VGSOM, IIT Kharagpur

Ph. D Entrance Examination: Written Test Sample Questions

Time: 2 Hours Total Marks: 100

Three sections:

Section 1: Quantitative Aptitude

Section 2: (Reading Comprehension and Verbal Ability)

Section 3: (Descriptive Section)

Sample Questions:

Note: the pattern of questions provided below may change depending upon department

requirements

SECTION 1: QUANTITATIVE APTITUDE

1. If ax = b, by = c and cz = a, then xyz is equal to:

(c) 0 (b) -1 (c) 1 (d) a+b+c

2. The equations ax – (a + b) y = 1 and (a – b)x + ay = 5 have a unique solution:

(a) For all values of a and b

(b) Only when a = b

(c) Only when a2 : b2 ≠ 1 : 2

(d) Only when a = 0 and b = 0

3. The sum of the digits of a number is subtracted from the number. The result is always

(a) Divisible by 6 (b) divisible by 9 (c) Not divisible by 6 (d) not divisible by 9

4. The diagonals of a rhombus are 10 cm and 24 cm. The perimeter of the rhombus is

(a) 68 cm (b) 30 cm (c) 34 cm (d) 52 cm

5. The locus of the centres of the circles touching both the arms of an acute angle is (a) a concentric circle (b) a circle (c) a parallelogram (d) A bisector of the angle

6. There are 6 balls of different colours and 3 boxes of different sizes. Each box can hold all

the 6 balls. The balls are put in the boxes so that no box remains empty. The number of ways in which this can be done is :

(a) 534 (b) 543 (c)540 (d) 528

7. If the total numbers of relations from Set A to Set B is 1024, and n(A) > 1, n(B) > 1, then (a) n(A) = 2, n(B) = 5 (b) n(A) = 5, n(B) = 1 (c) n(A) = 10, n(B) = 1 (d) n(A) = 1, n(B) =

10

8. On a railway there are ten (10) stations. The number of types of tickets required in order that it may be possible to book a passenger from every station to every other is (a) 10/ 2 (b) 10 2 (c)10 / 8 (d) 10 8 2 (e)None of the above.

9. The number of ways in which the letters of the word “ARGUMENT” can be arranged so

that only consonants occurs at both the ends is: (a) 31*5! (b) 14400 (c) 41000 (d) none of these 10. If Ur denotes the number of one-one functions from (X1, X2, ...Xr) to (Y1, Y2,...Yr) such that f (XI) ≠ Y1 for 1 = 1, 2, 3, ...r then U4 is: (a) 9 (b) 44 (c)265 (d) None of these

Study the following example and answer questions 11-15: An electronic device rearranges numbers step-by-step in a particular order according to a set of rules. The device stops when the final result is obtained. In this case the device stops at Step V. Input: 85 16, 36 04 19 97 63 09 Step I 97 85 16 36 04 19 63 09 Step II 97 85 63 16 36 04 19 09 Step III 97 85 63 36 16 04 19 09 Step IV 97 85 63 36 19 16 04 09 Step V 97 85 63 36 19 16 09 04 11 Which of the following will be Step III for the input below? Input: 09 25 16 30 32 18 17 06 (a) 32 09 25 16 30 18 17 06 (b) 32 30 09 25 16 19 17 06 (c) 32 30 09 25 16 18 17 06 (d) 32 30 25 09 16 18 17 06

12. What is the last step for the input below ? Input: 16 09 25 27 06 05

(a) Step II (b) Step III (c) Step IV (d) None of these

13. What is the output of Step V for the input below? Input: 25 08 35 11 88 67 23 (a) 88 67 35 25 23 11 08 (b) 88 67 35 25 23 08 11 (c) 08 11 23 25 35 67 88 (d) None of these

14. Which one of the following would be last step for the input below? Input: 03 31 43 22 11 09 (a) Step II (b) Step III (c) Step IV (d) None of these

15. If the output of Step IV is as given below, what was the input? Step IV:02 86 71 69 15 19 06 63 58

(a) 86 92 69 71 15 19 06 63 58 (b) 15 86 19 92 06 69 63 58 71 (c) 15 19 06 63 58 86 92 69 71 (d) None of these.

