CAT Exam Question Papers.......2007,2006,2005

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CAT 2007

Section I This section contains 25 questions
1. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?
(1) May 21
(2) April 11
(3) May 20
(4) April 10
(5) June 30
2. A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?
(1) –119
(2) –159
(3) –110
(4) –180
(5) –105
3. Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?
(1) Between 0 and 90
(2) Between 0 and 30
(3) Between 0 and 60
(4) Between 0 and 75
(5) Between 0 and 45
Directions for Questions 4 and 5: Let S be the set of all pairs (i, j) where 1 ≤ i < j ≤ n and n ≥ 4. Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise. For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3) are also friends, but (1, 4) and (2, 3) are enemies.
4. For general n, how many enemies will each member of S have?
(1) n – 3
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(2)
(3) 2n – 7
(4)
(5)
5. For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members?
(1)
(2) 2n – 6
(3)
(4) n – 2
(5)
Directions for Questions 6 and 7: Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others. Option A: Invest in a public sector bank. It promises a return of +0.10% Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3% Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%
6. The maximum guaranteed return to Shabnam is
(1) 0.25%
(2) 0.10%
(3) 0.20%
(4) 0.15%
(5) 0.30%
7. What strategy will maximize the guaranteed return to Shabnam?
(1) 100% in option A
(2) 36% in option B and 64% in option C
(3) 64% in option B and 36% in option C
(4) 1/3 in each of the three options
(5) 30% in option A, 32% in option B and 38% in option C
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Directions for Questions 8 and 9: Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.
Departure
Arrival
City
Time
City
Time
B
8:00 a.m.
A
3:00 p.m.
A
4:00 p.m.
B
8: p.m.
Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.
8. What is the time difference between A and B?
(1) 1 hour and 30 minutes
(2) 2 hours
(3) 2 hours and 30 minutes
(4) 1 hour
(5) Cannot be determined
9. What is the plane’s cruising speed in km per hour?
(1) 700
(2) 550
(3) 600
(4) 500
(5) Cannot be determined
10. Consider all four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?
(1) 3
(2) 2
(3) 4
(4) 0
(5) 1
11. In a tournament, there are n teams T1 , T2 ....., Tn with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common:
T1 & T2 , T2 & T3 ,......, Tn − 1 & Tn , and Tn & T1.
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No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together?
(1) n(k – 1)
(2) k(n – 1)
(3) n(k – 2)
(4) k(k – 2)
(5) (n – 1)(k – 1)
Directions for Questions 12 and 13: Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.
12. How many units should Mr. David produce daily?
(1) 130
(2) 100
(3) 70
(4) 150
(5) Cannot be determined
13. What is the maximum daily profit, in rupees, that Mr. David can realize from his business?
(1) 620
(2) 920
(3) 840
(4) 760
(5) Cannot be determined
Directions for Questions 14 and 15: Let a1 = p and b1 = q, where p and q are positive quantities. Define: an = pbn – 1 ; bn = qbn − 1 (for even n > 1) and an = pan – 1 ; bn = qan − 1 (for odd n > 1)
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14.
(1)
(2)
(3)
(4)
(5)
15. If p = 1/3 and q = 2/3, then what is the smallest odd n such that an + bn < 0.01?
(1) 7
(2) 13
(3) 11
(4) 9
(5) 15
Directions for Questions 16 through 19: Each question is followed by two statements A and B. Answer each question using the following instructions. Mark (1) if the question can be answered by using statement A alone but not by using statement B alone. Mark (2) if the question can be answered by using statement B alone but not by using statement A alone. Mark (3) if the question can be answered by using both the statements together but not by using either of the statements alone. Mark (4) if the question cannot be answered on the basis of the two statements.
16. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, WI, of Section I is smaller than the average weight, WII, of Section II. If the heaviest student, say Deepak, of Section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes WII and that of Section II becomes WI. What is the weight of Poonam?
A. WII – WI = 1.0
B. Moving Deepak from Section II to I (without any move from I to II) makes the average weights of the two sections equal.
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17. Consider integers x, y and z. What is the minimum possible value of x2 + y2 + z2 ?
A. x + y + z = 89
B. Among x, y, z two are equal.
18. Rahim plans to draw a square JKLM with a point O on the side JK but is not successful. Why is Rahim unable to draw the square?
A. The length of OM is twice that of OL.
B. The length of OM is 4 cm.
19. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC’s requirements?
A. The inner diameter of the tank is at least 8 meters.
B. The tank weighs 30,000 kg when empty, and is made of a material with density of 3 gm/cc.
20. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17
(2) 16
(3) 18
(4) 15
(5) 19
21. How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an odd integer less than 60?
(1) 6
(2) 4
(3) 7
(4) 5
(5) 3
22. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?
(1) Over Rupees 13 but less than Rupees 14
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(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5
23. Consider the set S = {2, 3, 4, ...., 2n + 1}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?
(1) 0
(2) 1
(3) n/2
(4) n + 1/2n
(5) 2008
24. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight member joint family is nearest to:
(1) 23 years
(2) 22 years
(3) 21 years
(4) 25 years
(5) 24 years
25. A function f(x) satisfies f (1) = 3600, and f(1) + f(2) + ... + f(n) = n² f(n), for all positive integers n >1. What is the value of f(9) ?
(1) 80
(2) 240
(3) 200
(4) 100
(5) 120
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Section II This section contains 25 questions Directions for Questions 26 to 29: Each question is followed by two statements, A and B. Answer each question using the following instructions: Mark (1) if the question can be answered by using the statement A alone but not by using the statement B alone. Mark (2) if the question can be answered by using the statement B alone but not by using the statement A alone. Mark (3) if the question can be answered by using either of the statements alone. Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone. Mark (5) if the question cannot be answered on the basis of the two statements.
26. In a football match, at half-time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match?
A. In the second half Mahindra and Mahindra Club scored four goals. B. The opponent scored four goals in the match.
27. In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school?
A. Sixty per cent of the top academic performers were not athletes.
B. All the top academic performers were not necessarily athletes.
28. Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz contest. They were ranked based on their scores in the contest. Dev got a higher rank as compared to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan’s rank was lower than the median. Who among the five got the highest rank?
A. Atul was the last rank holder. B. Bala was not among the top two rank holders.
29. Thirty per cent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background?
A. Twenty five per cent of the employees have engineering background.
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B. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background.
DIRECTIONS for Questions 30 to 33: Answer the following questions based on the information given below: The proportion of male students and the proportion of vegetarian students in a school are given below. The school has a total of 800 students, 80% of whom are in the Secondary Section and rest equally divided between Class 11 and 12.
Male (M)
Vegetarian (V)
Class 12
0.6
Class 11
0.55
0.5
Secondary Section
0.55
Total
0.475
0.53
30. What is the percentage of male students in the secondary section?
(1) 40
(2) 45
(3) 50
(4) 55
(5) 60
31. In Class 12, twenty five per cent of the vegetarians are male. What is the difference between the number of female vegetarians and male non-vegetarians?
(1) less than 8
(2) 10
(3) 12
(4) 14
(5) 16
32. What is the percentage of vegetarian students in Class 12?
(1) 40
(2) 45
(3) 50
(4) 55
(5) 60
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33. In the Secondary Section, 50% of the students are vegetarian males. Which of the following statements is correct?
(1) Except vegetarian males, all other groups have same number of students.
(2) Except non-vegetarian males, all other groups have same number of students.
(3) Except vegetarian females, all other groups have same number of students.
(4) Except non-vegetarian females, all other groups have same number of students
(5) All of the above groups have the same number of students.
Directions for Questions 34 to 37: Answer the following questions based on the information given below. The following table shows the break-up of actual costs incurred by a company in last five years (year 2002 to year 2006) to produce a particular product. The production capacity of the company is 2000 units. The selling price for the year 2006 was Rs. 125 per unit. Some costs change almost in direct proportion to the change in volume of production, while others do not follow any obvious pattern of change with respect to the volume of production and hence are considered fixed. Using the information provided for the year 2006 as the basis for projecting the figures for the year 2007, answer the following questions.
Year 2002
Year 2003
Year 2004
Year 2005
Year 2006
Volume of production
1000
900
1100
1200
1200
Costs (Rs.)
Material
50,000
45,100
55,200
59,900
60,000
Labour
20,000
18,000
22,100
24,150
24,000
Consumables
2,000
2,200
1,800
1,600
1,400
Rent of building
1,000
1,000
1,100
1,100
1,200
Rates and taxes
400
400
400
400
400
Repair and maintenance expenses
800
820
780
790
800
Operating cost of machines
30,000
27,000
33,500
36,020
36,000
Selling and marketing expenses
5,750
5,800
5,800
5,750
5,800
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34. What is the approximate cost per unit in rupees, if the company produces and sells 1400 units in the year 2007?
(1) 104
(2) 107
(3) 110
(4) 115
(5) 116
35. What is the minimum number of units that the company needs to produce and sell to avoid any loss?
(1) 313
(2) 350
(3) 384
(4) 747
(5) 928
36. If the company reduces the price by 5%, it can produce and sell as many units as it desires. How many units should the company produce to maximize its profit?
(1) 1400
(2) 1600
(3) 1800
(4) 1900
(5) 2000
37. Given that the company cannot sell more than 1700 units, and it will have to reduce the price by Rs.5 for all units, if it wants to sell more than 1400 units, what is the maximum profit, in rupees, that the company can earn?
(1) 25,400
(2) 24,400
(3) 31,400
(4) 32,900
(5) 32,000
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Directions for Questions 38 to 41: Answer the following questions based on the information given below. The table below shows the comparative costs, in US Dollars, of major surgeries in USA and a select few Asian countries.
Procedure
Comparative Costs in USA and some Asian Countries (in US Dollars)
USA
India
Thailand
Singapore
Malaysia
Heart Bypass
130000
10000
11000
18500
9000
Heart Valve Replacement
160000
9000
10000
12500
9000
Angioplasty
57000
11000
13000
13000
11000
Hip Replacement
43000
9000
12000
12000
10000
Hysterectomy
20000
3000
4500
6000
3000
Knee Replacement
40000
8500
10000
13000
8000
Spinal Fusion
62000
5500
7000
9000
6000
The equivalent of one US Dollar in the local currencies is given below.
1 US Dollar Equivalent
India
40.928
Rupees
Malaysia
3.51
Ringits
Thailand
32.89
Bahts
Singapore
1.53
$ Dollars
A consulting firm found that the quality of the health services were not the same in all the countries above. A poor quality of a surgery may have significant repercussions in future, resulting in more cost in correcting mistakes. The cost of poor quality of surgery is given in the table below.
Procedure
Comparative Costs in USA and some Asian Countries (in US Dollars ‘000)
USA
India
Thailand
Singapore
Malaysia
Heart Bypass
0
3
3
2
4
Heart Valve Replacement
0
5
4
5
5
Angioplasty
0
5
5
4
6
Hip Replacement
0
7
5
5
8
Hysterectomy
0
5
6
5
4
Knee Replacement
0
9
6
4
4
Spinal Fusion
0
5
6
5
6
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38. A US citizen is hurt in an accident and requires an angioplasty, hip replacement and a knee replacement. Cost of foreign travel and stay is not a consideration since the government will take care of it. Which country will result in the cheapest package, taking cost of poor quality into account?
(1) India
(2) Thailand
(3) Malaysia
(4) Singapore
(5) USA
39. Taking the cost of poor quality into account, which country/countries will be the most expensive for knee replacement?
(1) India
(2) Thailand
(3) Malaysia
(4) Singapore
(5) India and Singapore
40. Approximately, what difference in amount in Bahts will it make to a Thai citizen if she were to get a hysterectomy done in India instead of in her native country, taking into account the cost of poor quality? It costs 7500 Bahts for one-way travel between Thailand and India.
(1) 23500
(2) 40500
(3) 57500
(4) 67500
(5) 75000
41. The rupee value increases to Rs.35 for a US Dollar, and all other things, including quality, remain the same. What is the approximate difference in cost, in US Dollars, between Singapore and India for a Spinal Fusion, taking this change into account?
(1) 700
(2) 2500
(3) 4500
(4) 8000
(5) No difference
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Directions for Questions 42 to 46: Answer the following questions based on the information given below. A low-cost airline company connects ten Indian cities, A to J. The table below gives the distance between a pair of airports and the corresponding price charged by the company. Travel is permitted only from a departure airport to an arrival airport. The customers do not travel by a route where they have to stop at more than two intermediate airports.
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Sector No.
Airport of Departure
Airport of Arrival
Distance between the Airports (km.)
Price (Rs.)
1
A
B
560
670
2
A
C
790
1350
3
A
D
850
1250
4
A
E
1245
1600
5
A
F
1345
1700
6
A
G
1350
2450
7
A
H
1950
1850
8
B
C
1650
2000
9
B
H
1750
1900
10
B
I
2100
2450
11
B
J
2300
2275
12
C
D
460
450
13
C
F
410
430
14
C
G
910
1100
15
D
E
540
590
16
D
F
625
700
17
D
G
640
750
18
D
H
950
1250
19
D
J
1650
2450
20
E
F
1250
1700
21
E
G
970
1150
22
E
H
850
875
23
F
G
900
1050
24
F
I
875
950
25
F
J
970
1150
26
G
I
510
550
27
G
J
830
890
28
H
I
790
970
29
H
J
400
425
30
I
J
460
540
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42. What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from A to J?
(1) 2275
(2) 2850
(3) 2890
(4) 2930
(5) 3340
43. The company plans to introduce a direct flight between A and J. The market research results indicate that all its existing passengers travelling between A and J will use this direct flight if it is priced 5% below the minimum price that they pay at present. What should the company charge approximately, in rupees, for this direct flight?
(1) 1991
(2) 2161
(3) 2707
(4) 2745
(5) 2783
44. If the airports C, D and H are closed down owing to security reasons, what would be the minimum price, in rupees, to be paid by a passenger travelling from A to J?
(1) 2275
(2) 2615
(3) 2850
(4) 2945
(5) 3190
45. If the prices include a margin of 10% over the total cost that the company incurs, what is the minimum cost per kilometer that the company incurs in flying from A to J?
(1) 0.77
(2) 0.88
(3) 0.99
(4) 1.06
(5) 1.08
46. If the prices include a margin of 15% over the total cost that the company incurs, which among the following is the distance to be covered in flying from A to J that minimizes the total cost per kilometer for the company?
(1) 2170
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(2) 2180
(3) 2315
(4) 2350
(5) 2390
Directions for Questions 47 to 50: Answer the following questions based on the information given below. A health-drink company’s R&D department is trying to make various diet formulations, which can be used for certain specific purposes. It is considering a choice of 5 alternative ingredients (O, P, Q, R, and S), which can be used in different proportions in the formulations. The table below gives the composition of these ingredients. The cost per unit of each of these ingredients is O: 150, P: 50, Q: 200, R: 500, S: 100.
Composition
Ingredient
Carbohydrate %
Protein %
Fat %
Minerals %
O
50
30
10
10
P
80
20
0
0
Q
10
30
50
10
R
5
50
40
5
S
45
50
0
5
47. For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least 30% protein. In how many different ways can we prepare this diet by mixing at least two ingredients?
(1) One
(2) Two
(3) Three
(4) Four
(5) None
48. Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat and at least 30% protein? The diet has to be formed by mixing two ingredients.
(1) P and Q
(2) P and S
(3) P and R
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(4) Q and S
(5) R and S
49. In what proportion should P, Q and S be mixed to make a diet having at least 60% carbohydrate at the lowest per unit cost?
(1) 2 : 1 : 3
(2) 4 : 1 : 2
(3) 2 : 1 : 4
(4) 3 : 1: 2
(5) 4 : 1 : 1
50. The company is planning to launch a balanced diet required for growth needs of adolescent children. This diet must contain at least 30% each of carbohydrate and protein, no more than 25% fat and at least 5% minerals. Which one of the following combinations of equally mixed ingredients is feasible?
(1) O and P
(2) R and S
(3) P and S
(4) Q and R
(5) O and S
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Section III This section contains 25 questions Directions for Questions 51 to 53: In each question, there are four sentences. Each sentence has pairs of words/phrases that are italicized and highlighted. From the italicized and highlighted word(s)/phrase(s), select the most appropriate word(s)/phrase(s) to form correct sentences. Then, from the options given, choose the best one.
51. The cricket council that was[A]/were[B] elected last March is[A]/are[B] at sixes and sevens over new rules.
The critics censored[A]/censured[B] the new movie because of its social inaccessibility. Amit’s explanation for missing the meeting was credulous[A]/credible[B]. She coughed discreetly[A]/discretely[B] to announce her presence.
1) BBAAA
2) AAABA
3) BBBBA
4) AABBA
5) BBBAA
52. The further[A]/farther[B] he pushed himself, the more disillusioned he grew.
For the crowds it was more of a historical[A]/historic[B] event; for their leader, it was just another day. The old man has a healthy distrust[A]/mistrust[B] for all new technology. This film is based on a real[A]/true [B] story. One suspects that the compliment[A]/complement[B] was backhanded.
1) BABAB
2) ABBBA
3) BAABA
4) BBAAB
5) ABABA
53. Regrettably[A]/Regretfully[B] I have to decline your invitation.
I am drawn to the poetic, sensual[A]/sensuous[B] quality of her paintings. He was besides[A]/beside[B] himself with rage when I told him what I had done. After brushing against a stationary[A]/stationery[B] truck my car turned turtle. As the water began to rise over[A]/above[B] the danger mark, the signs of an imminent flood were clear.
1) BAABA
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2) BBBAB
3) AAABA
4) BBAAB
5) BABAB
Directions for Questions 54 to 56: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question. To discover the relation between rules, paradigms, and normal science, consider first how the historian isolates the particular loci of commitment that have been described as accepted rules. Close historical investigation of a given specialty at a given time discloses a set of recurrent and quasi-standard illustrations of various theories in their conceptual, observational, and instrumental applications. These are the community's paradigms, revealed in its textbooks, lectures, and laboratory exercises. By studying them and by practicing with them, the members of the corresponding community learn their trade. The historian, of course, will discover in addition a penumbral area occupied by achievements whose status is still in doubt, but the core of solved problems and techniques will usually be clear. Despite occasional ambiguities, the paradigms of a mature scientific community can be determined with relative ease. That demands a second step and one of a somewhat different kind. When undertaking it, the historian must compare the community's paradigms with each other and with its current research reports. In doing so, his object is to discover what isolable elements, explicit or implicit, the members of that community may have abstracted from their more global paradigms and deploy it as rules in their research. Anyone who has attempted to describe or analyze the evolution of a particular scientific tradition will necessarily have sought accepted principles and rules of this sort. Almost certainly, he will have met with at least partial success. But, if his experience has been at all like my own, he will have found the search for rules both more difficult and less satisfying than the search for paradigms. Some of the generalizations he employs to describe the community's shared beliefs will present more problems. Others, however, will seem a shade too strong. Phrased in just that way, or in any other way he can imagine, they would almost certainly have been rejected by some members of the group he studies. Nevertheless, if the coherence of the research tradition is to be understood in terms of rules, some specification of common ground in the corresponding area is needed. As a result, the search for a body of rules competent to constitute a given normal research tradition becomes a source of continual and deep frustration.
