Graduate Aptitude Test in Engineering 2017

Question Paper Name: Production and Industrial Engineering 5th Feb 2017

Subject Name: Production and Industrial Engineering

Duration : 180

Total Marks: 100

1. Divergence of the curl of a twice differentiable continuous vector function is

(A) unity

(B) infinity

(D) a unit vector

Ans: (C)

2. For two non-zero vectors is perpendicular to then

(A) the magnitude of is twice the magnitude of

(B) the magnitude of is half the magnitude of

(D) the magnitudes of and are equal

Ans: (D)

3. For an orthogonal matrix Q, the valid equality is

(A) Q^T = Q⁻¹

(B) Q = Q⁻¹

(D) det(Q) = 0

Ans: (A)

4. The product of a complex number z = x + iy and its complex conjugate is

(A) x²

(B) y²

(D) x² + y²

Ans: (D)

5. Using Simpson’s 1/3 rule for numerical integration, the consecutive points are joined by a

(A) line

(B) parabola

(D) polynomial with power 1/3

Ans: (B)

6. For a two dimensional state-of-stress defined as σ_xx = σ_yy = τ_xy = S, the Mohr’s circle of stress has

(A) center at (S, 0) and radius S

(B) center at (0, 0) and radius S

(D) center at (S/2, 0) and radius 2S

Ans: (A)

7. A specimen of steel has yield strength of 700 MPa. The specimen is subjected to a state of plane-stress with σ₁ = σ₂ = 500 MPa. The factor of safety according to the von-Mises theory of failure is _______

Ans: (1.4)

8. The inside and outside radii of a thick-walled cylindrical pressure vessel are denoted by a and b, respectively. If the vessel is subjected to an internal pressure P, then the magnitude of the radial stress σ_rr is

(A) zero at r = a and maximum at r = b

(B) maximum at r = a and zero at r = b

(D) zero at both r = a and r = b

Ans: (B)

9. A metallic cylindrical casing of an exhaust pipe has inner radius 50 mm and wall thickness 7 mm. If the thermal conductivity of the material of the casing is 50 W/m-K, then the thermal resistance of the casing in K/kW is _____(up to three decimal places).

Ans: (0.41 to 0.42)

10. In Value Engineering approach, the value of the product is

(A) inversely proportional to its functions and directly proportional to its cost

(B) directly proportional to its functions and inversely proportional to its cost

(D) directly proportional to its functions as well as its cost

Ans: (B)

11. Match the ASME process charge symbols with their correct description

(A) P-3, Q-4, R-1, S-5, T-2

(B) P-4, Q-2, R-5, S-1, T-3

(D) P-1, Q-5, R-3, S-2, T-4

Ans: (C)

12. In Glass fiber Reinforce Plastic (GFRP) composites with long fibers, the role matrix is to

(P) support and transfer the stresses to the fibers

(Q) reduce propagation of cracks

(R) carry the entire load

(S) protect the fibers against damage

The correct statements are

(A) P, Q and R

(B) Q, R and S

(D) P, R and S

Ans: (C)

13. Turning, drilling, boring and milling are commonly used machining operations. Among these, the operation(s) performed by a single point cutting tool is (are)

(A) turning only

(B) drilling and milling only

(D) boring only

Ans: (C)

14. In chemical machining, the etch factor is expressed as

(A)

(B)

(C)

(D)

Ans: (A)

15. A Shewhart was developed for an in-control process. Considering the probability of a point falling outside the 3σ control limits as 0.0026, the value of average run length for this chart is ______

Ans: (384 to 385)

16. Accuracy of measuring instrument is expressed as

(A) true value – measured value

(B) measured value – true value

(C)

(D)

Ans: (C)

17. The operating characteristic curves of three single sampling plans X, Y and Z with same lot size and acceptance number are shown in the Figure.

Considering the above operating characteristic curves, the correct relationship of the plans with respect to sample size is

(A) sample size of X < sample size of Y < sample size of Z

(B) sample size of X = sample size of Y = sample size of Z

(D) sample size of X > sample size of Y < sample size of Z

Ans: (C)

18. In carbon dioxide molding process, the binder used is

(A) Sodium bentonite

(B) Calcium bentonite

(D) Phenol formaldehyde

Ans: (C)

19. A steel wire of 2 mm diameter is to be drawn from a wire of 5 mm diameter. The value of true s train developed is _____(up to three decimal places).

