GATE question paper Production and Industrial Engineering 2009 (PI)

1.

The homogeneous part of the differential equation

 (p, q and r are constants) has real distinct roots if

(A) p² - 4q > 0

(B) p² - 4q < 0

(C) p² - 4q = 0

(D) p² - 4q = r

2.

The total derivative of the function 'x y' is

(A) xdy + ydx

(B) xdx + ydy

(C) dx + dy

(D) dx dy

3.

A helical compression spring has: d = wire diameter, D = mean coil diameter, E = Young's modulus, G = modulus of rigidity and N_a = number of active coils. The spring stiffness is

(A)

(B)

(C)

(D)

4.

Which of the following processes is NOT executed by an ideal Rankine cycle with no superheat?

(A) Isentropic expansion

(B) Isentropic compression

(C) constant temperature heat addition

(D) Constant temperature heat rejection

5.

During the numerical solution of a first order differential equation using the Euler (also known as Euler Cauchy) method with step size h, the local truncation error is of the order of

(A) h²

(B) h³

(C) h⁴

(D) h⁵

6.

For a granted patent to last for 20 years, the patent must be

(A) owned by the investor          

(B) renewed and maintained

(C) novel                      

(D) non-obvious

7.

As per Kendall's notation in M/G/c queuing system, the number of arrivals in a fixed time follows

(A) beta distribution

(B) Normal distribution

(C) Poisson distribution

(D) Uniform distribution

8.

Which of the following forecasting models explicitly accounts for seasonality of demand?

(A) Simple moving average model

(B) Simple exponential smoothing model

(C) Holt's model

(D) Winter's model

9.

A typical Fe-C alloy containing greater than 0.8% C is known as

(A) Eutectoid steel         

(B) Hypoeutectoid steel

(C) Mild steel

(D) Hypereutectoid steel

10.

The capacity of a material to absorb energy when deformed elastically, and to release it back when unloaded is termed as

(A) toughness

(B) resilience

(C) ductility                   

(D) malleability

11.

The product of the complex numbers (3 - i2) and (3 + 4) results in

(A) (1 + i6)

(B) (9 - i8)

(C) (9 + i8)

(D) (17 + i6)

12.

The value of the determinant  is

(A) -28

(B) -24

(C) 32

(D) 36

13.

If module and number of teeth of a spur gear with an involute profile are 3 mm and 23 respectively, then the pitch diameter (in mm) of the spur gear is

(A) 7.67

(B) 15.34

(C) 34.50

(D) 69.00

14.

Hot chamber die casting process is NOT suited for

(A) lead and its alloy

(B) Zinc and its alloys

(C) Tin and its alloys

(D) aluminum and its alloys

15.

The total angular movement (in degrees) of a lead-screw with a pitch of 5.0 mm to drive the work-table by a distance of 200 mm in a NC machine is

(A) 14400

(B) 28800

(C) 57600

(D) 72000

16.

Anisotropy in rolled components is caused by

(A) change in dimensions

(B) scale formation

(C) closure of defects

(D) grain orientation

17.

Which of the following processes is used to manufacture products with controlled porosity?

(A) Casting

(B) Welding

(C) forming

(D) Powder metallurgy

18.

Which of the following powders should be fed for effective oxy-fuel cutting of stainless steel?

(A) Steel

(B) Aluminum

(C) Copper

(D) Ceramic

19.

An autocollimator is used to

(A) measure small angular displacements on flat surface

(B) compare known and unknown dimensions

(C) measure the flatness error

(D) measure roundness error between centers

20.

Diamond cutting tools are not recommended for machining of ferrous metals due to

(A) high tool hardness

(B) high thermal conductivity of work material

(C) poor tool toughness

(D) chemical affinity of tool material with iron

21.

The value of x₃ obtained by solving the following system of linear equations is

x₁ + 2x₂ - 2x₃ = 4

2x₁ + x₂ + x₃ = -2

-x₁ + x₂ - x₃ = 2

(A) -12

(B) -2

(C) 0

(D) 12

22.