Recognizing that frustration, however, makes it possible to diagnose its source. Scientists can agree that a Newton, Lavoisier, Maxwell, or Einstein has produced an apparently
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permanent solution to a group of outstanding problems and still disagree, sometimes without being aware of it, about the particular abstract characteristics that make those solutions permanent. They can, that is, agree in their identification of a paradigm without agreeing on, or even attempting to produce, a full interpretation or rationalization of it. Lack of a standard interpretation or of an agreed reduction to rules will not prevent a paradigm from guiding research. Normal science can be determined in part by the direct inspection of paradigms, a process that is often aided by but does not depend upon the formulation of rules and assumption. Indeed, the existence of a paradigm need not even imply that any full set of rules exists.
54. What is the author attempting to illustrate through this passage?
(1) Relationships between rules, paradigms, and normal science.
(2) How a historian would isolate a particular ‘loci of commitment’.
(3) How a set of shared beliefs evolve in to a paradigm.
(4) Ways of understanding a scientific tradition.
(5) The frustrations of attempting to define a paradigm of a tradition
55. The term ‘loci of commitment’ as used in the passage would most likely correspond with which of the following?
(1) Loyalty between a group of scientists in a research laboratory.
(2) Loyalty between groups of scientists across research laboratories.
(3) Loyalty to a certain paradigm of scientific inquiry.
(4) Loyalty to global patterns of scientific inquiry.
(5) Loyalty to evolving trends of scientific inquiry.
56. The author of this passage is likely to agree with which of the following?
(1) Paradigms almost entirely define a scientific tradition.
(2) A group of scientists investigating a phenomenon would benefit by defining a set of rules.
(3) Acceptance by the giants of a tradition is a sine qua non for a paradigm to emerge.
(4) Choice of isolation mechanism determines the types of paradigm that may emerge from a tradition.
(5) Paradigms are a general representation of rules and beliefs of a scientific tradition.
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Directions for Questions 57 to 59: Each of the following questions has a paragraph from which the last sentence has been deleted. From the given options, choose the sentence that completes the paragraph in the most appropriate way.
57. Characters are also part of deep structure. Characters tie events in a story together and provide a thread of continuity and meaning. Stories can be about individuals, groups, projects or whole organizations, so from an organizational studies perspective, the focal actor(s) determine the level and unit of analysis used in a study. Stories of mergers and acquisitions, for example, are common place. In these stories whole organizations are personified as actors. But these macro-level stories usually are not told from the perspective of the macro-level participants, because whole organizations cannot narrate their experiences in the first person.
(1) More generally, data concerning the identities and relationships of the characters in the story are required, if one is to understand role structure and social networks in which that process is embedded.
(2) Personification of a whole organization abstracts away from the particular actors and from traditional notions of level of analysis.
(3) The personification of a whole organization is important because stories differ depending on who is enacting various events.
(4) Every story is told from a particular point of view, with a particular narrative voice, which is not regarded as part of the deep structure.
(5) The personification of a whole organization is a textual device we use to make macro-level theories more comprehensible.
58. Nevertheless, photographs still retain some of the magical allure that the earliest daguerreotypes inspired. As objects, our photographs have changed; they have become physically flimsier as they have become more technologically sophisticated. Daguerre produced pictures on copper plates; today many of our photographs never become tangible thins, but instead remain filed away on computers and cameras, part of the digital ether that envelops the modern world. At the same time, our patience for the creation of images has also eroded. Children today are used to being tracked from birth by digital cameras and video recorders and they expect to see the results of their poses and performances instantly. The space between life as it is being lived and life as it is being displayed shrinks to a mere second.
(1) Yet, despite these technical developments, photographs still remain powerful because they are reminders of the people and things we care about.
(2) Images, after all, are surrogates carried into battle by a soldier or by a traveller on holiday.
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(3) Photographs, be they digital or traditional, exist to remind us of the absent, the beloved, and the dead.
(4) In the new era of the digital image, the images also have a greater potential for fostering falsehood and trickery, perpetuating fictions that seem so real we cannot tell the difference.
(5) Anyway, human nature being what it is, little time has passed after photography’s inventions became means of living life through images.
59. Mma Ramotswe had a detective agency in Africa, at the foot of Kgale Hill. These were its assets; a tiny white van, two desks, two chairs, a telephone, and an old typewriter. Then there was a teapot, in which Mma Ramotswe - the only private lady detective in Botswana - brewed red bush tea. And three mugs - one for herself, one for her secretary and one for the client. What else does a detective agency really need? Detective agencies rely on human intuition and intelligence, both of which Mma Ramotswe had in abundance.
(1) But there was also the view, which again would appear on no inventory.
(2) No inventory would ever include those, of course.
(3) She had an intelligent secretary too.
(4) She was a good detective and a good woman.
(5) What she lacked in possessions was more than made up by a natural shrewdness.
Directions for Questions 60 to 62: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question
The difficulties historians face in establishing cause-and-effect relations in the history of human societies are broadly similar to the difficulties facing astronomers, climatologists, ecologists, evolutionary biologists, geologists, and palaeontologists. To varying degrees each of these fields is plagued by the impossibility of performing replicated, controlled experimental interventions, the complexity arising from enormous numbers of variables, the resulting uniqueness of each system, the consequent impossibility of formulating universal laws, and the difficulties of predicting emergent properties and future behaviour. Prediction in history, as in other historical sciences, is most feasible on large spatial scales and over long times, when the unique features of millions of small-scale brief events become averaged out. Just as I could predict the sex ratio of the next 1,000 newborns but not the sexes of my own two children, the historian can recognize factors that made inevitable the broad outcome of the collision between American and Eurasian societies after 13,000 years of separate developments, but not the outcome of the 1960 U.S. presidential election. The details of which candidate said what during a single televised
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debate in October 1960 could have given the electoral victory to Nixon instead of to Kennedy, but no details of who said what could have blocked the European conquest of Native Americans. How can students of human history profit from the experience of scientists in other historical sciences? A methodology that has proved useful involves the comparative method and so-called natural experiments. While neither astronomers studying galaxy formation nor human historians can manipulate their systems in controlled laboratory experiments, they both can take advantage of natural experiments, by comparing systems differing in the presence or absence (or in the strong or weak effect) of some putative causative factor. For example, epidemiologists, forbidden to feed large amounts of salt to people experimentally, have still been able to identify effects of high salt intake by comparing groups of humans who already differ greatly in their salt intake; and cultural anthropologists, unable to provide human groups experimentally with varying resource abundances for many centuries, still study long-term effects of resource abundance on human societies by comparing recent Polynesian populations living on islands differing naturally in resource abundance. The student of human history can draw on many more natural experiments than just comparisons among the five inhabited continents. Comparisons can also utilize large islands that have developed complex societies in a considerable degree of isolation (such as Japan, Madagascar, Native American Hispaniola, New Guinea, Hawaii, and many others), as well as societies on hundreds of smaller islands and regional societies within each of the continents. Natural experiments in any field, whether in ecology or human history, are inherently open to potential methodological criticisms. Those include confounding effects of natural variation in additional variables besides the one of interest, as well as problems in inferring chains of causation from observed correlations between variables. Such methodological problems have been discussed in great detail for some of the historical sciences. In particular, epidemiology, the science of drawing inferences about human diseases by comparing groups of people (often by retrospective historical studies), has for a long time successfully employed formalized procedures for dealing with problems similar to those facing historians of human societies. In short, I acknowledge that it is much more difficult to understand human history than to understand problems in fields of science where history is unimportant and where fewer individual variables operate. Nevertheless, successful methodologies for analyzing historical problems have been worked out in several fields. As a result, the histories of dinosaurs, nebulae, and glaciers are generally acknowledged to belong to fields of science rather than to the humanities.
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60. Why do islands with considerable degree of isolation provide valuable insights into human history?
(1) Isolated islands may evolve differently and this difference is of interest to us.
(2) Isolated islands increase the number of observations available to historians.
(3) Isolated islands, differing in their endowments and size may evolve differently and this difference can be attributed to their endowments and size.
(4) Isolated islands, differing in their endowments and size, provide a good comparison to large islands such as Eurasia, Africa, Americas and Australia.
(5) Isolated islands, in so far as they are inhabited, arouse curiosity about how human beings evolved there.
61. According to the author, why is prediction difficult in history?
(1) Historical explanations are usually broad so that no prediction is possible.
(2) Historical out comes depend upon a large number of factors and hence prediction is difficult for each case.
(3) Historical sciences, by their very nature, are not interested in a multitude of minor factors, which might be important in a specific historical outcome.
(4) Historians are interested in evolution of human history and hence are only interested in log term predictions.
(5) Historical sciences suffer from the inability to conduct controlled experiments and therefore have explanations based on a few long-term factors.
62. According to the author, which of the following statements would be true?
(1) Students of history are missing significant opportunities by not conducting any natural experiments.
(2) Complex societies inhabiting large islands provide great opportunities for natural experiments.
(3) Students of history are missing significant opportunities by not studying an adequate variety of natural experiments.
(4) A unique problem faced by historians is their inability to establish cause and effect relationships.
(5) Cultural anthropologists have overcome the problem of confounding variables through natural experiments.
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Directions for Questions 63 to 65: In each question, there are five sentences or parts of sentences that form a paragraph. Identify the sentence(s) or part(s) of sentence(s) that is/are correct in terms of grammar and usage. Then, choose the most appropriate option.
63.
A. When I returned to home, I began to read
B. everything I could get my hand on about Israel.
C. That same year Israel’s Jewish Agency sent
D. a Shaliach a sort of recruiter to Minneapolis.
E. I became one of his most active devotees.
(1) C & E
(2) C only
(3) E only
(4) B, C & E
(5) C, D & E
64.
A. So once an economy is actually in recession,
B. The authorities can, in principle, move the economy
C. Out of slump - assuming hypothetically
D. That they know how to - by a temporary stimuli.
E. In the longer term, however, such policies have no affect on the overall behaviour of the economy.
(1) A, B & E
(2) B, C & E
(3) C & D
(4) E only
(5) B only
65.
A. It is sometimes told that democratic
B. government originated in the city-states
C. of ancient Greece. Democratic ideals have been handed to us from that time.
D. In truth, however, this is an unhelpful assertion.
E. The Greeks gave us the word, hence did not provide us with a model.
(1) A, B & D
(2) B, C & D
(3) B & D
(4) B only
(5) D only
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Directions for Questions 66 to 68: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question. Human Biology does nothing to structure human society. Age may enfeeble us all, but cultures vary considerably in the prestige and power they accord to the elderly. Giving birth is a necessary condition for being a mother, but it is not sufficient. We expect mothers to behave in maternal ways and to display appropriately maternal sentiments. We prescribe a clutch of norms or rules that govern the role of a mother. That the social role is independent of the biological base can be demonstrated by going back three sentences. Giving birth is certainly not sufficient to be a mother but, as adoption and fostering show, it is not even necessary! The fine detail of what is expected of a mother or a father or a dutiful son differs from culture to culture, but everywhere behaviour is coordinated by the reciprocal nature of roles. Husbands and wives, parents and children, employers and employees, waiters and customers, teachers and pupils, warlords and followers; each makes sense only in its relation to the other. The term ‘role’ is an appropriate one, because the metaphor of an actor in a play neatly expresses the rule-governed nature or scripted nature of much of social life and the sense that society is a joint production. Social life occurs only because people play their parts (and that is as true for war and conflicts as for peace and love) and those parts make sense only in the context of the overall show. The drama metaphor also reminds us of the artistic licence available to the players. We can play a part straight or, as the following from J.P. Sartre conveys, we can ham it up. Let us consider this waiter in the cafe. His movement is quick and forward, a little too precise, a little too rapid. He comes towards the patrons with a step a little too quick. He bends forward a little too eagerly; his voice, his eyes express an interest a little too solicitous for the order of the customer. Finally there he returns, trying to imitate in his walk the inflexible stiffness of some kind of automaton while carrying his tray with the recklessness of a tightrope-walker....All his behaviour seems to us a game....But what is he playing? We need not watch long before we can explain it: he is playing at being a waiter in a cafe. The American sociologist Erving Goffman built an influential body of social analysis on elaborations of the metaphor of social life as drama. Perhaps his most telling point was that it is only through acting out a part that we express character. It is not enough to be evil or virtuous; we have to be seen to be evil or virtuous.
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There is distinction between the roles we play and some underlying self. Here we might note that some roles are more absorbing than others. We would not be surprised by the waitress who plays the part in such a way as to signal to us that she is much more than her occupation. We would be surprised and offended by the father who played his part ‘tongue in cheek’. Some roles are broader and more far-reaching than others. Describing someone as a clergyman or faith healer would say far more about that person than describing someone as a bus driver.
66. What is the thematic highlight of this passage?
(1) In the absence of strong biological linkages, reciprocal roles provide the mechanism for coordinating human behaviour.
(2) In the absence of reciprocal roles, biological linkages provide the mechanism for coordinating human behaviour.
(3) Human behaviour is independent of biological linkages and reciprocal roles.
(4) Human behaviour depends on biological linkages and reciprocal roles.
(5) Reciprocal roles determine normative human behavior in society.
67. Which of the following would have been true if biological linkages structured human society?
(1) The role of mother would have been defined through her reciprocal relationship with her children.
(2) We would not have been offended by the father playing his role ‘tongue in cheek’.
(3) Women would have adopted and fostered children rather than giving birth to them.
(4) Even if warlords were physically weaker than their followers, they would still dominate them.
(5) Waiters would have stronger motivation to serve their customers.
68. It has been claimed in the passage that “some roles are more absorbing than others”. According to the passage, which of the following seem(s) appropriate reason(s) for such a claim?
A. Some roles carry great expectations from the society preventing manifestation of the true self.
B. Society ascribes so much importance to some roles that the conception of self may get aligned with the roles being performed.
C. Some roles require development of skill and expertise leaving little time for manifestation of self.
(1) A only
(2) B only
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(3) C only
(4) A & B
(5) B & C
Directions for Questions 69 to 72: In each question, there are five sentences/paragraphs. The sentence/ paragraph labelled A is in its correct place. The four that follow are labelled B, C, D and E, and need to be arranged in the logical order to form a coherent paragraph/passage. From the given options, choose the most appropriate option. 69.
A. In America, highly educated women, who are in stronger position in the labour market than less qualified ones, have higher rates of marriage than other groups.
B. Some work supports the Becker thesis, and some appears to contradict it.
C. And, as with crime, it is equally inconclusive.
D. But regardless of the conclusion of any particular piece of work, it is hard to establish convincing connections between family changes and economic factors using conventional approaches.
E. Indeed, just as with crime, an enormous academic literature exists on the validity of the pure economic approach to the evolution of family structures.
(1) BCDE
(2) DBEC
(3) BDCE
(4) ECBD
(5) EBCD
70.
A. Personal experience of mothering and motherhood are largely framed in relation to two discernible or “official” discourses: the “medical discourse and natural childbirth discourse”. Both of these tend to focus on the “optimistic stories” of birth and mothering and underpin stereotypes of the “godmother”.
B. At the same time, the need for medical expert guidance is also a feature for contemporary reproduction and motherhood. But constructions of good mothering have not always been so conceived - and in different contexts may exist in parallel to other equally dominant discourses.
C. Similarly, historical work has shown how what are now taken-for-granted aspects of reproduction and mothering practices result from contemporary “pseudoscientific directives” and “managed constructs”. These changes have led to a reframing of modern discourses that pattern pregnancy and motherhood leading to an acceptance of the need for greater expert management.
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D. The contrasting, overlapping and ambiguous strands within these frameworks focus to varying degrees on a woman’s biological tie to her child and predisposition to instinctively know and be able to care for her child.
E. In addition, a third, “unofficial popular discourse” comprising “old wives” tales and based on maternal experiences of childbirth has also been noted. These discourses have also been acknowledged in work exploring the experiences of those who apparently do not “conform” to conventional stereotypes of the “good mother”
(1) EDBC
(2) BCED
(3) DBCE
(4) EDCB
(5) BCDE
71.
A. Indonesia has experienced dramatic shifts in its formal governance arrangements since the fall of President Soeharto and the close of his centralized, authoritarian "New Order" regime in 1997.
B. The political system has taken its place in the nearly 10 years since Reformasi began. It has featured the active contest for political office among a proliferation of parties at central, provincial and district levels; direct elections for the presidency (since 2004); and radical changes in centre-local government relations towards administrative, fiscal, and political decentralization.
C. The mass media, once tidily under Soeharto's thumb, has experienced significant liberalization as has the legal basis for non-governmental organizations, including many dedicated to such controversial issues as corruption control and human rights.
D. Such developments are seen optimistically by a number of donors and some external analysts, who interpret them as signs of Indonesia's political normalization.
E. A different group of analysts paint a picture in which the institutional forms have changed, but power relations have not. Vedi Hadiz argues that Indonesia's "democratic transition" has been anything but linear.
(1) BDEC
(2) CBDE
(3) CEBD
(4) DEBC
(5) BCDE
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72.
A. I had six thousand acres of land, and had thus got much spare land besides the coffee plantation. Part of the farm was native forest, and about one thousand acres were squatters' land, what [the Kikuyu] called their shambas.
B. The squatters' land was more intensely alive than the rest of the farm, and was changing with the seasons the year round. The maize grew up higher than your head as you walked on the narrow hard-trampled footpaths in between the tall green rustling regiments.
C. The squatters are Natives, who with their families hold a few acres on a white man's farm, and in return have to work for him a certain number of days in the year. My squatters, I think, saw the relationship in a different light, for many of them were born on the farm, and their fathers before them, and they very likely regarded me as a sort of superior squatter on their estates.
D. The Kikuyu also grew the sweet potatoes that have a vine like leaf and spread over the ground like a dense entangled mat, and many varieties of big yellow and green speckled pumpkins.
E. The beans ripened in the fields, were gathered and thrashed by the women, and the maize stalk and coffee pods were collected and burned, so that in certain seasons thin blue columns of smoke rose here and there all over the farm.
(1) CBDE
(2) BCDE
(3) CBED
(4) DBCE
(5) EDBC
Directions for Questions 73 to 75: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question. Every civilized society lives and thrives on a silent but profound agreement as to what is to be accepted as the valid mould of experience. Civilization is a complex system of dams, dykes, and canals warding off, directing, and articulating the influx of the surrounding fluid element; a fertile fenland, elaborately drained and protected from the high tides of chaotic, unexercised, and inarticulate experience. In such a culture, stable and sure of itself within the frontiers of 'naturalized' experience, the arts wield their creative power not so much in width as in depth. They do not create new experience, but deepen and purify the old. Their works do not differ from one another like a new horizon from a new horizon, but like a madonna from a madonna.