Ans: (1.80 to 1.85)

20. In gas tungsten arc welding process, the material coated on pure tungsten electrode to enhance its current carrying capacity is

(A) Titanium

(B) Manganese

(D) Thorium

Ans: (D)

21. In powder metallurgy, the process ‘atomization refers to a method of

(A) producing powders

(B) compaction of powders

(D) blending of metal powders

Ans: (A)

22. The ideal stress-strain behavior for a completely brittle material during tensile testing up to failure is described by

(A)

(B)

(C)

(D)

Ans: (B)

23. With reference to Iron-Carbon equilibrium phase diagram, the crystal structure of 0.3% plain carbon steel at 1, 100℃ is

(A) HCP

(B) BCT

(D) FCC

Ans: (D)

24. If E is the modulus of elasticity in GPa, G is the shear modulus in GPa and v is the Poisson’s ratio of a linear elastic and isotropic material, the three terms are related as

(A) E = G(1− 2v)

(B) E = 2G(1 – v)

(D) E = 2G(1 + v)

Ans: (D)

25. A machined surface with standard symbols indicating the surface texture is shown in the Figure. (All dimensions in the Figure are in micrometer).

The waviness height (in micrometer) of the surface is

(A) 1

(B) 50

(D) 120

Ans: (B)

26. The improper integral converges to

(A) 0

(B) 1.0

(D) 2.0

Ans: (C)

27. The local minima of the function f(x) = x² – x⁴ in the range −8 ≤ x ≤ 0.8 is located at

(A)

(B)

(C)

(D)

Ans: (A)

28. Runge-Kutta fourth order method is used to solve the differential equation If the initial value y(0) = 2 and step-size is 0.1, then the value of y(0.1) is _______(up to three decimal places)

Ans: (2.2 to 2.3)

29. Two machines are defective in a lot of 10. A combination of four machines is to be picked at a time from the lot. The maximum number of combinations that can be obtained without any defective machine is ______

Ans: (70)

30. The simply-supported beam shown in the Figure is loaded symmetrically using two equal point loads P. The radius of curvature of deflection-curve is 15m for the portion of the beam that is subjected to pure bending. The vertical deflection (in mm) at point M, equidistant from both the supports, is _____(up to two decimal places).

Ans: (18.00 to 19.00)

31. A solid circular shaft is subjected to a bending moment M and torque T simultaneously. Neglecting the effects of stress concentration, the equivalent bending moment is expressed as

(A)

(B)

(C)

(D)

Ans: (A)

32. A pair of spur gears with 20° full-depth involute teeth is used to transmit 3.5 kW of power. The pinion rotates at 700 rpm and has pitch circle diameter of 100 mm. Assuming a single pair of teeth in contact, the total force acting on a gear tooth (in kN) is

(A) 0.347

(B) 0.954

(D) 1.302

Ans: (C)

33. A manometer is used for the pressure measurement in a closed tank. The three fluids f1, f2 and f3 have specific weights γ, 2γ and 0.5γ, respectively. The schematic arrangement with manometric readings and other dimensions are shown in the Figure. In order to ensure zero gauge pressure in the tank at the mid-height level (h/2), the height of the tank h(in m) is _______

Ans: (2.0)

34. A pipeline with variable cross-section contains water with specific weight 10⁴N/m³. The flow conditions at two points 1 and 2 on the axis of the pipe are:

P₁ = 3 bar, V₁ = 10 m/s

P₂ = 1 bar, V₂ = 20 m/s

Consider frictional losses to be negligible. For no-flow condition between points 1 and 2(as shown in Figure), if the height z₁ from the datum is 1 m, then the height z₂(in m) is _______

(g = 9.81 m/s²)

Ans: (5.5 to 6.0)

35. A reversible heat engine (E) operating in a cycle interacts with three reservoirs 1, 2 and 3 maintained at temperatures T₁ = 500 K, T₂ = 400 K and T₃ = 300 K, respectively. The engine receives 10 kJ of heat from reservoir 1 and rejects 3 kJ to reservoir 3. The net work output, W_net(in kJ) from the engine is ______

Ans: (3)

