Cl Mock Cat 2

Mock CAT - 2

Test Booklet Serial Number: 7 7 0 3 6 0

INSTRUCTIONS Before the Test: 1. 2.

3. 4. 5. 6.

DO NOT OPEN THIS BOOKLET UNTIL THE SIGNAL TO START IS GIVEN. Keep only the Admit Card, pencil, eraser and sharpener with you. DO NOT KEEP with you books, rulers, slide rules, drawing instruments, calculators (including watch calculators), pagers, cellular phones, stop watches or any other device or loose paper. These should be left at a place as indicated by the invigilator. Use only an HB pencil to fill in the Answer Sheet. Enter in your Answer Sheet: (a) in Box 10 the Test Form Number, which appears at the bottom of this page, (b) in Box 11 the Test Booklet Serial number, which appears at the top of this page. Ensure that your personal data have been entered correctly on Side 1 of the Answer Sheet. Check whether you have entered your 7-digit Enrollment ID in Box 2 of the Answer sheet correctly.

At the Start of the Test: 1. As soon as the signal to start is given, open the Booklet. 2. This Test booklet contains 27 pages, including the blank ones. Immediately after opening the Test Booklet, verify that all the pages are printed properly and are in order. Also that the Test form Number indicated on the cover page and at the bottom of the inner pages is the same. If there is a problem with your Test Booklet, immediately inform the invigilator/supervisor. You will be provided with a replacement. How to answer: 1. This test has three sections which examine various abilities. These 3 sections have 90 questions in all with each section having 30 questions. You will be given two and half hours to complete the test. In distributing the time over the three sections, please bear in mind that you need to demonstrate your competence in all three sections. 2. Directions for answering the questions are given before some of the questions wherever necessary. Read these directions carefully and answer the questions by darkening the appropriate circles on the Answer Sheet. There is only one correct answer to each question. 3. Each section carries 100 marks. Each section is divided into two sub-sections, A and B. All Questions in sub-sections I-A, II-A and III-A carry two marks each. All Questions in sub sections I-B, II-B and III-B carry four marks each. Wrong answers will attract a penalty of one-fourth the marks allotted to the questions. 4. Do your rough work only on the Test Booklet and NOT on the Answer Sheet. 5. Follow the instructions of the invigilator. Candidates found violating the instructions will be disqualified. After the Test: 1. At the end of the test, remain seated. The invigilator will collect the Answer Sheet from your seat. Do not leave the hall until the invigilator announces. “You may leave now.” The invigilator will make the announcement only after collecting the Answer Sheets from all the candidates in the room. 2. You may retain this Test Booklet with you. Candidates giving assistance or seeking/receiving help from any source in answering questions or copying in any manner in the test will have their Answer Sheets cancelled.

MCT-0006/08

Test Form Number:

002

SECTION – I Sub-section I-A: Number of Questions = 10 Note: Questions 1 to 10 carry 2 marks each. DIRECTIONS for questions 1 to 3: Answer the questions on the basis of the information given below. The following table provides information about twenty Presidents of United States of America. They belong to one out of the three different parties namely Democrat (D), Whig (W) and Republic (R). The table also provides information about the tenure of their Presidentship and the state which they belong to. The dates in the “Duration of Service” should be read as Year – Month – Date. For example, 1841 – 04 – 06 should be read as 6th of April in the year 1841.

S.No.

Persons

Party

Duration of Service (Both Inclusive)

State

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

John Tyler James K. Polk Zachary Taylor Millard Fillmore Franklin Pierce James Buchanan Abraham Lincoln Andrew Johnson Ulysses S. Grant Rutherford B. Hayes James Garfield Chester A. Arthur Grover Cleveland Benjamin Harrison Grover Cleveland William McKinley Theodore Roosevelt William Howard Taft Woodrow Wilson Warren G. Harding

W D W W D D R R R R R R D R D R R R D R

1841-04-06 to 1845-03-03 1845-03-04 to 1849-08-01 1849-08-02 to 1850-07-09 1850-07-10 to 1853-11-03 1853-11-04 to 1857-03-03 1857-03-04 to 1861-09-03 1861-09-04 to 1865-04-15 1865-04-16 to 1869-03-03 1869-03-04 to 1877-12-30 1877-12-31 to 1881-03-03 1881-03-04 to 1881-09-19 1881-09-20 to 1886-03-03 1886-03-04 to 1889-03-03 1889-03-04 to 1893-03-03 1893-03-04 to 1898-03-03 1898-03-04 to 1901-09-13 1901-09-14 to 1909-03-03 1909-03-04 to 1913-03-03 1913-03-04 to 1921-03-03 1921-03-04 to 1927-03-09

Virginia Tennessee Louisiana New York New Hampshire Pennsylvania Illinois Tennessee Illinois Ohio Ohio New York New York Indiana New York Ohio New York Ohio New Jersey Ohio

1.

Among the following, who was the President of United States of America for the maximum duration? (1) Grover Cleveland (2) Theodore Roosevelt (3) Woodrow Wilson (4) Ulysses S. Grant (5) None of these

2.

How many of these persons belonged to the Republic party and were the President of United States of America for a tenure ranging from 2 to 5 years? (1) Five (2) Six (3) Seven (4) Eight (5) Nine

3.

A group out of these persons is formed in which, for every person in the group there is at least one more person who belonged to the same party and the same state as him/her. The number of Presidents in this group cannot exceed (1) 9 (2) 10 (3) 14 (4) 12 (5) 11

002

1

DIRECTIONS for Questions 4 to 7: Answer the questions on the basis of the information given below. MS, MBA, LLB, MD and MHM are the five most sought after professional degree programmes in each of the five countries viz. India, US, UK, Austrailia, and Singapore. To complete any of these degrees, students can choose to study in any of these five countries. After the completion of their degrees, these students become professionals employable in all the five countries. The following table lists the total Expenses Incurred (EI) on these professional degrees and the Annual Incomes (AI) earned by the professionals, in their first job after the completion of their degrees, in each of these five countries in the local currencies. Expenses Incurred(EI) and Annual Incomes (AI) Degree

India (INR)

US (USD)

UK (GBP)

Austrailia (AUD) Singapore (SGD)

EI

AI

EI

AI

EI

AI

EI

AI

EI

AI

50000

600000

36500

40000

30000

20000

35000

30000

50000

60000

MBA

400000 800000

45000

30000

28000

10000

40000

60000

55000

90000

LLB

300000 500000

35000

50000

20000

40000

32000

40000

42000

120000

MD

1500000 2000000 62000

60000

25000

80000

28000

70000

40000

100000

180000 240000

70000

70000

90000

20000

25000

40000

60000

MS

MHM

50000

Using the following table, the EI and the AI figures of different countries can be compared.

Exchange Rates Currency

Equivalent to INR

One USD

39.8

One GBP

79

One AUD

35.9

One SGD

28.7

Assume that the data given in the above two tables is valid for every year. Also assume that professionals receive no increment in their salaries, unless specified. 4.

Studying in which of these five countries, a student gets the best return on the expense incurred by him, at the end of one year, if he completes MHM degree and works in the same country ? (1) India (2) US (3) UK (4) Australia (5) Singapore

5.

Mr. Smith works in Australia for an Australian company. The company sponsors him an interest free loan of 75% of the total expense on his MBA degree in UK. In return, Mr. Smith has to serve the company for three consecutive years in Australia after completing his MBA. The salary net of deductions that the company can pay Mr. Smith, when employing him again, for full recovery of the loan amount over the period of three years cannot be more than (1) 44600 AUD (2) 25600 AUD (3) 15400 AUD (4) 18400 AUD (5) None of these

2

002

6.

Mr. H. Gopal Shastry lives in India. In a few days, he will leave for UK to pursue a one year MBA degree. Airfare from India to UK is INR 16500 and that from UK to India is GBP 386. Before completing his degree, he wishes to visit India. Before allocating money for his expense on his MBA degree in UK, his total Budget for tuition and travel is INR 2340000 only. How many times, from UK, can he make a return trip to India ? (1) Only Once (2) Only Twice (3) Only Thrice (4) Only Four Times (5) Only Five Times

7.

Amol and Bimal completed their MS degrees in Singapore and in US respectively funded through a zero interest loan. After completion of their degrees, Amol started working in US and Bimal started working in Singapore. Taking into account, their expenditures on degrees and their salaries only, the difference in the income available to be spent for Amol and Bimal after repaying their study loans, at the end of first year of their jobs is approximately (1) 2820 USD (2) 3055 USD (3) 3925 USD (4) 4300 USD (5) 10700 USD

DIRECTIONS for Questions 8 to 10: Answer the questions on the basis of the information given below. The result of AIEEE 2008 for 17 Indian states is given below. The table provides both State Rank and All India rank for a certain set of people. For example there are 200 students in Haryana who had a state rank ranging from 800 to 1600 and an All India Rank ranging from 4000 to 5000. No two students can have same All India Rank, or even same state rank from the same state.

S.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 8.

002

State Kerala Tamil Nadu Delhi Andhra Pradesh Uttar Pradesh Madhya Pradesh Bihar Rajasthan Haryana Himachal Pradesh Jharkhand Maharashtra Karnataka Orissa Uttaranchal Punjab West Bengal

State rank All India Rank 1-400 2000-4000 200 -400 3000-5000 500-900 1000-2000 500-1000 4000-5000 600-1200 500-2500 1000-1500 3500-4500 2000-2500 4000-5000 100-300 500-1000 800-1600 4000-5000 700-1000 3000-4000 100-300 500-1000 200-800 1000-2000 400-700 3000-3500 500-1000 300-600 1000-1500 6000-7000 300-800 2500-3000 400-1000 2000-3000

Number of students 250 100 400 250 150 300 400 100 200 100 150 300 100 50 400 200 250

The number of students that have State Rank greater than 450 and an All India Rank less than or equal to 2000 out of the students given in the table is atleast (1) 500 (2) 450 (3) 900 (4) 350 (5) 499

3

9.

TIIT Hyderabad has an admission criteria for its students which requires both state and All India rank to be less than or equal to 1000 . If every student who qualifies this criteria gets admitted from these 17 states, the number of seats in TIIT, Hyderabad is atmost (1) 550 (2) 450 (3) 400 (4) 300 (5) 451

10.

Dali College of Engineering has admission criteria for every aspirant that he / she must have a state rank less than or equal to 500 in their respective states. Which state has the maximum number of students in Dali College of Engineering if every student applies there for admission? (1) Kerala (2) Maharashtra (3) Punjab (4) Jharkhand (5) Cannot be determined

4

002

Sub-section I-B: Number of Questions = 20 Note: Questions 11 to 30 carry 4 marks each. DIRECTIONS for Questions 11 to 14: Each question is followed by two statements, A and B. Answer each question using the following instructions: Mark (1) Mark (2) Mark (3) Mark (4) Mark (5) 11.

if the question can be alone. if the question can be alone. if the question can be if the question can be statements alone. if the question cannot

answered by using the statement A alone but not by using the statement B answered by using the statement B alone but not by using the statement A answered by using either of the statements alone. answered by using both the statements together but not by either of the be answered on the basis of the two statements.

Is b2 + 2ab − 48a 2 > 0 A: ax 2 + bx + 4a > 0, for every real x. B: 2ax + 4bx + 3 = 0 for only one real x.

12.

In a quadrilateral ABCD, BD = 10 cm, AB = 6 cm and CD = 8 cm. Determine the area of quadrilateral ABCD? A: M1 and M2 are midpoints AB and CD respectively. M1M2 = 5 cm and ∠BDC = 30°. B: M1 and M2 are midpoints of AB and AD respectively. M1M2 = 5 cm and ∠ABD = 45°.

13.

Ryan, Samar, Julie, Merissa, Sandy and Nicole are siblings. Sandy is younger than both Merissa and Ryan. Julie is older than Samar. Merissa is younger than Samar but older than Nicole. Who is the oldest among them? A: The aggregate age of Samar and Ryan is less than the aggregate age of Nicole and Merissa. B: The aggregate age of Julie and Merissa is less than the aggregate age of Ryan and Nicole.

14.

Jerry, Sherry and Larry played one out of the three sports namely badminton, squash and table tennis . Their respective opponents in these sports is one among the three persons namely Dhiru, Veeru and Neeru. All games are played between exactly two people. Who is the opponent of Larry? A: Veeru is not the opponent of Larry and Jerry did not play table tennis B: Veeru did not play badminton and Dhiru played squash.

002

5

DIRECTIONS for Questions 15 to 18: Answer the questions on the basis of the information given below. A car manufacturing company XYZ sold 10000 cars in the year 2007. Out of the twelve months in the year, the number of months in which the company sold more than 1000 cars is five and each of these five months is termed “Productive” by the company. The company formed 12 groups of months such that each group had six months each. Out of the 12 groups, there is only 1 group in which there are no “Productive” month and 1 group in which there are exactly 5 “Productive” months. The group in which there are exactly 5 “Productive” months is Group 7. The following table provides information about the composition of each of the 12 groups formed by the company.

Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 Group 9 Group 10 Group 11 Group 12

Month 1 November June January June August December January June December February November February

Month 2 Month 3 October January November July February March March October February November March January April September November May June March May August December March March June

Month 4 June October April December September February July October September April May January

Month 5 March September July November July April May March July January October December

Month 6 February March August April May July August December May July June October

15.

Which of the following months is not termed “Productive” by the company? (1) January (2) May (3) September (4) April (5) August

16.

How many groups have four “Productive” months? (1) 5 (2) 1 (3) 2

(4) 3

(5) 4

17.

Which of the following statements is/are NOT true? A. There is only 1 group in which the number of months that are not termed “Productive” by the company is 4. B. There are exactly two pairs of consecutive months that are termed “Productive” by the company. C. There are exactly four pairs of consecutive months that are not termed “Productive” by the company. (1) Only A (2) Only C (3) Both B and C (4) Both A and C (5) Neither A nor B nor C.

18.

In how many groups the number of “Productive” months is not more than the number of months that are not “Productive”? (1) 9 (2) 8 (3) 7 (4) 10 (5) None of these

6

002

DIRECTIONS for Questions 19 to 22: Answer the questions on the basis of the information given below. Many Asian countries including China, Japan, Kazakhstan, India, Singapore, Malaysia and Jordon participated in one or more sporting events held at the 2006 Asian Games. In each sporting event at least three countries participated. At the end of each sporting event, the country finishing at the first, the second and the third positions were awarded a gold, a silver and a bronze medal respectively. The following bar graph shows distribution of the three types of medals. In this graph, the parts marked by “Data Not Available” may have belonged to one or more of all the participating countries.

100%

10.50%

90%

23.00%

80%

14.50%

70%

12.50%

60%

10.00%

50%

31.00%

15.50%

10.00%

20.50%

15.00%

12.50%

16.50%

18.00%

12.50%

10.50%

15.00%

15.50%

40% 30% 20%

37.50%

10% 0% Gold China India Jordon

Silver Japan Singapore Data Not Available

Bronze Kazakhstan Malaysia

19.

Which of the following could not have been the sum of the number of silver and the number of bronze medals won by Malaysia ? (1) 142 (2) 164 (3) 213 (4) 284 (5) 355

20.

What was the ratio of the number of gold medals won by Singapore to the number of silver medals won by Jordon ? (1) 21 : 31 (2) 4 : 5 (3) 31 : 33 (4) 29 : 31 (5) Cannot be determined

21.

The total number of medals won by India was at least what percentage of the total number of medals won by China? (1) 31.12% (2) 75.80% (3) 62.24% (4) 39.50% (5) Cannot be determined

22.

It is given that the parts of the graph marked as “Data Not Available” belonged to exactly one of the seven countries that are mentioned above but was not included in the respective bar in the graph. When arranged in an ascending order of the total number of medals won, which of the following will never be a possible case ? (1) Jordon, Japan, Kazakhstan (2) Malaysia, India, Singapore (3) Japan, China, Singapore (4) Japan, Singapore, Jordon (5) Malaysia, India, Kazakhstan

002

7

DIRECTIONS for Questions 23 to 26: Answer the questions on the basis of the information given below. A public poll was conducted to find the most popular sportsman in the year 2007. The public poll was conducted in five rounds namely Round I, Round II, Round III ,Round IV and Round V in that particular order. The same group of 200 people voted in each of the five rounds. The nominees for the most popular sportsman award were P, Q, R, S, T and U. The following table provides information about the number of votes received by each of these six nominees in the given rounds. One person can vote for only one nominee in the given rounds.

P Q R S T U

I 34 26 52 21 43 24

II 39 39 32 34 43 13

III 43 31 43 28 36 19

IV 29 35 36 29 35 36

V 34 29 41 28 44 24

Additional Information Given: 1. Persons, who voted for P in any round, voted for either S or T in the following round. 2. Only those persons, who voted for Q or U in any round, voted for P in the following round. 3. Persons, who voted for T in any round, voted for either R or U in the following round. 4. Persons who voted for S in round I, voted for S in each of the next three rounds. 23.

Magic number for a nominee is defined as the number of nominees who have got lesser number of votes than him/her in exactly two rounds. Find the aggregate sum of the magic numbers for all the nominees. (1) 0 (2) 1 (3) 2 (4) 3 (5) 4

24.

Out of the number of persons who voted for P in any round, the number of persons who voted for S is at least (1) 10 (2) 12 (3) 9 (4) 8 (5) 11

25.

The number of persons who voted for the same nominee across all the five rounds is at most (1) 36 (2) 31 (3) 35 (4) 39 (5) 32

26.

If out of the persons who voted for Q in round IV, maximum number of persons voted for R in round V, then out of the persons who voted for U in round IV, at most how many persons voted for Q in round V? (1) 7 (2) 13 (3) 9 (4) 8 (5) 11

8

002

DIRECTIONS for Questions 27 to 30: Answer the questions on the basis of the information given below. Five guests namely A, B, C, D and E are staying in a hotel. Each of theses five mentioned guests ordered one item each for breakfast, lunch and dinner. The items ordered by the guests are distinct. The following table provides information about the items ordered for breakfast, lunch and dinner by these mentioned guests.

Item 1 Item 2 Item 3 Item 4 Item 5 Breakfast Biscuit Eggs Milk Salad Toast Lunch Burger Continental Dosa Fruits Rice Dinner Chicken Chinese Pizza Rotis Upma Additional Information Given: 1. The only items that are classified as “Non – Vegetarian” are eggs, continental, chicken and burger. Further, each of A, B and C did not order “Non – Vegetarian” items 2. B is a patient and ordered milk in the breakfast. 3. The items ordered by C have at least two items whose names start with the same alphabet. This holds true for D as well as E. 4. E ordered exactly two “Non – Vegetarian” items but did not order chicken. 5. Out of the mentioned guests, there is only one guest who is from south India and he/she ordered both dosa and upma. 6. The guest who ordered toast also ordered fruits. 27.

Which of the mentioned guests is from south India? (1) A (2) B (3) C

(4) D

(5) E

28.

Which of the following item is also ordered by the guest who ordered fruits? (1) Rice (2) Biscuit (3) Rotis (4) Pizza (5) None of these

29.

Which of the following is not the guest who did not order Salad? (1) E (2) D (3) B (4) A

30.

002

(5) C

Which of the following items is not ordered by the guest who ordered Rotis? (1) Salad (2) Rice (3) Burger (4) Both (1) and (2) (5) Both (2) and (3)

9

SECTION – II Sub-section II-A: Number of Questions = 10 Note: Questions 31 to 40 carry 2 marks each. DIRECTIONS for Questions 31 to 34: The passage given below is followed by a set of questions. Choose the best answer to each question.

PASSAGE Wittgenstein’s Philosophical Investigations says that: “For a large class of cases - though not for all - in which we employ the word “meaning” it can be defined thus: the meaning of a word is its use in the language.” It is quite clear that here Wittgenstein is not offering the general theory that “meaning is use,” as he is sometimes interpreted as doing. The main rival views that Wittgenstein warns against are that the meaning of a word is some object that it names - in which case the meaning of a word could be destroyed, stolen or locked away, which is nonsense - and that the meaning of a word is some psychological feeling - in which case each user of a word could mean something different by it, having a different feeling, and communication would be difficult if not impossible. Knowing the meaning of a word can involve knowing many things: to what objects the word refers (if any), whether it is slang or not, what part of speech it is, whether it carries overtones, and if so what kind they are, and so on. To know all this, or to know enough to get by, is to know the use. And generally knowing the use means knowing the meaning. Philosophical questions about consciousness, for example, then, should be responded to by looking at the various uses we make of the word “consciousness.” Scientific investigations into the brain are not directly relevant to this inquiry (although they might be indirectly relevant if scientific discoveries led us to change our use of such words). The meaning of any word is a matter of what we do with our language, not something hidden inside anyone’s mind or brain. This is not an attack on neuroscience. It is merely distinguishing philosophy (which is properly concerned with linguistic or conceptual analysis) from science (which is concerned with discovering facts). One exception to the meaning-is-use rule of thumb is given in Philosophical Investigations Sect.561, where Wittgenstein says that “the word “is” is used with two different meanings (as the copula and as the sign of equality)” but that its meaning is not its use. That is to say, “is” has not one complex use (including both “Water is clear” and “Water is H2O”) and therefore one complex meaning, but two quite distinct uses and meanings. It is an accident that the same word has these two uses. It is not an accident that we use the word “car” to refer to both Fords and Hondas. But what is accidental and what is essential to a concept depends on us, on how we use it. This is not completely arbitrary, however. Depending on one’s environment, one’s physical needs and desires, one’s emotions, one’s sensory capacities, and so on, different concepts will be more natural or useful to one. This is why “forms of life” are so important to Wittgenstein. What matters to you depends on how you live (and vice versa), and this shapes your experience. So if a lion could speak, Wittgenstein says, we would not be able to understand it. We might realize that “roar” meant zebra, or that “roar, roar” meant lame zebra, but we would not understand lion ethics, politics, aesthetic taste, religion, humor and such like, if lions have these things. We could not honestly say “I know what you mean” to a lion. Understanding another involves empathy, which requires the kind of similarity that we just do not have with lions, and that many people do not have with other human beings.

10

002

When a person says something what he or she means depends not only on what is said but also on the context in which it is said. Importance, point, meaning are given by the surroundings. Words, gestures, expressions come alive, as it were, only within a language game, a culture, a form of life. If a picture, say, means something then it means so to somebody. Its meaning is not an objective property of the picture in the way that its size and shape are. The same goes of any mental picture. Hence Wittgenstein’s remark that “If God had looked into our minds he would not have been able to see there whom we were speaking of.” Any internal image would need interpretation. If I interpret my thought as one of Hitler and God sees it as Charlie Chaplin, who is right? Which of the two famous contemporaries of Wittgenstein’s I mean shows itself in the way I behave, the things I do and say. It is in this that the use, the meaning, of my thought or mental picture lies. “The arrow points only in the application that a living being makes of it.” 31.

What is the central theme of the passage? (1) The meaning of a word is its use in the language. (2) Meaning of a word is usually context dependent. (3) How you live shapes your application. (4) Empathy can help one understand word meanings accurately. (5) Generally, knowing the use of a word means knowing its meaning.

32.

Which of the following inferences is not true as per the passage? a. ‘What is accidental and what is essential’ is not completely arbitrary because what is natural to a lion may not be natural to a human being. b. Wittgenstein offers at times the general theory that “meaning is use”. c. God is unable to understand the thoughts going on in a human being’s mind owing to the objective nature of human thoughts. (1) a and b (2) Only a (3) Only b (4) b and c (5) a, b and c

33.

Wittgenstein would be most likely to agree with which of the following statements? (1) Scientific investigations are irrelevant when it comes to inquiry into the meanings of words. (2) The contextual nature of word meanings makes communication easy. (3) If one could standardize word meanings then ways of living would also get standardized. (4) One should be content if one is able to ‘get by’ in one’s interactions. (5) None of the above.

34.

The last statement of the passage implies that (1) The arrow represents what is considered as false. (2) Application mitigates the validity of interpretation. (3) Living beings cannot do without application. (4) Application is the cause of interpretation. (5) Interpretation cannot be validated without seeing the application.

002

11

DIRECTIONS for Questions 35 to 37: The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences among the given choices to construct a coherent paragraph. 35.

A. The word failure, it seems, is not good for building self-esteem in school children. B. Liz Beattie, a 37-year old veteran primary-level instructor, proposed that the word failure should be banned from classrooms and replaced with the more appealing phrase deferred success so as not to discourage students from continuing efforts to achieve. C. Although the motion ultimately experienced its own “deferred success,” it was not without supporters among the 35,000-member teacher’s association. D. One Wesley Paxton, a member of the PAT Council, expressed his enthusiastic agreement, saying: “It’s time we made the word ‘fail’ redundant and replaced it with ‘please do a bit more’.” E. In the summer of 2005, a British school teacher proposed a rather controversial motion to her union, the Professional Association of Teachers (PAT). (1) ADBCE

36.

(4) CEDAB

(5) ABCDE

(2) BDACE

(3) DABEC

(4) ABEDC

(5) ABECD

A. Enter the virtual assistants who are entrepreneurial partners - highly skilled in their profession and able to have an impact on the productivity of those they work with. B. But most of the small businesses started today will reach an impasse very quickly - they will be spending so much time on administrative tasks that they can no longer concentrate on growing their business. C. On the contrary, some believe that increasing numbers of small businesses will afford administrative support experts with entrepreneurial spirit opportunities that have never before been possible. D. Traditionally, the need for assistance has left the small business owner with several bleak optionshire an expensive “temp” for a band-aid-style solution, take on a great deal of expense and responsibility with a “permanent” employee, or-perhaps worst of all-turn away the work. E. Corporate downsizing and the move towards small, home-based businesses could appear to be bad news for the over 3 million people whose expertise lies in the administrative support arena. (1) DCABE

12

(3) EBCDA

A. In art, essentialism is the idea that certain concepts may be expressed organically in certain media. B. Each medium has its own particular strengths and weaknesses, contingent on its mode of communication. C. This idea may be further refined and it may be said that the haiku is a poor vehicle for describing a lover’s affection as opposed to the more organically correct sonnet. D. Essentialism is attractive to artists because it not only delineates the role of art and media but also prescribes a method for evaluating art. E. A chase scene may be appropriate for motion pictures, but poorly realised in poetry because the essential components of the poetic medium are ill suited to convey the information of a chase scene. (1) DCEBA

37.