The periods of art which are most vigorous in creative passion seem to occur when the established pattern of experience loosens its rigidity without as yet losing its force. Such a
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period was the Renaissance, and Shakespeare its poetic consummation. Then it was as though the discipline of the old order gave depth to the excitement of the breaking away, the depth of job and tragedy, of incomparable conquests and irredeemable losses. Adventurers of experience set out as though in lifeboats to rescue and bring back to the shore treasures of knowing and feeling which the old order had left floating on the high seas. The works of the early Renaissance and the poetry of Shakespeare vibrate with the compassion for live experience in danger of dying from exposure and neglect. In this compassion was the creative genius of the age. Yet, it was a genius of courage, not of desperate audacity. For, however elusively, it still knew of harbours and anchors, of homes to which to return, and of barns in which to store the harvest. The exploring spirit of art was in the depths of its consciousness still aware of a scheme of things into which to fit its exploits and creations. But the more this scheme of things loses its stability, the more boundless and uncharted appears the ocean of potential exploration. In the blank confusion of infinite potentialities flotsam of significance gets attached to jetsam of experience; for everything is sea, everything is at sea - .... The sea is all about us; The sea is the land's edge also, the granite Into which it reaches, the beaches where it tosses Its hints of earlier and other creation ... - and Rilke tells a story in which, as in T.S. Eliot's poem, it is again the sea and the distance of 'other creation' that becomes the image of the poet's reality. A rowing boat sets out on a difficult passage. The oarsmen labour in exact rhythm. There is no sign yet of the destination. Suddenly a man, seemingly idle, breaks out into song. And if the labour of the oarsmen meaninglessly defeats the real resistance of the real waves, it is the idle single who magically conquers the despair of apparent aimlessness. While the people next to him try to come to grips with the element that is next to them, his voice seems to bind the boat to the farthest distance so that the farthest distance draws it towards itself. 'I don't know why and how,' is Rilke's conclusion, 'but suddenly I understood the situation of the poet, his place and function in this age. It does not matter if one denies him every place - except this one. There one must tolerate him.'
73. In the passage, the expression “like a madonna from a madonna” alludes to
(1) The difference arising as a consequence of artistic license.
(2) The difference between two artistic interpretations.
(3) The difference between ‘life’ and ‘interpretation of life’.
(4) The difference between ‘width’ and ‘depth’ of creative power.
(5) The difference between the legendary character and the modern day singer.
74. The sea and ‘other creation’ leads Rilke to
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(1) Define the place of the poet in his culture.
(2) Reflect on the role of the oarsman and the singer.
(3) Muse on artistic labour and its aimlessness.
(4) Understand the elements that one has to deal with.
(5) Delve into natural experience and real waves.
75. According to the passage, the term “adventurers of experience” refers to
(1) Poets and artists who are driven by courage.
(2) Poets and artists who create their own genre.
(3) Poets and artists of the Renaissance.
(4) Poets and artists who revitalize and enrich the past for us.
(5) Poets and artists who delve in flotsam and jetsam in sea.



Answer the questions 1 to 5 on the basis of the information given below. In a Class X Board examination, ten papers are distributed over five Groups – PCB, Mathematics, Social Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a student is calculated in the following manner. First, the Group Scores are obtained by averaging marks in the papers within the Group. The final score is the simple average of the Group Scores. The data for the top ten students are presented below. (Dipan’s score in English Paper II has been intentionally removed in the table).
PCB Group
Mathematics Group
Social Science Group
Vernacular Group
English Group
Final Score
Name of the student
Phy.
Chem.
Bio.
Hist.
Geo.
Paper I
Paper II
Paper I
Paper II
Ayesha (G)
98
96
97
98
95
93
94
96
96
98
96.2
Ram (B)
97
99
95
97
95
96
94
94
96
98
96.1
Dipan (B)
98
98
98
95
96
95
96
94
96
??
96.0
Sagnik (B)
97
98
99
96
96
98
94
97
92
94
95.9
Sanjiv (B)
95
96
97
98
97
96
92
93
95
96
95.7
Shreya (G)
96
89
85
100
97
98
94
95
96
95
95.5
Joseph (B)
90
94
98
100
94
97
90
92
94
95
95.0
Agni (B)
96
99
96
99
95
96
82
93
92
93
94.3
Pritam (B)
98
98
95
98
83
95
90
93
94
94
93.9
Tirna (G)
96
98
79
99
85
94
92
91
87
96
93.7
Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.
1. How much did Dipan get in English Paper II?
(1) 94
(2) 96.5
(3) 97
(4) 98
(5) 99
Solution: Dipan’s Group Scores are as follows:
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Mathematics Group = 95 Dipan’s final score = 96 ∴ Sum of Dipan’s Group Scores = 96 × 5 = 480 ∴ x = 97 Dipan scored 97 marks in English Paper II. Hence, option 3.
2. Students who obtained Group Scores of at least 95 in every group are eligible to apply for a prize. Among those who are eligible, the student obtaining the highest Group Score in Social Science Group is awarded this prize. The prize was awarded to:
(1) Shreya
(2) Ram
(3) Ayesha
(4) Dipan
(5) no one from the top ten
Solution: From the table we can observe that only Dipan is eligible to apply for the prize. So Dipan gets the prize. Hence, option 4.
3. Among the top ten students, how many boys scored at least 95 in at least one paper from each of the groups?
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
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Solution: Dipan was the only boy to score at least 95 in at least one paper from each of the groups. Hence, option 1.
4. Each of the ten students was allowed to improve his/her score in exactly one paper of choice with the objective of maximizing his/her final score. Everyone scored 100 in the paper in which he or she chose to improve. After that, the topper among the ten students was:
(1) Ram
(2) Agni
(3) Pritam
(4) Ayesha
(5) Dipan
Solution: In order to maximize scores, each student would choose to improve his/her score in the paper which would affect the group score the most. Consider the options. Ram chooses Vernacular Paper I or II. His original group score in Vernacular group = 94 His new score = 96.1 + 0.6 = 96.7 Agni chooses Vernacular Paper I. His original group score in Vernacular group = 87.5 His new score = 94.3 + 1.8 = 96.1 Pritam chooses History. His original group score in Social Science group = 89
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His new score = 93.9 + 1.7 = 95.6 Ayesha chooses Geography. Her original group score in Social Science group = 94 Her new score = 96.2 + 0.7 = 96.9 Dipan chooses Mathematics. His original group score in Mathematics group = 95 His new score = 96 + 0.6 = 97, which is the highest among the five options. Hence, option 5.
5. Had Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the Social Science Group, then their standing in decreasing order of final score would be:
(1) Pritam, Joseph, Tirna, Agni
(2) Joseph, Tirna, Agni, Pritam
(3) Pritam, Agni, Tirna, Joseph
(4) Joseph, Tirna, Pritam, Agni
(5) Pritam, Tirna, Agni, Joseph
Solution: Group scores of Joseph, Agni, Pritam and Tirna in Social Science Group are 95.5, 95.5, 89 and 89.5 respectively. Their final scores are 95, 94.3, 93.9, 93.7 respectively. If their group scores in social science change to hundred their final scores will be affected by 4.5/5, 4.5/5, 11/5 and 10.5/5 respectively. Their new final scores would be 95.9, 95.2, 96.1 and 95.8 respectively. Their standing in decreasing order of final score would be Pritam, Joseph, Tirna, Agni. Hence, option 1.
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Answer questions 6 to 10 on the basis of the information given below. Mathematicians are assigned a number called Erdös number, (named after the famous mathematician, Paul Erdös). Only Paul Erdös himself has an Erdös number of zero. Any mathematician who has written a research paper with Erdös has an Erdös number of 1. For other mathematicians, the calculation of his/her Erdös number is illustrated below: Suppose that a mathematician X has co-authored papers with several other mathematicians. From among them, mathematician Y has the smallest Erdös number. Let the Erdös number of Y be y. Then X has an Erdös number of y + 1. Hence any mathematician with no co-authorship chain connected to Erdös has an Erdös number of infinity. In a seven day long mini-conference organized in memory of Paul Erdös, a close group of eight mathematicians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the conference, A was the only participant who had an infinite Erdös number. Nobody had an Erdös number less than that of F. On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdös number of the group of eight mathematicians to 3. The Erdös numbers of B, D, E, G and H remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdös number of the group of eight to as low as 3. At the end of the third day, five members of this group had identical Erdös numbers while the other three had Erdös numbers distinct from each other. On the fifth day, E co-authored a paper with F which reduced the group‘s average Erdös number by 0.5. The Erdös numbers of the remaining six were unchanged with the writing of this paper. No other paper was written during the conference.
6. The person having the largest Erdös number at the end of the conference must have had Erdös number (at that time):
(1) 5
(2) 7
(3) 9
(4) 14
(5) 15
Solution: Let F and E have Erdös numbers f and e respectively, at the beginning of the conference. On the third day, A’s and C’s Erdös numbers become (f + 1) The sum of Erdös numbers changed to 8 × 3 = 24 At the end of the third day, five members had identical Erdös numbers while the other three had distinct ones.
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On the fifth day, E’s Erdös numbers became f + 1 and this reduced the group’s average by 0.5. This means that E’s Erdös numbers was not f + 1 on the third day. Thus we have, At the end of the third day, 5(f + 1) + f + e + y = 24 Hence 6f + 5 + e + y = 24 Hence 6f + e + y = 19 At the end of the fifth day, 6(f + 1) + f + y = 2.5 × 8 = 20 Hence 7f + y = 14 Among the eight mathematicians, F has the smallest Erdös number. Let f = 2 ∴ y = 0 However, only Paul Erdös himself has an Erdös number of 0. So f cannot be equal to 2. Any other value greater than 2, would render y as a negative number, which is also not possible. So, f = 1 ∴ y = 7 ∴ e = 6 Now, we can solve all the questions. From the above explanation, the largest Erdös number at the end of the conference would be 7. Hence, option 2.
7. How many participants in the conference did not change their Erdös number during the conference?
(1) 2
(2) 3
(3) 4
(4) 5
(5) Cannot be determined
Solution: As per the explanation given in the first question, the Erdös numbers of B, D, G, H and F did not change during the conference. Hence, option 4.
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8. The Erdös number of C at the end of the conference was:
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Solution: As follows from the explanation given in the first question, C’s Erdös number was f + 1 = 2 on the third day and thereafter. Hence, option 2.
9. The Erdös number of E at the beginning of the conference was:
(1) 2
(2) 5
(3) 6
(4) 7
(5) 8
Solution: It can be inferred from the common explanation that E’s Erdös number was 6. Hence, option 3.
10. How many participants had the same Erdös number at the beginning of the conference?
(1) 2
(2) 3
(3) 4
(4) 5
(5) Cannot be determined
Solution: Since 5 participants had identical Erdös numbers at the end of day three and two of these were A and C whose Erdös numbers had changed on the same day, three had the same Erdös numbers at the beginning of the conference. Hence, option 2.
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Answer questions 11 to 15 on the basis of the information given below. Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs. 100, while at the end of the fifth day it was priced at Rs. 110. At the end of each day, the MCS share price either went up by Rs. 10, or else, it came down by Rs. 10. Both Chetan and Michael took buying and selling decisions at the end of each trading day. The beginning price of MCS share on a given day was the same as the ending price of the previous day. Chetan and Michael started with the same number of shares and amount of cash, and had enough of both. Below are some additional facts about how Chetan and Michael traded over the five trading days. Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other hand, each day if the price went down, he bought 10 shares at the closing price. If on any day, the closing price was above Rs. 110, then Michael sold 10 shares of MCS, while if it was below Rs. 90, he bought 10 shares, all at the closing price.
11. If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3?
(1) Rs. 90
(2) Rs. 100
(3) Rs. 110
(4) Rs. 120
(5) Rs. 130
Solution: Let the price of the share rise on x days and fall on y days. As the price increases by Rs. 10 in the five days, we have: x + y = 5 and 10x – 10y = 10 Solving the above two equations simultaneously, we have x = 3 and y = 2 The price of the share goes up on 3 days and falls on 2 days. The three days on which the price rises can be selected in 5C3 = 10 ways The following are the 10 cases:
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Day 1
Day 2
Day 3
Day 4
Day 5
Chetan
Michael
Cash
Shares
Cash
Shares
Case 1
Opening
100
110
120
130
120
1300
–10
3700
–30
Closing
110
120
130
120
110
Case 2
Opening
100
90
80
90
100
1300
–10
–800
10
Closing
90
80
90
100
110
Case 3
Opening
100
90
100
110
120
1300
–10
1200
–10
Closing
90
100
110
120
110
Case 4
Opening
100
110
100
110
100
1300
–10
0
0
Closing
110
100
110
100
110
Case 5
Opening
100
110
120
110
120
1300
–10
2400
–20
Closing
110
120
110
120
110
Case 6
Opening
100
110
120
110
100
1300
–10
1200
–10
Closing
110
120
110
100
110
Case 7
Opening
100
90
100
110
100
1300
–10
0
0
Closing
90
100
110
100
110
Case 8
Opening
100
110
100
110
120
1300
–10
1200
–10
Closing
110
100
110
120
110
Case 9
Opening
100
90
100
90
100
1300
–10
0
0
Closing
90
100
90
100
110
Case 10
Opening
100
110
100
90
100
1300
–10
0
0
Closing
110
100
90
100
110
Consider Case 5 Chetan sells on Days 1, 2 and 4 and buys on days 3 and 5. Change in the number of shares he has = –30 + 20 = –10 Change in his cash = 10 × (110 + 120 + 120) – 10 × (110 + 110) = Rs. 1300 Michael sells on days 2 and 4, but never buys as the share price does not go below Rs. 90. Change in the number of shares he has = –20 Change in his cash = 10 × (120 + 120) = Rs. 2400 The other cases are evaluated in a similar manner and the data is tabulated as shown above. Chetan sold on three consecutive days Cases 1, 2 and 3. Michael sold only once Case 3.
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∴ The price of the share at the end of day 3 = Rs. 110 Hence, option 3.
12. If Michael ended up with Rs. 100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan (at the end of day 5)?
(1) Michael had 10 less shares than Chetan.
(2) Michael had10 more shares than Chetan.
(3) Chetan had 10 more shares than Michael.
(4) Chetan had 20 more shares than Michael.
(5) Both had the same number of shares.
Solution: Referring to the formulated table of the first question, Michael ends up with Rs. 100 less cash than Chetan in cases 3, 6 and 8. In each of these cases, both of them hold the same number of shares at the end of day 5. Hence, option 5.
13. If Chetan ended up with Rs. 1300 more cash than Michael at the end of day 5, what was the price of MCS share at the end of day 4?
(1) Rs. 90
(2) Rs. 100
(3) Rs. 110
(4) Rs. 120
(5) Not uniquely determinable
Solution: This information corresponds to cases 4, 7, 9 and 10 from the solution table. The price at the end of day 4 in each of these cases is Rs. 100. Hence, option 2.
14. What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day?
(1) Rs. 3700
(2) Rs. 4000
(3) Rs. 4700
(4) Rs. 5000
(5) Rs. 6000
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Solution: The maximum increase in combined cash balance of Chetan and Michael = 1300 + 3700 = Rs. 5000 (case 1 from the table) Hence, option 4.
15. If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the share at the end of day 3?
(1) Rs. 90
(2) Rs. 100
(3) Rs. 110
(4) Rs. 120
(5) Rs. 130
Solution: This information corresponds to case 2 from the table. The price at the end of day 3 was Rs. 90. Hence, option 1. Answer questions 16 to 20 on the basis of the information given below. A significant amount of traffic flows from point S to point T in the one-way street network shown below. Points A, B, C, and D are junctions in the network, and the arrows mark the direction of traffic flow. The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street.
Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum. If two or more routes have the same least travel cost, then motorists are indifferent between them. Hence, the traffic gets evenly distributed among all the least cost routes.
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The government can control the flow of traffic only by levying appropriate toll at each junction. For example, if a motorist takes the route S-A-T (using junction A alone), then the total cost of travel would be Rs. 14 (i.e. Rs. 9 + Rs. 5) plus the toll charged at junction A.
16. If the government wants to ensure that all motorists travelling from S to T pay the same amount (fuel costs and toll combined) regardless of the route they choose and the street from B to C is under repairs (and hence unusable), then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:
(1) 2, 5, 3, 2
(2) 0, 5, 3, 1
(3) 1, 5, 3, 2
(4) 2, 3, 5, 1
(5) 1, 3, 5, 1
Solution: Let the toll charged at junctions A, B, C and D be a, b, c and d respectively. Since the cost of travel including toll on routes S-A-T, S-D-T, S-B-A-T and S-D-C-T is the same. ∴ 14 + a = 13 + d = 9 + a + b = 10 + c + d Thus, b = 5, d – a = 1, c = 3 If a = 0, d = 1, If a = 1, d = 2 and if a = 2, d = 3 Hence, both options 2 and 3 satisfy the given criteria. Note: The question makers took care of this inconsistency while calculating scores.
17. If the government wants to ensure that no traffic flows on the street from D to T, while equal amount of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:
(1) 1, 5, 3, 3
(2) 1, 4, 4, 3
(3) 1, 5, 4, 2
(4) 0, 5, 2, 3
(5) 0, 5, 2, 2
Solution: Since the cost of travel including toll on routes S-A-T, S-B-C-T, S-B-A-T and S-D-C-T is the same. ∴ 14 + a = 7 + b + c = 9 + a + b = 10 + c + d ∴ b = 5, d = 2, c – a = 2
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Only option 5 satisfies these criteria. Hence, option 5.
18. If the government wants to ensure that all routes from S to T get the same amount of traffic, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:
(1) 0, 5, 2, 2
(2) 0, 5, 4, 1
(3) 1, 5, 3, 3
(4) 1, 5, 3, 2
(5) 1, 5, 4, 2
Solution: Since the cost of travel including toll on all routes is the same. ∴ 14 + a = 7 + b + c = 13 + d = 9 + a + b = 10 + c + d ∴ b = 5, d = 2, c = 3 and a = 1 Hence, option 4.
19. If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:
(1) 0, 5, 4, 1
(2) 0, 5, 2, 2
(3) 1, 5, 3, 3
(4) 1, 5, 3, 2
(5) 0, 4, 3, 2
Solution: If we make the cost of travelling on all the routes equal, traffic along S-B will be twice that along S-A. But we want traffic along S-A, S-B and S-D to be the same. As routes lead to C from both B and D, we can increase the toll at C so that the cost of travelling along S-B-C-T and S-D-C-T is more than that along the other three routes. Now, 14 + a = 9 + b = 13 + d ∴ a = 0, b = 5 and d =1 Also, 7 + b + c > 14 and 10 + d + c > 14 ∴ c > 3 Hence, option 1.
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20. The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:
(1) Rs. 7
(2) Rs. 9
(3) Rs. 10
(4) Rs. 13
(5) Rs. 14
Solution: If toll charges at all junctions are made 0, 100% traffic will pass through S-B-C-T. This is not possible. If toll charges at A and B are made 0, then 100% traffic will pass through S-B-A-T. This is also not possible. If toll charges at C and D are made 0, that at B are made Rs.3, then the traffic will get equally divided between S-D-C-T and S-B-C-T. Thus, the cost incurred will be Rs. 10. Hence, option 3. Answer questions 21 to 25 on the basis of the information given below. K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions: A team must include exactly one among P, R, and S. A team must include either M or Q, but not both. If a team includes K, then it must also include L, and vice versa. If a team includes one among S, U, and W, then it must also include the other two. L and N cannot be members of the same team. L and U cannot be members of the same team. The size of a team is defined as the number of members in the team.
21. What could be the size of a team that includes K?
(1) 2 or 3
(2) 2 or 4
(3) 3 or 4
(4) Only 2
(5) Only 4
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Solution: As K is included, L is included. So, N and U cannot be included. As U is not included, S and W are not included. One out of M and Q and one out of P and R will be included. Thus, the team will include: K, L, (M or Q) and (P or R). Hence, option 5.
