GATE PI 2013 PYQ

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field defined with respect to a Cartesian coordinate system having and as unit base vectors. where

The probability that a student knows the correct answer to a multiple choice question is . If the student does not know the answer, then the student guesses the answer. The probability of the guessed

The value of the definite integral is

A company manufactures 1000 toys every day. On an average, 10% of the toys are defective and 40% of the defective toys can be reworked into defect-free ones. The average number of defect-free toys man

The partial differential equation is a

The function satisfies the differential equation and the auxiliary conditions, . The Laplace transform of is given by

Let be a normal random variable with mean 1 and variance 4. The probability is

The eigenvalues of a symmetric matrix are all

Match the CORRECT pairs. Numerical Integration Scheme Order of Fitting Polynomial P. Simpson's 3/8 Rule 1. First Q. Trapezoidal Rule 2. Second R. Simpson's 1/3 Rule 3. Third

Choose the CORRECT set of functions, which are linearly dependent.

The solution to the differential equation where is a constant, subjected to the boundary conditions and , is

Find the sum of the expression

Were you a bird, you __________ in the sky.

What will be the maximum sum of 44, 42, 40, ......?

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

In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the t

Which one of the following is modeled based on adaptation capabilities of biological systems?

A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey i

Complete the sentence: Universalism is to particularism as diffuseness is to __________

The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost

After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, t

Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

For a ductile material, toughness is a measure of

Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below: Specific enthalpy (kJ/kg) Velocity (m/s) Inlet steam condition 3250 180 Ex

A metric thread of pitch 2 and thread angle 60° is inspected for its pitch diameter using 3-wire method. The diameter of the best size wire in is

A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details. plate width = 200 mm plate thickness = 5 mm number of rivets = 3 rivet

A planar closed kinematic chain is formed with rigid links PQ = 2.0 , QR = 3.0 , RS = 2.5 and SP = 2.7 with all revolute joints. The link to be fixed to obtain a double rocker (rocker- rocker) mechani

For steady, fully developed flow inside a straight pipe of diameter , neglecting gravity effects, the pressure drop over a length and the wall shear stress are related by

Match the CORRECT pairs. Processes Characteristics / Applications P. Friction Welding 1. Non-consumable electrode Q. Gas Metal Arc Welding 2. Joining of thick plates R. Tungsten Inert Gas Welding 3. C

A cylinder contains 5 of an ideal gas at a pressure of 1 . This gas is compressed in a reversible isothermal process till its pressure increases to 5 . The work in required for this process is

A simply supported beam of length is subjected to a varying distributed load Nm , where the distance is measured from the left support. The magnitude of the vertical reaction force in N at the left su

A rod of length having uniform cross-sectional area is subjected to a tensile force as shown in the figure below. If the Young's modulus of the material varies linearly from to along the length of the

Consider one-dimensional steady state heat conduction along -axis ( ), through a plane wall; with the boundary surfaces ( and ) maintained at temperatures of 0°C and 100°C. Heat is generated uniformly

A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 rad/s. If the total fluctuation of speed is not to exceed , the mass moment of ine

Following data refers to an automat and a center lathe, which are being compared to machine a batch of parts in a manufacturing shop. Automat Center Lathe Machine Set-up Time in min 120 30 Machine Set

A firm produces 120 units of product in every 8 hour shift. Four operations as given below are needed to manufacture each unit of product. Operation Precedence Processing time (in min) P none 1 Q P 2

The fixed cost and the variable cost of production of a product are Rs. 20000 and Rs. 50 per unit, respectively. The demand for the item is 500 units. To break even, the unit price of the items in Rs.

Match the CORRECT pairs. Group I Group II P. Man-machine chart 1. Determines standard time of jobs Q. Learning curve 2. Finds the preferred method of doing work R. Time study 3. Measures work improvem

Therbligs refer to the

Cylindrical pins of mm diameter are electroplated in a shop. Thickness of the plating is micron. Neglecting gage tolerances, the size of the GO gage in mm to inspect the plated components is

Circular blanks of 10 diameter are punched from an aluminum sheet of 2 thickness. The shear strength of aluminum is 80 . The minimum punching force required in is

Neglecting the contribution of the feed force towards cutting power, the specific cutting energy in is

In the 3-2-1 principle of fixture design, 3 refers to the number of

Assuming approach and over-travel of the cutting tool to be zero, the machining time in min is

The orthogonal rake angle of the cutting tool in degree is

In water jet machining, the water jet is issued through a 0.3 mm diameter orifice at a pressure of 400 MPa. The density of water is 1000 kg/m . The coefficient of discharge is 1.0. Neglecting all loss

A steel bar 200 in diameter is turned at a feed of 0.25 with a depth of cut of 4 . The rotational speed of the workpiece is 160 . The material removal rate in is

Two cutting tools are being compared for a machining operation. The tool life equations are: Carbide tool: HSS tool: where is the cutting speed in m/min and is the tool life in min. The carbide tool w

The normal force acting at the chip-tool interface in N is

During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = 2) at current of 1000 A with 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If Titani

In a rolling process, the state of stress of the material undergoing deformation is

A cube shaped casting solidifies in 5 . The solidification time in for a cube of the same material, which is 8 times heavier than the original casting, will be

To avoid stock out situations, the retailer needs to place orders when the inventory level (in kg) drops to

Let (P) denote the linear programming formulation of a transportation problem with sources and destinations. Then, the dual linear program of (P) has

Customers arrive at a ticket counter at a rate of 50 per and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 . Assuming that customer arrivals form a

The critical path of the project, based on the mean activity duration, is

Consider a two machine flow shop where jobs are first processed in Machine X and then in Machine Y, in the same sequence. The processing times of four jobs (1, 2, 3 and 4) on the machines are: Job Pro

If the retailer uses an optimum order policy to minimize the total cost, the saving in Rs. in the total cost as compared to the current policy will be

Let denote the cumulative distribution function of the standard normal random variable. The probability that all activities on the critical path, based on the mean activity duration, are completed in

A linear programming problem is shown below. Maximize Subject to It has

In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

The type of control chart used to monitor the amount of dispersion in a sample is

A manufacturer produces bars designed to be of 10 mm diameter with a tolerance of mm. Historical data indicates that manufactured bars have an average diameter of 9.98 mm with a standard deviation of

A company plans to purchase a machine whose uptime needs to be atleast 95%. They have shortlisted two models of the machine with the following operational characteristics: Machine MTBF (hr) MTTR (hr)