16. In 4 years, the –simple interest on a certain sum of money is 7/25 of the principal. What is the annual rate of interest? (a) 4% (b) 4.5% (c) 7% (d) 9%

17. There are thirty days in April, June, September, and November. Some months are of thirty one days. A month is chosen at random. Then its probability of having exactly three days less than maximum of 31 is (a) 15/16 (b) 1 (c)3/48 (d) None of these

18. Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of 1st escalator is 2:3 (steps). The ratio of 2nd person’s speed to that of 2nd escalator is 3:5 (steps). Find the total number of steps they both have taken together. (a) 85 (b) 93 (c)80 (d) 75 19. The table below shows the temperatures in degrees Mon Tue Wed Thu Fri Sat Sun 66 78 75 69 78 77 70 Noon time Temperature If ‘m’ represents the median temperature, ‘f’ represents the temperature that occurs most often and ‘a’ represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f and a ? (a) a < m > f (b) a < m < f (c) m < a < f (d) m < f < a

20. Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the park are exactly double the corresponding sides of the flower bed. The ratio of the areas of the path to the flower bed is: (a) 1 : 1 (b) 1 : 2 (c) 1 : 3 (d) 3 : 1 Directions for Questions 21-24: A survey of movie goers from five cities A, B, C, D and E is summarized below. The first column gives the percentage of viewers in each city who watch less than one movie a week. The second column gives the total number of viewers who view one or more movies per week. City I II A 60 2400 B 20 3000 C 85 2400 D 55 2700 E 75 8000

21. How many viewers in city C watch less than one movie a week? (a) 2040 (b) 13600 (c)16000 (d) 3600

22. Which city has the highest number of viewers who watch less than one movie a week? (a) City E (b) City D (c) City B (d) City C

23. A city with the second lowest number of movie watchers is

(a) City E (b) City D (c) City B (d) City C

24. The total number of all movie goers in the five cities who watch less than one movie per week is (a) 50000 (b) 36000 (c)18500 (d) 45250

25. The 288th term of the sequence a, b, b, c, c, c, d, d, d, d,....is

(a) 2/5 (b) 1/5 (c) 1/6 (d) None of these. 26. A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was a four is (a) 2/5 (b) 1/5 (c) 1/6 (d) None of these.

27. A boat covers a distance of 30 kms downstream in 2 hours while it takes 6 hours to cover the same distance upstream. What is the speed of the boat in kms per hour? (a) 5 (b) 7.5 (c) 13 (d) 18 28. A five digit number is formed by using the digits 1, 2, 3, 4, and 5 without repetitions. What is the probability that the number is divisible by 4? (a) 1/5 (b) 5/6 (c) 4/5 (d) None of these

29. If the algebraic sum of deviations of 20 observations from 23 is 70, mean of these observations would be (a) 24 (b) 25 (c)26 (d) None of these.

30. An alloy of gold and silver weighs 50 gms. It contains 80% gold. How much gold should be added to the alloy so that percentage of gold is increased to 90? (a) 50 gms (b) 60 gms (c)30 gms (d) 40 gms

SECTION 2 : (READING COMPREHENSION AND VERBAL ABILITY)

Directions:

Read the following passage carefully and answer the questions given below it. Certain

words are printed in bold to help you locate them while answering some of the questions.

Many people believe that science and religion are contrary to each other. But this

notion is wrong. As a matter of fact, both are complementary to each other. The aim of

both these institutions is to explain different aspects of life, universe and human existence.

There is no doubt that the methods of science and religion are different. The method of

science is observation, experimentation and experience. Science takes its recourse to

progressive march towards perfection. The tools of religion are faith, intuition and spoken

word of the enlightened. In general, while science is inclined towards reason and

rationality, spiritualism is the essence of religion.

In earlier times when man appeared on earth, he was over-awed at the sight of

violent and powerful aspects of nature. In certain cases, the usefulness of different natural

objects of nature overwhelmed man. Thus, began the worship of forces of nature – fire, the

sun, the rivers, the rocks, the trees, the snakes, etc. The holy scriptures were written by

those who had developed harmony between external nature and their inner self. Their

object was to ennoble, elevate and liberate the human spirit and mind. But the priestly class

took upon itself the monopoly of spiritual knowledge and interpretation to its own

advantage. Thus, the entire human race was in chains. Truth was flouted and progressive,

liberal and truthful ideas or ideas expressing doubts and scepticism were suppressed and

their holders punished. It was in these trying circumstances that science emerged as a

saviour of mankind. But its path was not smooth and safe. The scientists and free thinkers

were tortured. This was the fate of Copernicus, Galileo, Bruno and others. But by and by

science gained ground.

31. Why does man worship the forces of nature?

(a) The holy scriptures advocate the worship of forces of nature.

(b) The worship elevates and liberates the human spirit and mind.

(c) The worship makes man believe in faith and intuition.

(d) Forces of nature teach us spiritualism.