The displacement and acceleration of a cam follower mechanism are plotted in the following fitures:

The nature of the displacement curve is

(A) Cubic          

(B) Quadratic

(C) Simple harmonic

(D) Linear

23.

The solution of the differential equation  = 0 with boundary conditions: (i)  = 1 at x = 0 and (ii)  = 1 at x = 1, is

(A) y = 1

(B) y = x

(C) y = x + C, where C is an arbitrary constant

(D) y = C₁x + C₂, where C₁ and C₂ are arbitrary constants

24.

The line integral of the vector function  along the x-axis from x = 1 to x = 2 is

(A) 0

(B) 2.33

(C) 3

(D) 5.33

25.

using direct extruction process, a round billet of 100 mm length and 50 mm diametr is extruded. considering an ideal deformation process (no friction and no redundant work), extrusion ratio 4, and average flow stress of material 300 MPa, the pressure (in MPa) on the ram will be

(A) 416

(B) 624

(C) 700

(D) 832

26.

A friction clutch is designed to transmit 15 horsepower at 1500 rpm. the torque (in N×m) experienced by the clutch is

(A) 1.19

(B) 7.46

(C) 71.24

(D) 447.61

27.

A manufacturer has set up an assembly line where first, Task I is performed in Workstation 1 for 0.3 minutes; then Task II is performed in Workstation 2 for 0.4 minutes; and finally Task III is performed in workstation 3 for 0.3 minutes. The efficiency (in %) of this assembly line setup is

(A) 33.33

(B) 64.33

(C) 75.33

(D) 83.33

28.

A biaxial stress element in subjected to tensile and shear stresses as shown n the figure. If s_y = 20 MPa and t_xy = t_yx = 15MPa. the principal normal stress (in MPa) are:

(A) 5 and 55

(B) 10 and 30

(C) 12 and 48

(D) 20 and 42

29.

The area under the curve shown, between x = 1 and x = 3 is to be evaluated using the trapezoidal rule. The following points on the curve are given.

The evaluated area in (in m²) will be

(A) 7

(B) 8.67

(C) 9

(D) 18

30.

The pressure drop for laminar flow of a liquid in a smooth pipe at normal temperature and pressure is

(A) directly proportional to density          

(B) inversely proportional to density

(C) independent of density

(D) proportional to (density)^0.75

31.

A titanium sheet of 5.0 mm thickness is cut by wire-cut EDM process using a wire of 1.0 mm diameter. A uniform spark gap of 0.5 mm on both sides of the wire is maintained during cutting operation. If the feed rate of the wire into the sheet is 20 mm/min, the material removal rate
(in mm³/min) will be

(A) 150

(B) 200

(C) 300

(D) 400

32.

Autogenous gas tungsten are welding of a steel plate is carried out with welding current of 500 a, voltage of 20 V, and weld speed of 20 mm/min. Consider the heat transfer efficiency from the arc to the weld pool as 90%. the heat input per unit length (in kJ/mm) is

(A) 0.25

(B) 0.35

(C) 0.45

(D) 0.55

33.

Consider steady flow of water in a situation where two pipe lines (Pipe 1 and Pipe 2) combine into a single pipe line (Pipe 3) as shown in the figure. the cross-sectional areas of all three pipelines are constant. The following data is given:

Assuming the water properties and the velocities to be uniform across the cross section of the inlet and the outlet, the exit velocity (in m/s) in pipe 3 is

(A) 1

(B) 1.5

(C) 2

(D) 2.5

34.

Match the following:

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

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

(C) P - 2, Q - 1, r - 4, S - 3

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

35.

Consider the joint probability mass function of random variables X and Y as shown in the table below:

For instance, P {X = 1, Y = 2} = 0.3

The value of P {X = 2 | Y = 2} is

(A) 0.10

(B) 0.25

(C) 0.40

(D) 0.75

36.