22. In how many ways a team can be constituted so that the team includes N?
(1) 2
(2) 3
(3) 4
(4) 5
(5) 6
Solution: If the team includes N, it does not include L and K. One out of M and Q can be included and one out of P, S and R can be included. If S is a member, so are U and W. Thus the possible teams are:
1. N, M, P
2. N, M, R
3. N, Q, P
4. N, Q, R
5. N, M, S, U, W
6. N, Q, S, U, W
Hence, option 5.
23. What would be the size of the largest possible team?
(1) 8
(2) 7
(3) 6
(4) 5
(5) Cannot be determined
Solution: If S is not included, the team can have P or R, M or Q, K and L. If S is included, the team will have S, U, W, M or Q, N. This is the largest possible team. Hence, option 4.
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24. Who can be a member of a team of size 5?
(1) K
(2) L
(3) M
(4) P
(5) R
Solution: If K or L are included, N, U, S and W are excluded. One out of P and R and one out of M and Q are included. Thus the team has only 4 members. If P or R are included, the team can have M or Q, K and L. This team also has 4 members. A team having M can have S, U, W and N i.e., 5 members. Hence, option 3.
25. Who cannot be a member of a team of size 3?
(1) L
(2) M
(3) N
(4) P
(5) Q
Solution: A team sized 3 has to have M or Q and P or R. The only other member that can be selected all alone is N. L cannot be selected as K has to be selected with him. Hence, option 1.
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Section II Directions for Questions 26 to 30: Each of the questions below has a set of sequentially ordered statements. Each statement can be classified as one of the following:
A. Facts, which deal with the pieces of information that one has heard, seen or read, and which are open to discovery or verification (the answer option indicates such a statement with an ‘F’)
B. Inferences, which are conclusions drawn about the unknown, on the basis of the known (the answer option indicates such a statement with an ‘I’)
C. Judgements, which are opinions that imply approval or disapproval of persons, objects, situations and occurrences in the past, the present or the future (the answer option indicates such a statement with a ‘J’)
Select the answer option that best describes the set of statements.
26.
1. So much of our day-to-day focus seems to be on getting things done, trudging our way through the tasks of living - it can feel like a treadmill that gets you nowhere; where is the childlike joy?
2. We are not doing the things that make us happy; that which brings us joy; the things that we cannot wait to do because we enjoy them so much.
3. This is the stuff that joyful living is made of – identifying your calling and committing yourself wholeheartedly to it.
4. When this happens, each moment becomes a celebration of you; there is a rush of energy that comes with feeling completely immersed in doing what you love most.
(1) IIIJ
(2) IFIJ
(3) JFJJ
(4) JJJJ
(5) JFII
Solution: Statement 1 states, “It can feel like a treadmill that gets you nowhere”. This can neither be experienced nor verified as it is a personal viewpoint, hence a judgement. Statement 2 is a personal viewpoint not necessarily agreed to by many. It is a judgement. Statement 3 is an opinion, neither verifiable nor directly experienced. It is a judgement. Statement 4 is someone’s personal assessment of his own experience. It is also a judgement. Hence, option 4.
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27.
1. Given the poor quality of service in the public sector, the HIV/AIDS affected should be switching to private initiatives that supply anti-retroviral drugs (ARVs) at a low cost.
2. The government has been supplying free drugs since 2004, and 35000 have benefited up to now - though the size of the affected population is 150 times this number.
3. The recent initiatives of networks and companies like AIDSCare Network, Emcure, Reliance-Cipla-CII, would lead to availability of much-needed drugs to a larger number of affected people.
4. But how ironic it is that we should face a perennial shortage of drugs when India is one of the world‘s largest suppliers of generic drugs to the developing world.
(1) JFIJ
(2) JIIJ
(3) IFIJ
(4) IFFJ
(5) JFII
Solution: The given options require you to evaluate statement 1 as either a Judgement or an Inference. ‘Given the poor quality of services in the public sector … ’ is more of a judgement than an inference. Based on this the conclusion “should be switching….” establishes statement 1 as a judgement. This eliminates option 3 and 4. The numbers in statement 2 are a result of direct verification. Hence it is easy to see that statement 2 is a fact. This eliminates option 2. Evaluating options 1 and 5, both of which say statement 4 is an inference, one has to now establish whether statement 5 is an inference or a judgement (as per the options 1 and 5). “… how ironic it is..” is neither verified nor verifiable through facts. Statement 4 is a judgement. Hence, option 1.
28.
1. According to all statistical indications, the Sarva Shiksha Abhiyan has managed to keep pace with its ambitious goals.
2. The Mid-day Meal Scheme has been a significant incentive for the poor to send their little ones to school, thus establishing the vital link between healthy bodies and healthy minds.
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3. Only about 13 million children in the age group of 6 to 14 years are out of school.
4. The goal of universalisation of elementary education has to be a pre-requisite for the evolution and development of our country.
(1) IIFJ
(2) JIIJ
(3) IJFJ
(4) IJFI
(5) JIFI
Solution: Statement 1 is an inference. “According to statistical indications ….” tells us that what follows is based on statistics, hence an inference. This eliminates options 2 and 5. In statement 2 (to be evaluated as Judgement or Inference), though ‘significant incentive’ may be inferred by checking with available data, ‘the vital link between healthy bodies and healthy minds’ cannot be investigated for data – medical or otherwise. Hence, it is a judgement. Options 3 and 4 remain. The options state that sentence 3 is Fact. Sentence 4 needs to be evaluated as either an Inference or a Judgement. “… has to be a prerequisite for the evolution….” cannot be verified from facts making sentence 4 a Judgement. Hence, option 3.
29.
1. We should not be hopelessly addicted to an erroneous belief that corruption in India is caused by the crookedness of Indians.
2. The truth is that we have more red tape - we take eighty-nine days to start a small business, Australians take two.
3. Red tape leads to corruption and distorts a people‘s character.
4. Every red tape procedure is a point of contact with an official, and such contacts have the potential to become opportunities for money to change hands.
(1) JFIF
(2) JFJJ
(3) JIJF
(4) IFJF
(5) JFJI
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Solution: Several things make statement 1 a judgement – 'should not be', 'hopelessly addicted', 'erroneous belief', and ‘crookedness of Indians’; none of them are facts, nor verifiable inferences. Statement 2 is a combination of inference and facts. ‘we have more red tape’ is an inference, but ‘we take 89 days etc..” is a fact. Since the thrust of the statement is based on the facts it has to be classified as a fact. Therefore options 3 and 4 are eliminated. Options 1, 2 and 5 remain. Statement 3 is clearly a judgement or an opinion and is classified in both options 2 and 5 as a Judgement. Eliminate option 1. Statement 4 is to be evaluated a Judgement or an Inference. The first part of sentence 4 is a fact. In the second part, ‘potential’ is inferred based on facts/experiences. Hence it is an inference. This eliminates option 2. Hence, the correct answer is option 5.
30.
1. Inequitable distribution of all kinds of resources is certainly one of the strongest and most sinister sources of conflict.
2. Even without war, we know that conflicts continue to trouble us - they only change in character.
3. Extensive disarmament is the only insurance for our future; imagine the amount of resources that can be released and redeployed.
4. The economies of the industrialized western world derive 20% of their income from the sale of all kinds of arms.
(1) IJJI
(2) JIJF
(3) IIJF
(4) JIIF
(5) IJIF
Solution: The first sentence is to be evaluated as a Judgement or an Inference. ‘Most sinister’ is neither verified nor verifiable. It is clearly an opinion, making it a Judgement. This eliminates options 1, 3 and 5. Evaluating options 2 and 4, one has to decide whether statement 3 is an Inference or a Judgement. ‘Only insurance’ is neither a verified fact nor a verifiable inference. Hence it is a judgement, which eliminates option 4. Hence, option 2.
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Directions for Questions 31 to 35: 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.
31. I am sometimes attacked for imposing 'rules‘. Nothing could be further from the truth. I hate rules. All I do is report on how consumers react to different stimuli. I may say to a copywriter, “Research shows that commercials with celebrities are below average in persuading people to buy products. Are you sure you want to use a celebrity?” Call that a rule? Or I may say to an art director, “Research suggests that if you set the copy in black type on a white background, more people will read it than if you set it in white type on a black background.”
(1) Guidance based on applied research can hardly qualify as ‘rules’.
(2) Thus, all my so called ‘rules’ are rooted in applied research.
(3) A suggestion perhaps, but scarcely a rule.
(4) Such principles are unavoidable if one wants to be systematic about consumer behaviour.
(5) Fundamentally it is about consumer behaviour - not about celebrities or type settings.
Solution: It is not a difficult choice, when one understands that the concluding sentence of a paragraph should fulfill the purpose for which the paragraph is written, leaving no loose ends that may require further clarification. The first three sentences of the paragraph establish this purpose. Then the writer provides certain example situations. Option 3 concludes the paragraph smoothly – the writer tells us what his ‘alleged’ rules are. In consistence with the conversational tone of the paragraph, the writer does not assert even his explanation with undue vigor in the last sentence. Option 1 is contrary to the purpose of the paragraph because ‘guidance based on applied research’ makes his actions more binding on others than are rules. Options 2 and 4 are also eliminated for the same reason. Option 5 talks about one of the examples and not related to the purpose of the paragraph. Hence, option 3.
32. Relations between the factory and the dealer are distant and usually strained as the factory tries to force cars on the dealers to smooth out production. Relations between the dealer and the customer are equally strained because dealers continuously adjust prices - make deals - to adjust demand with supply while maximizing profits. This becomes a system marked by a lack of long-term
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commitment on either side, which maximize feelings of mistrust. In order to maximize their bargaining positions, everyone holds back information - the dealer about the product and the consumer about his true desires.
(1) As a result, ‘deal making’ becomes rampant, without concern for customer satisfaction.
(2) As a result, inefficiencies creep into the supply chain.
(3) As a result, everyone treats the other as an adversary, rather than as an ally.
(4) As a result, fundamental innovations are becoming scarce in the automobile industry.
(5) As a result, everyone loses in the long run.
Solution: All options begin with “as a result”. One has the freedom to ignore this or to work intensely on this phrase. ‘As a result’ indicates that one needs to discover the immediate consequence of the details given in the paragraph. Option 4 is the first to get eliminated as it is not a consequence at all. Options 1 and 2 are not consequences but what may currently exist in the industry; as explained in the paragraph. Option 3 brings in ‘adversary’ and ‘ally’. This is hardly sustained by the data in the paragraph, unless one justifies them. If one justifies them, the option gets eliminated, because again, it is not a consequence, but what exists there. The direct consequence is stated briefly in option 5 bringing the paragraph to a smooth closure as no further clarification is required. “As a result” has to be worked upon and not ignored. Hence, option 5.
33. In the evolving world order, the comparative advantage of the United States lies in its military force. Diplomacy and international law have always been regarded as annoying encumbrances, unless they can be used to advantage against an enemy. Every active player in world affairs professes to seek only peace and to prefer negotiation to violence and coercion.
(1) However, diplomacy has often been used as a mask by nations which intended to use force.
(2) However, when the veil is lifted, we commonly see that diplomacy is understood as a disguise for the rule of force.
(3) However, history has shown that many of these nations do not practice what they profess.
(4) However, history tells us that peace is professed by those who intend to use violence.
(5) However, when unmasked, such nations reveal a penchant for the use of force.
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Solution: The word 'professes' towards the end is significant. ‘However’ is constant in the options. One needs to pick out the best contrast. Options 3 and 4 get easily eliminated as they contain ‘history’, which will require a lot of explanation in the context. The last sentence will not contain any new ideas requiring further clarification. Option 5 is eliminated because of ‘penchant’ – the paragraph does not make such assertions. For the same reason, the ‘intention’ in option 1 gets it eliminated. The word 'professes’ in the paragraph directly leads to the ‘veil’ and ‘understood’ in option 2. Hence, option 2.
34. Age has a curvilinear relationship with the exploitation of opportunity. Initially, age will increase the likelihood that a person will exploit an entrepreneurial opportunity because people gather much of the knowledge necessary to exploit opportunities over the course of their lives, and because age provides credibility in transmitting that information to others. However, as people become older, their willingness to bear risks declines, their opportunity costs rise, and they become less receptive to new information.
(1) As a result, people transmit more information rather than experiment with new ideas as they reach an advanced age.
(2) As a result, people are reluctant to experiment with new ideas as they reach an advanced age.
(3) As a result, only people with lower opportunity costs exploit opportunity when they reach an advanced age.
(4) As a result, people become reluctant to exploit entrepreneurial opportunities when they reach an advanced age.
(5) As a result, people depend on credibility rather than on novelty as they reach an advanced age.
Solution: 'As a result' is a constant in the options. One needs to identify the direct consequence of what is stated in the paragraph. Also establish the purpose of the paragraph by looking at the first and the last sentences given to you. ('Age has …' and 'however, as people become older...'). Options 3 and 5 get eliminated most easily. Neither of these options is a consequence of the curvilinear relationship between age and exploitation of opportunity.
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The reluctance to “experiment with new ideas” (options 1 and 2) does not necessarily translate into the ‘entrepreneurial opportunity” given in the paragraph. Option 4 includes all this and is specific to the ideas presented in the paragraph and is a direct consequence. Hence, option 4.
35. We can usefully think of theoretical models as maps, which help us navigate unfamiliar territory. The most accurate map that it is possible to construct would be of no practical use whatsoever, for it would be an exact replica, on exactly the same scale, of the place where we were. Good maps pull out the most important features and throw away a huge amount of much less valuable information. Of course, maps can be bad as well as good - witness the attempts by medieval Europe to produce a map of the world. In the same way, a bad theory, no matter how impressive it may seem in principle, does little or nothing to help us understand a problem.
(1) But good theories, just like good maps, are invaluable, even if they are simplified.
(2) But good theories, just like good maps, will never represent unfamiliar concepts in detail.
(3) But good theories, just like good maps, need to balance detail and feasibility of representation.
(4) But good theories, just like good maps, are accurate only at a certain level of abstraction.
(5) But good theories, just like good maps, are useful in the hands of a user who knows their limitations.
Solution: 'We can usefully think of theoretical models as maps.' The first sentence has established the purpose of the paragraph which is to understand the usefulness of theoretical models using the comparison of maps. This purpose is fulfilled in option 1 that they are invaluable. That theoretical models ‘will never represent' (option 2), ‘need to balance” (option 3), ‘are accurate only' (option 4) do not fulfill this purpose. Option 5 is a generalization that the paragraph does not support. Hence, option 1.
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Directions for Questions 36 to 40: The passage given below is followed by a set of questions. Choose the most appropriate answer to each question. Fifteen years after communism was officially pronounced dead, its spectre seems once again to be haunting Europe. Last month, the Council of Europe‘s parliamentary assembly voted to condemn the crimes of totalitarian communist regimes,“ linking them with Nazism and complaining that communist parties are still legal and active in some countries.“Now Goran Lindblad, the conservative Swedish MP behind the resolution, wants to go further. Demands that European Ministers launch a continent-wide anti-communist campaign - including school textbook revisions, official memorial days, and museums - only narrowly missed the necessary two-thirds majority. Mr. Lindblad pledged to bring the wider plans back to the Council of Europe in the coming months. He has chosen a good year for his ideological offensive: this is the 50th anniversary of Nikita Khrushchev‘s denunciation of Josef Stalin and the subsequent Hungarian uprising, which will doubtless be the cue for further excoriation of the communist record. Paradoxically, given that there is no communist government left in Europe outside Moldova, the attacks have if anything, become more extreme as time has gone on. A clue as to why that might be can be found in the rambling report by Mr. Lindblad that led to the Council of Europe declaration. Blaming class struggle and public ownership, he explained different elements of communist ideology such as equality or social justice still seduce many“ and a sort of nostalgia for communism is still alive.” Perhaps the real problem for Mr. Lindblad and his right-wing allies in Eastern Europe is that communism is not dead enough - and they will only be content when they have driven a stake through its heart.
The fashionable attempt to equate communism and Nazism is in reality a moral and historical nonsense. Despite the cruelties of the Stalin terror, there was no Soviet Treblinka or Sorbibor, no extermination camps built to murder millions. Nor did the Soviet Union launch the most devastating war in history at a cost of more than 50 million lives - in fact it played the decisive role in the defeat of the German war machine. Mr. Lindblad and the Council of Europe adopt as fact the wildest estimates of those killed by communist regimes (mostly in famines) from the fiercely contested Black Book of Communism, which also underplays the number of deaths attributable to Hitler. But, in any case, none of this explains why anyone might be nostalgic in former communist states, now enjoying the delights of capitalist restoration. The dominant account gives no sense of how communist regimes renewed themselves after 1956 or why Western leaders feared they might overtake the capitalist world well into the 1960s. For all its brutalities and failures, communism in the Soviet Union, Eastern Europe, and elsewhere delivered rapid industrialization, mass education, job security, and huge advances in social and gender
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equality. Its existence helped to drive up welfare standards in the West, and provided a powerful counterweight to Western global domination. It would be easier to take the Council of Europe‘s condemnation of communist state crimes seriously if it had also seen fit to denounce the far bloodier record of European colonialism - which only finally came to an end in the 1970s. This was a system of racist despotism, which dominated the globe in Stalin‘s time. And while there is precious little connection between the ideas of fascism and communism, there is an intimate link between colonialism and Nazism. The terms lebensraum and konzentrationslager were both first used by the German colonial regime in south-west Africa (now Namibia), which committed genocide against the Herero and Nama peoples and bequeathed its ideas and personnel directly to the Nazi party. Around 10 million Congolese died as a result of Belgian forced labour and mass murder in the early twentieth century; tens of millions perished in avoidable or enforced famines in British-ruled India; up to a million Algerians died in their war for independence, while controversy now rages in France about a new law requiring teachers to put a positive spin on colonial history. Comparable atrocities were carried out by all European colonialists, but not a word of condemnation from the Council of Europe. Presumably, European lives count for more. No major twentieth century political tradition is without blood on its hands, but battles over history are more about the future than the past. Part of the current enthusiasm in official Western circles for dancing on the grave of communism is no doubt about relations with today‘s Russia and China. But it also reflects a determination to prove there is no alternative to the new global capitalist order - and that any attempt to find one is bound to lead to suffering. With the new imperialism now being resisted in the Muslim world and Latin America, growing international demands for social justice and ever greater doubts about whether the environmental crisis can be solved within the existing economic system, the pressure for alternatives will increase.
36. Among all the apprehensions that Mr. Goran Lindblad expresses against communism, which one gets admitted, although indirectly, by the author?
(1) There is nostalgia for communist ideology even if communism has been abandoned by most European nations.
(2) Notions of social justice inherent in communist ideology appeal to critics of existing systems.
(3) Communist regimes were totalitarian and marked by brutalities and large scale violence.
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(4) The existing economic order is wrongly viewed as imperialistic by proponents of communism.
(5) Communist ideology is faulted because communist regimes resulted in economic failures.
Solution: It is stated in the passage: “Despite the cruelties of the Stalin terror, there was no Soviet Treblinka or Sorbibor, no extermination camps built to murder millions.” Later on, “For all its brutalities and failures, communism in the Soviet union, …” There is no evidence to support the other options. Hence, option 3.
37. What, according to the author, is the real reason for a renewed attack against communism?
(1) Disguising the unintended consequences of the current economic order such as social injustice and environmental crisis.
(2) Idealising the existing ideology of global capitalism.
(3) Making communism a generic representative of all historical atrocities, especially those perpetrated by the European imperialists.