(2) BACDE

(2) ECBDA

(3) DBACE

(4) EDCBA

(5) CDEBA

002

DIRECTIONS for Questions 38 to 40: In each question, the word at the top is used in five different ways, numbered (1) to (5). Choose the option in which the usage of the word is incorrect or inappropriate. 38.

Beam (1) The work at the site came to a temporary halt when a worker was struck by a falling beam (2) His only response to the news of his brother’s return was to beam in joy (3) I was dazzled by a beam of sunlight that entered the dark room through a crack in the wall. (4) In the end it was decided to beam the last episode on both the channels. (5) IBA 2007 is a major international forum to discuss recent research and future prospects in Ion Beam Analysis.

39.

Face (1) We were surprised when Paul did an about face on the plan we had agreed upon (2) She persevered in the face of apparently insurmountable odds. (3) Jim’s proposal was accepted even though it flew off the face of all conventional wisdom. (4) Her friends were surprised at the way a timid speaker like Jenny could face down an experienced debater like Mike. (5) We had the opportunity to sit down face-to-face with Max Spevack, chairman of the Fedora project, at the Red Hat Summit.

40.

Act (1) After the performance, everyone agreed that the new acrobat in the circus was a classy act. (2) We had to cancel the inauguration when the air conditioning chose to act up again. (3) The defence counsel asked the accused to act out the events of the fateful Saturday evening for his benefit. (4) The ambassador censured the attack on the border as an uncalled for act of belligerence. (5) The genesis of an Act of Parliament is often a formal written proposal known as a White Paper, which if accepted will be prepared in the form of a proposed law known as a Bill.

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Sub-section II-B: Number of Questions = 20 Note: Questions 41 to 60 carry 4 marks each. DIRECTIONS for Questions 41 to 47: Each of the two passages given below is followed by a set of questions. Choose the best answer to each question.

PASSAGE – 1 The question of silence is inseparable from a certain atopia. It is no-where to be heard, as there is no such thing as a place without sound of any kind. Everyone knows that outer space, to be sure, is silent, but this silence is only technical, and is a kind of limit-possibility, is an absolute in the way that death is an absolute. It is always on the other side of the loud and noisy, bustling with activity so unlike death. Our science fiction films always give us the roar of the rockets, the booming explosions, and the affective omniscience of film music—the silence of space is made loud and noisy, bustling with activity so unlike death. The occasional films which omit sound when outside the spacecraft still have to contend with the candy wrappers and plastic lids and the coughing of the theatre space, so the silence of space can only be alluded to, barely auditioned. Perhaps the closest we get to the silence of space is the tinny voice of the headset, and the rhythm of breathing amplified in the astronaut’s helmet, the claustrophobia of atmospheric recirculation, such that silence is brought so close that it frames our perceptions and the action. Silence then takes on the explosiveness of an immanent possibility. Like death. It is no accident that we bring up cosmic space in our first consideration of the thematic of silence. For we can say, silence is the sound of space, quiet is always the sound of a place. For the closest approximation to silence is quiet, but to think of quiet is always to suggest a quiet: the quiet of the library, of a forest clearing, of anywhere at three in the morning. Silence, however, is a corollary of absolute space, of pure, uninterrupted extension, the space of Descartes and Newton, amongst others, or space uninflected, the happy medium for grids of all kinds. Noise localizes, for sounds have sources. They emanate from centers, or multiple centers, as in the accumulation of the traffic hum which is the acoustic signature of urban spaces. Silence is as well the transposition onto the acoustic plane of the blankness of paper, whether white or yellowy. Western art music shares this white silence with writing and painting. Rauschenberg had presented, in the early fifties, a series of monochrome paintings entitled the White Paintings. Here, too, the apparent emptiness reveals an active vitality and presence of light, color, and movement. Rauschenberg’s radical move towards white paintings certainly drove Cage to present his own “white” work, the silent piece. The imperative of silence for music, one can imagine, originates from the margins of the notation system, the white in-between of notes and staff lines, as well as the silence that is reading and writing, i.e. the silence of speechlessness, St. Augustine’s instinctive horror at the silence of the figure at the lectern, the silence of unvocalized interiority, the silence necessary as the medium of thought. The superabundant display of vitality, which takes the form of knocking, hammering, and tumbling things about, has proved a daily torment for some people. There are people, it is true—nay, a great many people— who smile at such things, because they are not sensitive to noise; but they are just the very people who are not sensitive to argument, or thought, or poetry, or art, in a word, to any kind of intellectual influence. On the other hand, noise is a torment to intellectual people. In the biographies of almost all the great writers, or wherever their personal utterances are recorded, complaints have been found regarding it. Silence is an effect, specifically, a technological and architectural effect, a type of quiet that perhaps can trace its lineage to the invention of masonry walls, i.e. walls composed of solid planes and thus impermeable to the sounds that might creep in through a mesh of leaves or the gaps in bundled saplings. Silence as a fantasy or an act of imagination will thus be linked to a certain stage of civilization. For we can imagine the difference

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between death in the jungle and death in the polis. In the former situation, one imagines that the cessation of movement on the part of the deceased may lead to a heightened sensitivity to the surrounding activity of the place - the animal sounds, the wind in the foliage; in other words, all that may have been tuned out when giving attention to another would uncannily return to the foreground. By contrast, city death implies the silence of the tomb, prepared somewhat by the echoey sonorousness of the temple. Thus silence can be linked to a certain stony sense of enclosure and interiority. 41.

What does the author imply by stating that ‘silence of space is a kind of limit possibility’? (1) The concept of silence of space is very restricted in nature. (2) The occurrence of space silence is less in everyday life because of the constant sound of other different things such as the roaring of rockets. (3) The silence of space occurs outside the earth and it also attracts for itself an active search for other types of noises which can substitute for this assumed silence. (4) The space is presented as a busy place always bustling with some type of activity or the other. (5) Human beings compensate for the silence of space by creating various types of sounds and noises such as the moving of rockets, huge explosions etc.

42.

What does the author imply by comparing silence with the space of Descartes and Newton? (1) The author tries to state the relationship between cosmic space and the concept of silence. (2) The author tries to focus on the localization of noise and the sources from where they emerge. (3) The author tries to state the relevance of Descartes and Newton’s theories with respect to space. (4) The author tries to emphasize on the closeness between silence and quiet. (5) The author makes an indirect reference to the unaltered original space that was referred to by Descartes and Newton.

43.

The above passage does not imply that: (1) Vitality cannot be expressed through science. (2) The concept of silence is a condition of inherent possibility and represents a rigid form of closeness. (3) Silence is many times approximated with quiet. (4) Silence is a type of technological and architectural effect. (5) Silence is important for music.

44.

Which of the following statements can be inferred from the passage? (1) St Augustine was filled with remorse at the silence of the figure of the lectern. (2) Silence can be as explosive as quiet. (3) Silence can be seen as a corollary of absolute space, unlike quiet. (4) Intellectual people are insensitive to noise. (5) It is preferable to die in a city rather than in a jungle as one can die peacefully.

PASSAGE – 2 There are grounds for thinking that, when compared to researchers in similar fields, management researchers are particularly susceptible to conflicts of interest and affiliation bias. In all areas of scientific study it is recognized that affiliations, particularly those related to funding, have the potential to influence the way that research issues are defined and findings presented. In fields such as medical research, it is a condition of publication that researchers must state any potential conflicts of interest so that their affiliations can be taken into account when reviewing the findings of a given study. However, it is rare for affiliations to be declared in the reviewing or publication of management research, despite the widespread practice of researchers engaging in management consultancy in areas related to their academic study. In addition, it is unusual for the adoption of joint research and consultancy roles to be seen as anything other than an advantage to the community,

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leading to greater congruence between practitioner and researcher concerns. Another contextual factor that affects management researchers differently from other social scientists stems from their engagements with powerful individuals and organizations. One of the main purposes of ethical regulation in social research is to protect vulnerable research participants from exploitation and potential harm, which might result from their involvement in the research process. The burden of responsibility for ensuring informed consent to research participation rests with the researcher even though the extent to which participants can ever be fully informed of the demands and uses of research is questionable. The principle of informed consent can be traced to the formation of the Nuremburg Code, which has informed subsequent ethics codes and human rights treatises throughout the world. The Nuremberg Code represented an attempt to formulate a universal natural law standard for human experimentation. Its importance stemmed from the appalling nature of the atrocities that stimulated its formation, and the desire of Nuremberg Trial judges to go beyond charging and convicting individual doctors in paving the way for a reconstituted moral vision. At the heart of the code is the principle of informed consent, which forms the basis for ensuring the protection of vulnerable people. However, this strong pronouncement on the rights of research subjects was almost immediately undermined by later codes, which isolated the Nazi experiments, treating them as a barbaric aberration that could not occur elsewhere in the Western world. The Nuremberg Code was therefore superseded by the Declaration of Helsinki, which sought to balance the interests of the subject against the need for scientific research. Despite these modifications, the protection of human subjects through informed consent remains a fundamental principle in most ethics codes in the social as well as biological sciences. In psychological research, power relations tend to favour the researcher who is often a professional psychologist carrying out research on their own patients. In education, research participants are often children who are at a power disadvantage relative to those who are carrying out the studies. The question for management researchers is whether the principle of informed consent is an appropriate mechanism for dealing with the ethical implications of relationships with research participants in this field of study. There are undoubtedly some instances when it is, such as when university students are asked to participate in research. However, unlike many other social researchers, the relationships between management researchers and their participants are often characterized by a power imbalance that favours the research subject rather than the researcher. 45.

What is the author attempting to illustrate through this passage? (1) Relationship between medical, psychological and management research. (2) How the present limitations in the field of research are a disadvantage to the management researcher. (3) The effects of set codes in the fields of research. (4) Ways to approach management research. (5) The unique effects of certain factors on management researchers.

46.

According to the author, which of the following statements would be true? (1) The objective of research supersedes the need for protection of human subjects. (2) The appropriate use of the principle of informed consent depends on the individual field of study. (3) The Declaration of Helsinki was formulated to restore the power to the researcher. (4) Affiliations are declared in the publication of management research issues. (5) Power relations cease to produce an effect on research projects.

47.

According to the passage, which of the following is a marked achievement of the Nuremberg code? (1) The formation of the Declaration of Helsinki. (2) The formation of an ideal law for human experimentation. (3) The formation of an ethical grounding in research. (4) The formation of a law. (5) The formation of a balance between the interests of the subject with the need for scientific research.

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Directions for questions 48 to 50: Each of the following questions has a paragraph from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way. 48.

Existentialism is the view of life which focuses on “a man” and in so doing denies that any man is to be measured or equated against any class called “man” in any sense of experience. Since “man” traditionally is classified in terms of his mind, body and will against the framework of an external world, the existential position denies, utterly, the certainty of any external world, as object, and denies, utterly, the assertion that any rule – physical, emotive, or intellectual - is valid in relation to the single individual. __________________ . (1) The exponent of existentialism considers the traditional world to be one of illusion. (2) Man is not an accidental expression of colliding atoms which continuously move in a random fashion. (3) It is quite interesting to analyze organized religion with this background. (4) It is the consciousness of a man that he is existing in terms of his own flowing of experience, a flow which is governed by natural laws. (5) Therefore, the existentialist is free to choose because there are no objective standards to inhibit or constrain his choice.

49.

What is nonlinear science all about? The core ideas are not hard to describe. Nonlinear dynamics arise from repeated iteration or feedback. A system, whether physical or mathematical, starts in some initial state. That initial state provides the input to a feedback mechanism which determines the new state of the system. The new state then provides the input through which the feedback mechanism determines the system’s next state and so on. Each successive state is causally dependent on its predecessor. __________________ . (1) Mathematics aside, nonlinearity has a crucial contribution to make towards general friction regardless of technological developments. (2) Sometimes the fundamentals of nonlinear science evade understanding. (3) The dynamics of non-linear science are being deeply pondered by scientists. (4) The attempt to apply the ideas of nonlinear science are resisted by the widespread predominance of linear modes of thought. (5) But what happens to the system over the course of many iterations can be more complex and less predictable than one might suppose.

50.

Anyone who’s ever played with an Erector Set knows intuitively that as long as the structural members remain well-connected, a framework may become twisted and distorted if you throw it to the floor, but it will never just collapse into pieces under any scenario involving self-related and self-proportional forces. Even if a giant came along and stomped on one of the Towers, the continuous vertical strength of the specially fabricated multi-story core columns, with their welded connections and dense crossbracing, would cause the building to split out over a multi-floor region. _____________________ (1) The vertical spacing of the office floors did not correlate to periodic points of weakness in the column assemblies. (2) This would be very much like the effect of a thunderstorm on a boat. (3) This would be very similar to the effect of an earthquake on a bridge. (4) This would be very much like the forces operating on a truss. (5) This would be very much like pushing down on a bundle of archery bows.