(e) None of these.

32. According to the passage, science and religion both

(a) Rely on the spoken word of the enlightened.

(b) Emerged out of the fear of man

(c) Emerged from the desire of man to worship the forces of nature.

(d) Employ different methods of enquiry.

(e) Work at the cross-purpose of each other.

33. Which of the following statements is not true in the context of the passage?

(a) Man worships the forces of nature.

(b) Methods of science and religion are different.

(c) Regimental religion got degenerated into orthodoxy.

(d) Galileo and Bruno were disciples of Copernicus.

34. Choose the word which is most nearly the same in meaning as the word “flouted” as used in the passage? (A) Mocked (B) Nourished (C) Expressed (D) Concealed

.35. Choose the word which is most opposite in meaning of the word “enlightened” as used in the passage? (A) Uninformed (B) Derogatory (C) Downtrodden (D) Educated

Directions for questions 36-40: Mark one of the phrases (A), (B), (C) or (D) which can replace the phrase given in BOLD to make the

sentence grammatically meaningful and correct. If the sentence is correct as it is and no correction

is required, mark (E) as the answer.

36. The donation amount was such that as I was expected him to donate. (A) so that as I expected (B) such that I expected of (C) such as that I expect (D) exactly as I had expected (E) no correction required

37. It is a pity that no one in the family disapproves by his getting up late.

(A) disapproved by his getting up (B) disapproves of his getting up (C) disapproved that he is getting up (D) disapproved why he got up (E) No correction required

38. He will be greatly surprised if he was felicitated by his staff members.

(A) if he will have felicitated (B) unless he was felicitated (C) if he is felicitated (D) if he would have felicitated (E) No correction required

39. Do you know when shall he be leaving for his higher studies in the USA?

(A) should he be left (B) he would be leaving

(C) he would be left (D) would he have left (E) No correction required

40. Using it wisely, leisure promotes health, efficiency and happiness.

(A) Use it wisely (B) If it is used wisely (C) Having used it wisely (D) Because of its wise use (E) No correction required

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Directions for questions 41 to 42: Sentences given in the question, when properly sequenced, form a

coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of these

sentences from among the four given alternatives to construct a coherent paragraph.

41. 1. Ignorance is the opposite of knowledge, i.e, want of knowledge. 2. To deal with uncertainty and ignorance economists have recognized the entrepreneur as

possessing this non-rational form of knowledge. 3. Like some ancient priest-king. The entrepreneur ‘knows’ the future and leads his people. 4. Entrepreneurial knowledge is essentially intuitive. 5. It involves seeing and realizing a vision of future markets, products and/or other

opportunities (A) 32145 (B) 43125 (C) 12453 (D) 45123

42.

1. Risk-stemming from fluctuations in exchange rate loans hover constantly on the horizon of foreign investment.

2. In view of the higher risk, a firm contemplating foreign investment would naturally expect a higher rate of return.

3. A multinational company may be accused of ‘profiteering’ even when it may simply be following the sound financial practice of asking for a higher rate of return commensurate with risks characterizing the project.

4. In addition, a foreign investment is subject to discriminatory treatment and selection control in various forms. (A) 1423 (B) 3421 (C) 1324 (D) 2134

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Directions for questions 43 to 46: From the given alternatives, choose the word that is most nearly

similar in meaning to the word given in CAPITAL letters.

43. PLACATE (A) Pacify (B) Transmit (C) Allow (D) Define 44. PROGNOSIS (A) Sample (B) Discussion (C) Forecast (D) Depression 45 BRACKISH (A) Salty (B) Wet (C) Rough (D) Rude 46 COPIUS (A) Pious (B) Covered (C) Plentiful (D) Cheating

Directions for questions 47 to 50: From the given alternatives, choose the word that is most nearly opposite in meaning to the word given in CAPITAL letters. 47. VACILLATION (A) Remorse (B) Steadfastness (C) Inoculation (D) Relief 48. COALESCE (A) Ossify (B) Dislocate (C) Disaggregate (D) Enervate 49. RESTIVE (A) Patient (B) Rigorous (C) Deceptive (D) Active 50 NEBULOUS (A) Ambiguous (B) Definite (C) Deceptive (D) Lazy

SECTION 3 : (DESCRIPTIVE SECTION)

Critically comment on any two topics (within 500 words).

1. Can money act as a motivating factor in one’s personal and professional life?

2. If the product is good, it does not require market

3. How to solve recent chit funds (like Saradha) related problems?

4. Supply chain management is important for manufacturing sector.

5. Competitiveness of Indian ITES sector

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