(4) Communism still survives, in bits and pieces, in the minds and hearts of people.
(5) Renewal of some communist regimes has led to the apprehension that communist nations might overtake the capitalists.
Solution: From the last paragraph: “Part of the current enthusiasm in official western circles for dancing on the grave of communism is no doubt about relations with today’s Russia and China. But it also reflects a determination to prove there is no alternative to the new global capitalist order – and that any attempt to find one is bound to lead to suffering.” From the second paragraph: “Blaming class struggle and public ownership, …….. and they will only be content when they have driven a stake through its heart.” This part of the passage also gives certain reasons which will answer the above question. Based on these two parts of the passage, the options to be evaluated are option 2 and option 4. Option 4 gets eliminated because the question asks the ‘real’ reason. If communism did not pose a threat to capitalism, there is no need to destroy it completely. Mere survival of something cannot be sufficient reason to destroy it, unless it is a threat to something else. As a result option 2 becomes the real reason and not option 4. Hence, option 2.
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38. The author cites examples of atrocities perpetrated by European colonial regimes in order to
(1) compare the atrocities committed by colonial regimes with those of communist regimes.
(2) prove that the atrocities committed by colonial regimes were more than those of communist regimes.
(3) prove that, ideologically, communism was much better than colonialism and Nazism.
(4) neutralise the arguments of Mr.Lindblad and to point out that the atrocities committed by colonial regimes were more than those of communist regimes.
(5) neutralise the arguments of Mr. Lindblad and to argue that one needs to go beyond and look at the motives of these regimes.
Solution: The reason why the writer cites examples of colonial atrocities has to be inferred from the passage. The writer’s apparently pro-communism stand is attributable to his comparison of communism, colonialism, and Nazism. Comparing these three the writer argues that communism is the least evil of the three. The writer compares Colonialism to Nazism because the Council of Europe (Mr. Lindblad) and the ‘anti-communists’ compare communism to Nazism. The writer argues that colonialism is closer to Nazism than is communism because of the motives of each. The writer terms colonialism and Nazism as ‘racist despotism’ whereas communism had helped a large number of people. He states: “It would be easier to take the Council of Europe’s condemnation of communist state crimes seriously if it had also seen fit to denounce the far bloodier record of European colonialism …” The atrocities attributed to colonialism neutralizes the arguments of Lindblad against communism, and calls for an objective evaluation of communism, colonialism, and Nazism as mentioned in option 5. The other options may appear close when the comprehension of the passage is not adequate. One may mistakenly choose option 4 in this case. However, option 4 though correct in the light of the passage is not the writer’s purpose in citing the example. Hence, option 5.
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39. Why, according to the author, is Nazism closer to colonialism than it is to communism?
(1) Both colonialism and Nazism were examples of tyranny of one race over another.
(2) The genocides committed by the colonial and the Nazi regimes were of similar magnitude.
(3) Several ideas of the Nazi regime were directly imported from colonial regimes.
(4) Both colonialism and Nazism are based on the principles of imperialism.
(5) While communism was never limited to Europe, both the Nazis and the colonialists originated in Europe.
Solution: The writer, in the passage, establishes greater similarity between colonialism and Nazism than communism and Nazism because “the fashionable attempt (by Lidblad) to equate communism and Nazism is in reality a moral and historical nonsense.” If communism has less to do with Nazism the question actually is what makes colonialism closer to Nazism? Option 3 may be chosen mistakenly if one is trying to find one of the intimate links between Nazism and colonialism without any reference to communism. Also, note that the options states “imported from colonial regimes”, whereas the text below shows that it was the German colonial regime. From the fourth and fifth paragraphs of the passage: “The terms lebensraum and konzentrationslager were both first used by the German colonial regime in south-west Africa (now Namibia), which committed genocide against the Herero and Nama peoples and bequeathed its ideas and personnel directly to the Nazi party. Around 10 million Congolese died as a result of Belgian forced labour and mass murder in the early twentieth century; tens of millions perished in avoidable or enforced famines in British-ruled India; up to a million Algerians died in their war for independence, while controversy now rages in France about a new law requiring teachers to put a positive spin on colonial history.” Option 1 answers the question by covering the gist of the two paragraphs that are relevant to the question: that both are examples of tyranny …. or ‘racist despotism’. The other options are not supported by the passage. Hence, option 1.
40. Which of the following cannot be inferred as a compelling reason for the silence of the Council of Europe on colonial atrocities?
(1) The Council of Europe being dominated by erstwhile colonialists.
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(2) Generating support for condemning communist ideology.
(3) Unwillingness to antagonize allies by raking up an embarrassing past.
(4) Greater value seemingly placed on European lives.
(5) Portraying both communism and Nazism as ideologies to be condemned.
Solution: All options are compelling reasons for the silence of the Council of Europe about colonial atrocities, whereas option 4 is the compelling reason for its (council of Europe’s) condemnation of communism. Hence, option 4 Directions for Questions 41 to 45: The passage given below is followed by a set of five questions. Choose the most appropriate answer to each question. My aim is to present a conception of justice which generalizes and carries to a higher level of abstraction the familiar theory of the social contract. In order to do this we are not to think of the original contract as one to enter a particular society or to set up a particular form of government. Rather, the idea is that the principles of justice for the basic structure of society are the object of the original agreement. They are the principles that free and rational persons concerned to further their own interests would accept in an initial position of equality. These principles are to regulate all further agreements; they specify the kinds of social cooperation that can be entered into and the forms of government that can be established. This way of regarding the principles of justice, I shall call justice as fairness. Thus, we are to imagine that those who engage in social cooperation choose together, in one joint act, the principles which are to assign basic rights and duties and to determine the division of social benefits. Just as each person must decide by rational reflection what constitutes his good, that is, the system of ends which it is rational for him to pursue, so a group of persons must decide once and for all what is to count among them as just and unjust. The choice which rational men would make in this hypothetical situation of equal liberty determines the principles of justice.
In ‘justice as fairness’, the original position is not an actual historical state of affairs. It is understood as a purely hypothetical situation characterized so as to lead to a certain conception of justice. Among the essential features of this situation is that no one knows his place in society, his class position or social status, nor does anyone know his fortune in the distribution of natural assets and abilities, his intelligence, strength, and the like. I shall even assume that the parties do not know their conceptions of the good or their special psychological propensities. The principles of justice are chosen behind a veil of ignorance. This ensures that no one is advantaged or disadvantaged in the choice of principles by the outcome of natural chance or the contingency of social circumstances. Since all are
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similarly situated and no one is able to design principles to favor his particular condition, the principles of justice are the result of a fair agreement or bargain. Justice as fairness begins with one of the most general of all choices which persons might make together, namely, with the choice of the first principles of a conception of justice which is to regulate all subsequent criticism and reform of institutions. Then, having chosen a conception of justice, we can suppose that they are to choose a constitution and a legislature to enact laws, and so on, all in accordance with the principles of justice initially agreed upon. Our social situation is just if it is such that by this sequence of hypothetical agreements we would have contracted into the general system of rules which defines it. Moreover, assuming that the original position does determine a set of principles, it will then be true that whenever social institutions satisfy these principles, those engaged in them can say to one another that they are cooperating on terms to which they would agree if they were free and equal persons whose relation with respect to one another were fair. They could all view their arrangements as meeting the stipulations which they would acknowledge in an initial situation that embodies widely accepted and reasonable constraints on the choice of principles. The general recognition of this fact would provide the basis for a public acceptance of the corresponding principles of justice. No society can, of course, be a scheme of cooperation which men enter voluntarily in a literal sense; each person finds himself placed at birth in some particular position in some particular society, and the nature of this position materially affects his life prospects. Yet a society satisfying the principles of justice as fairness comes as close as a society can to being a voluntary scheme, for it meets the principles which free and equal persons would assent to under circumstances that are fair.
41. A just society, as conceptualized in the passage, can be best described as:
(1) A Utopia in which everyone is equal and no one enjoys any privilege based on their existing positions and powers.
(2) A hypothetical society in which people agree upon principles of justice which are fair.
(3) A society in which principles of justice are not based on the existing positions and powers of the individuals.
(4) A society in which principles of justice are fair to all.
(5) A hypothetical society in which principles of justice are not based on the existing positions and powers of the individuals.
Solution:
Options 2 and 5 are eliminated because though the passage mentions a hypothetical situation in which ‘justice as fairness’ could be formulated, the society
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described/conceptualized in the passage is in no way ‘hypothetical’ as given in options 2 and 5. Option 1 is eliminated because ‘a just society’ is not a Utopia. Between options 3 and 4, the idea of fairness, which is casually mentioned in option 4, is fully explained in option 3 and is essential to answer the question, because the word ‘fair’ has a special and specific definition in the passage. Hence, option 3.
42. The original agreement or original position in the passage has been used by the author as:
(1) A hypothetical situation conceived to derive principles of justice which are not influenced by position, status and condition of individuals in the society.
(2) A hypothetical situation in which every individual is equal and no individual enjoys any privilege based on the existing positions and powers.
(3) A hypothetical situation to ensure fairness of agreements among individuals in society.
(4) An imagined situation in which principles of justice would have to be fair.
(5) An imagined situation in which fairness is the objective of the principles of justice to ensure that no individual enjoys any privilege based on the existing positions and powers.
Solution: The passage states: "In ‘justice as fairness’, the original position is not an actual historical state of affairs. It is understood as a purely hypothetical situation characterized so as to lead to a certain conception of justice. Among the essential features of this situation is that no one knows his place in society, his class position or social status, nor does anyone know his fortune in the distribution of natural assets and abilities, his intelligence, strength, and the like.” This makes option 1 correct and a mere repetition of what is stated in the passage. Options 4 and 5 are eliminated due to “would have to be fair” and “ensure” respectively. There is no data in the passage to indicate compulsion. Option 3 loses out similarly due to “ensure” Between options 1 and 2, option 1 resonates better with the ideas presented with “original position”. Hence, option 1.
43. Which of the following best illustrates the situation that is equivalent to choosing "the principles of justice" behind a "veil of ignorance"?
(1) The principles of justice are chosen by businessmen, who are marooned on an uninhabited island after a shipwreck, but have some possibility of returning.
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(2) The principles of justice are chosen by a group of school children whose capabilities are yet to develop.
(3) The principles of justice are chosen by businessmen, who are marooned on an uninhabited island after a shipwreck and have no possibility of returning.
(4) The principles of justice are chosen assuming that such principles will govern the lives of the rule makers only in their next birth if the rule makers agree that they will be born again.
(5) The principles of justice are chosen by potential immigrants who are unaware of the resources necessary to succeed in a foreign country.
Solution: The passage states the conditions termed as ‘veil of ignorance’ thus: “In ‘justice as fairness’, the original position …… is understood as a purely hypothetical situation characterized so as to lead to a certain conception of justice. Among the essential features of this situation is that no one knows his place in society, his class position or social status, nor does anyone know his fortune in the distribution of natural assets and abilities, his intelligence, strength, and the like. I shall even assume that the parties do not know their conceptions of the good or their special psychological propensities. The principles of justice are chosen behind a veil of ignorance.” Option 4 fulfills these conditions best. The rule makers in the options cannot know even their sex in the next birth – a clear case of veil of ignorance. Situations in all the other options exhibit some degree of knowledge or awareness of their position etc. The businessmen, school children, and immigrants have some degree of awareness of their existence. Hence, option 4.
44. Why, according to the passage, do principles of justice need to be based on an original agreement?
(1) Social institutions and laws can be considered fair only if they conform to principles of justice.
(2) Social institutions and laws can be fair only if they are consistent with the principles of justice as initially agreed upon.
(3) Social institutions and laws need to be fair in order to be just.
(4) Social institutions and laws evolve fairly only if they are consistent with the principles of justice as initially agreed upon.
(5) Social institutions and laws conform to the principles of justice as initially agreed upon.
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Solution: One may evaluate options 1, 2 and 5 as likely answers. Options 3 and 4 are quickly eliminated. Option 3 is eliminated because ‘fair in order to be just’ is vague does not relate to the ‘original agreement’ included in the question. Option 4 talks about the ‘evolution’ of social institutions which is completely new to the ideas presented in the passage. Between options 1, 2 and 5 option 2 is the best answer because options 1 and 5 are partial. Option 1 leaves out ‘original agreement’ which is required to answer the question, and option 5 leaves out the idea of ‘fairness’ which is the crux of the passage. Hence, option 2.
45. Which of the following situations best represents the idea of justice as fairness, as argued in the passage?
(1) All individuals are paid equally for the work they do.
(2) Everyone is assigned some work for his or her livelihood.
(3) All acts of theft are penalized equally.
(4) All children are provided free education in similar schools.
(5) All individuals are provided a fixed sum of money to take care of their health.
Solution: The idea of ‘justice as fairness” can be explained thus: From a hypothetical “initial position of equality” and “behind a veil of ignorance”, “a group of persons must decide once and for all what is to count among them as just and unjust.” The initial equality and veil of ignorance are crucial. From such a position what one can choose as fair is only option 4. The passage further states that “Since all are similarly situated and no one is able to design principles to favour his particular condition, the principles of justice are the result of a fair agreement or bargain. “ All other options would be considered unfair from a position of ‘no knowledge’ and the members are not “similarly situated”. If all children were to be given free education in similar schools, it immediately places them in similar situations. The initial position is now fair- Children may make use of their education (resources) differently, but will have to accept the later inequalities (that may develop) because the initial position was just and fair. Hence, option 4.
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Directions for Questions 46 to 50: The passage given below is followed by a set of five questions. Choose the most appropriate answer to each question. Our propensity to look out for regularities, and to impose laws upon nature, leads to the psychological phenomenon of dogmatic thinking or, more generally, dogmatic behaviour: we expect regularities everywhere and attempt to find them even where there are none; events which do not yield to these attempts we are inclined to treat as a kind of ‘background noise‘; and we stick to our expectations even when they are inadequate and we ought to accept defeat. This dogmatism is to some extent necessary. It is demanded by a situation which can only be dealt with by forcing our conjectures upon the world. Moreover, this dogmatism allows us to approach a good theory in stages, by way of approximations: if we accept defeat too easily, we may prevent ourselves from finding that we were very nearly right. It is clear that this dogmatic attitude, which makes us stick to our first impressions, is indicative of a strong belief; while a critical attitude, which is ready to modify its tenets, which admits doubt and demands tests, is indicative of a weaker belief. Now according to Hume‘s theory, and to the popular theory, the strength of a belief should be a product of repetition; thus it should always grow with experience, and always be greater in less primitive persons. But dogmatic thinking, an uncontrolled wish to impose regularities, a manifest pleasure in rites and in repetition as such, is characteristic of primitives and children; and increasing experience and maturity sometimes create an attitude of caution and criticism rather than of dogmatism. My logical criticism of Hume‘s psychological theory, and the considerations connected with it, may seem a little removed from the field of the philosophy of science. But the distinction between dogmatic and critical thinking, or the dogmatic and the critical attitude, brings us right back to our central problem. For the dogmatic attitude is clearly related to the tendency to verify our laws and schemata by seeking to apply them and to confirm them, even to the point of neglecting refutations, whereas the critical attitude is one of readiness to change them - to test them; to refute them; to falsify them, if possible. This suggests that we may identify the critical attitude with the scientific attitude, and the dogmatic attitude with the one which we have described as pseudo-scientific. It further suggests that genetically speaking the pseudo-scientific attitude is more primitive than, and prior to, the scientific attitude: that it is a pre-scientific attitude. And this primitivity or priority also has its logical aspect. For the critical attitude is not so much opposed to the dogmatic attitude as super-imposed upon it: criticism must be directed against existing and influential beliefs in need of critical revision - in other words, dogmatic beliefs. A critical attitude needs for its raw material, as it were, theories or beliefs which are held more or less dogmatically.
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Thus, science must begin with myths, and with the criticism of myths; neither with the collection of observations, nor with the invention of experiments, but with the critical discussion of myths, and of magical techniques and practices. The scientific tradition is distinguished from the pre-scientific tradition in having two layers. Like the latter, it passes on its theories; but it also passes on a critical attitude towards them. The theories are passed on, not as dogmas, but rather with the challenge to discuss them and improve upon them. The critical attitude, the tradition of free discussion of theories with the aim of discovering their weak spots so that they may be improved upon, is the attitude of reasonableness, of rationality. From the point of view here developed, all laws, all theories, remain essentially tentative, or conjectural, or hypothetical, even when we feel unable to doubt them any longer. Before a theory has been refuted we can never know in what way it may have to be modified.
46. In the context of science, according to the passage, the interaction of dogmatic beliefs and critical attitude can be best described as:
(1) A duel between two warriors in which one has to die.
(2) The effect of a chisel on a marble stone while making a sculpture.
(3) The feedstock (natural gas) in fertilizer industry being transformed into fertilizers.
(4) A predator killing its prey.
(5) The effect of fertilizers on a sapling.
Solution: The answer is derived from “For the critical attitude is not so much opposed to the dogmatic attitude as super-imposed upon it: criticism must be directed against existing and influential beliefs in need of critical revision - in other words, dogmatic beliefs. A critical attitude needs for its raw material, as it were, theories or beliefs which are held more or less dogmatically.” Based on this principle option 1 is eliminated there is neither raw material nor any critical revision in the example of warriors. Option 3 is eliminated because it talks about a transformation, whereas the passage only talks about a refinement. Options 4 and 5 talk about something ‘feeding’ or ‘growing’ on something else. Science does not ‘feed’ or ‘grow’ on dogma. Both are eliminated. Hence, option 2.
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47. According to the passage, the role of a dogmatic attitude or dogmatic behaviour in the development of science is
(1) critical and important, as, without it, initial hypotheses or conjectures can never be made.
(2) positive, as conjectures arising out of our dogmatic attitude become science.
(3) negative, as it leads to pseudo-science.
(4) neutral, as the development of science is essentially because of our critical attitude.
(5) inferior to critical attitude, as a critical attitude leads to the attitude of reasonableness and rationality.
Solution: The writer believes that dogma is important, because dogmas are refined into science with time. With this comprehension one is able to eliminate options 3, 4 and 5. Between options 1 and 2, option 2 erroneously states that dogmas become science whereas dogma merely provide the substance or the hypothesis that later on get refined into science. Hence option 2 is eliminated. Hence, option 1.
48. Dogmatic behaviour, in this passage, has been associated with primitives and children. Which of the following best describes the reason why the author compares primitives with children?
(1) Primitives are people who are not educated, and hence can be compared with children, who have not yet been through school.
(2) Primitives are people who, though not modern, are as innocent as children.
(3) Primitives are people without a critical attitude, just as children are.
(4) Primitives are people in the early stages of human evolution; similarly, children are in the early stages of their lives.
(5) Primitives are people who are not civilized enough, just as children are not.
Solution: The answer is available with the analysis of this part of the passage: “But dogmatic thinking, an uncontrolled wish to impose regularities, a manifest pleasure in rites and in repetition as such, is characteristic of primitives and children; and increasing experience and maturity sometimes create an attitude of caution and criticism rather than of dogmatism.” Option 1 is eliminated because ‘education’ is not the reason that the writer associates dogma with primitives and children. Option 2 is eliminated for ‘innocence’.
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Option 3 is contrary to the italicized part of the sentence. Option 5 is eliminated for ‘civilization’. Hence, option 4.