36. A schematic diagram of peripheral milling is shown in the Figure.

If t is the depth of cut and d is the diameter of the milling cutter, then the length of approach (l_a) is expressed as

(A)

(B)

(C)

(D)

Ans: (C)

37. An electrical appliances showroom sells 2,400 ceiling fans in one year (52 weeks). The holding cost is 10% the cost of the ceiling fan. The cost of one ceiling fan is Rs. 600. The cost incurred for placing an order is Rs. 201. There is a lead time of 5 weeks. The economic order quantity (EOQ) and the reorder level, respectively (rounded to the next higher integer) are

(A) 231, 127

(B) 38, 231

(D) 127, 13

Ans: (C)

38. In a calendar year, the demand forecast of motorbikes for the month of June is 200. The actual demand of motorbikes for the month of June and July are 300 and 350, respectively. If single exponential smoothing method with smoothing constant 0.7 is used, then the demand forecast for the month of August is _____

Ans: (326)

39. In a project, tasks, A, B, C, D, E, F, G, H, I and J are to be performed. The precedence relationships and the time required (in days) to complete the tasks are given in the Table.

The time required (in days) to complete the project along the critical path is ______

Ans: (48)

40. The potential production alternative for manufacturing a product along with their unit cost and monthly capacity are given in the Table.

The inventory at the end of July is 100 units. If the demand for the month of August is 620, then the minimum total cost (in Rs.) to meet the demand is _______

Ans: (2900)

41. The preparatory and miscellaneous codes used in CNC part programming and the functions are given in the Table.

The correct combinations of code and the respective function is

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

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

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

Ans: (A)

42. A surface of 30 mm × 30 mm of an iron block is machined using electrochemical machining process. The atomic weight and valency of iron of 55.85 and 2, respectively. The density o f iron is 7,860 kg/m³. If input current is 1,000 A and Faraday’s constant is 96,540 Coulombs, then the feed rate (in mm/min) is _______(up to two decimal places).

Ans: (2.40 to 2.50)

43. Quality control department of a company maintains ‘c’ chart to assess the quality of laptops. In this process, twenty laptops are examined randomly. The number of nonconformities observed per laptop is given in the Table.

Based on the data, the upper control limit for the ‘c’ chart is _______(up to two decimal places).

Ans: (11.00 to 11.20)

44. The Merchant circle diagram showing various forces associated with a cutting process using a wedge-shaped tool is given in the Figure.

The coefficient of friction can be estimated from the ratio

(A)

(B)

(C)

(D)

Ans: (D)

45. An air conditioner unit is expected to run continuously. The mean time between failures (MTBF) for this unit is 2,000 hours and the mean time to repair (MTTR) is 48 hours. The availability of the air conditioning unit is ______(up to three decimal places).

Ans: (0.970 to 0.980)

46. A firm manufactures capacitors using a specialized process. The desired specification for the capacitance is 40 ≠ 10 picofarads (pF). The process used is in statistical control. If the process mean is 41 pF and the estimated standard deviation is 3 pF, then the process capability index C_pk is _______

Ans: (1)

47. A metallic strip having thickness of 12 mm is to be rolled using two steel rolls, each of 800 mm diameter. It is assumed that there is no change in width of the strip during rolling. In order to achieve 10% reduction in cross-sectional area of the strip after rolling, the angle subtended (in degrees) by the deformation zone at the center of the roll is

(A) 1.84

(B) 3.14

(D) 8.23

Ans: (B)

48. An electron beam welding process uses 15 mA beam current at an accelerating voltage of 150 kV. The energy released per second by the beam (in J) is ______(up to one decimal place).

(1 Ampere = 6.28 × 10¹⁸ electrons per second, 1 eV= 1.6 × 10⁻¹⁹ J)

Ans: (2250 to 2265)

49. In a machine shop, four jobs need to be assigned to four different machines. Each of the jobs is to be assigned to one machine only at a time. The time taken to complete the job in different machines is given in the Table.

