Volume of 1

1440 part = 6 litres.

Volume of whole = (1440 × 6) litres = 8640 litres. 16. (b) The pattern is x2 + 3, where x = 4, 5, 6, 7, 8, 9 etc. But 102 is out of pattern.

17. (a) limx→∞ x+ 1

x+2

2x+1 = limx→∞ 1 −

1

x+2

2x+1

= limx→∞ 1 −1

𝑥+2

x+2

2𝑥+1

𝑥+2

= 𝑒lim 𝑥 → ∞ −

2+1𝑥

1+2𝑥 = 𝑒−2

18. (c) p ⋀ q means Mathematics is interesting and Mathematics is difficult. 19. (d) At the time of meeting, let the distance travelled by the second train be x km.

Then, distance covered by the first train is (x + 100) km.

𝑥

40=

𝑥+100

50 50x = 40x + 4000 x = 400.

So, distance between P and Q = (x + x + 100) km = 900 km. 20. (d) Let the parts be x, y and [2600 –(x + y)]. Then,

𝑥×4×1

100=

𝑦×6×1

100=

2600− 𝑥+𝑦 ×8×1

100

𝑦

𝑥=

4

6=

2

3 𝑜𝑟 𝑦 =

2

3𝑥.

So, 𝑥×4×1

100=

2600−5

3𝑥 ×8

100

4x = 7800−5𝑥 ×8

3 52x = (7800 × 8) x =

7800×8

52 = 1200.

Money invested at 4% = Rs. 1200

14

MOCK PAPER 1I

21. (c) Here, limx→0f x2 − f(x)

𝑓 𝑥 −𝑓(0)

= limx→0𝑓 ′ (x)2x − 𝑓′(x)

𝑓′ 𝑥 =

−𝑓 ′ (0)

𝑓 ′ (0)= −1

22. (d) Since the classification of the students on the basis of their results and sections form independent groups, so the total number of students in the class: = (28 + 23 + 17 + 27 + 14 + 12 + 8 + 13 + 6 + 17 + 9 + 15 + 64 + 55 + 46 + 76) = 430.

23. (d) Total number of failures in half – yearly exams in a section = [(Number of students failed in both exams) + (Number of students failed in half-yearly but passed in Annual exams)] in that section Failure rate in half-yearly exams in Section A

= 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑜𝑓 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝐴 𝑓𝑎𝑖𝑙𝑑 𝑖𝑛 𝐻𝑎𝑙𝑓 −𝑦𝑒𝑎𝑟𝑙𝑦

𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑖𝑛 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝐴× 100 %

= 28+14

28+14+6+64 × 100 % =

42

112× 100 % = 37.5%

Similarly, failure rate in half-yearly exams in:

Section B = 23+12

23+12+17+55 × 100 % =

35

107× 100 % = 32.71%

Section C = 17+8

17+8+9+46 × 100 % =

25

80× 100 % = 31.25%

Section D = 𝟐𝟕+𝟏𝟑

27+13+15+76 × 100 % =

40

131× 100 % = 30.53%

Clearly, the failure rate in minimum for Section D. 24. (a) Total number of students passed in annual exams in a section.

= [(Number of students failed in half-yearly but passed in annual exams) + Number of students passed in both exams)] in that section Success rate in annual examination in Section A

= 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑜𝑓 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝐴 𝑝𝑎𝑠𝑠𝑒𝑑 𝑖𝑛 𝑎𝑛𝑛𝑢𝑎𝑙 𝑒𝑥𝑎𝑚𝑠

𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑖𝑛 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝐴× 100 %

= 14+64

28+14+6+64 × 100 % =

78

112× 100 % = 69.64%

Similarly, success rate in annual examinations in:

Section B = 12+55

23+12+17+55 × 100 %

67

107× 100 % = 62.62%

Section C = 8+46

17+8+9+46 × 100 % =

54

80× 100 % = 67.5%

Section D= 13+76

27+13+15+76 × 100 % =

89

131× 100 % = 67.94%

Clearly, the success rate in annual examination in maximum for Section A. 25. (d) Pass percentage in at least one of the two examinations for different sections are:

For Section A = 14+6+64

28+14+6+64 × 100 % =

84

112× 100 % = 75%

For Section B = 12+17+55

23+12+17+55 × 100 %

63

80× 100 % = 78.75%

For Section C = 8+9+46

17+8+9+46 × 100 % =

63

80× 100 % = 78.75%

For Section D = 13+15+76

27+13+15+76 × 100 % =

104

131× 100 % = 79.39%

Clearly, the pass percentage in maximum for Section D. 26. (c) There are 6 letters in the given word, out of which there are 3 vowels are 3 consonants.

