GATE PI 2012 PYQ

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

lim is

At , the function has

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

The system of algebraic equations given above has

Consider the function in the interval . At the point , is

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

The inverse Laplace transform of the function is given by

Consider the differential equation with the boundary conditions of and . The complete solution of the differential equation is

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

Water ( ) at enters a counterflow heat exchanger with a mass flow rate of . Air ( ) enters at with a mass flow rate of . If the effectiveness of the heat exchanger is 0.8, the LMTD (in ) is

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.

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: Do

For an opaque surface, the absorptivity( ), transmissivity ( ) and reflectivity ( ) are related by the equation:

Choose the grammatically INCORRECT sentence:

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

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

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, Ev

Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If and are the diameters of the inner and outer tubes respectively, then the view factor is given b

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.

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 one

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 where y is the height of the arch in meters.

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

The cost function for a product in a firm is given by , where q is the amount of production. The firm can sell the product at a market price of ₹ 50 per unit. The number of units to be produced by the

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

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

In a DC arc welding operation, the voltage-arc length characteristic was obtained as where the arc length was varied between 5 mm and 7 mm. Here denotes the arc voltage in Volts. The arc current was v

The state of stress at a point under plane stress condition is The radius of the Mohr's circle representing the given state of stress in MPa is

An ideal gas of mass and temperature undergoes a reversible isothermal process from an initial pressure to final pressure . The heat loss during the process is . The entropy change of the gas 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

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

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 satu

A cantilever beam of length is subjected to a moment at the free end. The moment of inertia of the beam cross section about the neutral axis is and the Young's modulus is . The magnitude of the maximu

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

During normalizing process of steel, the specimen is heated

Match the following plastic products with their most appropriate materials. Products Materials 1. Gears P. Polymethylmethacrylate (PMMA) 2. Helmets Q. Polyamides (PA) 3. Lenses R. Polyethylene (PE) 4.

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 calcul

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

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 dime

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

For a linear programming problem, the set of constraints and leads to

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

Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, ) of length 500 m. The volumetric flow rate is 0.2 . The head loss (in m) due to friction is (assume )

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

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

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 numb

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

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

Data for four jobs that need to be processed on a single machine are given below. Job P Q R S Processing time (days) 12 9 21 10 Due date (days) 20 40 30 19 All the four jobs are available at time zero

The net cash flow is

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

The profit after tax (PAT) is

Mean undeformed chip thickness (in microns) is

Match the following metal forming processes with their associated stresses in the workpiece. Metal forming process Type of stress 1. Coining P. Tensile 2. Wire Drawing Q. Shear 3. Blanking R. Tensile

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 in the anti clockwise direction about the Z-axis with A fixed at the or

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

A mould having dimensions is filled with molten metal through a gate as shown in the figure. For height and cross-sectional area , the mould filling time is . The height is now quadrupled and the cros

Machining time for a single pass (in seconds) is

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

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

The time for one cycle, in milliseconds, is

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

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

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

Average power input (in kW) is