A grocery store faces a demand of 50 units of soap per day. The store orders soap periodically. it costs Rs. 100 to initiate a purchase order. It costs Rs. 0.04 per soap per day to store the soap. The lead time between placing and receiving the order is 4 days. The optimal inventory policy for ordering soap is to

(A) order 500 unit of soap whenever inventory level drops to 200 units

(B) order 500 units of soap whenever inventory level drops to 100 units

(C) order 1000 units of soap whenever inventory level drops to 200 units

(D) order 1000 units of soap whenever inventory level drops to 100 units

37.

A disk of 200 mm diameter is blanked from a strip of an aluminum alloy of thickness 3.2 mm. The material shear strength to fracture is 150 MPa. The blanking force (in kN) is

(A) 291

(B) 301

(C) 311

(D) 321

38.

Match the following:

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

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

(C) P - 1, Q - 4, R - 2, s - 3

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

39.

Match the following:

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

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

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

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

40.

The spur gear having a pressure angle of 20°, module of 3 mm and 40 teeth is to be inspected for its pitch circle diameter using two rollers (test plug method). If the centres of the rollers lie on the pitch circle, the suitable roller diameter (in mm) and the resulting distance 9in mm) between the rollers placed in opposite spaces will respectively be

(A) 2.9 and 82.9

(B) 2.9 and 165.9

(C) 5.9 and 82.9

(D) 5.9 and 165.9

41.

A company makes a product using three independent components I, II, and III with reliabilities of 0.80, 0.85 and 0.90 respectively. If the company decides to add one redundant unit of component I to improve reliability, then the reliability of the product is

(A) 0.612

(B) 0.734

(C) 0.837

(D) 0.969

42.

Given:

Assertion [a]: managers spend time on job analysis and job rating.

Reason [r]: Scientific management of wage structures through job evaluation helps increase productivity.

(A) Both [a] and [r] are true and [r] is the correct reason for [a].

(B) Both [a] and [r] are true, but [r] is not the correct reason for [a].

(C) Both [a] and [r] are false.

(D) [a] is true but [r] is false.

43.

A spare parts retain shop has sales of Rs. 4,00,000 and a profit of Rs. 50,000 for a product, in its first quarter. The profit volume (PV) ratio is 25%. The margin of safety = profit / PV ratio. The break even point of sales (in Rs.) is

(A) 20,000

(B) 40,000

(C) 2,00,000

(D) 4,00,000

44.

The following information relates to worker's payment in a company:

Standard production of a worker = 12 jobs per hour

Standard job rate = Rs. 3.00 per job

Pay for production less than standard = 85% of standard job rate

Pay for production more than standard = 120% of standard job rate

Three workers produce at the rate of 11, 13 and 15 jobs per hour. The total pay for three workers per hour based on differential wage incentive scheme is

(A) Rs. 117.00

(B) Rs. 128.85

(C) Rs. 1404.00

(D) Rs. 1546.20

45.

Match the following:

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

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

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

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

46.

Match the following:

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

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

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

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

47.

In an orthogonal machining operation, the tool life obtained is 10 min at a cutting speed of 100 m/min, while at 75 m/min cutting speed, the tool life is 30 min. The value of index (n) in the Taylor's tool life equation

(A) 0.262

(B) 0.323

(C) 0.423

(D) 0.521

48.

A solid cylinder of diameter D and height equal to D, and a solid cube of side L are being sand cast by using the same material. Assuming there is no superheat in both the cases, the ratio of solidification time of the cylinder to the solidification time of the cube is

(A) (L/D)²

(B) (2L/D)²

(C) (2D/L)²

(D) (D/L)²

49.

Following are some possible characteristics of a pile of power mixture:

P. Low inter particle friction

Q. High inter particle friction

R. Low porosity

S. High porosity

If the angle of repose for a pile of power mixture is low, it will exhibit

(A) P and R

(B) P and S

(C) Q and S

(D) Q and R

50.