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DIRECTIONS for Questions 51 and 52: In each of the following questions a paragraph is given followed by five summaries. Choose the best summary. 51.

Studying the phenomenon of childhood brings on also issues relating to children burial rites in all types of communities. Children burials and children graves are inherent parts of archaeological discoveries made at Moravian settlement agglomerations. In the recent years, extensive archaeological rescue research – especially in Central Moravia – has considerably extended the amount of knowledge on the Neolithic burial rite. Most new findings come from the Linear Pottery Culture period, while the period of the Culture with Stroke-Ornamented Pottery shows constant stagnation, and the Moravian Painted Ware Pottery Culture has yielded only random individual finds. (1) Extensive archaeological rescue research – especially in Central Moravia – has considerably extended the amount of knowledge on Neolithic burial rites. (2) Archaeological discoveries made at Moravian settlement agglomerations, especially in Central Moravia – have considerably extended the amount of knowledge on children burial rites, though the number of findings from each culture period varies. (3) Archaeological discoveries made at Moravian settlement agglomerations, have considerably increased the number of findings from each culture period because of the renewed interest in children burial rites. (4) Children burials and children graves are inherent parts of archaeological discoveries made at Moravian settlement agglomerations, which exhibit different findings from recent culture periods. (5) Archaeological discoveries made at Moravian settlement agglomerations exhibit different number of findings from different culture periods.

52.

The priestly caste of Jews - called Cohanim in Hebrew - have recently been conducting DNA tests to see whether or not they are actually linked to Aaron, the brother of Moses, as written in the Jewish Bible. This arose when a tribe in South Africa, known as the Lemba, wanted to find out more about their heritage. Claiming they were Jews because they followed dietary laws similar to those of Kashruth, scientists in England decided that they could perform DNA tests of Jews who claimed to be Cohanim and the Lemba to see if there were any similarities in the readings. Because neither Aaron’s nor Moses’ grave are to be found, as written in the last chapter of Deuteronomy, the scientists had to figure out how they were going to go about proving this. (1) Because neither Aaron’s nor Moses’ grave are to be found, Scientists in England decided that they could perform DNA tests of Jews who claimed to be Cohanim and the Lemba to see if there were any similarities in the readings. (2) Scientists were reluctant to figure out how they were going to perform DNA tests of Jews who claimed to be Cohanim and the Lemba because neither Aaron’s nor Moses’ grave are to be found. (3) Scientists had to figure out how they were going to perform DNA tests of Jews who claimed to be Cohanim and the Lemba as their claims appeared to be apocryphal. (4) Scientists in England decided that they could perform DNA tests of Jews who claimed to be Cohanim and the Lemba to see if there were any similarities in the readings. (5) Scientists in England decided to perform DNA tests of Jews who claimed to be Cohanim and the Lemba to validate their claims of lineage, but they were to figure out the mode as they faced constraints.

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DIRECTIONS for Questions 53 to 56: In each question there are five sentences or parts of sentences that form a paragraph. Identify the sentence(s) or part(s) that is/are correct in terms of grammar and usage. Then choose the most appropriate option. 53.

A. B. C. D. E.

It is an irony given that Brasilia was built at breakneck speed. The dream of moving the capital from Rio on the Atlantic coast to the centre of the country, had existed for above a century but Kubitschek pursued it with urgency. Commercial and residential zones were seeming meticulously demarcated. Cars zipped alongside wide highways past buildings that projected simplicity and modernity with fine lines and waves.

(1) A & B 54.

A. B. C. D. E.

(5) A, B & C

(2) A, B & E

(3) A, C, D & E

(4) C & E

(5) A, C & E

(2) A & B

(3) B, D & E

(4) A, C & E

(5) A, B & C

A. If staying outside the park boundaries precludes dawn and dusk animal sighting, daytime drives and walks make up for that. B. This rolling wilderness, studded with the great angular-branched baobab trees, and intersected by the Ruaha river, C. is known for its magnificent elephant population as well as for other mammals and, in particular, its bird life. D. A driving safari can cover the ground and will deliver you to concentrations of animals - anxious zebras, shifty buffaloes, distinguished elephants – but E. walking safaris take you closer, physically and mentally both, to the soil. (1) A & B

002

(4) A, B & E

Obviously, they have to be extended and silly, but still characters that you could definitely meet rather than over-the-top caricature. They also have to be fun to do; You have to enjoy playing the character. If people look alike they’re enjoying themselves, that comes across on screen and that’s how you find your fan base.

(1) A & D 56.

(3) A, B, D & E

A. Young describes the sight of a room full of B. major celebrities as “overpowering seductive”. C. I think they look silly parked alongside one another, like the Ferraris at the super car show I stumbled upon on a recent trip to Florida. D. The owners of these status symbols thought they would be looking even cooler clustered together with others of their kind. E. Big mistake! Once your eyes had adjusted to the glare from the bonnets, you saw them for what they were - a paltry collection of consumer durables. (1) A, B & C

55

(2) B & C

(2) B, C & D

(3) C & E

(4) C, D & E

(5) E only

19

Directions for questions 57 to 60: Each of the following questions has a paragraph with one italicized word that does not make sense. Choose the most appropriate replacement for that word from the options given below the paragraph. 57.

Haldiman was an experienced military commander. However, he still needed timely intelligence on enemy troop movements if he were to have any hope of stopping a large force. Couriers attempting to get from Lake Champlain to Clinton’s Headquarters in New York were continually intercepted .Clinton seemed to consider Haldimand’s need for information as secondary to the main war effort. There were hints of frustration in some of Haldimand’s letters at this seemingly factacious behavior on the part of Clinton. (1) devastating (2) caustic (3) recalcitrant (4) pernicious (5) acerbic

58.

The principle of fairness grounds a moral obligation not to bamboole as part of a fair scheme of cooperation, also called ‘the duty of fair play.’ The principle is standardly summarized as follows. If some people are contributing to the production of a public good, one should not simply enjoy the benefits without doing one’s share in the production of that good. (1) exhaust (2) constrain (3) intrude (4) manipulate (5) free ride

59.

Conflict has continued between Ireland and England for centuries. In spite of this, the two languages spoken by the English and Irish existed side by side, with many of the English living in Ireland learning the native language. However in Ireland, a change was to come. In an attempt to enforce complete annixation, the English passed laws to suppress the native Irish language. (1) subjugation (2) downthrow (3) regimen (4) abstinence (5) forbearance

60.

In a short time the family realized that the dog had many positive attributes. It had large bat-like ears that were sensitive and had strong attention. In fact the family realized that apart from a cuntimecious taste that it had shown towards books, eating the first edition copy of a famous Memoir, the dog had been purpose- built. (1) intense (2) extraneous (3) perverse (4) incendiary (5) beguilement

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SECTION – III Sub-section III-A: Number of Questions = 10 Note: Questions 61 to 70 carry 2 marks each.

61.

x−y Given that   % of x+y

(x2 − y2 ) +  xx +− yy  % of

( x − y )2 = 40,

where x ≠ ± y and x ≠ 0.

 2  x+y Find the value of  % of  .   x2 − y2   x    (1) 2 × 10–5

(2) 10–6

(3) 2 × 10–6

(4) 10–5

(5) None of these

62.

Let A be a two-digit number and B be another two-digit number formed by reversing the digits of A. If A + B + (Product of digits of the number A) = 145, then what is the sum of the digits of A? (1) 12 (2) 10 (3) 13 (4) 9 (5) 11

63.

Suresh and Ramesh are playing a game with a fair die marked 1, 2, 3, 4, 5 and 6 on its six faces. On his turn, a player rolls the die and notes the number s obtained. They roll the die turn by turn. The player, who gets 6 first wins the game. If Suresh gets the first turn to roll the die, then the probability of Ramesh winning the game is (1)

64.

1 6

(2)

5 6

(3)

6 11

(4)

5 11

(5)

1 11

The nth term of two different series are Rn = R1 × Sn–1 and Sn = S1 × Rn–1. If R1 = x, S1 = y (where x, y > 0 ), then which of the following is equal to Rn + Sn (if n > 3)? (1) 2x2y2 (4) xy(Rn–2 + Sn –2)

(2) 2xy(Rn–2 + Sn–2) (5) None of these

(3) xy(Rn–3 + Sn–3)

65.

When a two–digit number N is divided by the sum of its digits, the result is Q. Find the minimum possible value of Q. (1) 10 (2) 2 (3) 5.5 (4) 1.9 (5) 7

66.

In a quadrilateral ABCD, E is a point on AB. If ∠ADE = ∠DEC = ∠ECB = 30°, AD = 2 units and BC = 4 units, then what is the area of the ∆DEC? (1) 4 sq. units (2) 6 sq. units (3) 2 sq. units (4) 1 sq. units (5) 3 sq. units

67.

What is the sum of the roots of all the quadratic equations that can be formed such that both the roots of the quadratic equation are common with the roots of equation (x – a)(x – b)(x – c) = 0 ? (1) 3(a + b + c) (2) 2(a + b + c) (3) (a + b + c) (4) 4(a + b + c) (5) 3a + 3b + 4c

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68.

There is a 5 digit natural number N1 = abcde whose digits a, b, c, d and e are in an arithmetic progression and there is another 4 digit number N2 = ABCD whose digits A, B, C, D are in a geometric progression. Which of the following statements is invalid ? (1) Sum of digits of N2 is 15 (2) N1 has 12 possible values (3) N1 + N2 has 24 possible values (4) N1 is never divisible by 4 (5) None of these

DIRECTIONS for Questions 69 and 70: Answer the questions on the basis of the information given below. A very large open tub is circular in shape and is filled with water. From a point X, two friends Jack and Straw start swimming simultaneously at constant speeds in the opposite directions. The tub has a circumference of 100 metres. The water inside the tub flows in the clockwise direction at a uniform speed. Jack swims along the water flow. The two friends meet for the first time, at a distance of 30 metres from the point X in the clockwise direction. Straw reversed the direction in which he was swimming immediately after they met for the first time. The time duration from the 1st meeting to the 2nd meeting is 10 seconds.

S tra w

X Jack

69.

Find the distance between the point X and the point at which they meet for the second time. (1) 60 metres in the clockwise direction. (2) 90 metres in the clockwise direction. (3) 45 metres in the anticlockwise direction. (4) 0 metres. (5) Cannot be determined.

70.

If the ratio of the speeds of Jack and Straw is 2:5, then the speed at which water flows is (1) 3 m/s

22

(2) 1 m/s

(3)

2 m/s 3

(4)

1 m/s 3

(5)

4 m/s 3

002

Sub-section III-B: Number of Questions = 20 Note: Questions 71 to 90 carry 4 marks each. 71.

In an island, which had a total population of 55009, a war was fought between ‘Benos’ and ‘Malos’ the only tribes residing in the island. During the war every ‘Benos’ fought with a different number of ‘malos’. One of them fought with exactly 140 ‘Malos’, a second one fought with exactly 141 ‘Malos’, a third one fought with exactly 142 ‘Malos’, a fourth one with with exactly 143 ‘Malos’ and so on till one of them fought with every ‘Malos’ residing in the island. Find the number of ‘Malos’ residing in the island. (1) 27435 (2) 33000 (3) 30000 (4) 27574 (5) 50000

DIRECTIONS for Questions 72 and 73: Answer the questions on the basis of the information given below. In a class comprising of boys and girls, ‘k’ oranges were distributed such that everyone in the class gets at least one orange and atmost three oranges. The aggregate number of boys and girls who got three oranges is 40. The aggregate number of boys who got at least two oranges and the number of girls who got at least 1 orange is 100. The aggregate number of boys and girls who got at least two oranges is 60 and the aggregate number of boys who got atleast one orange and the number of girls who got exactly three oranges is 100. 72.

Which of the following value of ‘k’ is consistent with the information given above? (1) 225 (2) 230 (3) 255 (4) 270 (5) 265

73.

Which of the following can be the number of girls who got exactly two oranges? (1) 17 (2) 19 (3) 23 (4) Both (1) and (2) (5) Both (2) and (3)

74.

When Saurav was born, his mother Lakshmi was 24 years old. When Saurav turned 50, his mother was still alive. In these 50 years how many times was Lakshmi’s age divisible by Saurav’s age? (Assume that the number that denotes the age of a person is always an integer.) (1) 6 (2) 7 (3) 8 (4) 12 (5) 24

75.

A is the set of first 40 natural numbers. B is a subset of A such that there exist atleast 2 pairs of elements in B whose difference is 12. If n is the number of elements in B, then which of the following is correct? (1) n ≥ 14 (2) n ≥ 24 (3) n ≥ 26 (4) n ≥ 28 (5) n ≥ 30

76.

The sum of the number of factors of the number N and N2 is 34. How many such distinct numbers N < 150 exist ? (1) 6 (2) 5 (3) 4 (4) 3 (5) 2

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23

77.

Let f(x) be a function that satisfies f(x – 2) = – f (x + 2) for every real number x. From x = – 2 to x = 2, the graph of f(x) is as shown below.

Which of the following shows the correct graph of f(x) from x = 96 to x = 104?

(1)

(2)

(3)

(4)

(5) None of these 78.

