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

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