Production And Industrial Engineering - PI 2012 GATE Paper (Practice Test) - GATE

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

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

Mitigate

Q. 6 - Q. 10 carry two marks each.

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

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

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

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?

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

Q. 11 – Q. 35 carry one mark each.

For the spherical surface the unit outward normal vector at the point  is given by

Consider the function f (x) = |x| in the interval -1 <x <1. At the point x = 0, f(x) is

At x = 0, the function f(x) = x³ + 1 has

The area enclosed between the straight line y = x and the parabola y = x² in the x-y plane is

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 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 cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of the beam cross section about the neutral axis is I and the Young’s modulus is E. The magnitude of the maximum deflection is

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

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

Note: All dimensions are in mm.

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

A n ideal gas of mass m and temperature T₁ undergoes a reversible isothermal process from an initial pressure P₁ to final pressure P₂. The heat loss during the process is Q. The entropy change ΔS of the gas is

F or an opaque surface, the absorptivity (α ) , transmissivity (τ) and reflectivity (ρ) are related by the equation:

W hich one of the following configurations has the highest fin effectiveness?

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

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

In an interchangeable assembly, shafts of size   mm mate with holes of size  mm. The maximum interference (in microns) in the assembly is

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

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

During normalizing process of steel, the specimen is heated

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

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

Which one of the following is NOT associated with the process of new product development?

A process needs to be standardized for method and time. Which one of the following represents the sequence of work study experiments?

Reduction in the variability of manufactured product characteristics will definitely result in observations close to

Q. 36 - Q. 65 carry two marks each.

Q. 

The system of algebraic equations given above has

For the matrix A = , ONE of the normalized eigen vectors is given as

Consider the differential equation  with the boundary conditions of
y(0) = 0 and y(1) = 1. The complete solution of the differential equation is

The inverse Laplace transform of the function    is given by

A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is

T he state of stress at a point under plane stress condition is

σ_xx = 40 MPa, σ_yy = 100 MPa and τ_xy = 40 MPa.

The radius of the Mohr’s circle representing the given state of stress in MPa is

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

Water (C_p = 4.18 kJ/kg.K) at 80°C enters a counterflow heat exchanger with a mass flow rate of 0.5 kg/s. Air (C_p = 1 kJ/kg.K) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in °C) is

C onsider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If D₁ and D₂ are the diameters of the inner and outer tubes respectively, then the view factor F₂₂ is given by

A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in h₁, h₂ and h₃ are negligible, the instantaneous discharge velocity is

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

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

A mould having dimensions 100 mm × 90 mm × 20 mm is filled with molten metal through a gate as shown in the figure. For height h and cross-sectional area A, the mould filling time is t₁. The height is now quadrupled and the cross-sectional area is halved. The corresponding filling time is t₂. The ratio t₂/t₁ is

A thin square plate ABCD with side of unit length is kept in the X-Y plane as shown in the figure. The plate is first rotated by 30° in the anti clockwise direction about the Z-axis with A fixed at the origin. The plate is then rotated by 90° in the anti clockwise direction about the X-axis with A fixed at the origin. The final co-ordinates of C are

A sine bar has a length of 250 mm. Each roller has a diameter of 20 mm. During taper angle measurement of a component, the height from the surface plate to the centre of a roller is 100 mm. The calculated taper angle (in degrees) is

M atch the following plastic products with their most appropriate materials.

In a shaping process, the number of double strokes per minute is 30 and the quick return ratio is 0.6. If the length of the stroke is 250 mm, the average cutting velocity in m/min is

For a linear programming problem, the set of constraints x+y ≤ 2, 3x+5y ≥ 15, x ≥ 0 and y ≥ 0 leads to

A milk vendor incurs an overstocking cost of Rs. 2 per litre and a shortage cost of Rs. 0.5 per litre.
The demand is uniformly distributed between 1 litre and 6 litres. Using the Newsvendor Model, the
maximum quantity of milk in litre(s) the vendor should order is

The specification limits for the weight of a product are 13.1 kg and 15 kg. If the process has a variance of weight 0.05 kg², then the process capability index is

On an average, there are 30 customers in a queue. If the arrival rate of customers into the system is 16 customers per hour and on average 32 customers leave the system per hour, then the average number of customers in the system is

Data for four jobs that need to be processed on a single machine are given below.

All the four jobs are available at time zero. If the jobs are scheduled using the Earliest Due Date (EDD) algorithm, then the job with maximum tardiness is

Common Data Questions

Common Data for Questions 58 and 59:

Two steel truss members, AC and BC, each having cross sectional area of 100 mm², are subjected to a horizontal force F as shown in figure. All the joints are hinged.

Q. 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 100 MPa is

Common Data Questions

Common Data for Questions 58 and 59:

Two steel truss members, AC and BC, each having cross sectional area of 100 mm², are subjected to a horizontal force F as shown in figure. All the joints are hinged.

.

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

Common Data for Questions 50 and 51:

Data for a plain milling operation are given below.

Q. Mean undeformed chip thickness (in microns) is

Common Data for Questions 50 and 51:

Data for a plain milling operation are given below.


Q. M achining time for a single pass (in seconds) is

Linked Answer Questions

Statement for Linked Answer Questions 52 and 53:

In an EDM process using RC relaxation circuit, a 12 mm diameter through hole is made in a steel plate of
50 mm thickness using a graphite tool and kerosene as dielectric. Assume discharge time to be negligible.
Machining is carried out under the following conditions:

Resistance 40 Ω
Capacitance 20 μF
Supply voltage 220 V
Discharge voltage 110 V

Q. The time for one cycle, in milliseconds, is

Linked Answer Questions
 

Statement for Linked Answer Questions 62 and 63:

In an EDM process using RC relaxation circuit, a 12 mm diameter through hole is made in a steel plate of
50 mm thickness using a graphite tool and kerosene as dielectric. Assume discharge time to be negligible.
Machining is carried out under the following conditions:

Resistance 40 Ω
Capacitance 20 μF
Supply voltage 220 V
Discharge voltage 110 V

Q. Average power input (in kW) is

Statement for Linked Answer Questions 64 and 65:

In a particular year, an organization earns cash revenues of Rs. 2,00,000. Total material and labour expenses are Rs. 1,09,000. The depreciation claimed on the equipment is Rs. 25,000. The tax rate is 20%.

Q. The profit after tax (PAT) is

Statement for Linked Answer Questions 54 and 55:

In a particular year, an organization earns cash revenues of Rs. 2,00,000. Total material and labour expenses are Rs. 1,09,000. The depreciation claimed on the equipment is Rs. 25,000. The tax rate is 20%.

Q. The net cash flow is