In order ensure that the total time required to complete all the jobs is minimum, the optimal assignment of the job is

(A) J₁ ⇒ M₄, J₂ ⇒ M₂, J₃ ⇒ M₃, J₄ ⇒ M₁

(B) J₁ ⇒ M₂, J₂ ⇒ M₁, J₃ ⇒ M₄, J₄ ⇒ M₃

(D) J₁ ⇒ M₄, J₂ ⇒ M₂, J₃ ⇒ M₁, J₄ ⇒ M₃

Ans: (B)

50. A hose coupling manufacturing company has production capacity of 2,500 units per year. The unit selling price of the item is Rs. 150/ The fixed cost of production is Rs. 80,000 and variable cost of production per unit its Rs. 70. If the company wishes to achieve a profit of Rs. 20,000 during the calendar year, then the minimum quantity to be produced is ______

Ans: (1250)

51. Schematic diagram of pouring basin and sprue of a gating system is shown in the Figure. Depth of molten metal in the pouring basin is 100 mm and the height of the sprue is 1,500 mm.

Consider the cross-section of the sprue is circular, the ratio d₁ : d₂ to avoid aspiration is

(A) 3 : 2

(B) 5 : 6

(D) 1 : 2

Ans: (D)

52. In a numerical control (NC) machine positioning system, the measures of precision are expressed by considering a single axis as shown in the Figure.

If σ is standard deviation of the error distribution, then l, m and n are

(A) l = Accuracy, m = Repeatability, n = control resolution

(B) l = Repeatability, m = Accuracy n = control resolution

(D) l = Accuracy, m = Control resolution, n = Repeatability

Ans: (A)

53. In a machining operation with turning tool, the tool life (T) is related to cutting speed v(m/s), feed f(mm) and depth of cut d(mm) as

T=Cv⁻^2.5f⁻^0.9d⁻^0.15

where, C is a constant. The suggested values for the cutting parameters are: v = 1.5 m/s, f = 0.25 mm and d = 3 mm for normal rough turning. If the operation is performed at twice the cutting speed and the other parameters remain unchanged, the corresponding percentage change in tool life is ______

Ans: (80 to 84)

54. The annual demand of wrist produced on an assembly line is 1,03,125 units. The line operates 50 weeks/year, 5 shifts/week and 7.5 hours/shift. The uptime efficiency of the line is 99%. The cycle time (T_c) of the assembly line (in minutes/unit) is _____(up to two decimal places).

Ans: (1.00 to 1.10)

55. In a gear manufacturing company, three orders P, Q and R are to be processed on a hobbing machine. The orders were received in the sequence P – Q – R. The Table indicates the process time remaining and production calendar due date for each order.

Considering today as the Day 10 in the production calendar of the Hobbing Shop, the sequence of the order scheduled using the ‘Critical Ratio’ rule is

(A) P – Q – R

(B) P – R – Q

(D) Q – R – P

Ans: (D)

56. She has a sharp tongue and it occasionally turn _______

(A) hurtful

(B) left

(D) vital

Ans: (A)

57. I_____ made arrangements had I _______ informed earlier.

(A) could have, been

(B) would have, being

(D) had been, been

Ans: (A)

58. In the summer, water consumption is known to decrease overall by 25%. A Water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.

Which of the following statements is correct?

(A) The ratio of household to other consumption is 8/17

(B) The ratio of household to other consumption is 1/17

(D) There are errors in the official’s statement.

Ans: (D)

59. 40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represents this as a slice of a pie chart is

(A) 120

(B) 144

(D) 212

Ans: (B)

60. Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be deduced from the preceding sentences?

i. At least one bench is a table

ii. At least one shelf is a bench

iii. At least one chair is a table

iv. All benches are chairs

(A) Only i

(B) Only ii

(D) Only iv

Ans: (B)

61. ‘If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these page; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”.

Here, the word ‘antagonistic’ is closest in meaning to

(A) impartial

(B) argumentative

(D) hostile

Ans: (D)

62. S, T, U, V, W, X, Y, and Z are seated around a circular table. T’s neighbours are Y and V, Z is seated third to the left of T and second to the right of S,. U’s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?

(A) X

(B) W

(D) T

Ans: (A)

63. Trucks (10 m long) and cars (5 m long) go on a single lane bridge.. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?

(A) 1440

(B) 1200

(D) 600

Ans: (A)

64. There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

(A) 56

(B) 52

(D) 44

Ans: (A)

65. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.

The path from P to Q is best described by

(A) Up-Down-Up-Down

(B) Down-Up-Down-Up

(D) Up-Down-Up

Ans: (C)

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