49. Which of the following statements best supports the argument in the passage that a critical attitude leads to a weaker belief than a dogmatic attitude does?
(1) A critical attitude implies endless questioning, and, therefore, it cannot lead to strong beliefs.
(2) A critical attitude, by definition, is centred on an analysis of anomalies and “noise”.
(3) A critical attitude leads to questioning everything, and in the process generates “noise” without any conviction.
(4) A critical attitude is antithetical to conviction, which is required for strong beliefs.
(5) A critical attitude leads to questioning and to tentative hypotheses.
Solution: The last paragraph of the passage completely supports option 5. The question asks you to best support “critical attitude leads to a weaker belief”. Option 5 supports this by stating that critical attitude leads to questioning and hypothesis – these weaken beliefs. Option 1 states ‘cannot lead to strong beliefs’. As we are in fact, asked to support this; it is not the best option. Options 2 and 3 are eliminated for the ‘noise’, which does not suffice to support the notion. Option 4 states what is required for ‘strong beliefs’ and does not support the thesis, 'critical attitude leads to a weaker belief'. Hence, option 5.
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50. According to the passage, which of the following statements best describes the difference between science and pseudo-science?
(1) Scientific theories or hypothesis are tentatively true whereas pseudo-sciences are always true.
(2) Scientific laws and theories are permanent and immutable whereas pseudo-sciences are contingent on the prevalent mode of thinking in a society.
(3) Science always allows the possibility of rejecting a theory or hypothesis, whereas pseudo-sciences seek to validate their ideas or theories.
(4) Science focuses on anomalies and exceptions so that fundamental truths can be uncovered, whereas pseudo-sciences focus mainly on general truths.
(5) Science progresses by collection of observations or by experimentation, whereas pseudo-sciences do not worry about observations and experiments.
Solution: From paragraph 3: “For the dogmatic attitudes clearly related to the tendency to verify our laws and schemata by seeking to apply them and to confirm them, even to the point of neglecting refutations, whereas the critical attitude is one of readiness to change them - to test them; to refute them; to falsify them, if possible. This suggests that we may identify the critical attitude with the scientific attitude, and the dogmatic attitude with the one which we have described as pseudo-scientific.” Only option 3 best answers about the difference between science and pseudo-science. Hence, option 3.
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Section III
51. If x = −0.5, then which of the following has the smallest value?
(1)
(2)
(3)
(4)
(5)
Solution: All the others are positive. Hence, option 2.
52. Which among 2 1/2, 3 1/3, 4 1/4 , 6 1/6 and 12 1/12 is the largest ?
(1) 21/2
(2) 31/3
(3) 41/4
(4) 61/6
(5) 121/12
Solution: 21/2 = 26/12 = (26)1/12 = 641/12 Similarly, 31/3 = 811/12 , 41/4 = 641/12, 61/6 = 361/12 Now, all the powers are equal. Thus the option with the largest base is the largest. 31/3 is the largest. Hence, option 2.
53. (1) 3/8 (2) 27/8 (3) 3/4 (4) 27/4 (5) 1/4
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Solution: Hence, option 1.
54. The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
(1) remain the same
(2) decrease by 13.64%
(3) decrease by 15%
(4) decrease by 18.75%
(5) decrease by 30%
Solution: Let the original length, breadth and height of the room be 3x, 2x and x respectively. ∴ The new length, breadth and height are 6x, x and x/2 respectively. Area of four walls = (2 × length × height) + (2 × breadth × height) Original area of four walls = 6x2 + 4x2 = 10x2 New area of four walls = 6x2 + x2 = 7x2 ∴ Area of wall decreases by [(10x2 − 7x2)/10x2] × 100 = 30% Hence, option 5.
55.
(1)2/495 (2) 2/477 (3) 12/55 (4) 1/1485 (5)1/2970
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Solution: . . .
Hence, option 1.
56. A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?
(1) 3
(2) 4
(3) 5
(4) 6
(5) 7
Solution: Let there be n rows and a students in the first row. ∴ Number of students in the second row = a + 3 ∴ Number of students in the third row = a + 6 and so on. ∴ The number of students in each row forms an arithmetic progression with common difference = 3 The total number of students = The sum of all terms in the arithmetic progression
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Now consider options. 1. n = 3 ∴ a = 207 2. n = 4 ∴ a = 153 3. n = 5 ∴ a = 120 4. n = 6 5. n = 7 ∴ a = 81 As a is an integer, only n = 6 is not possible. Hence, option 4.
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57. What are the values of x and y that satisfy both the equations?
2 0.7x × 3−1. 25y = 8√6/27 40.3x × 90.2y = 8 × (81)1/5
(1) x = 2, y = 5
(2) x = 2.5, y = 6
(3) x = 3, y = 5
(4) x = 3, y = 4
(5) x = 5, y = 2
Solution: 20.7x × 3−1.25y = 27/2 × 3−5/2 = 20.7× 5 × 3−1.25 × 2 ∴ x = 5 and y = 2 These values of x and y satisfy the second equation also. Hence, option 5.
58. The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:
(1) 7
(2) 13
(3) 14
(4) 18
(5) 20
Solution: 2x + y = 40 ∴ y = 40 – 2x x and y are positive integers and x ≤ y If x = 1, y = 38 x = 2, y = 36 x = 3, y = 34 . . x = 12, y =16 x = 13, y = 14 x = 14, y = 12
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∴ For x > 13, y ≤ x ∴ There are 13 solutions to the given equation. Hence, option 2.
59. A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below:
Only September: 18; September but not August: 23; September and July: 8; September: 28; July: 48; July and August: 10; None of the three months: 24. What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?
(1) 7
(2) 9
(3) 12
(4) 14
(5) 17
Solution:
100 – 24 = 76 had read at least one issue. If x people read all the three issues, then (8 – x) people read only the September and July issues.
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23 people read the September issue but not the August issue. ∴ 18 + 8 – x = 23 ∴ x = 3 As 28 people read the September issue, [28 – (8 – 3) – 3 – 18] = 2 people read only the August and September issues. As 10 people read the July and August issues, 10 – 3 = 7 people read only the July and August issues. ∴ The number of people who have read exactly two consecutive issues = 7 + 2 = 9 Hence, option 2.
60. The sum of four consecutive two digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?
(1) 21
(2) 25
(3) 41
(4) 67
(5) 73
Solution: The four consecutive two-digit odd numbers will have (1, 3, 5, 7) or (3, 5, 7, 9) or (5, 7, 9, 1) or (7, 9, 1, 3) as units digits. As the sum divided by 10 yields a perfect square, the sum is a multiple of 10. ∴ The units digits have to be (7, 9, 1, 3). Thus the four numbers will be (10x + 7), (10x + 9), (10x + 11) and (10x + 13), where 0 < x < 9 (as each of these numbers is a two digit number) Sum of these numbers = 40x + 40 = 40(x + 1) Now, 40(x + 1)/10 = 4(x + 1) is a perfect square As 4 is a perfect square (x + 1) is some perfect square < 10 x + 1 = 4, x = 3, and the four numbers are 37, 39, 41 and 43 x + 1 = 9, x = 8, and the four numbers are 87, 89, 91 and 93 Hence, option 3.
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61. The graph of y – x against y + x is as shown below.
(All graphs in this question are drawn to scale and the same scale has been used on each axis). Then, which of the options given shows the graph of y against x. (1)
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(2)
(3)
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(4)
(5)
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Solution: All the given graphs are drawn to the same scale. We can see that the line makes an angle which is more than 45° with the horizontal axis. ∴ The slope of the line is greater than 1. Let the slope be k. ∴ (y – x) = k(y + x) {∵ k > 1} ∴ y – x = ky + kx ∴ The graph of y against x will be such that when x is positive, y is negative and |x| < |y|, except at (0, 0). Hence, option 4.
62. Consider the set S = {1, 2, 3, …, 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?
(1) 3
(2) 4
(3) 6
(4) 7
(5) 8
Solution: Let there be n terms (n ≥ 3) in the arithmetic progression having 1 as the first term and 1000 as the last. Let d be the common difference. 1000 = 1 + (n – 1) × d ∴ 999 = (n – 1) × d ... (i) ∴ Factors of 999 are 1, 3, 9, 27, 37, 111, 333 and 999
Substituting in equation (i)
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If d = 1, n = 1000 If d = 3, n = 334 If d = 9, n = 112 If d = 27, n = 38 If d = 37, n = 28 If d = 111, n = 10 If d = 333, n = 4 If d = 999, n = 2, which is not possible as n > 2 ∴ 7 arithmetic progressions can be formed. Hence, option 4.
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Answer Questions 63 and 64 on the basis of the information given below: A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminum of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.
63. The proportion of the sheet area that remains after punching is:
(1)
(2)
(3)
(4)
(5)
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Solution:
Let PQRS be the square sheet and let the hole have centre O. As P lies on the circumference of the circle and as m ∠APC = 90°, AC is a diameter. ∵ BP is a diameter, m ∠PAB = m ∠BCP = 90° ∵ BP = AC, ABCP is a square. ∴ m∠POC = 90° and OP = OC = 1 unit The area of part of the circle falling outside the square sheet = 2 × (Area of sector POC – Area of Δ OPC) Area of part of hole on sheet = Area of hole − Area of part of the circle falling outside the square sheet
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Part of square remaining after punching = Area of square − Area of part of hole on sheet Hence, option 2.
64. Find the area of the part of the circle (round punch) falling outside the square sheet.
(1)
(2)
(3)
(4)
(5)
Solution: We have calculated this value while solving the previous question. Hence, option 4.
65.
(1) –8 ≤ x ≤ 1
(2) –1 ≤ x ≤ 8
(3) 1 < x < 8
(4) 1 ≤ x ≤ 8
(5) –8 ≤ x ≤ 8
Solution: Then equation (i) becomes y2 + y – 2 ≤ 0 (y + 2)(y – 1) ≤ 0
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–2 ≤ y ≤ 1 –8 ≤ x ≤ 1 Hence, option 1.
66. Let f(x) = max (2x + 1, 3 − 4x), where x is any real number. Then the minimum possible value of (x) is:
(1) 1/3
(2) 1/2
(3) 2/3
(4) 4/3
(5) 5/3
Solution:
Let the two lines represent the equations y = 2x + 1 and y = 3 – 4x respectively. The greater value between 2x + 1 and 3 – 4x is greater than 5/3, when x < 1/3 or x > 1/3.
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The greater value is minimum at x = 1/3 and this value is 5/3. Hence, option 5. Note: In general, the minimum value of the function f(x) = max (ax + b, cx + d) occurs when ax + b = cx + d Answer Questions 67 and 68 on the basis of the information below: An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.
67. What is the weight of Praja‘s luggage?
(1) 20 kg
(2) 25 kg
(3) 30 kg
(4) 35 kg
(5) 40 kg
Solution: Let f kg be the free luggage allowance and let Raja and Praja have r kg and p kg excess luggage respectively. Let x be the fixed rate per kg for excess luggage. ∴ 2f + r + p = 60 ... (i) rx = 1200 ... (ii) px = 2400 ... (iii) (60 – f)x = 5400 ... (iv) From (ii) and (iii), p = 2r ... (v)
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Substituting in (i), 2f + 3r = 60 ∴ f = 30 – 3r/2 ... (vi) Substituting in (iv), (60 – 30 + 3r/2)x = 5400 ∴ 30x + 3rx/2 = 5400 From (ii), rx = 1200 ∴ 30x = 3600 ∴ x = 120 ∴ r = 10, p = 20 and f = 15 Hence, option 4.
68. What is the free luggage allowance?
(1) 10 kg
(2) 15 kg
(3) 20 kg
(4) 25 kg
(5) 30 kg
Solution: f = 15 kg Hence, option 2.
69. Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?
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(1) 3
(2) 3.5
(3) 4
(4) 4.5
(5) 5
Solution: Arun has travelled 60 km when Barun starts. Barun overtakes Arun in 60/(40 – 30) = 6 hrs In this time, Barun travels 6 × 40 = 240 km from the starting point. Kiranmala overtakes Arun at the same point. Kiranmala takes 240/60 = 4 hrs to reach there. Arun takes 240/30 = 8 hrs to reach there. ∴ Kiranmala starts 8 – 4 = 4 hrs after Arun. Hence, option 3.
70. When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?
(1) 5
(2) 6
(3) 7
(4) 8
(5) 10
Solution: Let 10x + y be a two digit number, where x and y are positive single digit integers and x > 0. Its reverse = 10y + x Now, 10y + x – 10x – y = 18 ∴ 9(y – x) = 18 ∴ y – x = 2 Thus y and x can be (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8) and (7, 9) ∴ Other than 13, there are 6 such numbers. Hence, option 2.
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71. A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semicircle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semicircle (in sq. cm.) will be:
(1) 32π
(2) 50π
(3) 40.5π
(4) 81π
(5) undeterminable
Solution:
Let CB = x cm Δ ACD and Δ ADB are similar triangles. ∴ AD/AB = AC/AD ∴ AD2 = AC × AB ∴(AC2 + CD2) = 2 × (2 + x) ∴ 40 = 2 × (2 + x) ∴ x = 18 ∴ Diameter AB = 20 cm ∴ Radius = 10 cm ∴ Area = 50π sq. cm. Hence, option 2.
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72. There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?
(1) 144
(2) 180
(3) 192
(4) 360
(5) 716
Solution: Task 2 can be assigned in 2 ways (either to person 3 or person 4). Task 1 can then be assigned in 3 ways (persons 3 or 4, 5 and 6) The remaining 4 tasks can be assigned to the remaining 4 persons in 4! = 24 ways ∴ The assignment can be done in 24 × 2 × 3 = 144 ways Hence, option 1.
73. The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:
(1) 101 : 88
(2) 87 : 100
(3) 110 : 111
(4) 85 : 98
(5) 97 : 84
Solution: Consider options. As the number of employees is prime we can add the numerator and denominator of ratios directly to find the number of employees. 1. Number of employees = 101 + 88 = 189 Number of employees = 189, which is not a prime number. ∴ Option 1 is eliminated. 2. Number of employees = 87 + 100 = 187 Number of employees = 187, which is not a prime number. ∴ Option 2 is eliminated.
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3. Number of employees = 110 + 111 = 221 Number of employees = 221, which is not a prime number. ∴ Option 3 is eliminated. 4. Number of employees = 85 + 98 = 183 Number of employees = 183, which is not a prime number. ∴ Option 4 is eliminated. 5. Number of employees = 97 + 84 = 181 Number of employees = 181, which is a prime number. ∴ The ratio of employees = 97:84 Hence, option 5.
74.
then which of the following pairs of values for (a, b) is not possible?
(1)
(2) 1, 1
(3) 0.4, 2.5
(4)
(5) 2, 2
Solution:
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Only option 5 does not satisfy this. Hence, option 5.
75. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?
(1) 75
(2) 90
(3) 120
(4) 135
(5) 150
Solution:
BP = PC = BC m ∠BPC = m ∠PCB = m ∠PBC = 60° Also, PC = CD = BP = AB
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Δ ABP and Δ PCD are isosceles triangles. m ∠ABP = m ∠PCD = 90 – 60 = 30° ∴ m ∠APB = m ∠DPC = (180 – 30)/2 = 75° ∴ m ∠APD = 360 – (m ∠APB + m ∠DPC + m ∠BPC) = 360 – (75 + 75 + 60) = 150° Hence, option 5.



CAT 2005

Examination duration: 2 hours SECTION I Sub-section I-A: Number of Questions = 10 Note: Questions 1 to 10 carry one mark each. Directions for Questions 1 to 5: Answer the questions independently of each other.
1. If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of
(1) 0
(2) 1
(3) 69
(4) 35
2. A chemical plant has four tanks (A, B, C, and D), each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows:
From A to B @ 20 litres/minute From C to A @ 90 litres/minute From A to D @ 10 litres/minute From C to D @ 50 litres/minute From B to C @ 100 litres/minute From D to B @ 110 litres/minute Which tank gets emptied first and how long does it take (in minutes) to get empty after pumping starts?
(1) A, 16.66
(2) C, 20
(3) D, 20
(4) D, 25
3. Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is
(1)
(2)
(3)
(4)
4. A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the
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rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?
(1) 3.88%
(2) 4.22%
(3) 4.44%
(4) 4.72%
5. In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is
(1) 200
(2) 216
(3) 235
(4) 256
Directions for Questions 6 and 7: Answer the questions on the basis of the information given below. Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.
6. At what time do Ram and Shyam first meet each other?
(1) 10:00 a.m.
(2) 10:10 a.m.
(3) 10:20 a.m.
(4) 10:30 a.m.
7. At what time does Shyam overtake Ram?
(1) 10:20 a.m.
(2) 10:30 a.m.
(3) 10:40 a.m.
(4) 10:50 a.m.
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Directions for Questions 8 to 10: Answer the questions independently of each other.
8.
(1) 0 < R ≤ 0.1
(2) 0.1 < R ≤ 0.5
(3) 0.5 < R ≤ 1.0
(4) R > 1.0
9. What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?
(1) 1 or 7
(2) 2 or 14
(3) 3 or 21
(4) 4 or 28
10. For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?
x² – y² = 0 (x – k)² + y² = 1
(1) 2
(2) 0
(3)
(4)
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Sub-section I-B: Number of Questions = 20 Note: Questions 11 to 30 carry two marks each. Directions for Questions 11 to 30: Answer the questions independently of each other.
11. Let n! = 1 × 2 × 3 × ... × n for integer n ≥ 1. If p = 1! + (2 × 2!) + (3 × 3!) + … + (10 × 10!), then p + 2 when divided by 11! leaves a remainder of
(1) 10
(2) 0
(3) 7
(4) 1
12. Consider a triangle drawn on the X-Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is
(1) 780
(2) 800
(3) 820
(4) 741
13. The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B > A and B − A is perfectly divisible by 7, then which of the following is necessarily true?
(1) 100 < A < 299
(2) 106 < A < 305
(3) 112 < A < 311
(4) 118 < A < 317
14. If a1 = 1 and an + 1 – 3an + 2 = 4n for every positive integer n, then a100 equals
(1) 399 – 200
(2) 399 + 200
(3) 3100 – 200
(4) 3100 + 200
15. Let S be the set of five digit numbers formed by the digits 1, 2, 3, 4 and 5, using each digit exactly once such that exactly two odd positions are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in S?
(1) 228
(2) 216
(3) 294
(4) 192
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16. The rightmost non-zero digit of the number 302720 is
(1) 1
(2) 3
(3) 7
(4) 9
17. Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is
(1)
(2) 1 + π
(3)
(4) 5
18. If x ≥ y and y > 1, then the value of the expression
(1) -1
(2) -0.5
(3) 0
(4) 1
19. For a positive integer n, let Pn denote the product of the digits of n, and Sn denote the sum of the digits of n. The number of integers between 10 and 1000 for which Pn + Sn = n is
(1) 81
(2) 16
(3) 18
(4) 9
20. Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is
(1) 4
(2) 5
(3) 6
(4) 7
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21. In the X-Y plane, the area of the region bounded by the graph of |x + y| + |x – y| = 4 is
(1) 8
(2) 12
(3) 16
(4) 20
22. In the following figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that AE:EB = 1:2, and DF is perpendicular to MN such that NL:LM = 1:2. The length of DH in cm is
(1)
(2)
(3)
(4)
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23. Consider the triangle ABC shown in the following figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and ∠BCD = ∠BAC. What is the ratio of the perimeter of the triangle ADC to that of the triangle BDC?