Amol owns a factory that can produce a maximum of 1300 units in one day. The variable cost of producing each unit is same. The fixed cost of running the factory for one day is Rs. 20000 and the total cost of producing 1200 units in a day is Rs. 200000. The selling price is Rs. 190 per unit when 1000 units are produced in a day. For every subsequent increase of 100 units in the production, the selling price per unit reduces by Rs. 5. The maximum possible profit that can be earned in one day is (1) Rs. 20000 (2) Rs. 18000 (3) Rs. 18700 (4) Rs. 16000 (5) None of these

24

002

79.

80.

x x Find the number of positive integral solutions of the equation   =    28   37  Here, [x] denotes the greatest integer less than or equal to x. (1) 27 (2) 28 (3) 38 (4) 58 (5) 57 Raju travels from town A to town B, by road. The road map that he uses as a guide is as given below.

A

B

Each of the straight line drawn in the map above is a road on which he cannot travel more than once. In how many ways can Raju travel from town A to town B ? (1) 32 ways (2) 81 ways (3) 145 ways (4) 243 ways (5) 729 ways 81.

In the figure given below, ABCD is a rectangle. Under a rectangular co-ordinate system X-Y, coordinates of the vertices A and C are (5, 0) and (0, –10) respectively and diagonal BD lies on the straight line L. The position of the rectangle is now changed is a way such that the coordinates of vertices A and C are (0, 10) and (5, 0) respectively and diagonal BD lies on the straight line M. Find the point of intersection of lines L and M. BC = 10 m, AB = 5 m.

B

5m

A

10 m

C

(1) (0, 0)

82.

 5  (2)  − , 5   2 

D

 5 (3)  5,   2

(4) (5, 0)

(5) (0, –5)

In the figure given below, ABC, DEF and GHI are equilateral triangles having the same area. It is also given that BD = DG = GC. Find the ratio of the area of the figure EJKL to the area of the figure AKHIB. A

E J

H L

K B

(1)

002

3 17

(2)

1 6

D

(3)

2 19

G

C

F

(4)

3 11

I

(5)

2 17

25

83.

A rod of length ‘L’ cm is broken into two parts of lengths L1 cm and L2 cm, where L1 = 2a × 3b and L2 = 3a × 2b. If the mid-point of the rod is at a distance of 90 cm from the ends, then find the value of L1 × L2 (Here, a and b are positive integers). (1) 7776 (2) 8176 (3) 8076 (4) 7716 (5) Data insufficient

84.

Gopal is a shopkeeper who has put two articles viz. P and Q on sale. He has offered two discount schemes viz. A and B under either of which a customer ends up paying the same amount of money. Scheme A: With the purchase of article P, 50% discount is given on the article Q, if purchased. Scheme B: With the purchase of article Q, 40% discount is given on the article P, if purchased. Now, Gopal decided to give a discount of 40% instead of 50% on the article Q in scheme A. What should be the discount offered on the article P in scheme B such that the customer will still pay the same amount irrespective of the scheme he chooses ? (1) 30% (2) 24% (3) 36% (4) 40% (5) 32%

85.

The radius of the circle with center at O is 5 cm. The length of each of the chords PQ and RS is 8 cm. Another circle with center at C is drawn such that it touches the circle and the chords PQ and RS. Given that the line joining the centers of the two circles passes through M, find the radius of the circle C.

P O R

C

M

S

Q

(1) 1 + 2 2 cm

(2) 2 + 3 cm

(3) 2 + 2 cm

(4) 3 +

3 cm 2

(5) 2 3 cm

86.

The terms of the sequence x1, x2, x3…..xn satisfies the relation xn – xn–1 + xn–2 = 0, where n > 2. If the (x + x 2 ) sum of first 88 terms and the first 89 terms is 150 and 120 respectively, then find the value of 1 . 2 (1) 124 (2) – 124 (3) – 30 (4) 30 (5) 90

87.

ABCD is a rectangle such that DC = 8 cm. E is a point on the side AB. The line DE is extended to a point F outside the rectangle. If the ratio of the area of the ∆ADE, ∆BEF and the quadrilateral EBCD is 1:3:6, then the ratio of the area of the ∆AEF to the area of the ∆AED is (1) 6 : 5 (2) 5 : 6 (3) 15 : 2 (4) 7 : 2

88.

A, B and C are positive integers (A, C ≠ 1) that satisfy A × B = C and B × C = A. Which of the following is equal to the expression (A logC BC × BlogCB + BlogACA × ClogAC ) ? (1) AB + C (2) B(C + A) (3) C(A + B) (4) B(B + C)

26

(5) None of these

(5) AC + B

002

89.

In the figure given below ABCD is an isosceles trapezium and PQSR is a square. If the length of the segment BC, PQ and AD is 2, 3 and 6 units respectively, then find the area of the trapezium ABCD.

B

C

P

A (1) 14 sq. units 90.

002

(2) 12 sq. units

Q

R (3) 16 sq. units

S

D (4) 18 sq. units

(5) 20 sq. units

P is the set of all the triplets of distinct natural numbers, which are in an arithmetic progression. If the product of the numbers in each triplet is less than 100 then the number of elements in the set P is (1) 20 (2) 10 (3) 14 (4) 8 (5) 18

27

Space for rough work

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Mock CAT – 2

Answers and Explanations 1

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3

5

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1

MY PERFORMANCE Total Time Taken Total Correct Incorrect Net Questions (Min) Attempts Attempts Attempts Score Section I – A

10

Section I – B

20

Language Comprehension Section II – A and English Usage Section II – B

10

Section III – A

10

Section III – B

20

Logical Reasoning based Data Interpretation

20

Quantitative Ability TOTAL

90

150

Discuss this test online at PREPZONE http://www.careerlauncher.co.in/prepzone Check detailed analysis of this test at http://www.careerlauncher.com/sis

MCT-0006/08 002

1

1. 4

Out of the mentioned persons, the only person who was the president of the United States of America for more than eight years is Ulysses S. Grant.

2. 3

The persons belonging to the Republic party were the presidents of the United States of America for not less than 2 years and not more than 5 years are Abraham Lincoln, Andrew Johnson, Rutherford B. Hayes, Chester A. Arthur, Benjamin Harrison, William McKinley and William Howard Taft. Therefore, there are seven such persons.

3. 5

4. 5

For Amol, Net balance = USD 40000 – SGD 50000 = INR (39.8 × 40000) – INR (28.7 × 50000) = 157000 For Bimal, Net balance = SGD 60000 – USD 36500 = INR (28.7 × 60000) – INR (39.8 × 36500) = 269300 Total difference = INR (269300 – 157000) = INR 112300 = 2820 USD Hence (1) is correct. 8. 5

The number of persons who belong to the state Virginia, Tennessee, Louisiana, New York, New Hampshire, Pennsylvania, Illinois, Ohio, Indiana and New Jersey are 1, 2, 1, 5, 1, 1, 2, 5, 1 and 1 respectively. The two persons who belong to the state Tennessee belong to different parties. Out of the five persons who belong to the state New York, the number of persons who belong to the Republic and the Democrat party are 2 and 2 respectively. The two persons who belong to the state Illinois belong to the same party. All the five persons from the state Ohio belong to the Republic party. Therefore, maximum possible number of persons in the group are (2 + 2) (New York) + 2(Illinois) + 5(Ohio) = 11

States

250

2000-2249

Tamil Nadu

100

3000-3099

Delhi

400

1000-1399

Andhra Pradesh

250

4000-4249

Uttar Pradesh

150

500-649

Madhya Pradesh

300

3500-3799

Bihar

400

4250-4649

Rajasthan

100

625-724

Haryana

200

4650-4849

Himachal Pradesh

100

3100-3199

Jharkhand

150

725-874

Total Expense on a UK MBA Degree = 28000 GBP. Amount Sponsored by the Company = 0.75 × 28000 = 21000 GBP

Maharashtra

300

1400-1699

Karnataka

100

3200-3299

Orissa

50

300-349

79.0 AUD = 46200 AUD = 21000 × 35.9 For a repayment of this amount, over a period of three years,

Uttaranchal

400

6000-6399

Punjab

200

2500-2699

West Bengal

250

2700-2949

Return on expense can be calculated by the ratio

60000 This ratio is maximum for Singapore as = 1.5 40000 Hence (5) is the correct answer.

46200 his company must pay him = 15400 AUD lesser than 3 what he would have been paid annually, otherwise. ⇒ The maximum salary that the company can offer him = (60000 – 15400) = 44600 AUD. For the period of three years the maximum salary that the company can offer him = 44600 × 3 = 133800 AUD. Hence option (5) is the correct choice. 6. 2

Cost of one return trip to India = (INR 16500 + GBP 386) = INR 47000. Total expense on a UK MBA degree = GBP 28000 = INR 2212000 The money available = INR 2340000 – INR 2212000 = INR 128000 Total money available for return trip from UK = 128000 – 386 × 79 = 97500

97500 ; 2, he can make a maximum of two return trips. 47000 Hence (2) is the correct answer.

As

7. 1

2

Number of Students All India Rank

Kerala

Annual SalaryRecieved . Total Expense Incurred

5. 5

Delhi, Maharashtra and Orissa satisfy the criteria (Even 1 student of West Bengal can, but we have to consider the minimum case in the question, so it can be omitted). Whatever be the allotment of ranks all students of Delhi and Orissa (wiz 400 + 50) will meet the criteria. To get the minimum number we can allot state rank 200 to 499 to the 300 students of Maharashtra (All India Rank can be any for these students in the given range).This way we get minimum 49 students from Maharashtra that meet the criteria. Hence total number of students = 400 + 50 + 49 = 499.

Expe ns e s

Incom e s

Am ol

SGD 50000

USD 40000

Bim al

USD 36500

SGD 60000

For both Amol and Bimal, Net balance = (Income – Expenses)

Note: Merely assigning All India rank to students of above 3 states will not suffice, we need to be sure that rest of states also show coherency in data. Based on the assignment of All India Ranks in Q8 of three states, rest all states can occupy ranks as above which satisfy all the constraints in the table. 9. 5

The table below represents the allotment of All India ranks in which maximum students meet the admission criteria of TIIT Hyderabad.

State

All India Rank Num be r of Stude nts

Delhi

1000

1

Uttar Pradesh

500 - 650

150

Rajasthan

651 - 751

100

Jharkhand

752 - 902

150

Orissa

300 - 350

50

All India Rank 1000 can also be occupied by a student of Maharashtra. It can be verified that students in rest of the state can also occupy rest of All India ranks by shuffling data in table of Q8. Hence Maximum number of students is 451. Option (5) is the correct choice.

002

10. 5 S.No.

State

Students that meet criteria

Total number of students

1

Kerala

250

250

2

Tamil Nadu

100

100

3

Rajasthan

100

100

4

Jharkhand

150

150

5

Maharashtra

Maximum 300

300

6

Karnataka

Maximum 100

100

7

Punjab

Maximum 200

200

8

West Bengal

Maximum 100

250

Above table indicates number of students from each state that meet the admission criteria of Dali College of Engineering. Though number of students from state 1 to 4 in the table that meet the criteria are fixed, it’s not the case for rest of the states where the maximum number is denoted. Since 300 students of Maharashtra can also have state ranks from 501 - 800, number of students that meet the criteria can vary from 0 to 300, which may or may not exceed the fixed number of students from Kerala (wiz 250). Hence (5). Cannot be determined. 11. 3

D M2 A

As 2ax + 4bx + 3 = 0 for only one real x, discriminant = 0. ⇒ Discriminant = ( 4b )2 − 4(2a)(3) = 0 ⇒ Discriminant = (b − 6a) = 0

⇒ b2 + 2ab − 48a2 = (b − 6a)(b + 8a) = 0 Hence (B) alone is also sufficient to answer the question and the answer is “no”. 12. 1

Using the statement given in A, we can draw the quadrilateral ABCD, as below. D 3 0° M 2 C

A M1

G

C

As α cannot be determined uniquely, are cannot determine BC, uniquely. Hence, we cannot determine the area of quadrilateral ABCD. The information M1M2 = 5cm, is redundant The area of quadrilateral cannot be determined, using statement B alone. 13. 3

Using the information given in the question the following can be concluded: 1. Age (Merissa), Age (Ryan) > Age (Sandy) 2. Age (Julie) > Age (Samar) 3. Age (Samar) > Age (Merissa) > Age (Nicole) Therefore, Age (Julie) > Age (Samar) > Age (Merissa) > Age (Sandy), Age (Nicole) Using Statement A: Age (Samar) + Age (Ryan) < Age (Nicole) + Age (Merissa) Since Age (Samar) > Age (Merissa), therefore Age (Nicole) > Age (Ryan). So it can now be concluded that Julie is the oldest of all the siblings.

Statement A: As ax2 + bx + 4a > 0 for all values of x, we must have a > 0 and

Statement B:

α

4 5° M1 B

b2 + 2ab – 48a2 = (b – 6a)(b + 8a)

Discriminant < 0. or a > 0 and b2 – 16a2 < 0 or a > 0 and (b – 4a)(b + 4a) < 0 or (b – 4a) < 0 and (b + 4a) > 0 ⇒ (b – 6a) < 0 and (b + 8a) > 0 ⇒ b2 + 2ab – 48a2 < 0 Hence (A) alone is sufficient to answer the question and the answer is “no”.

