GATE ME-2

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1. Match the Machine Tools (Group A) with the probable Operations

(A) P-1, Q-2, R-4, S-3

(B) P-2, Q-1, R-4, S-3

(D) P-3, Q-4, R-2, S-1

2. With respect to metal working, match Group A with Group B:

(A) P-II, Q-III, R-VI, S-V

(B) P-III, Q-I, R-VI, S-V

(D) P-I, Q-II, R-V, S-VI

An analytic function of a complex variable z = x + i y is expressed as f (z) = u(x, y) + i v(x, y), where i = -1 . If u(x, y) = 2 x y, then v(x, y) must be

(A) x² + y² + constant

(B) x² - y² + constant

(D) - x² - y² + constant

4.Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true?

(A) I yields after II

(B) II yields after I

(D) Nothing can be said about their relative yielding

5.For the CNC part programming, match Group A with Group B:

(A) P-II, Q-III, R-I, S-IV

(B) P-I, Q-III, R-II, S-IV

(D) P-II, Q-I, R-III, S-IV

6.A hole of 20 mm diameter is to be drilled in a steel block of 40 mm thickness. The drilling is performed at rotational speed of 400 rpm and feed rate of 0.1 mm/rev. The required approach and over run of the drill together is equal to the radius of drill. The drilling time (in minute) is

(A) 1.00

(B) 1.25

(D) 1.75

7.A rectangular hole of size 100 mm × 50 mm is to be made on a 5 mm thick sheet of steel having ultimate tensile strength and shear strength of 500 MPa and 300 MPa, respectively. The hole is made by punching process. Neglecting the effect of clearance, the punching force (in kN) is

(A) 300

(B) 450

(D) 750

8.Which one of the following is NOT a decision taken during the aggregate production planning stage?

(A) Scheduling of machines

(B) Amount of labour to be committed

(D) Inventory to be carried forward

9. A CNC vertical milling machine has to cut a straight slot of 10mm width and 2mm depth by a cutter of 10mm diameter between points (0,0) and (100,100) on the XY plane (dimensions in mm). The feed rate used for milling is 50mm/min. milling time for the slot (in seconds) is

(A) 120

(B) 170

(D) 240

10.A solid cylinder of diameter 100mm and height 50mm is forged between two frictionless flat dies to a height of 25mm. The percentage change in diameter is

(A) 0

(B) 2.07

(D) 41.4

11. The velocity triangles at the inlet and exit of the rotor of a turbo machine are shown. V denotes the absolute velocity of the fluid, W denotes the relative velocity of the fluid, and U denotes the blade velocity. Subscripts 1 and 2 refer to inlet and outlet respectively. If V2 = W1 and V1 = W2, then the degree of reaction is

(A) 0

(B) 1

(D) 0.25

12. Which one of the following configurations has the highest fin effectiveness?

(A) Thin, closely spaced fins

(B) Thin, widely spaced fins

(D) Thick, closely spaced fins

13. In the mechanism given below, if the angular velocity of the eccentric circular disc is 1rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is

(A) 0.05

(B) 0.1

(D) 10.0

14. A circular solid disc of uniform thickness 20mm, radius 200mm and mass 20kg, is used as a flywheel. If it rotates at 600rpm, the kinetic energy of the flywheel, in Joules is

(A) 395

(B) 790

(D) 3160

15. For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

(A) 1

(B) 2

(D) 8

16. At x=0, the function f x  x3  1 has

(A) A maximum value

(B) A minimum value

(D) A point of inflection

17. Match the following metal forming processes with their associated stresses in the workpiece.

(A) P-4, Q-1, R-2, S-3

(B) P-4, Q-1, R-3, S-2

(D) P-1, Q-3, R-2, S-4

18. In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, the material removal rate

(A) Increases continuously

(B) Decreases continuously

(D) Increases, becomes stable and then decreases

19. During normalizing process of steel, the specimen is heated

(A) Between the upper and lower critical temperature and cooled in still air

(B) Above the upper critical temperature and cooled in furnace

(D) Between the upper and lower critical temperature and cooled in furnace

20. Oil flows through a 200mm diameter horizontal cast iron pipe (friction factor, f=0.0225) of length 500m. The volumetric flow rate is (in m) due to friction is ( assume g=9.81m/s2 ) 0.2m3 / s . The head loss

(A) 116.18

(B) 0.116

(D) 232.36

21.Steam enters an adiabatic turbine operating at steady state with an enthalpy of 3251.0kJ/kg and leaves as a saturated mixture at 15kPa with quality (dryness fraction) 0.9. The enthalpies of the saturated liquid and vapour at 15kPa are h_f=225.94kJ/kg and h_g=2598.3kJ/kg respectively. The mass flow rate of steam is 10kg/s. Kinetic and potential energy changes are negligible. The power output of the turbine in MW is:

(A) 6.5

(B) 8.9

(D) 27.0

22. The following are the data for two crossed helical gears used for speed reduction: Gear I: Pitch circle diameter in the plane of rotation 80mm and helix angle 30º. Gear II: Pitch circle diameter in the plane of rotation 120mm and helix angle 22.5º

If the input speed is 1440rpm, the output speed in rpm is

(A) 1200

(B) 900

(D) 720

23. A solid disc of radius r rolls without slipping on the horizontal floor with angular velocity  and angular acceleration  . The magnitude of acceleration of the point of contact on the disc is

(A) Zero

(B) ra

(C)

(D) rw²

24. A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

(A) 0

(B) 1

(D) 2.02

25.The area enclosed between the straight line y=x and the parabola x-y plane is y = x²in the

(A) 1/6

(B) 1/4

(D) 1/2

26.Calculate the punch size in mm, for a circular blanking operation for which details are given below:

Size of the blank    25mm
Thickness of the sheet     2mm
Radial clearance between punch and die        0.06mm
Die allowance                        0.05mm

(A) 24.83

(B) 24.89

(D) 25.17

27. In a single pass rolling process using 410mm diameter steel rollers, a strip of width 140mm and thickness 8mm undergoes 10% reduction of thickness. The angle of bite in radians is

(A) 0.006

(B) 0.031

(D) 0.600

28.In a DC arc welding operation, the voltage-arc length characteristic was obtained as Varc = 20 + 5l where the arc length l was varied between 5mm and 7mm. Here Varcdenotes the arc voltage in Volts. The arc current was varied from 400A to 500A. Assuming linear power source characteristic, the open circuit voltage and short circuit current for the welding operation are:

(A) 45V, 450A

(B) 75V, 550A

(D) 150V, 1500A

29. A solid circular shaft needs to be designed to transmit a torque of 50Nm. If the allowable shear stress of the material is 140MPa, assuming a factor of safety of 2, the minimum allowable design diameter in mm is

(A) 8

(B) 16

(D) 32

30.A force of 400N is applied to the brake drum of 0.5m diameter in a band brake system as shown in the figure, where the wrapping angle is 180º. If the coefficient of friction between the drum and the band is 0.25, the braking torque applied, in Nm is

(A) 100.6

(B) 54.4

(D) 15.7

31.The system of algebraic equations given below has

x + 2y + z = 4
2x + y + 2z = 5
x - y + z = 1

(A) A unique solution of x=1, y=1 and z=1

(B) Only the two solutions of (x=1, y=1 and z=1) and (x=2, y=1 and z=0)

(D) No feasible solution

32. In a single pass drilling operation, a through hole of 15mm diameter is to be drilled in a steel plate of 50mm thickness. Drill spindle speed is 500rpm, feed is 0.2mm/rev and drill point angle is 118º. Assuming 2mm clearance at approach and exit, the total drill time in seconds is

(A) 35.1

(B) 32.4

(D) 30.1

33. A room contains 35kg of dry air and 0.5g of water vapour. The total pressure and temperature of air in the room are 100kPa and 25ºC respectively. Given that the saturation pressure for water at 25ºC is 3.17kPa, the relative humidity of the air in the room is

(A) 67%

(B) 55%

(D) 71%

34. A fillet-welded joint is subjected to transverse loading F as shown in the figure. Both legs of the fillets are of 10mm size and the weld length is 30mm. If the allowable shear stress of the weld is 94MPa, considering the minimum throat area of the weld, the maximum allowable transverse load in kN is

(A) 14.44

(B) 17.92

(D) 22.16

35.The state of stress at a point under plane stress condition is

sxx = 40MPa; syy = 100MPa and txy = 40MPa
The radius of the Mohr's circle representing the given state of stress in MPa is

(A) 40

(B) 50

(D) 100

36. The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100MPa is

(A) 8.17

(B) 11.15

(D) 22.30

37. If F =1kN , the magnitude of the vertical reaction force developed at the point B in KN is

(A) 0.63

(B) 0.32

(D) 1.46

38. The power required for the compressor in kW is

(A) 5.94

(B) 1.83

(D) 39.5

39. The rate at which heat is extracted in kJ/s from the refrigerated space is

(A) 28.3

(B) 42.9

(D) 14.6

40. The critical path for the project is

(A) a-b-e-g-h

(B) a-c-g-h

(D) a-b-c-f-h

41. If the duration of activity f alone is changed from 9 to 10 days, then the

(A) Critical path remains the same and the total duration to complete the project changes to 19days