(1) 7/9
(2) 8/9
(3) 6/9
(4) 5/9
24. P, Q, S, and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR?
(1)
(2)
(3)
(4)
25. Let S be a set of positive integers such that every element n of S satisfies the conditions
a) 1000 ≤ n ≤ 1200 b) every digit in n is odd Then how many elements of S are divisible by 3?
(1) 9
(2) 10
(3) 11
(4) 12
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26.
(1) 3
(2)
(3)
(4)
27. Let g(x) be a function such that g(x + 1) + g(x – l) = g(x) for every real x. Then for what value of p is the relation g(x + p) = g(x) necessarily true for every real x?
(1) 5
(2) 3
(3) 2
(4) 6
28. A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs. 250 and Rs. 300 per day respectively. In addition, a male operator gets Rs. 15 per call he answers and a female operator gets Rs. 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?
(1) 15
(2) 14
(3) 12
(4) 10
29. Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?
(1) 5
(2) 10
(3) 9
(4) 15
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30. A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is
(1) 10
(2) 12
(3) 14
(4) 16
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SECTION II Sub-section II-A: Number of Questions =10 Note: Questions 31 to 40 carry one mark each. Directions for Questions 31 to 34: The passage given below is followed by a set of four questions. Choose the best answer to each question. A game of strategy, as currently conceived in game theory, is a situation in which two or more "players" make choices among available alternatives (moves). The totality of choices determines the outcomes of the game, and it is assumed that the rank order of preferences for the outcomes is different for different players. Thus the "interests" of the players are generally in conflict. Whether these interests are diametrically opposed or only partially opposed depends on the type of game. Psychologically, most interesting situations arise when the interests of the players are partly coincident and partly opposed, because then one can postulate not only a conflict among the players but also inner conflicts within the players. Each is torn between a tendency to cooperate, so as to promote the common interests, and a tendency to compete, so as to enhance his own individual interests. Internal conflicts are always psychologically interesting. What we vaguely call "interesting" psychology is in very great measure the psychology of inner conflict. Inner conflict is also held to be an important component of serious literature as distinguished from less serious genres. The classical tragedy, as well as the serious novel, reveals the inner conflict of central figures. The superficial adventure story, on the other hand, depicts only external conflict; that is, the threats to the person with whom the reader (or viewer) identifies stem in these stories exclusively from external obstacles and from the adversaries who create them. On the most primitive level this sort of external conflict is psychologically empty. In the fisticuffs between the protagonists of good and evil, no psychological problems are involved or, at any rate, none are depicted in juvenile representations of conflict.
The detective story, the "adult" analogue of a juvenile adventure tale, has at times been described as a glorification of intellectualized conflict. However, a great deal of the interest in the plots of these stories is sustained by withholding the unraveling of a solution to a problem. The effort of solving the problem is in itself not a conflict if the adversary (the unknown criminal) remains passive, like Nature, whose secrets the scientist supposedly unravels by deduction. If the adversary actively puts obstacles in the detective's path toward the solution, there is genuine conflict. But the conflict is psychologically interesting only to the extent that it contains irrational components such as a tactical error on the criminal's part or the detective's insight into some psychological quirk of the criminal or something of this sort. Conflict conducted in a
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perfectly rational manner is psychologically no more interesting than a standard Western. For example, Tic-tac-toe, played perfectly by both players, is completely devoid of psychological interest. Chess may be psychologically interesting but only to the extent that it is played not quite rationally. Played completely rationally, chess would not be different from Tic-tac-toe. In short, a pure conflict of interest (what is called a zero-sum game) although it offers a wealth of interesting conceptual problems, is not interesting psychologically, except to the extent that its conduct departs from rational norms.
31. According to the passage, internal conflicts are psychologically more interesting than external conflicts because
(1) internal conflicts, rather than external conflicts, form an important component of serious literature as distinguished from less serious genres.
(2) only juveniles or very few "adults" actually experience external conflict, while internal conflict is more widely prevalent in society.
(3) in situations of internal conflict, individuals experience a dilemma in resolving their own preferences for different outcomes.
(4) there are no threats to the reader (or viewer) in case of external conflicts.
32. Which, according to the author, would qualify as interesting psychology?
(1) A statistician's dilemma over choosing the best method to solve an optimisation problem.
(2) A chess player's predicament over adopting a defensive strategy against an aggressive opponent.
(3) A mountaineer's choice of the best path to Mt. Everest from the base camp.
(4) A finance manager's quandary over the best way of raising money from the market.
33. According to the passage, which of the following options about the application of game theory to a conflict-of-interest situation is true?
(1) Assuming that the rank order of preferences for options is different for different players.
(2) Accepting that the interests of different players are often in conflict.
(3) Not assuming that the interests are in complete disagreement.
(4) All of the above.
34. The problem solving process of a scientist is different from that of a detective because
(1) scientists study inanimate objects, while detectives deal with living criminals or law offenders.
(2) scientists study known objects, while detectives have to deal with unknown criminals or law offenders.
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(3) Scientists study phenomena that are not actively altered, while detectives deal with phenomena that have been deliberately influenced to mislead.
(4) Scientists study psychologically interesting phenomena, while detectives deal with “adult” analogues of juvenile adventure tales.
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 from among the given choices to construct a coherent paragraph.
35.
A. Similarly, turning to caste, even though being lower caste is undoubtedly a separate cause of disparity, its impact is all the greater when the lower-caste families also happen to be poor.
B. Belonging to a privileged class can help a woman to overcome many barriers that obstruct women from less thriving classes.
C. It is the interactive presence of these two kinds of deprivation - being low class and being female - that massively impoverishes women from the less privileged classes.
D. A congruence of class deprivation and gender discrimination can blight the lives of poorer women very severely.
E. Gender is certainly a contributor to societal inequality, but it does not act independently of class.
(1) EABDC
(2) EBDCA
(3) DAEBC
(4) BECDA
36.
A. When identity is thus ‘defined by contrast’, divergence with the West becomes central.
B. Indian religious literature such as the Bhagavad Gita or the Tantric texts, which are identified as differing from secular writings seen as ‘western’, elicits much greater interest in the West than do other Indian writings, including India's long history of heterodoxy.
C. There is a similar neglect of Indian writing on non-religious subjects, from mathematics, epistemology and natural science to economics and linguistics.
D. Through selective emphasis that point up differences with the West, other civilizations can, in this way, be redefined in alien terms, which can be exotic and charming, or else bizarre and terrifying, or simply strange and engaging.
E. The exception is the Kamasutra in which western readers have managed to cultivate an interest.
(1) BDACE
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(2) DEABC
(3) BDECA
(4) BCEDA
37.
A. This is now orthodoxy to which I subscribe - up to a point.
B. It emerged from the mathematics of chance and statistics.
C. Therefore the risk is measurable and manageable.
D. The fundamental concept: Prices are not predictable, but the mathematical laws of chance can describe their fluctuations.
E. This is how what business schools now call modern finance was born.
(1) ADCBE
(2) EBDCA
(3) ABDCE
(4) DCBEA
Directions for Questions 38 to 40: In each question, the word at the top is used in four different ways, numbered 1 to 4. Choose the option in which the usage of the word is incorrect or inappropriate.
38. NEAR
(1) I got there just after you left – a near miss!
(2) She and her near friend left early.
(3) The war led to a near doubling of prices.
(4) They came near to tears seeing the plight of the victims.
39. HAND
(1) I have my hand full, I cannot do it today.
(2) The minister visited the jail to see the breach at first hand.
(3) The situation is getting out of hand here.
(4) When the roof of my house was blown away, he was willing to lend me a hand.
40. FOR
(1) He has a great eye for detail.
(2) We are waiting for the day.
(3) I can’t bear for her to be angry.
(4) It couldn’t be done for ever.
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Sub-section II–B: Number of Questions = 20 Note: Questions 41 to 60 carry two marks each. Directions for Questions 41 to 48: Each of the two passages given below is followed by a set of four questions. Choose the best answer to each question. PASSAGE I Crinoline and croquet are out. As yet, no political activists have thrown themselves in front of the royal horse on Derby Day. Even so, some historians can spot the parallels. It is a time of rapid technological change. It is a period when the dominance of the world's superpower is coming under threat. It is an epoch when prosperity masks underlying economic strain. And, crucially, it is a time when policy-makers are confident that all is for the best in the best of all possible worlds. Welcome to the Edwardian Summer of the second age of globalisation. Spare a moment to take stock of what's been happening in the past few months. Let's start with the oil price, which has rocketed to more than $65 a barrel, more than double its level 18 months ago. The accepted wisdom is that we shouldn't worry our little heads about that, because the incentives are there for business to build new production and refining capacity, which will effortlessly bring demand and supply back into balance and bring crude prices back to $25 a barrel. As Tommy Cooper used to say, 'just like that'. Then there is the result of the French referendum on the European Constitution, seen as thick-headed luddites railing vainly against the modern world. What the French needed to realise, the argument went, was that there was no alternative to the reforms that would make the country more flexible, more competitive, more dynamic. Just the sort of reforms that allowed Gate Gourmet to sack hundreds of its staff at Heathrow after the sort of ultimatum that used to be handed out by Victorian mill owners. An alternative way of looking at the French "non" is that our neighbours translate "flexibility" as "you're fired". Finally, take a squint at the United States. Just like Britain a century ago, a period of unquestioned superiority is drawing to a close. China is still a long way from matching America's wealth, but it is growing at a stupendous rate and economic strength brings geopolitical clout. Already, there is evidence of a new scramble for Africa as Washington and Beijing compete for oil stocks. Moreover, beneath the surface of the US economy, all is not well. Growth looks healthy enough, but the competition from China and elsewhere has meant the world's biggest economy now imports far more than it exports. The US is living beyond its means, but in this time of studied complacency a current account deficit worth 6 percent of gross domestic product is seen as a sign of strength, not weakness.
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In this new Edwardian summer, comfort is taken from the fact that dearer oil has not had the savage inflationary consequences of 1973-74, when a fourfold increase in the cost of crude brought an abrupt end to a postwar boom that had gone on uninterrupted for a quarter of a century. True, the cost of living has been affected by higher transport costs, but we are talking of inflation at 2.3 per cent and not 27 per cent. Yet the idea that higher oil prices are of little consequence is fanciful. If people are paying more to fill up their cars it leaves them with less to spend on everything else, but there is a reluctance to consume less. In the 1970s unions were strong and able to negotiate large, compensatory pay deals that served to intensify inflationary pressure. In 2005, that avenue is pretty much closed off, but the abolition of all the controls on credit that existed in the 1970s means that households are invited to borrow more rather than consume less. The knock-on effects of higher oil prices are thus felt in different ways - through high levels of indebtedness, in inflated asset prices, and in balance of payments deficits. There are those who point out, rightly, that modern industrial capitalism has proved mightily resilient these past 250 years, and that a sign of the enduring strength of the system has been the way it apparently shrugged off everything - a stock market crash, 9/11, rising oil prices - that have been thrown at it in the half decade since the millennium. Even so, there are at least three reasons for concern. First, we have been here before. In terms of political economy, the first era of globalisation mirrored our own. There was a belief in unfettered capital flows, in free trade, and in the power of the market. It was a time of massive income inequality and unprecedented migration. Eventually, though, there was a backlash, manifested in a struggle between free traders and protectionists, and in rising labour militancy. Second, the world is traditionally at its most fragile at times when the global balance of power is in flux. By the end of the nineteenth century, Britain's role as the hegemonic power was being challenged by the rise of the United States, Germany, and Japan while the Ottoman and Hapsburg empires were clearly in rapid decline, Looking ahead from 2005, it is clear that over the next two or three decades, both China and India - which together account for half the world's population - will flex their muscles. Finally, there is the question of what rising oil prices tell us. The emergence of China and India means global demand for crude is likely to remain high at a time when experts say production is about to top out. If supply constraints start to bite, any declines in the price are likely to be short-term cyclical affairs punctuating a long upward trend.
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41. By the expression 'Edwardian Summer', the author refers to a period in which there is
(1) unparalleled luxury and opulence.
(2) a sense of complacency among people because of all-round prosperity.
(3) a culmination of all-round economic prosperity.
(4) an imminent danger lurking behind economic prosperity.
42. What, according to the author, has resulted in a widespread belief in the resilience of modern capitalism?
(1) Growth in the economies of Western countries despite shocks in the form of increase in levels of indebtedness and inflated asset prices.
(2) Increase in the prosperity of Western countries and China despite rising oil prices.
(3) Continued growth of Western economies despite a rise in terrorism, an increase in oil prices and other similar shocks.
(4) The success of continued reforms aimed at making Western economies more dynamic, competitive and efficient.
43. Which of the following best represents the key argument made by the author?
(1) The rise in oil prices, the flux in the global balance of power and historical precedents should make us question our belief that the global economic prosperity would continue.
(2) The belief that modern industrial capitalism is highly resilient and capable of overcoming shocks will be belied soon.
(3) Widespread prosperity leads to neglect of early signs of underlying economic weakness, manifested in higher oil prices and a flux in the global balance of power.
(4) A crisis is imminent in the West given the growth of countries like China and India and the increase in oil prices.
44. What can be inferred about the author's view when he states, 'As Tommy Cooper used to say "just like that"'?
(1) Industry has incentive to build new production and refining capacity and therefore oil prices would reduce.
(2) There would be a correction in the price levels of oil once new production capacity is added.
(3) The decline in oil prices is likely to be short-term in nature.
(4) It is not necessary that oil prices would go down to earlier levels.
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PASSAGE II While complex in the extreme, Derrida's work has proven to be a particularly influential approach to the analysis of the ways in which language structures our understanding of ourselves and the world we inhabit, an approach he termed deconstruction. In its simplest formulation, deconstruction can be taken to refer to a methodological strategy which seeks to uncover layers of hidden meaning in a text that have been denied or suppressed. The term 'text', in this respect, does not refer simply to a written form of communication, however. Rather, texts are something we all produce and reproduce constantly in our everyday social relations, be they spoken, written or embedded in the construction of material artifacts. At the heart of Derrida's deconstructive approach is his critique of what he perceives to be the totalitarian impulse of the Enlightenment pursuit to bring all that exists in the world under the domain of a representative language, a pursuit he refers to as logocentrism. Logocentrism is the search for a rational language that is able to know and represent the world and all its aspects perfectly and accurately. Its totalitarian dimension, for Derrida at least, lies primarily in its tendency to marginalize or dismiss all that does not neatly comply with its particular linguistic representations, a tendency that, throughout history, has all too frequently been manifested in the form of authoritarian institutions. Thus logocentrism has, in its search for the truth of absolute representation, subsumed difference and oppressed that which it designates as its alien 'other'. For Derrida, western civilization has been built upon such a systematic assault on alien cultures and ways of life, typically in the name of reason and progress. In response to logocentrism, deconstruction posits the idea that the mechanism by which this process of marginalization and the ordering of truth occurs is through establishing systems of binary opposition. Oppositional linguistic dualisms, such as rational/irrational, culture/nature and good/bad are not, however, construed as equal partners as they are in, say, the semiological structuralism of Saussure. Rather, they exist, for Derrida, in a series of hierarchical relationships with the first term normally occupying a superior position. Derrida defines the relationship between such oppositional terms using the neologism différance. This refers to the realization that in any statement, oppositional terms differ from each other (for instance, the difference between rationality and irrationality is constructed through oppositional usage), and at the same time, a hierarchical relationship is maintained by the deference of one term to the other (in the positing of rationality over irrationality, for instance). It is this latter point which is perhaps the key to understanding Derrida's approach to deconstruction,
For the fact that at any given time one term must defer to its oppositional 'other', means that the two terms are constantly in a state of interdependence. The presence of one is dependent upon the absence or 'absent-presence' of the 'other', such as in the case of good and evil, whereby to understand the nature of one, we must constantly relate it to the absent term in order to grasp its meaning. That is, to do good, we must understand that our act is not evil for without that comparison the term becomes meaningless. Put
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simply, deconstruction represents an attempt to demonstrate the absent-presence of this oppositional 'other', to show that what we say or write is in itself not expressive simply of what is present, but also of what is absent. Thus, deconstruction seeks to reveal the interdependence of apparently dichotomous terms and their meanings relative to their textual context; that is, within the linguistic power relations which structure dichotomous terms hierarchically. In Derrida's own words, a deconstructive reading "must always aim at a certain relationship, unperceived by the writer, between what he commands and what he does not command of the patterns of a language that he uses. . . .[It] attempts to make the not-seen accessible to sight." Meaning, then, is never fixed or stable, whatever the intention of the author of a text. For Derrida, language is a system of relations that are dynamic, in that all meanings we ascribe to the world are dependent not only on what we believe to be present but also on what is absent. Thus, any act of interpretation must refer not only to what the author of a text intends, but also to what is absent from his or her intention. This insight leads, once again, to Derrida's further rejection of the idea of the definitive authority of the intentional agent or subject. The subject is decentred; it is conceived as the outcome of relations of différance. As author of its own biography, the subject thus becomes the ideological fiction of modernity and its logocentric philosophy, one that depends upon the formation of hierarchical dualisms, which repress and deny the presence of the absent 'other'. No meaning can, therefore, ever be definitive, but is merely an outcome of a particular interpretation.
45. According to the passage, Derrida believes that:
(1) Reality can be construed only through the use of rational analysis.
(2) Language limits our construction of reality.
(3) A universal language will facilitate a common understanding of reality.
(4) We need to uncover the hidden meaning in a system of relations expressed by language.
46. To Derrida, 'logocentrism' does not imply:
(1) A totalitarian impulse.
(2) A domain of representative language.
(3) Interdependence of the meanings of dichotomous terms.
(4) A strategy that seeks to suppress hidden meanings in a text.
47. According to the passage, Derrida believes that the system of binary opposition
(1) represents a prioritization or hierarchy.
(2) reconciles contradictions and dualities.
(3) weakens the process of marginalization and ordering of truth.
(4) deconstructs reality.
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48. Derrida rejects the idea of 'definitive authority of the subject' because
(1) interpretation of the text may not make the unseen visible.
(2) the meaning of the text is based on binary opposites.
(3) the implicit power relationship is often ignored.
(4) any act of interpretation must refer to what the author intends.
Directions for Questions 49 to 52: 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.
49. The audiences for crosswords and sudoku, understandably, overlap greatly, but there are differences, too. A crossword attracts a more literary person, while sudoku appeals to a keenly logical mind. Some crossword enthusiasts turn up their noses at sudoku because they feel it lacks depth. A good crossword requires vocabulary, knowledge, mental flexibility and sometimes even a sense of humor to complete. It touches numerous areas of life and provides an "Aha!" or two along the way.
(1) Sudoku, on the other hand, is just a logical exercise, each one similar to the last.
(2) Sudoku, incidentally, is growing faster in popularity than crosswords, even among the literati.
(3) Sudoku, on the other hand, can be attempted and enjoyed even by children.
(4) Sudoku, however, is not exciting in any sense of the term.
50. Most firms consider expert individuals to be too elitist, temperamental, egocentric, and difficult to work with. Force such people to collaborate on a high-stakes project and they just might come to fisticuffs. Even the very notion of managing such a group seems unimaginable. So most organizations fall into default mode, setting up project teams of people who get along nicely.
