Ph.D Admission Test Dec 2011 - iitbmonash

Ph.D Admission Test
Dec 2011

Instructions
• This question paper has two parts, Part-A (multiple choice) and Part-B (descriptive).

• You have a max of 45 minutes to answer questions in Part A & B.

• Please do not make any markings on the question papers. Use the answer sheets for all your workings
and your responses.

• There are 40 problems in Part-A. Correct answer will get 3 points and wrong answer will get -1 point.
You have to answer at most 20 questions of your choice. You may answer any 20 of the 40 problems.

• You may answer more than 20 questions. However, only your best 20 questions will receive a score.

• There are 8 problems of which you must answer 2 in Part-B. Only your first two problems will be graded.
You must show your work to receive credit.

• Make and necessary assumptions wherever required. Please don’t ask for any clarifications on questions.

• Write your name, FAN and question numbers clearly on your answer sheet.

• In your answer sheet, mark clearly the questions that you are attempting in Part-A and Part-B before
you provide your answer to these.

Part-A

1. Complete the sequence 1, 2, 5, 13, 34, . . .

(A) 74 (B) 89 (C) 55 (D) 69

2. Which of the following bonds will be most difficult to break?

(A) C − O (B) C − C (C) C − N (D) C − S

3. Where would the spark plug for the typical automobile diesel engine be located?
(A) Under the Engine (for uniformly igniting fuel in entire combustion chamber)
(B) Above the Engine (for easy accessibility and maintenance)
(C) To the side of engine with the injectors
(D) Typical automobile diesel engine does not have a spark plug

4. Which of the following straight lines passes through the point (1,2)

(A) y = 2x + 3 (B) y = 5x − 3 (C) y = 3x + 2 (D) y = 3x − 5

* Some of the questions are taken/inspired from IIT/IISc/GATE/UGC model question papers and other entrance examinations
of prominent universities in India and abroad.

1

IMURA Admission Test - Dec 2011 2

5. Mercury is closer to the Sun than Venus. Yet Venus is hotter because it has:

(A) a dominant CO2 atmosphere (B) a dominant methane atmosphere

(C) sulphuric acid clouds (D) an atmosphere devoid of oxygen

6. In a permanent magnet DC motor, the direction of rotation can be changed by
(A) reducing the supply voltage
(B) reducing the armature current
(C) reversing the polarity of the stator current
(D) reversing the polarity of the supply voltage

7. If the viscosity of water in a swimming pool were to be reduced by 10% by some process (while all other

properties remained unchanged), what would the difference for a human swimmer in the pool be?

(A) No difference (B) Can swim faster with same effort

(C) Will swim slower with same effort (D) Answer differs depending on the ”stroke” be-

ing used

8. Which of the following expresses the Second law of thermodynamics?

(A) ∆F ≤ W (B) ∆S < Q/T (C) ∆U = Q + W (D) ∆S ≤ 0

9. Today is Monday. After 89 days, it will be:

(A) Wednesday (B) Saturday (C) Tuesday (D) Thursday

10. Which adaptation assists temperature regulation in plants?

(A) Large leaves for cooling (B) Increased production of seeds

(C) Movement of glucose to roots (D) Evaporation of water from stomates

11. The graph shows the forces experienced by an astronaut during a rocket launch into a stable orbit. In
which time interval was the acceleration of the rocket the greatest?

(A) S-T (B) T-U (C) U-V (D) V-W

12. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many

days will 5 women and 10 children take to complete the work?

(A) 3 (B) 5 (C) 7 (D) None of these

13. Diamond is an allotropic form of

(A) Germanium (B) Carbon (C) Silicon (D) Sulphur

14. In a certain code language, the word SNAKE is written as 14,5,8,0,12 and the word COMPUTER is

written as 33,48,9,11,36,83,12,91. Assuming consistency of the coding patterns, which of the following

could be the correct code for WEST ?