Let us mark these positions as under:

15

MOCK PAPER 1I

(1) (2) (3) (4) (5) (6) Now, 3 vowels can be placed at any of the three placed out of 4, marked 1, 3, 5. Number of ways of arranging the vowels = 3P3 = 3! = 6. Also, the 3 consonants can be arranged at the remaining 3 positions. Number of ways of these arrangements = 3P3 = 3! = 6. Total number of ways = (6 × 6) = 36.

27. (d) Area = 1 hect. = 10000 sq. m side = 10000 m = 100 m. Side of the other square = 101 m. Difference in their areas = [(101)2 – (1002)]m2 =[(101 + 100)(101 – 100)]m2 = 201m2.

28. (b) P(None is defective) = 16𝐶2

20𝐶2

= 16×15

2×1×

2×1

20×19 =

12

19

P(at least one is defective) = 1 −12

19 =

7

19 .

29. (c) We know that by Newton‟s Leibnitz formula

If I = f t dx,v

u

then 𝑑𝐼

𝑑𝑥= 𝑓 𝑣

𝑑𝑣

𝑑𝑥− 𝑓 𝑢

𝑑𝑢

𝑑𝑥

When u and v are functions of x.

𝑑𝑥

𝑑𝑦=

1

1+9𝑦2

𝑑𝑦

𝑑𝑥= 1 + 9𝑦2

𝑑2𝑦

𝑑𝑥2 =9𝑦

1+9𝑦2 .

𝑑𝑦

𝑑𝑥

= 9𝑦

1+9𝑦2 1 + 9𝑦2 = 9𝑦

30. (a) Let AB be the tower and C and D be the two positions of the boats. Then, ∠ACB = 450, ∠ADB = 300 and AC = 60 m. Let AB = h.

Then, 𝐴𝐵

𝐴𝐶= tan 450 = 1 𝐴𝐵 = 𝐴𝐶 𝑕 = 60 𝑚.

and, 𝐴𝐵

𝐴𝐷= tan 300 =

1

3 𝐴𝐷 = 𝐴𝐵 × 3 = 60 3 𝑚.

CD = (AD – AC) = 60( 3 − 1) m.

Hence, required speed =

60 3− 1

5 𝑚/𝑠

𝑠= (12 × 0.73) m/s

= 12 × 0.73 ×18

5 km/hr = 31.5 km/hr ≈ 32 km/hr.

31. (a) Let A = 𝑎1 , 𝑎2 , 𝑎3 , ………… . , 𝑎𝑛 . Since f: A A is a one-one function. Therefore, f(a1), f(a2), ….., f(an) are distance element of set A. But, A has one n elements. Therefore, {f(a1), f(a2), …., f(an)} = A But, A is a finite set consisting of n element. Therefore, f(a1), f(a2), f(a3), …., f(an) are distinct elements of A. Hence, f: A A is ONTO.

32. (c) Absolute max. value = 56 at x = 5 Absolute Min. value = 24 at x = 1

33. (b) - 3 2

5 𝑒2 + 1

34. (c) a + b + c = 0

16

MOCK PAPER 1I

(a + b + c)2 = 0

𝑖. 𝑒. , 𝑎2 + 𝑏2 + 𝑐2 + 2 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 = 0

𝑎2 + 𝑏2 + 𝑐2 = −2(𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎) = - 2[a(b + c) + bc]

= - 2[a(-a) + bc]

= - 2[- 𝑎2 + bc] = 2 [𝑎2 - bc]

given expression becomes = - 2

36. (c) Area of square ABCD = 2 sq unit

Area of circle = sq unit

Required area = ( - 2) sq unit 37. (c) Number of students who passed half-yearly exams in the school

= (Number of students passed in half-yearly but failed in annual exams) + (Number of students passed in both exams) = (6 + 17 + 9 + 15) + (64 + 55 + 46 + 76) = 288 Also, Number of students who passed annual exams in the school = (Number of students failed in half – yearly but passed in annual exams) + (Number of students passed in both exams) = (14 + 12 + 8 + 13) + (64 + 55 + 46 + 76) = 288 Since, the number of students passed in half – yearly = the number of students passed in annual exams, therefore, it can be inferred that both the examinations had almost the same difficulty level. Thus, Statements (a), (b) and (d) are false and Statement (c) is true.

38. (c) 1

42

39. (a) 0.0071 40. (d) The equation of all the straight lines passage through origin (0, 0) is

y = mx …………… (i) Hence, required differential equation of all such lines is

𝑦 = 𝑑𝑦

𝑑𝑥 𝑥 ∵ 𝑚 =

𝑑𝑦

𝑑𝑥

49. (a) BC make combination (change or reshape of environment). 55. (a) Relation > Studies object – Studying person 56. (c) Relation > Renouncer – Renounced thing 57. (d) Relation > Minor act – Major version _______ 58. (a) Relation > Similar 64. (d) Refer the third – last sentence of the passage. 66. (b) Refer “derisive phase”. 68. (a) Refer the fourth and fifth sentences of the passage. 70. (b) Refer the first sentences of the passage.