(B) Critical path and the total duration to complete the project remain the same

(D) Critical path changes and the total duration to complete the project changes to 17days

42. The exit temperature of the air is

(A) 516K

(B) 532K

(D) 468K

43. The exit area of the nozzle in cm2 is

(A) 90.1

(B) 56.3

(D) 12.9

44. The cost function for a product in a firm is given by 5q2 , where q is the amount of production. The firm can sell the product at a market price of Rs.50 per unit. The number of units to be produced by the firm such that the profit is maximized is

(A) 5

(B) 10

(D) 25

45. Choose the most appropriate alternative from the options given below to complete the following sentence:

Suresh's dog is the one was hurt in the stampede

(A) that

(B) which

(D) whom

46. Choose the grammatically INCORRECT sentence:

(A) They gave us the money back less the service charges of Three Hundred rupees.

(B) This country's expenditure is not less than that of Bangladesh.

(D) This country's expenditure on educational reforms is very less

47. Which one of the following options is the closest in meaning to the word given below?

Mitigate

(A) Diminish

(B) Divulge

(D) Denote

48. Choose the most appropriate alternative from the options given below to complete the following sentence:

Despite several the mission succeeded in its attempt to resolve the conflict.

(A) attempts

(B) setbacks

(D) delegations

49. Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economic data. Requirements: High School-pass, must be available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.

Which one of the following is the best inference from the above advertisement?

(A) Gender-discriminatory

(B) Xenophobic

(D) Not gender-discriminatory

50. Given the sequence of terms, AD CG FK JP, the next term is

(A) OV

(B) OW

(D) PW

51. Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list

Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list

S: Doubling each entry in a list leaves the standard deviation of the list unchanged

(A) P, Q

(B) Q, R

(D) R, S

52. An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable Of X's shock absorbers, 96% are reliable. Of Y's shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

(A) 0.288

(B) 0.334

(D) 0.720

53.A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x - 0.1x2 where y is the height of the arch in meters. The maximum possible height of the arch is

(A) 8 meters

(B) 10 meters

C) 12 meters

D) 14 meters

54. Choose the correct verb to fill in the blank below:

Let us

(A) Introvert

(B) alternate

(D) Altruist

55. Choose the most suitable one word substitute for the following expression:

Connotation of a road or way

(A) Pertinacious

(B) Viaticum

(D) Ravenous

56. Find the missing sequence in the letter series below:

A, CD, GHI, ? , UVWXY

(A) LMN

(B) MNO

(D) NOPQ

57. Choose the most appropriate word from the options given below to complete the following sentence

If the athlete had wanted to come first in the race, he several hours every day.

(A) should practise

(B) Should have practiced

(D) Should be practicing

58.Ram and Shyam shared a secret and promised to each other that it would remain between them. Ram expressed himself in one of the following ways as given in the choices below. Identify the correct way as per standard English

(A) It would remain between you and me

(B) It would remain between I and you

(D) It would remain with me

59. In the following question, the first and the last sentence of the passage are in order and numbered 1 and 6. The rest of passage is split into 4 parts and numbered as 2,3,4 and 5. These 4 parts are not arranged in proper order. Read the sentences and arrange them in logical sequence to make a passage and choose the correct sequence from the given options.

On Diwali, the family rises early in the morning
The whole family, including the young and old enjoy doing
Children let off fireworks later in the night with their
At sunset, the lamps are lit and the family performs various
Father, mother and children visit relatives and exchange gifts and

6.Houses look so pretty with lamps all around

(A) 2, 5, 3, 4

(B) 5, 2, 4, 3

(D) 4, 5, 2, 3

60.A gas is stored in a cylindrical tank of inner radius 7 m and wall thickness 50 mm. The gage pressure of the gas is 2 MPa. The maximum shear stress (in MPa) in the wall is

(A) 35

(B) 70

(D) 280

61. Which of the following statements regarding a Rankine cycle with reheating are TRUE ?

(I)Increase in average temperature of heat addition
(II)reduction in thermal efficiency
(III) drier steam at the turbine

(A) only (i) and (ii) are correct

(B) only (ii) and (iii) are correct

(i) , (ii) and (iii) are correct

62. Within a boundary layer for a steady incompressible flow, the Bernoulli equation

(A) holds because the flow is steady

(B) holds because the flow is incompressible

(D) does not hold because the flow is frictional

63. At least one eigenvalue of a singular matrix is

(A) Positive

(B) Zero

(D) Imaginary

64. At x= 0, the function f(x) = |x| has

(A) a minimum

(B) a maximum

(D) neither a maximum nor minimum

65. For the truss shown in figure , the magnitude of the force (in kN)ni the member SR is

(A) 10

(B) 14.14

(D) 28.28

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