θ

Using Statement B: Age (Julie) + Age (Merissa) < Age (Ryan) + Age (Nicole) Since Age (Merissa) > Age (Nicole), therefore Age (Ryan) > Age (Julie). Hence Ryan the oldest of all the siblings. So, statement B alone is sufficient to answer the question. Hence, option (3) is the correct choice. 14. 5

Veeru must be playing Table tennis since Dhiru is playing Squash and Veeru is not playing Badminton. Also Sherry must be playing Table tennis with Veeru since Veeru is not playing with Larry and Jerry is not playing table tennis. With the same facts, we can easily say that Neeru must be playing Badminton. Here either Larry or Jerry could play with Dhiru or Neeru. Hence option (5) is the correct choice.

For questions 15 to 18: Given that the number of months that are termed “Productive” by the company is 5. It is also known that Group 7 has five “Productive” months. The six months in Group 7 are January, April, September, July, May and August. Out of these six months, there is one month that is not termed “Productive” by the company. The six months that are not in Group 7 are February, March, June, October, November and December; therefore these six months are not termed “Productive” by the company. Now in order to find out of the months in Group 7, which is not termed “Productive” by the company we need to find which group has no “Productive” month.

B

As measurement of AB, BD, CD and M1M2 are known and ∠BDC = 30° is known, ∠ABD = θ can be determined, uniquely. Hence, AD and BC can also be measured, Hence, the area of quadrilateral ABCD can be determined, using statement A alone, Using statement B: The figure can be drawn as below.

002

If in any group there are at least two months that are also in Group 7, then that particular group cannot be the group that has no “Productive” month. So, following this logic it can be concluded that Group 2 or Group 3 or Group 5 or Group 6 or Group 9 or Group 10 cannot be the group that has no “Productive” month.

3

Therefore, Group 1 or Group 4 or Group 8 or Group 11 or Group 12 can be the group that has no “Productive” month.

21. 3

We will assume that all the silver medals won by “others” were won by China only.

Consider Group 1 and Group 12: If January is the month that is not termed “Productive”, then there will be two groups with no “Productive” months. Hence, this is not possible.

Number of medals won by India =

Consider Group 8 and Group 11: If May is the month that is not termed “Productive”, then there will be two groups with no “Productive” months. Hence, this is not possible.

=

N 9N 33N 47N + + = 8 50 200 100

Number of medals won by China

3N 3N 23N 151N + + = 8 20 100 200

⇒ Number of medals won by India is at least

Therefore Group 4 is the group that has no “Productive” month and out of the months in Group 7, April is the month that is not termed “Productive” by the company. 15. 4

1

2

3

4

5

6

7

8

9

10 11 12

1

2

3

0

4

3

5

1

3

4

1

22. 4

The number of groups in which there are four “Productive” months is 2.

17. 5

From the table given above, there is only 1 group (Group 2) in which there are 4 months that are not termed “Productive” by the company. Hence, Statement A is true. The pairs of consecutive months that are termed “Productive” are (July and August) and (August and September). Hence Statement B is true. The pairs of consecutive months that are not termed “Productive” are (February and March); (March and April); (October and November); (November and December). Hence Statement C is true. Hence option (5) is the correct choice.

46N and all of them may have belonged either to 200 China or to Japan. Bronze Medals: The number of bronze medals whose data is

62N and all of them may have belonged either 200 to Kazakhstan or to Singapore. Hence for each of the seven countries, there are only two possible values for the total number of medals. These values are tabulated below: not available is

The groups in which the number of “Productive” months is more than the number of months that are not termed “Productive” by the company are Group 5, Group 7 and Group 10. Therefore, the number of groups in which the number of “Productive” months is not more than the number of months that are not termed “Productive” by the company is 12 – 3 = 9.

20. 4

29N  Number of gold medals won by Singapore =    200  31N  Number of Silver medals won by Jordon =    200  Hence the required ratio is 29:31. Hence (4) is the correct option.

4

Minimum Medals

Maximum Medals

China

105N/200

151N/200

Japan

56N/200

102N/200

Kazakhstan

41N/200

103N/200

India

94N/200

94N/200

Singapore

54N/200

116N/200

Malaysia

71N/200

92N/200

Jordon

51N/200

72N/200

116N 56N 102N , Japan Could have had either or medals in 200 200 200 all. As Jordon can have a maximum of

72N medals only, this 200

option is not valid.

Sum of the numbers of silver and bronze medals won by

71N Malaysia = . As this sum must be an integer, it will be a 200 multiple of 71. Accordingly, 142, 213, 284 and 355 all are possible values. Only 164 is not a multiple of 71 and hence (2) is the correct answer.

Country

All the options except option (4) show a valid arrangement. In option (4) the total number of medals with Singapore must be

For questions 19 to 22: At the end of each event exactly one each of gold, silver and bronze medals were awarded hence the total number of gold or silver or bronze medals must be the same. Let there be N number each of gold, silver and bronze medals. 19. 2

Gold Medals: The number of gold medals whose data is not available is (21N/200) and all of them may have belonged either to Malaysia or to Jordon. Silver Medals: The number of silver medals whose data is not available is

1

16. 3

18. 1

of the number of medals won by China.

Out of the given options April is not termed “Productive” by the company.

Gr oup Num be r Num be r of Pr oductive m onths

94 = 62.24% 151

Note: No intermediate values are possible between the respective maximum & the minimum values for any of the seven countries. 23. 3

Magic Number for P, Q, R, and S is 0 and magic number for T and U is 1. (T - R) and (U - S) Required sum is 2.

24. 5

Since out of the number of persons who voted for P in any round, the number of persons who voted for S should be least, we need to maximize the number of persons who voted for P in any round and then voted for T in the next round. (Additional Information (1)). 34 persons who voted for P in round I, voted for T in round II. Out of the 39 persons who voted for P in round II, 36 voted for T in round III and 3 voted for S in round III.

002

Out of the 43 persons who voted for P in round III, 35 voted for T in round III and only 8 can vote for S in round IV as out of the 29 persons who voted for S in round IV, 21 have to be those who voted for S in round I. (Additional Information IV) Out of the 29 persons who voted for P in round IV, 29 voted for T in round V) Therefore, out of the persons who voted for P in any round, the number of persons who voted for S is at least 3 + 8 = 11. 25. 5

26. 1

Number of persons who voted for P in every round = 0. Number of persons who voted for Q in every round is at most = 9 (In round II number of persons voting for Q and U is 39 and 13 respectively and the number of persons voting for P in round III is 43). This is possible when the persons who voted for U in any round always voted for P in the next round. Number of persons who voted for R in every round is at most = 2 (Number of persons who voted for T in round I is 43 and the sum total of persons who voted for R and U in round II is 45). Therefore, the number of persons who voted for the same nominee in every round is at most 9 + 2 + 21(S) = 32. Note: 21(S) means votes for S. Since the persons who voted for T in any round, voted for either R or U in the following round and out of the persons who voted for Q in round IV, we need to maximize the number of persons who voted for R in round V, therefore following conditions must hold true. 1. Out of the persons who voted for T in round IV, 24 persons will vote for U in round V. This will leave 11 persons who voted for T in round IV to vote for R in round V. 2. Out of the persons who voted for Q in round IV, maximum number of persons who voted for R in round V will be 41 – 11 = 30. Now, out of the persons who voted for U in round IV, we need to maximize the number of persons who voted for Q in round V. So, following conditions must hold true. 1. The 35 – 30 = 5 persons who voted for Q in round IV will vote for P in round 5. This will leave 34 – 5 = 29 votes still to be given to P and this will be done by 29 persons who voted for U in round IV (Remember additional information 2). So out of the persons who voted for U in round IV, at most 36 – 29 = 7 persons could have voted for Q in round V.

31. 5

Option 1 is incorrect because the statement is generally true and does not hold for all cases. Option 2 is too specific to qualify as the central theme. Option 3 is too general. Option 4 is true, but not broad enough to encompass the whole passage. Option 5 is the main idea being discussed in the passage and hence is the best choice.

32. 5

Statement a cannot be inferred as the basis or reasoncomparison between a lion and a human being - is too narrow. b cannot be inferred as it is given at the start of the second paragraph that Wittgenstein has been interpreted by some people to be giving the general theory. We cannot conclusively say whether he has really offered the theory. The first half of statement c is Wittgenstein’s personal opinion. The reason “objective nature of human thoughts” seems far fetched when seen in the light of the passage. Statement c, on the whole, cannot be conclusively inferred to be generally true. Hence option 5 is the best option.

33. 5

None of the statements are logically complete and fit to be called as statements which Wittgenstein would agree to.

34. 5

The last 2 sentences of the passage and especially the last sentence are indicating the importance of Application in facilitating correct interpretation. In fact the last sentence is emphatic on the point that only application is important. Option 1 is incorrect as the arrow should represents the truth and not the false. Option 2 is the opposite of what is indicated by the last line. Option 3 is general and does not talk about the specific implication. Option 4 also goes off-track as interpretation can happen without application, but the validity will be under question. Option 5 represents the implication of the last line correctly.

35. 3

The central theme of the paragraph revolves around the initiative taken by a British school teacher to abandon the word “failure” from being used in classrooms as it creates negative vibes among the innocent minds of school children. Therefore, the starting link should be a sentence which introduces the new step taken by the British teacher. Hence the first sentence starting the paragraph should be sentence E. Obviously the next sentence following it should be a sentence which describes the teacher’s name and the details of the initiative or motion taken by her. So the sentence following E should be sentence B. Hence there is an evident EB link. Sentence C should definitely follow sentence B because of the use of the word “motion” in C which refers to the initiative taken by Beattie in sentence B. Similarly there is also a direct link between sentences C and D which is clear by the usage of the word “agreement” in sentence D. Finally the conclusion that failure lowers the confidence and self-esteem of school children is stated in sentence A. Hence, the correct answer has to be option (3).

36. 5

The paragraph primarily revolves around the idea of “essentialism” and how it focusses on expressing various concepts separately through different media so that their true value is realized to their full extent. Hence the starting sentence has to be A. Therefore, options (1), (2) and (3) can be safely eliminated. Clearly sentence B elaborates further on the thought stated in sentence A by emphasizing that each medium has different levels of strengths and weaknesses and hence the concepts that have to be expressed through them have to be obviously different. Therefore, there is a direct AB link. The sentence following B’s line of thought has to be E as it provides an example of how one concept suitable for a particular medium becomes poor in perception if it is expressed through any other medium. The EC link is quite prominent because C provides more examples in relation to the idea expressed in E. Finally

For questions 27 and 30: There are 4 Non-vegetarian item and only 2 Non – vegetarian D& E, implies both have exactly two non Veg items (from statement 2) According to information no (1) the meals taken by C, D, E could be a. Biscuit and burger b. Rice and rotis (this has to go with C as only vegetarian combination) c. Continental and Chinese d. Continental and chicken. Toast and Fruit can only go to A (this should go to a vegetarian)and Now Dosa & Upma combination has to go to B only. As E doesn’t like chicken this should go to D this implies Continental Chinese combination should go E and Biscuit Burger combination to D Hence the meal arrangement will be:

Breakfast

Lunch

A

Toast

Fruits

Pizza

B

Milk

Dosa

Upma

C

Salad

Rice

Rotis

D

Biscuit

Burger

Chicken

E

Eggs

Continental

Chinese

27. 2

002

28. 4

29. 5

30. 3

Dinner

5

sentence D has to be the concluding sentence because it proves why essentialism is liked by artists because of the systematic method of separating art and media. Hence the correct link at the end has to be CD and not DC and so the correct answer has to option (5). 37. 2

According to the given options, D, C or E could be the opener. Sentence C cannot be the opener as it is presenting a contradiction but one does not know what is being contradicted here. Sentence D may seem like the opener but the idea in E is more general as compared to D. So, E is the opener. It presents the problem that is being faced by small, home-based businesses. EC is a mandatory pair as Sentence C contradicts the problem (revealed in E) and shows that this problem is actually an opportunity. So, option 2 contains the correct order. Further, B presents another possible problem that these small businesses will be facing in the near future. Sentence D further presents the problems that were faced by entrepreneurs. Sentence A provides the solution to the whole issue and concludes the paragraph.

38. 2

Beam: Option (2) is wrong because ‘beam in’ is an incorrect phrasal verb; ‘beam with’ joy is the right usage.

39. 3

Face: Option (3) is wrong. ‘Flew in the face of…’ is the right idiom to use.

40. 1

Act: Option (1) is wrong because the colloquially used idiom is ‘class act’ and not ‘classy act’.

41. 3

Option (1) is out of context as it is nowhere mentioned in the given passage. Again Option (2) speaks about the frequency of occurrence of space silence in daily life which has no relevance with the given question. The question is asking to find the hidden meaning of the phrase’ silence of space is a kind of limit possibility’ and hence space being a busy place bustling with a lot of activity is not of our concern. So we can eliminate Option (4). Option (5) gives partial information for the question because it neglects the aspect of space silence occurring outside the earth which makes it an unqualified concept in terms of defining silence in its proper tone. Therefore, the correct answer is Option (3) because it includes both the points indicated in the passage which make the silence of space a kind of limit possibility such as the point of space silence occurring outside the earth and space silence attracting an active search for other types of noise which can compensate for this stated silence.