(1) The result, however, is disastrous.
(2) The result is mediocrity.
(3) The result is creation of experts who then become elitists.
(4) Naturally, they drive innovations.
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51. Federer's fifth grand slam win prompted a reporter to ask whether he was the best ever. Federer is certainly not lacking in confidence, but he wasn't about to proclaim himself the best ever. "The best player of this generation, yes", he said, "But nowhere close to ever. Just look at the records that some guys have. I'm a minnow".
(1) His win against Agassi, a genius from the previous generation, contradicts that.
(2) Sampras, the king of an earlier generation, was as humble.
(3) He is more than a minnow to his contemporaries.
(4) The difference between 'the best of this generation' and 'the best ever' is a matter of perception.
52. Thus the end of knowledge and the closing of the frontier that it symbolizes is not a looming crisis at all, but merely one of many embarrassing fits of hubris in civilization's long industry. In the end, it will pass away and be forgotten. Ours is not the first generation to struggle to understand the organizational laws of the frontier, deceive itself that it has succeeded, and go to its grave having failed.
(1) One would be wise to be humble.
(2) But we might be the first generation to actually reach the frontier.
(3) But we might be the first generation to deal with the crisis.
(4) However, this time the success is not illusory.
Directions for Questions 53 to 56: Each question consists of four sentences on a topic. Some sentences are grammatically incorrect or inappropriate. Select the option that indicates the grammatically correct and appropriate sentence(s).
53.
A. When virtuoso teams begin their work, individuals are in and group consensus is out.
B. As project progresses, however, the individual stars harness themselves to the product of the group.
C. Sooner or later, the members break through their own egocentrism and become a plurality with single-minded focus on the goal.
D. In short, they morph into a powerful team with a shared identity.
(1) A & C
(2) A & D
(3) B & D
(4) A, C & D
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54.
A. Large reductions in the ozone layer, which sits about 15-30 km above the Earth, take place each winter over the Polar regions, especially the Antarctic, as low temperatures allow the formation of stratospheric clouds that assist chemical reactions breaking down ozone.
B. Industrial chemicals containing chlorine and bromine have been blamed for thinning the layer because they attack the ozone molecules, making them to break apart.
C. Many an offending chemicals have now been banned.
D. It will still take several decades before these substances have disappeared from the atmosphere.
(1) D only
(2) B & D
(3) A & D
(4) A & C
55.
A. The balance of power will shift to the East as China and India evolve.
B. Rarely the economic ascent of two still relatively poor nations has been watched with such a mixture of awe, opportunism, and trepidation.
C. Postwar era witnessed economic miracles in Japan and South Korea, but neither was populous enough to power worldwide growth or change the game in a complete spectrum of industries.
D. China and India, by contrast, possess the weight and dynamism to transform the 21st-century global economy.
(1) A, B & C
(2) A & D
(3) C
(4) C & D
56.
A. People have good reason to care about the welfare of animals.
B. Ever since Enlightenment, their treatment has been seen as a measure of mankind's humanity.
C. It is no coincidence that William Wilberforce and Sir Thomas Foxwell Buxton, two leaders of the movement to abolish the slave trade, helped found the Royal Society for the Prevention of Cruelty to Animals in 1820s.
D. An increasing number of people go further: mankind has a duty not to cause pain to animals that have the capacity to suffer.
(1) A & D
(2) B
(3) A & C
(4) C & D
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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. Intelligent design derives from an early 19th-century explanation of the natural world given by an English clergyman, William Paley. Paley was the populariser of the famous watchmaker analogy. Proponents of intelligent design are crupping Paley's argument with a new gloss from molecular biology.
(1) destroying
(2) testing
(3) resurrecting
(4) questioning
58. Women squat, heads covered, beside huge piles of limp fodder and blunk oil lamps, and just about all the cows in the three towns converge upon this spot. Sinners, supplicants and yes, even scallywags hand over a few coins for a crack at redemption and a handful of grass.
(1) shining
(2) bright
(3) sputtering
(4) effulgent
59. It is klang to a sensitive traveller who walks through this great town, when he sees the streets, the roads, and cabin doors crowded with beggars, mostly women, followed by three, four, or six children, all in rags and importuning every passenger for alms.
(1) amusing
(2) irritating
(3) disgusting
(4) distressing
60. Or there is the most fingummy diplomatic note on record: when Philip of Macedon wrote to the Spartans that, if he came within their borders, he would leave not one stone of their city, they wrote back the one word - "If".
(1) witty
(2) rude
(3) simple
(4) terse
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SECTION III Sub-section III-A: Number of Questions = 10 Note: Questions 61 to 70 carry one mark each. Answer Questions 61 to 64 on the basis of the information given below: A management institute was established on January 1, 2000 with 3, 4, 5, and 6 faculty members in the Marketing, Organisational Behaviour (OB), Finance, and Operations Management (OM) areas respectively, to start with. No faculty member retired or joined the institute in the first three months of the year 2000. In the next four years, the institute recruited one faculty member in each of the four areas. All these new faculty members, who joined the institute subsequently over the years, were 25 years old at the time of their joining the institute. All of them joined the institute on April 1. During these four years, one of the faculty members retired at the age of 60. The following diagram gives the area-wise average age (in terms of number of completed years) of faculty members as on April 1 of 2000, 2001, 2002, and 2003.
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61. From which area did the faculty member retire?
(1) Finance
(2) Marketing
(3) OB
(4) OM
62. Professors Naresh and Devesh, two faculty members in the Marketing area, who have been with the Institute since its inception, share a birthday, which falls on 20th November. One was born in 1947 and the other one in 1950. On April 1 2005, what was the age of the third faculty member who has been in the same area since inception?
(1) 47
(2) 50
(3) 51
(4) 52
63. In which year did the new faculty member join the Finance area?
(1) 2000
(2) 2001
(3) 2002
(4) 2003
64. What was the age of the new faculty member, who joined the OM area, as on April 1, 2003?
(1) 25
(2) 26
(3) 27
(4) 28
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Answer Questions 65 to 67 on the basis of the information given below: The table below reports annual statistics related to rice production in select states of India for a particular year.
State
Total Area (in million hectares)
% of Area Under Rice Cultivation
Production (in million tons)
Population (in millions)
Himachal Pradesh
6
20
1.2
6
Kerala
4
60
4.8
32
Rajasthan
34
20
6.8
56
Bihar
10
60
12
83
Karnataka
19
50
19
53
Haryana
4
80
19.2
21
West Bengal
9
80
21.6
80
Gujarat
20
60
24
51
Punjab
5
80
24
24
Madhya Pradesh
31
40
24.8
60
Tamilnadu
13
70
27.3
62
Maharashtra
31
50
48
97
Uttar Pradesh
24
70
67.2
166
Andhra Pradesh
28
80
112
76
65. Which two states account for the highest productivity of rice (tons produced per hectare of rice cultivation)?
(1) Haryana and Punjab
(2) Punjab and Andhra Pradesh
(3) Andhra Pradesh and Haryana
(4) Uttar Pradesh and Haryana
66. How many states have a per capita production of rice (defined as total rice production divided by its population) greater than Gujarat?
(1) 3
(2) 4
(3) 5
(4) 6
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67. An intensive rice producing state is defined as one whose annual rice production per million of population is at least 400,000 tons. How many states are intensive rice producing states?
(1) 5
(2) 6
(3) 7
(4) 8
Answer Questions 68 to 70 on the basis of the information given below: The table below reports the gender, designation and age-group of the employees in an organization. It also provides information on their commitment to projects coming up in the months of January (Jan), February (Feb), March (Mar) and April (Apr), as well as their interest in attending workshops on: Business Opportunities (BO), Communication Skills (CS), and E-Governance (EG).
Sl. No.
Name
Gender
Designation
Age Group
Committed to problems during
Interested in workshop on
1
Anshul
M
Mgr
Y
Jan, Mar
CS, EG
2
Bushkant
M
Dir
I
Feb, Mar
BO, EG
3
Charu
F
Mgr
I
Jan, Feb
BO, CS
4
Dinesh
M
Exe
O
Jan, Apr
BO, CS, EG
5
Eashwaran
M
Dir
O
Feb, Apr
BO
6
Fatima
F
Mgr
Y
Jan, Mar
BO, CS
7
Gayatri
F
Exe
Y
Feb, Mar
EG
8
Hari
M
Mgr
I
Feb, Mar
BO, CS, EG
9
Indira
F
Dir
O
Feb, Apr
BO, EG
10
John
M
Dir
Y
Jan, Mar
BO
11
Kalindi
F
Exe
I
Jan, Apr
BO, CS, EG
12
Lavanya
F
Mgr
O
Feb, Apr
CS, EG
13
Mandeep
M
Mgr
O
Mar, Apr
BO, EG
14
Nandlal
M
Dir
I
Jan, Feb
BO, EG
15
Parul
F
Exe
Y
Feb, Apr
CS, EG
16
Rahul
M
Mgr
Y
Mar, Apr
CS, EG
17
Sunita
F
Dir
Y
Jan, Feb
BO, EG
18
Urvashi
F
Exe
I
Feb, Mar
EG
19
Yamini
F
Mgr
O
Mar, Apr
CS, EG
20
Zeena
F
Exe
Y
Jan, Mar
BO, CS, EG
M = Male, F = Female; Exe = Executive, Mgr = Manager, Dir = Director; Y = Young, I = In-between, O = Old
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For each workshop, exactly four employees are to be sent, of which at least two should be Females and at least one should be Young. No employee can be sent to a workshop in which he or she is not interested in. An employee cannot attend the workshop on Communication Skills, if he or she is committed to internal projects in the month of January; Business Opportunities, if he or she is committed to internal projects in the month of February; E-governance, if he or she is committed to internal projects in the month of March.
68. Assuming that Parul and Hari are attending the workshop on Communication Skills (CS), then which of the following employees can possibly attend the CS workshop?
(1) Rahul and Yamini
(2) Dinesh and Lavanya
(3) Anshul and Yamini
(4) Fatima and Zeena
69. How many Executives (Exe) cannot attend more than one workshop?
(1) 2
(2) 3
(3) 15
(4) 16
70. Which set of employees cannot attend any of the workshops?
(1) Anshul, Charu, Eashwaran, and Lavanya
(2) Anshul, Bushkant, Gayatri, and Urvashi
(3) Charu, Urvashi, Bushkant, and Mandeep
(4) Anshul, Gayatri, Eashwaran, and Mandeep
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Sub-section III-B: Number of Questions = 20 Note: Questions 71 to 90 carry two marks each. Answer Questions 71 to 74 on the basis of the information given below: In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed # 32) which is designated match No. 1 of first round; the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In the second round, the winner of match No. 1 of first round plays the winner of match No. 16 of first round and is designated match No. 1 of second round. Similarly, the winner of match No. 2 of first round plays the winner of match No. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds as well.
Seed #
Name of Player
Seed #
Name of Player
Seed #
Name of Player
1
Maria Sharapova
12
Mary Pierce
23
Silvia Farina Elia
2
Lindsay Davenport
13
Anastasia Myskina
24
Tatiana Golovin
3
Amelie Mauresmo
14
Alicia Molik
25
Shinobu Asagoe
4
Kim Clijsters
15
Nathalie Dechy
26
Francesca Schiavone
5
Svetlana Kuznetsova
16
Elena Bovina
27
Nicole Vaidisova
6
Elena Dementieva
17
Jelena Jankovic
28
Gisela Dulko
7
Justine Henin
18
Ana Ivanovic
29
Flavia Pennetta
8
Serena Williams
19
Vera Zvonareva
30
Anna Chakvetadze
9
NadiaPetrova
20
Elena Likhovtseva
31
Ai Sugiyama
10
Venus Williams
21
Daniela Hantuchova
32
Anna-lena Groenefeld
11
Patty Schnyder
22
Dinara Safina
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71. If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?
(1) Justine Henin
(2) Nadia Petrova
(3) Patty Schnyder
(4) Venus Williams
72. If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petrova make it to the semifinals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?
(1) Dinara Safina
(2) Justine Henin
(3) Nadia Petrova
(4) Patty Schnyder
73. If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals?
(1) Anastasia Myskina
(2) Flavia Pennetta
(3) Nadia Petrova
(4) Svetlana Kuznetsova
74. If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?
(1) Amelie Mauresmo
(2) Elena Dementieva
(3) Kim Clijsters
(4) Lindsay Davenport
Answer Questions 75 to 78 on the basis of the information given below:
Venkat, a stockbroker, invested a part of his money in the stock of four companies - A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order. At the time of investment, the price of each stock was Rs.100. Venkat purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30%, and 40% from the stock of companies A, B, C and D, respectively. Returns are defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these
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two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or the IT industry with extraordinarily good results, the returns were twice that of the initially expected returns. For the company belonging to the Steel or the Auto industry, the returns on announcement of extraordinarily good results were only one and a half times that of the initially expected returns. For the remaining two companies, which did not announce extraordinarily good results, the returns realized during the year were the same as initially expected.
75. What is the minimum average return Venkat would have earned during the year?
(1) 30%
(2) 31.25%
(3) 32.5%
(4) Cannot be determined
76. If Venkat earned a 35% return on average during the year, then which of these statements would necessarily be true?
I. Company A belonged either to Auto or to Steel Industry.
II. Company B did not announce extraordinarily good results.
III. Company A announced extraordinarily good results.
IV. Company D did not announce extraordinarily good results.
(1) I and II only
(2) II and III only
(3) I and IV only
(4) II and IV only
77. If Venkat earned a 38.75% return on average during the year, then which of these statement(s) would necessarily be true?
I. Company C belonged either to Auto or to Steel Industry.
II. Company D belonged either to Auto or to Steel Industry.
III. Company A announced extraordinarily good results.
IV. Company B did not announce extraordinarily good results.
(1) I and II only
(2) II and III only
(3) I and IV only
(4) II and IV only
78. If Company C belonged to the Cement or the IT industry and did announce extraordinarily good results, then which of these statement(s) would necessarily be true?
I. Venkat earned not more than 36.25% return on average.
II. Venkat earned not less than 33.75% return on average.
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III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results.
IV. If Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel Industry.
(1) I and II only
(2) II and IV only
(3) II and III only
(4) III and IV only
Answer Questions 79 to 82 on the basis of the information given below: The year is 2089. Beijing, London, New York, and Paris are in contention to host the 2096 Olympics. The eventual winner is determined through several rounds of voting by members of the IOC with each member representing a different city. All the four cities in contention are also represented in IOC. In any round of voting, the city receiving the lowest number of votes in that round gets eliminated. The survivor after the last round of voting gets to host the event. A member is allowed to cast votes for at most two different cities in all rounds of voting combined. (Hence, a member becomes ineligible to cast a vote in a given round if both the cities (s)he voted for in earlier rounds are out of contention in that round of voting). A member is also ineligible to cast a vote in a round if the city (s)he represents is in contention in that round of voting. As long as the member is eligible, (s)he must vote and vote for only one candidate city in any round of voting.
The following incomplete table shows the information on cities that received the maximum and minimum votes in different rounds, the number of votes cast in their favour, and the total votes that were cast in those rounds.
Round
Total votes cast
Maximum votes cast
Eliminated
City
No. of votes
City
No. of votes
1
London
30
New York
12
2
83
Paris
32
Beijing
21
3
75
It is also known that: All those who voted for London and Paris in round 1, continued to vote for the same cities in subsequent rounds as long as these cities were in contention. 75% of those who voted for Beijing in round 1, voted for Beijing in round 2 as well.
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Those who voted for New York in round 1, voted either for Beijing or Paris in round 2. The difference in votes cast for the two contending cities in the last round was 1. 50% of those who voted for Beijing in round 1, voted for Paris in round 3.
79. What percentage of members from among those who voted for New York in round 1, voted for Beijing in round 2?
(1) 33.33
(2) 50
(3) 66.67
(4) 75
80. What is the number of votes cast for Paris in round 1?
(1) 16
(2) 18
(3) 22
(4) 24
81. What percentage of members from among those who voted for Beijing in round 2 and were eligible to vote in round 3, voted for London?
(1) 33.33
(2) 38.10
(3) 50
(4) 66.67
82. Which of the following statements must be true?
a. IOC member from New York must have voted for Paris in round 2.
b. IOC member from Beijing voted for London in round 3.
(1) Only a
(2) Only b
(3) Both a and b
(4) Neither a nor b
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Answer Questions 83 to 86 on the basis of the information given below: The table below presents the revenue (in million rupees) of four firms in three states. These firms, Honest Ltd., Aggressive Ltd., Truthful Ltd. and Profitable Ltd. are disguised in the table as A, B, C and D, in no particular order.
States
Firm A
Firm B
Firm C
Firm D
UP
49
82
80
55
Bihar
69
72
70
65
MP
72
63
72
65
Further, it is known that: In the state of MP, Truthful Ltd. has the highest market share. Aggressive Ltd.’s aggregate revenue differs from Honest Ltd.’s by Rs. 5 million.
83. What can be said regarding the following two statements?
Statement 1: Profitable Ltd. has the lowest share in MP market. Statement 2: Honest Ltd.’s total revenue is more than Profitable Ltd.
(1) If Statement 1 is true then Statement 2 is necessarily true.
(2) If Statement 1 is true then Statement 2 is necessarily false.
(3) Both Statement 1 and Statement 2 are true.
(4) Neither Statement 1 nor Statement 2 is true.
84. What can be said regarding the following two statements?
Statement 1: Aggressive Ltd.’s lowest revenues are from MP. Statement 2: Honest Ltd.’s lowest revenues are from Bihar.
(1) If Statement 2 is true then Statement 1 is necessarily false.
(2) If Statement 1 is false then Statement 2 is necessarily true.
(3) If Statement 1 is true then Statement 2 is necessarily true.
(4) None of the above.
85. What can be said regarding the following two statements?
Statement 1: Honest Ltd. has the highest share in the UP market. Statement 2: Aggressive Ltd. has the highest share in the Bihar market.
(1) Both statements could be true.
(2) At least one of the statements must be true.
(3) At most one of the statements is true.
(4) None of the above
86. If Profitable Ltd.’s lowest revenue is from UP, then which of the following is true?
(1) Truthful Ltd.’s lowest revenues are from MP.
(2) Truthful Ltd.’s lowest revenues are from Bihar.
(3) Truthful Ltd.’s lowest revenues are from UP.
(4) No definite conclusion is possible.
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Answer Questions 87 to 90 on the basis of the information given below: Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project. A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project. The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects. 17 volunteers are involved in the TR project. The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER Project alone. Ten volunteers involved in the TR project are also involved in at least one more project.
87. Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is:
(1) 1
(2) 3
(3) 4
(4) 5
88. Which of the following additional information would enable to find the exact number of volunteers involved in various projects?
(1) Twenty volunteers are involved in FR.
(2) Four volunteers are involved in all the three projects.
(3) Twenty three volunteers are involved in exactly one project.
(4) No need for any additional information.
89. After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project.
Which of the following statements, then, necessarily follows?
(1) The lowest number of volunteers is now in TR project.
(2) More volunteers are now in FR project as compared to ER project.
(3) More volunteers are now in TR project as compared to ER project.
(4) None of the above
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90. After the withdrawal of volunteers, as indicated in Question 89, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?
(1) ER
(2) FR
(3) TR
(4) Cannot be determined