Match the following:

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

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

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

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

Common Data Questions

Common Data for Questions 51 and 52

Consider the Linear Programming Problem (LPP)

Maximize           z = 4x₁ + 3x₂ + 2x₃

Subject to:

2x_i + x₂ + 2x₃ £ 50          (constraint 1)

x₁ + x₂ + x₃ £ 30 (constraint 2)

x₁, x₂, x₃ ³ 0

The associated simplex tableau at optimality is shown below, there s₁ and s₂ repreent the slacks for constraints 1 and 2, respectively.

51

Basic variables in the optimal solution are

(A) s₁ and s₂

(B) x₁ and x₂

(C) x_1, x₂ and x₃

(D) x₃, s₁ and s₂

52.

Suppose that in the LPP given, the right hand side of constraint 1 changes from 50 to 40. The new objective value is

(A) 90

(B) 100

(C) 110

(D) 120

Common Data for Questions 53 and 54:

In acceptance sampling, the probability distribution of the number of defectives X in a sample can be approximated as a Poisson distribution, Prob {X = k} = , for k = 0, 1, 2 ..., where n is the sample size and p is the actual proportion or percent of defective items in a batch.

a company receives a shipment batch of N = 2000 items. the sampling plan followed by the company is to sample n = 50 items from the batch and accept the batch if the number of defective items are 2 or less. let the acceptable Quality Level (AQL) be 0.02 and the Lot Tolerance Percent Defective (LTPD) be 0.05.

53

The probability of incorrectly rejecting a good batch or the Producer's risk is

(A) 0.0805

(B) 0.3678

(C) 0.5437

(D) 0.9195

54.

The probability of incorrectly accepting a bad batch or the Consumer's risk is

(A) 0.0805        

(B) 0.3678        

(C) 0.5437        

(D) 0.9195

Common Data for Questions 55 and 56:

An orthogonal turning operation is carried out at 20 m/min cutting speed, using a cutting tool of rake angle 15°. The chip thickness is 0.4 mm and the uncut chip thickness is 0.2 mm.

55.

The shear plane angle (in degrees) is

(A) 26.8

 (B) 27.8

(C) 28.8

(D) 29.8

56.

The chip velocity (in m/min) is

(A) 8

(B) 10

(C) 12

(D) 14

Linked Answer Questions

Statement for Linked Answer Questions 57 and 58:

Four jobs need to be processed sequentially on two machines, first on machine M and then on Machine N. Each machine can process only one job at a time. The processing time (in min) are given in the table below:

57.

The optimal sequence of jobs that will minimize makespan (total time required to complete all jobs) is

(A) I - II - III - IV                       

(B) III - II - I - IV

(C) IV - III - I - II                       

(D) III - I - IV - II

58.

When the jobs are processed based on the optimal sequence tha tminimizes makespan, the totla idle time (in min) on Machine N is

(A) 1

(B) 3

(C) 4

(D) 6

Statement for Linked Answer Questions 59 and 60:

Resistance spot welding of two steel sheets is carried out in lap joint configuration by using a welding current of 3 kA and a weld time of 0.2 s. A molten weld nugget of volume 20 mm³ is obtained. The effective contact resistance is 200 mW (micro-ohms). The material properties of steel are given as: (i) latent heat of melting: 1400 kJ/kg, (ii) density: 8000 kg/m³, (iii) melting temperature: 1520°C, (iv) specific heat: 0.5 kJ/kg°C. The ambient temperature is 25°C.

59.

Heat (in Joules) used for producing weld nugget will be (assuming 100% heat transfer efficiency)

(A) 324

(B) 334

(C) 344

(D) 354

60.

Heat (in Joules) dissipated to the base metal will be (neglecting all other heat losses)

(A) 10

(B) 16

(C) 22

(D) 32

End of the Question Paper