42. 5

Option (1) is irrelevant in terms of the given question because the author has not mentioned cosmic space with respect to the space of Descartes and Newton. Again Option (2) is out of context because ‘localization of noise’ is not our focus for the question. Option (3) is incorrect because the author has nowhere given the details of Descartes and Newton’s theories in the passage. Option (4) has no link with the given question as it does not mention the ‘space of Descartes and Newton’ which is the main topic of the question. Option (5) is the correct answer as it has been mentioned in the 4th sentence of the 2nd paragraph of the passage where the author gives a hint regarding the real space of Descartes and Newton which was ‘uninflected’ or unaltered.

43. 1

In the example of Rauschenberg’s paintings, it is stated that the apparent emptiness revealed an active vitality. Hence, it would be incorrect to infer that vitality cannot be expressed through science. The other options can be inferred from the passage.

6

44. 3

Refer to para 2 where Silence has been differentiated from quiet. Options 1 and 4 are incorrect. Option 2 is also incorrect. The passage nowhere talks of the explosiveness of quiet. Also - explosiveness of silence is spoken about in the context of silence becoming a definite possibility. Option 5 is an opinion which is unsubstantiated by the passage.

45. 5

Option (1) mentions the relationship between various researches whereas the passage talks about the comparison between various researchers. So, option 1 is incorrect. Option (2) refers to ‘present limitations in the field of research are a disadvantage’. This statement is too strong. The author explains that these factors ‘affect management researchers differently’ (para 2, line 1) and hence does not specifically refer to these as ‘disadvantages’. Option (3) presents only one aspect (of codes) from the passage. Option (4) refers to ‘ways to approach management research’ which is incorrect because it is not mentioned or discussed in the passage. Option (5) explains ‘the unique effects of certain factors on management researchers’. The passage mentions the effects of factors on management researchers vis-a-vis the effects on researchers from other fields of study. So, option (5) is the appropriate choice.

46. 2

Option (1) is clearly a statement which the author would disagree with. In the second paragraph, the Nuremberg code is discussed. The second paragraph explains, ‘At the heart of the code is the principle of informed consent, which forms the basis for ensuring the protection of vulnerable people’. Also, the last line of the second paragraph, ‘the protection of human subjects remains a fundamental principle’. Both these statements from the passage are contradictory to option 1. Option 3 is incorrect because the third last line of the second paragraph explains that ‘the Declaration of Helsinki, which sought to balance the interests of the subject against the need for scientific research.’ Option (4) directly contradicts the statement given in sixth line of the first paragraph, where the author explains that such a declaration is ‘rare in management research’. Option (5) is incorrect because in the last paragraph the author explains how ‘power relations’ affect research in different fields of study. Option (2) refers to ‘the appropriate use of the principle of informed consent’, ‘on the individual field of study’. In the last paragraph of the passage, the author explains that ‘the question for management researchers......whether the principle of informed consent is an appropriate mechanism.......with research participants in this field of study’. This justifies option (2) as a true statement.

47. 3

There is no proof available in the passage that justifies that the Nuremberg code led to the formation of the Declaration of Helsinki. So, option (1) is incorrect. Option (2) suggests that the Nuremberg code was an ‘ideal law’. This cannot be justified on the basis of the given passage. Whether it was ‘ideal’ or not, one cannot say. Option (4) is incomplete because it does not explain the nature of the law. Also, it does not highlight the importance of the law. Option (5) is incorrect because it refers to the achievement of the Declaration of Helsinki and not the Nuremberg code (second paragraph, last four lines). Option (3) mentions ‘ethical grounding in research’. This statement is justified by the example of the ‘Nuremberg Trial’. The author mentions that the Nuremberg code paved ‘the way for a reconstituted moral vision’ (second paragraph, line twelve). Hence, option (3) is the correct

48. 5

Option 1 seems like a repetition as the last sentence has spoken about the world and ended with the individual. Option 2 goes against the tone of the passage and is vague. Option 3 starts off on a different track –organized religion. Option 4 talks about man’s flow being governed by natural laws whereas the paragraph denies the existence of any rule.

002

Option 5 carries forward the theme of the paragraph and states a conclusion about the existentialist which is drawn from the paragraph. 49. 5

Option 5 correctly continues the theme of the paragraph. It talks about the behaviour of the nonlinear system. Options 1, 2, 3 and 4 are general in nature and do not specifically continue the idea left off in the last line of the paragraph.

50. 5

Option 1 is abruptly in the past tense. In options 2 and 3 the effect of the thunderstorm and the earthquake forces do not resemble the downward push / thrust of the giant stomping on the towers. Option 4 is vague. Option 5 is specific and similar to the example of the ‘giant’s stomp’ in the paragraph.

51. 2

Option 1 is incomplete. Option 3 is illogical and distorted when compared to the original paragraph. In Option 4, we cannot say that the findings are from recent culture periods. Option 5 is too specific as children and Neolithic burial rites are left out. Option 2 covers the main points of the paragraph and provides a good summary. Hence option 2 is the best choice.

52. 5

Option 1 is incorrect as the lack of evidence was not the reason for performing the DNA tests. Option 2 says that the scientists were ‘reluctant’ - which is nowhere given in the paragraph. Option 3 is incorrect as it cannot be said that the claims were ‘apocryphal’. Option 4 is incomplete when compared with option 5. Option 5 encompasses the core of the paragraph and hence is the best summary of the passage.

53. 1

54. 5

The correct option is 5 because ‘A, C and E’ have no errors. In ‘B’ the correct word (adverb) is ‘overpoweringly’ and not ‘overpowering’. In ‘D’ it should be ‘would look’, since the sentence is in past tense. The correct option is 4. A, C and E don’t have any grammatical error. In ‘D’ it should be ‘people look like..’ not ‘..alike’, because ‘alike’ is incorrect contextually. In ‘B’ it should be ‘caricatures’ and not ‘caricature.

56. 2

The correct option is 2. There are no errors in B, C and D. A is incorrect because it should be ‘sightings’ not ‘sighting’ since it is referring to more than one situation, that is ‘dawn and dusk animal …’. E is incorrect because ‘both’ should precede ‘physically and mentally’, since ‘both’ is a distributive pronoun.

57. 3

It is clearly evident from the passage that Clinton never gave priority to Haldiman’s need for timely information because of which Haldiman was disappointed. Hence, Clinton’s attitude towards the matter was one of strong opposition or resistance because of which he was not responding properly. Hence, devastating, caustic, pernicious and acerbic are out of context here because the passage is not talking about anything that is damaging or sarcastic by nature. The most appropriate answer would be “recalcitrant” which means providing resistance or obstruction to something.

002

59. 1

The last sentence of the passage clearly indicates that the English wanted to suppress the Irish language. Hence, the most appropriate word that would be closest to “suppress” is “subjugation” which means to bring about complete control or to conquer something. “Down throw” which means to throw down, “Regimen” which means governmental rule or procedure, “Abstinence” which means self-restraint and “Forbearance” which means refraining from doing something are unsuitable for the meaning of the sentence given.

60. 3

By referring to the last sentence of the passage, one can derive that the dog had a very opposing attitude towards books which is evident from its activity of eating the first edition of a famous Memoir. Hence, the suitable word to be used here is “perverse” which means to be marked by the disposition to oppose or contradict. “Intense” which means passionate, “Extraneous” which means irrelevant, “Incendiary” which means capable of causing fire and “Beguilement” which refers to the act of deceiving or misleading are not appropriate in terms of the paragraph stated.

61. 4

The first sentence of the passage is talking about the principle of fairness which speaks about the moral responsibility of contributing in the production of public goods rather than only enjoying the benefits. The usage of the word “not to” before the italicised word indicates that the answer would be “free ride” which means to obtain something without any effort. “Exhaust” which means to drain out of energy, “Constrain”

(

)

x−y x + y 2 2 2   % of x − y +   % of ( x − y ) = 40 x y x y + −    

⇒ ( x − y ) + x2 − y2 = 4 × 103 2

The correct option is 1 because ‘A’ and ‘B’ don’t have any error. In ‘C’ it should be ‘over’ not ‘above’. ‘D’ is incorrect because it should be ‘seemed’ not ‘were seeming’. In ‘E’ the correct preposition should be ‘along’ not ‘alongside’.

55. 4

58. 5

which means to force or compel, “Intrude” which means to interfere and “Manipulate” which means to influence or control shrewdly or deceitfully are not suitable in the given context.

⇒ x 2 − xy = 2 × 103 x+ y ∴  % of  x 

62. 5

 2  2 −2 −5  x 2 − y 2  = x ( x − y ) × 10 = 10  

∴ ab + ba + a × b = 145 ⇒ 10a + b + 10b + a + ab = 145

...(i)

145 − 11b 11 + b The possible values of ‘b’ and ‘a’ that satisfies the above equation are 3 and 8 or 8 and 3 respectively. ∴ Sum of the digits of A = 11. ⇒ a=

63. 4

Ramesh gets the second, fourth, sixth.... infinite turns to roll the die. The probability that he is the first to get number 6 as his outcome is given by: P( Ramesh Wins) = 5 5 1  5 5 5 5 5 1  5 1  5 × ×  +  × × × × ×  + .... ∞  × + × 6 6 6 6 6 6 6 6 6 6 6 6 5 1 6 × 6  = 5 =   5 5  11 1−  ×  6 6

64. 4

R1 = x

S1 = y

R2 = R1S1 = xy

S3 = S1R2 = y x

2 2

S4 = S1R3 = y × x

R3 = R1S2 = x y R 4 = R1S3 = x y 3 2

R5 = X y

S2 = S1R1 = yx

2

2

2

2

3 2

S5 = y x

R5 + S5 = xy(x2y + y2x) = xy(R3 + S3) Rn + Sn = xy(Rn–2 + Sn–2) Hence, option (4) is the correct answer.

7

65. 4

Let, N = ab

69. 5

∴ N = 10a + b

⇒Q=

   9  10a + b  9a  = 1+  = + 1    a+b a +b  1 + b  a 

Now, the value of Q will be minimum when the value of ‘b’ and ‘a’ is 9 and 1 respectively. So, the minimum possible value of Q is 1.9

66. 3

2

D

C

3 0°

3 0°

4

70. 4 E

B

Please note that ∆ADE is similar to ∆ECB since AD P EC and

The equations formed by the roots of the equation (x – a) (x – b)(x – c) can be as follows (i) (x – a)(x – b) ⇒ Roots are a, b (ii) (x – b)(x – c) ⇒ Roots are b, c (iii) (x – c)(x – a) ⇒ Roots are c, a (iv) (x – a)2 ⇒ Roots are a, a (v) (x – b)2 ⇒ Roots are b, b (vi) (x – c)2 ⇒ Roots are c, c Adding all these roots, we get 4(a + b + c). Hence option (4) is the correct choice. For option (1), N2 = 1248 or 8421 and sum of digits = 15. For option (2), N1 has six possible values when digits are in increasing arithmetic progression and other six possible values when they are in decreasing progression. Hence 12 values. Similarly N1 + N2 will have 24 possible values which means option (3) is also possible. When N 1 = 23456, it becomes divisible by 4.Hence option (4) is not possible. Note: Digits in N1 cannot have a common difference more than 2

X Straw

Jack

Let VJ and VS be ‘2x’ and ‘5x’ respectively. Solving equation (iii) & (iv)

∴W = 71. 4

10 m/s 3

10 20 m/s = 3 3

10 50 m/s = 3 3

⇒ W = 3×

1 1 ab sin30° = × 8 × sin30° = 2 units 2 2 Hence option (3) is the correct choice.

For questions 69 and 70:

…(ii)

VS = 5 ×

2 b = ⇒ ab = 8 a 4

Area of ∆DEC =

68. 4

100 = 10 VS – VJ

VJ = 2 ×

Q ∆ADE ~ ∆ECB

67. 4

…(i)

We get that x =

DE P BC . Let, DE = a and EC = b.

∴

30 70 = VJ + W VS – W

Solving equation (i) …(iii) 3VS – 7VJ = 10W Solving equation (ii) …(iv) VS – VJ = 10 Since, there are three unknowns and two equations, the equations cannot be solved for unique values of VS, VJ and W. Hence, option (5) is the correct choice.

3 0° A

Given that circumference of the path followed by the friends = 100 metres Let the speed of Jack be VJ m/s Let the speed of Straw be VS m/s Let the speed at which the water flows = W m/s

50 20 – 7× 3 3

1 m/s 3

Let the number of Benos be ‘B’ So, the number of Malos will be ‘139 + B’. Therefore, B + 139 + B = 55009 2B = 55009 – 139, B = 27435 Therefore the total number of Malos residing in the island = 55009 – B = 27574. Hence, option (4) is the correct choice.

