GATE ME-3

1 Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is

2. “Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”The word that best fills the blank in the above sentence is

3 Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

4 A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?

5 A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

7. From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?

9 For an Oldham coupling used between two shafts, which among the following statements are correct?I. Torsional load is transferred along shaft axis. II. A velocity ratio of 1:2 between shafts is obtained without using gears. III. Bending load is transferred transverse to shaft axis. IV. Rotation is transferred along shaft axis.

10 Which one of the following statements is correct for a superheated vapour?

11 In a linearly hardening plastic material, the true stress beyond initial yielding

12 Using the Taylor’s tool life equation with exponent n = 0.5, if the cutting speed is reduced by 50%, the ratio of new tool life to original tool life is

13 A grinding ratio of 200 implies that the

14 Interpolator in a CNC machine

15 The time series forecasting method that gives equal weightage to each of the m most recent observations is

16 The number of atoms per unit cell and the number of slip systems, respectively, for a facecentered cubic (FCC) crystal are

17 A six-faced fair dice is rolled five times. The probability (in %) of obtaining “ONE” at least four times is

18 “The dress _________ her so well that they all immediately _________ her on her appearance.”The words that best fill the blanks in the above sentence are

19 “The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”The word that best fills the blank in the above sentence is

20 Find the missing group of letters in the following series: BC, FGH, LMNO, _____

21 The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

22 Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

23 A wire would enclose an area of 1936 m2 , if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?

24. A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?

25 A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number. i. If the house number is a multiple of 3, then it is a number from 50 to 59. ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69. iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79. What is the house number?

26.An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials: (1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __. Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

27 Pre-tensioning of a bolted joint is used to

28.The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 µm. If the peak wavelength of emitted radiation changes to 2.90 µm, then the temperature (in K) of the black body is

29 Select the correct statement for 50% reaction stage in a steam turbine.

30.Denoting L as liquid and M as solid in a phase-diagram with the subscripts representing different phases, a eutectoid reaction is described by

31.During solidification of a pure molten metal, the grains in the casting near the mould wall are

32. Feed rate in slab milling operation is equal to

33 Metal removal in electric discharge machining takes place through

34.The preferred option for holding an odd-shaped workpiece in a centre lathe is

35.A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic order quantity of the tyres is

36.Let X1 and X2 be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X1, X2) is

37.“Going by the _________ that many hands make light work, the school _______ involved all the students in the task.” The words that best fill the blanks in the above sentence are

38. Which one of the following statements is TRUE for the ultrasonic machining (USM) process?

39. The standard deviation of linear dimensions P and Q are 3 m and 4 m, respectively. When assembled, the standard deviation (in m) of the resulting linear dimension (P+Q) is ________

40. The emissive power of a blackbody is P. If its absolute temperature is doubled, the emissive power becomes.

41.The determinant of a 2x2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is

42. Which one of the following statement is TRUE? A. Both Pelton and Francis turbines are impulse turbines. B. Francis turbine is a reaction turbine but Kaplan turbine is an impulse turbine. C. Francis turbine is an axial−flow reaction turbine. D. Kaplan turbine is an axial−flow reaction turbine. 8. Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is

43. It is desired to make a product having T-shaped cross-section from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength of the product?

44. The heat loss from a fin in 6W. The effectiveness and efficiency of the fin are 3 and 0.75, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base temperature, is ________.

45. For a single with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?

46.For the stability of a floating body the

47. For a loaded cantilever beam of uniform crosssection, the bending moment (in N.mm) along the length is M(x)=5x2+10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm is

49. A sample of 15 data is follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is

51.Given the atomic weight of Fe is 56 and that of C is 12, the weight percentage of carbon in cementite (Fe3C) is ________

52 In an orthogonal machining with a tool of 9° orthogonal rake angle, the uncut chip thickness is 0.2mm. The chip thickness fluctuates between 0.25 mm and 0.4 mm. The ratio of the maximum shear angel to the minimum shear angle during machining is _________

53. The crystal structure of aluminium is

54. A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPA. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _______

55. In a counter-flow heat exchanger, water is heated at the rate of 1.5kg/s from 40°C to 80°C by an oil entering at 120°C and leaving at 60°C. The specific heats of water and oil are 4.2kJ/kg/K and 2kJ/kg.K respectively. The overall heat transfer coefficient is 400 W/m2 .K. The required heat transfer surface area (in m2) is

56. For the laminar flow of water over a sphere, the drag force,  is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3 . When the diameter of the sphere is 10mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is_____

57. A rod of length 20mm is stretched to make a rod of length 40 mm. Subsequently, it is compressed to make a rod of final length 10 mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is

58.In the Rankine cycle for a steam power plant the turbine entry and exit enthalpies are 2803 kJ/kg and 1800 kJ/kg, respectively. The enthalpies of water at pump entry and exit are 121 kJ/kg and 124 kJ/kg, respectively. The specific steam consumption (in kg/k W.h) of the cycle is _______

59. A calorically perfect gas (specific heat at constant pressure 1000 J/kg.K) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are 1100 K and 400 K, respectively. The power produced is 4.6 MW and heat escapes at the rate of 300 kJ/s through the turbine casing. The mass flow rate of the gas (in kg/s) through the turbine is

60. The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is 2.87 m3 and 300K, respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is 0.5bar. If the gas constant of air is R=287 K/kg. K and the atmospheric pressure is 1 bar, the mass of air (in kg) in the vessel is

61. A strip of 120 mm width and 8 mm thickness is rolled between two 300 mm-diameter rolls to get a strip of 120 mm width and 7.2 mm thickness. The speed of the strip at the exit is 30 m/min. There is no front or back tension. Assuming uniform roll pressure of 200 MPa in the roll bite and 100% mechanical efficiency, the minimum total power (in kW) required to drive the two roll is _______.

62. A metal ball of diameter 60mm is initially at 220 °C. The ball is suddenly cooled by an air jet of 20°C. The heat transfer coeffient is 200 W/m2 .K and 9000kg/m2 , respectively. The ball temperature (in °C) after 90 seconds will be approximately.

63. single – plate clutch has a friction disc with inner and outer radii of 20 mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction  varies radially as =0.01 r, where r is in mm. The clutch needs to transmit a friction torque of 18.8k kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is ________

64. One kg of an ideal gas (gas constant R=287 J/kg.K) undergoes an irreversible process from state-1 (1 bar, 300 K) to state -2 (2 bar, 300 K). The change in specific entropy (s1-s2) of the gas (in J/kg.K) in the process is

65. During the turning of a 20mm-diameter steel bar at a spindle speed of 400 rpm, a tool life of 20 minute is obtained. When the same bar is turned at 200 rpm, the tool life become 60 minute. Assume that Taylor’s tool life equation is valid. When the bar is turned at 300 rpm, the tool lidfe (in minute) is approximately.

66. The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2 , the natural frequency (in radian/s) of the compound pendulum is ______

67. If you choose plan P, you will have to ______ plan Q, as these two are mutually _______.