(A) 33,12,14,83 (B) 7,12,14,83 (C) 14,5,14,83 (D) None of these

IMURA Admission Test - Dec 2011 3

15. Potassium Permanganate is used for purifying drinking water, because

(A) it is a sterilising agent (B) it dissolves the impurities of water

(C) it is a reducing agent (D) it is an oxidising agent

16. Eigen values of a matrix A is 2, 3, x (= 0) then eigen values of A−2 are

(A) 6, 9, x2 (B) 1/4, 1/3, 1/x2 (C) 1/2, 1/3, 1/16 (D)1/4, 1/9, 1/25

17. A spaceship is travelling at a very high speed. What effects would be noted by a stationary observer?
(A) Time runs slower on the spaceship and it contracts in length.
(B) Time runs faster on the spaceship and it contracts in length.
(C) Time runs slower on the spaceship and it increases in length.
(D) Time runs faster on the spaceship and it increases in length.

18. Which aqueous solution turns phenolphthalein pink?

(A) HCl (B)N aCl (C) N aOH (D) CH3OH

19. Roots of a 3rd degree polynomial x3 + a1x2 + a2x + a3 are α ≤ −8 , β ≥ 5 and -7. Which is the possible

value for a3

(A) 150 (B) 300 (C) -300 (D) −7αβ

20. If both x and y are prime numbers, which of the following CANNOT be the difference of x and y?

(A) 1 (B) 3 (C) 15 (D) 23

21. The equivalent DC voltage of an AC voltage is (B) 0.707 times the peak AC voltage
(A) 0.500 times the peak AC voltage (D) 3.300 times the peak AC voltage
(C) 1.412 times the peak AC voltage

22. The mean of 10 numbers is 21. If two more numbers are included, the mean is 25. What is the mean of

the two additional numbers

(A) 12 (B) 24 (C) 37 (D) 45

23. A politician has asserted that ”Less than half of my voters realize the fact that more than half of my
campaigners deserve to spend more than half of the rest of their lives behind the bars”. Which of the
following statements is closest to the politician’s statement?
(A) The politician will double the number of prisons
(B) The politician will close half the prisons
(C) The politician considers his voters as well informed and wants his campaigners to reach out to more
of of them
(D) The politician considers his voters to be uninformed about the criminal history of his campaigners

24. Which of these figures can be folded to form a triangular pyramid?

(A) I only (B) I and II (C) I, II and III (D) I and III
(C) 4/3 (D) 75/100
25. A probability of 75% is equal to the fraction

(A) 1/75 (B) 3/4

IMURA Admission Test - Dec 2011 4

26. A certain organization had 50 male and 48 female employees. Some of the employees left the organization.

No new employees joined the organization. Now the ratio of number of male employees to the number

of female employees in the organization is exactly 2:1. Which of the following could be total number of

employees currently working ?

(A) 59 (B) 81 (C) 60 (D) 99

27. If an electrical current varies inversely with resistance, what is the effect on the current when resistance

is doubled, keeping everything else the same

(A) current is doubled (B) current is halved

(C) current remains the same (D) current gets squared

28. In humans, brown eye colour is dominant and blue eye colour is recessive. A brown-eyed boy and a
blue-eyed girl have a blue-eyed mother. What eye colour does the father have and why?
(A) Brown, because the gene for brown eye colour is sex linked.
(B) Brown, because at least one of the parents must have brown eyes.
(C) Blue, because at least two other members of the family have blue eyes.
(D) Blue, because at least one of the parents must be heterozygous for eye colour.

29. An AC to DC rectification circuit is shown. What wave form would be displayed on the Oscilloscope?

30. Which of these statements best describes the forces acting on a satellite in orbit around Earth?
(A) Although gravity has no effect, there is still an outward force.
(B) The satellite is kept up by an outward force that balances the force due to gravity.
(C) Gravity is the only force acting on the satellite and this results in an inward acceleration.
(D) The effect of gravity is negligible, the satellite is kept in orbit by its momentum and the net force on
it is zero.