For questions 72 and 73: Let x be the number of girls who got exactly three oranges and y be the number of boys who got atleast two oranges. A t le as t 1 o r an g e 100 – x

A t le as t 2 o r an g e y

Gir ls

100 – y

60 – y

x

T o tal

200 – (x + y )

60

40

Bo ys

Now, 100 – x ≥ y ≥ 40 − x

...(i)

100 – y > 60 – y ≥ x

...(ii)

200 – (x + y) ≥ 60> 40

...(iii)

Exactly 3 o r an g e s 40 – x

(i) implies that 40 ≤ x + y ≤ 100 (ii) implies that x + y ≤ 60, (iii) implies that x + y ≤ 140 Combining all three results we get that 40 ≤ x + y ≤ 60. Also, 40 × 3 + (60 – 40) × 2 + (200 – (x + y) – 60) × 1 = K

8

002

⇒ 300 – (x + y) = K ⇒ x + y = 300 – K ∴ 40 ≤ 300 – K ≤ 60 ⇒ 240 ≤ K ≤ 260

72. 3

Only option (3), i.e. 255 lies within the permissible range of values of ‘K’.

73. 4

From the table, the number of girls who got exactly two oranges = 60 – y – x = 60 – (x + y) = 60 – (300 – K ) = K – 240 We know that 240 ≤ K ≤ 260 So, for K = 257, K – 240 = 17 and for K = 259, K – 240 = 19 Hence, option (4) is the correct choice.

As 96 is completely divisible by 8 and as 104 = 96 + 8, the graph of f(x) from x = 96 to x = 104 will be same as the graph of f(x) from x = 0 to x = 8. Hence option (3) is correct. 78. 5

74. 3

75. 3

L = S + 24 So, if L has to be divisible by S S + 24 has to be divisible by S. This means 24 has to be divisible by S. Hence, it can happen as many times as 24 has factors, which is 8. Let us find the maximum selection when there is no pair. Take a situation of taking the first 12 numbers 1 to 12. In this case we cannot have any other numbers from 13 to 24 otherwise difference of the two numbers will because 12. We can start from 25 and select till 36. Therefore there is no selection from 37 to 40. Hence we can select 24 numbers, (1, 2, ......, 12, 25, 26...... 36) and still have no pairs. Any new number selects with necessarily pair up with an existing number (pair is when difference is 12) So to get 2 pairs, we must select 26 numbers. If it is atleast 2 pairs n ≥ 26

76. 5

77. 3

We know that number of factors of a perfect square is always odd. ∴ Number of factors of N2 is odd. Now, we can conclude that number of factors of N is also odd. [odd + odd = even] ∴ N is also a perfect square. Since N < 150 and sum of the number of factors of N and N2 is 34, therefore N must have at least 2 prime factors. Consider, N = 36 = 22 × 32, N2 = 362 = 24 × 34 Sum of factors = 3 × 3 + 5 × 5 = 34 For, N = 100 = 22 × 52, N2 = 1002 = 24 × 54 Sum of factors = 3 × 3 + 5 × 5 = 34 ∴ There are only 2 such values of N < 150, i.e. N = 36 and N = 100. f(x – 2) + f(x + 2) = 0 ...(i) ⇒ f(x – 1) + f(x + 3) = 0 or f(x) + f(x + 4) = 0 ...(ii) or f(x + 1) + f(x + 5) = 0 or f(x + 2) + f(x + 6) = 0 or f(x + 3) + f(x + 7) = 0 or f(x + 4) + f(x + 8) = 0 ...(iii) from (ii) and (iii) f(x + 8) = f(x) ...(iv) ⇒ The graph of f(x), will get repeated after every interval of 8 units, from the given graph and by using (i) and (ii) above, we can draw the graph of f(x) from x = 0 to x = 8, as below

Profit is maximum when production is 1099 units/day and not 1000 units. Total cost when Production is 1099 units/day. fixed cost = Rs. 2000 Variable cost =

(200000 – 20000 ) = Rs. 150 / unit

1200 ∴ Total cost = 20000 + 150 × 1099 = Rs. 184850 Total selling price = 1099 × 190 = Rs. 208810 Total profit = 208810 – 184850 = Rs. 23960 (Further production increase will decrease the cost marginally but there will be a steep fall in selling price) [at 1199 and 1299 units total profit is less than Rs. 23960]

79. 5

 x   x  As 28 × 5 < 37 × 4, therefore the value of   =   can  28   37  be either 3 or 2 or 1 or 0. Case I:  x   x   28  =  37  = 3     Since, 28 × 4 – 37 × 3 = 1, therefore there is only 1 value of  x   x  ‘x’, i.e. x = 111 for which   =   = 3  28   37  Case II:  x   x   28  =  37  = 2     Since, 28 × 3 – 37 × 2 = 10, therefore there are 10 values  x   x  of ‘x’ for which   =   = 2  28   37  Case III:  x   x   28  =  37  = 1     Since, 28 × 2 – 37 × 1 = 19, therefore there are 19 values  x   x  of ‘x’ for which   =   = 1  28   37  Case IV:  x   x   28  =  37  = 0    

There are 27 values of x, i.e 0 ≤ x ≤ 27 for which  x   x   28  =  37  = 0     Hence, total number of positive integral solutions of the equation = 1 + 10 + 19 + 27 = 57

002

9

82. 5

I

80. 4

II P

A

III

IV

V

∆KGC : ∆JDC : ∆ABC.

x y

Q

Let the area of the ∆ABC be ‘a’ square units.

B

z

R

Q ∆KGC : ∆JDC : ∆ABC

There are 5 decision making stages. At each of these stages by there are 3 possibilities. At state I: One can take any of the three paths p, q, r. At stage II : If one goes via path P, will reach x - at this point one has 3 possible paths again as shown below.

a 4a ∆KGC = , ∆JDC = 9 9 Similarly, ∆GLF =

x y

4a a a − = 9 9 3

4a 9

Area of the figure BAJELHIB = a +

x y z

Re quired Ratio =

and this will be true at all the five stages. Hence number of routes = 35 = 243. Case I: A and C have co-ordinates (5, 0) and (0, –10) respectively.

A (5,0)

B (0,0)

2 a 19a 2a – a a

x

83. 1

⇒

⇒ Equation of straight line L is y = –2x. Case II: A and C have co-ordinates (0, 10) and (5, 0)

y

C (5 , 0 )

84. 5

x

Co-ordinates of vertices B and D are (5, 10) and (0, 0) respectively. Equation of the straight line M is:

y − 0 10 − 0 = =2 x−0 5−0 ⇒ Equation of straight line M is y = 2x Lines L (equation y = –2x) and M (equation y = 2x) intersect at (0, 0); the origin of the X-Y co-ordinate system.

2a .3b + 3a .2b = 90 2

⇒ 2a–2.3b-1+ 3a-1.2b-2 = 15 Note that in above expression, none of the terms in the L.H.S can be either a prime number or a multiple of 5. The only numbers left are 2, 4, 6, 8, 9. Now, only pair which add up to give 15 is 9 and 6. Hence, a = 3 and b = 2 or a = 2 and b = 3. Therefore, L1 × L2 = 7776. Hence, option (1) is the correct choice.

y − 0 0 − ( −10) = = −2 x−0 0−5

D (0 , 0 )

L1 + L2 = 90 2

⇒ 2a-1.3b + 3a.2b-1 = 90 ⇒ 6 (2a-2.3b-1+ 3a-1.2b-2) = 90

Co-ordinates of vertices B and D are (0, 0) and (5, –10). Equation of the straight line L is

B (5, 10 )

2 . 17

According to the question, we have

D (5 , – 10 )

A (0, 10 )

2 17

be divided into 9 equilateral ∆s of equal area. In the given diagram, there are total of 19 small equilateral triangles and figure EJKL includes 2 such triangles. Hence required ratio =

(0 ,– 10 ) C

=

5a 5a 19a + = 9 9 9

Alternative method: Use the fact that if each side of an equilateral triangle is divided into three equal parts, then the area of the triangle can

y

10

⇒ JKGD =

 4a a  2a ⇒ EJKL = a −  + =  9 3 9

x

81. 1

Since BD = DG = GC and ABC, DEF and GHI are equilateral triangles having the same area, therefore

Let the marked price of the articles P and Q be ‘p’ and ‘q’ respectively. Amount paid by the customer if he/she chooses scheme A will be p + (1 – 0.5)q = p + 0.5q Amount paid by the customer if he/she chooses scheme B will be q + (1 – 0.4)p = q + 0.6p Now, p + 0.5q = q + 0.6p ⇒ 0.4p = 0.5q ⇒ 4p = 5q New amount paid by the customer if he/she chooses scheme A = p + (1 – 0.4)q = p + 0.6q Let, K% be the discount offered on article P in scheme B. k   P Amount paid by the customer is = q +  1– 100   k  5  ⇒ q + 1 −  p = p + 0.6q and p = 4 q  100  ∴ k = 32 Hence, option (5) is the correct choice.

002

Note: Its a linear relation Scheme A: Scheme B = Discount offered are in the ratio

∴ EB = 8 − x cm Let, the length of BC be ‘h’ cm

4  5:4 which has to remain the same  40 = 50 ×  5 

∴ ∆AED =

4   ⇒  Re quired answer = 40 × = 32%  5  

EBCD =

⇒

P

85. 1

N

A E R

P1

C ircle C

∴ S

F B

88. 2

Q

∆AED x 1 16 = = ⇒x= cm EBCD 16 − x 6 7

∆AEF 6 = ∆AED 5

The expression is

(

)(

OM = OE2 + EM2 = 3 2 cm

OP1 = 5 − x, P1M = P1B2 + BM2 = 2 x cm

= A ( AB )

Also, P1O + OM = P1M

Now it is given that A × B = C and B × C = A.

= A

1+ logC B

OE = OP − PE = 5 − 4 = 3 cm 2

2

2

logC B

Given that xn – xn–1 + xn–2 = 0 or xn = xn–1 – xn–2 Now x1 = x1 x2 = x2 x3 = x2 – x1 x4 = x3 – x2 = x2 – x1 – x2 = –x1 x5 = x4 – x3 = –x1 – x2 + x1 = –x2 x6 = x5 – x4 = –x2 + x1 Now x1 + x2 + … + x6 = 0. Therefore for a gap of every 6 terms, the summation of terms becomes zero. The sum of first 88 terms of the sequence will be 2x2 – x1 since 88 = 6k + 4 and the sum of first 89 term of the sequence will be x2 – x1 since 89 = 6k + 5. Therefore, we can write here 2x2 – x1 = 150 x2 – x1 = 120

1 ⇒ ( x1 + x2 ) = –30. 2

D

)(C ) )

logA A + logA C

) + (B ) + (B.B

1+ logA C

logC B

)(C )(C

logA C

logA C

logA C

)

logA C

+ B (BC )

logA C

B

89. 3

…(i)

B

Q

M

A

S

R

D

Drop a perpendicular from point B on PQ. Q ABCD is an isosceles trapezium, therefore AS = RD. ⇒ AS = RD =

AD – PQ 3 = units. 2 2

Also, ∆BMP : ∆PSA ⇒

BM PS = MP SA

3  PQ – BC  ×  3  2  2

2 ×1 = 1 units 2 Area of trapezium ABCD ⇒ BM =

=

C

Given that the length of the line segment DC = 8 cm Let, the length of the line segment AE = x cm.

C

P

⇒ BM =

E

logC B

) + (B

= A(C)logCB + B(A)logA C = AB + BC = B(A + C)

F A

logC B

A(AB)logCB + B(BC)logA C

5+3 2 = 1 + 2 2 cm 1+ 2

87. 1

)(B )(B

logC B

⇒ 5 − x + 3 2 = 2x

⇒x=

logC C + logC B

)(B

)

( = (A = ( A. A

2

002

)(

 logC BC  logC B log CA log C C A + B A A  B  

Let P1 be the center of the circle C and N be the point where the circle C touches the circle having radius 5 cm. A and B are the points at which the circle C touches the chords PQ and RS respectively. E and F are the mid points of the chords PQ and RS respectively. Let the radius of the circle C be ‘x’ cm

86. 3

1 1 (8 − x + 8) × h = × (16 − x)h 2 2

∆EBF 3 ∆AEF x ∆EBF 16 3 = ⇒ = × = × ∆AED 1 ∆AED (8 – x) ∆AED 40 1

O M

1 × x×h 2

=

1 (BC + AD ) × (BM + PS ) 2

1 × 8 × 4 = 16 sq. units 2

11

90. 1

12

Let us suppose that the first term is ‘x’ and the common difference is ‘d’. All the different cases, as per the condition in the question, can be written as follows. x = 1, d = 1, 1 × 2 × 3 = 6 x = 1, d = 2, 1 × 3 × 5 = 15 x = 1, d = 3, 1 × 4 × 7 = 28 x = 1, d = 4, 1 × 5 × 9 = 45 x = 1, d = 5, 1 × 6 × 11 = 66 x = 1, d = 6, 1 × 7 × 13 = 91 x = 2, d = 1, 2 × 3 × 4 = 24 x = 2, d = 2, 2 × 4 × 6 = 48 x = 2, d = 3, 2 × 5 × 8 = 80 x = 3, d = 1, 3 × 4 × 5 = 60 Now every single case has two possibilities. For example 1 × 2 × 3 can be written as 3 × 2 × 1. Hence total of 20 solutions are possible.

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