31. What is the name of the compound shown?

(A) 1-chloro-1,2-difluoropropane (B) 3-chloro-2,3-difluoropropane
(C) 1,2-difluoro-1chloropropane (D) 1-chloro-1,2-difluoropentane

IMURA Admission Test - Dec 2011 5

32. Four years before today, Jack was twice as old as Jill. Four years later from now, Jill will be 3/4 of Jack’s

age. How old is Jack now?

(A) 6 years (B) 8 years (C) 12 years (D) 16 years

33. If a material is subjected to two incremental true strains namely 1 and 2, then the total true strain is:

(A) 1 ∗ 2 (B) 1 − 2 (C) 1 + 2 (D) 1/ 2

34. Macro-segregation can be removed by

(A) Annealing (B) Hot working (C) Both (D) None

35. Which blood vessels in humans contain structures that allow blood to flow in only one direction

(A) Arteries (B) Capillaries (C) Lymph Vessels (D) Veins

36. In the hydraulic system below, if the φ12mm input piston moves a distance of 20mm, how far will the
φ24mm output piston move?

(A) 5mm (B) 10mm (C) 20mm (D) 40mm

37. At the end of a Marathon race, a runner’s body is dehydrated. How does the body control the two
hormones, ADH and aldosterone, to help re-establish normal water balance?
(A) ADH is released and aldosterone is inhibited
(B) ADH is inhibited and aldosterone is released
(C) Both ADH and aldosterone are released
(D) Both ADH and aldosterone are released

38. What is the most likely effect of increasing the amount of the cross-linking of the polymer chains in rubber?
(A) The stiffness of the rubber increases
(B) The brittleness of the rubber reduces
(C) The rubber can be formed more easily
(D) The rubber can be stretched more easily

39. Why are high voltages (440kV) used in the transmission of electricity by the PowerGrid Corporation of

India? (B) To increase current
(A) To increase safety

(C) To reduce resistance (D) To reduce power loss

40. Why is water not used for frying of food items ? (B) Viscosity of water is too low
(A) Boiling point of water is too low (D) Smoke point of water is too low
(C) Density of water is too low

Part-B

[Try and show your workings clearly for these answers]

IMURA Admission Test - Dec 2011 6

1. A vendor has 6 different boxes which weigh 8, 16, 12, 20, 10 and 18 kg and cost Rs. 30, 35, 40, 45, 50 and
60 respectively. As a business (wo)man, you always try to get more quantity in all deals that you finalize.
What will your purchase plan be if you have a capital outlay of Rs.190.

2. A miner is trapped in a mine containing three doors. The first door leads to a tunnel that takes him out
to the surface after two hours of travel. The second door leads to a tunnel that returns him to the mine
after three hours of travel. The third door leads to a tunnel that also returns him to his mine after three
hours. Assuming that the miner is at all times equally likely to choose any one of the doors, (irrespective
of previous choices) what is probability that he will reach to the surface within 24 hours?

3. It is drizzling outside and you have to carry a cardboard box over a certain distance without cover or
umbrella etc. You can either walk slow to avoid the rain hitting the box from the front, or run fast to
spend least time in the rain. Which strategy out of these two will you choose to protect the box from
getting wet. Is there an optimum speed that you should go at?

4. Does eating fat make you fat? Justify your answer.

5. Munna Bhai is playing carrom, and wants to pocket the queen. The position of queen (φ = 2, mass=m),
cover (φ = 2, mass=m) and the hole for pocketing (φ = 2 + δ) is shown in the diagram below. The striker
(φ = 3, mass=2m) has to be put on the line A-B, without moving the cover. Choose the position of the
striker, and determine the velocity vector with which Munna has to release the striker to pocket the queen
in the hole.

6. Explain why black coloured dress is not preferred in summer season in plains.

IMURA Admission Test - Dec 2011 7

7. Two balls are thrown simultaneously from a same point. One is thrown vertical, and other at an angle of
θ to the vertical. Initial velocity of the bodies is v. Neglecting the air drag, and assuming gravity due to
acceleration = g, find the distance between the bodies at time t.

8. Write a pseudo-algorithm to sort 5 numbers. Give output of each step of your algorithm. Please assume
any non-negative integers.