GATE PI 2011 PYQ

The value of using Cauchy's integral around the circle , where , is

The eigen values of the following matrix are

If , and are three points defined in x, y, z coordinate system, then which one of the following vectors is perpendicular to both the line vectors and ?

The solution of the differential equation with and as constants is

If matrix and matrix , the transpose of product of these two matrices, i.e. is equal to

The output 'y' of a process is related to two independent and non-correlated process variables and through the following relation: The standard deviations of the variables and are 0.5 each. A portion

It is estimated that the average number of events during a year is three. What is the probability of occurrence of not more than two events over a two-year duration? Assume that the number of events f

The line integral from to along the semi-circle shown in the figure is

The value of , using trapezoidal rule for 10 trapezoids, is equal to

If defines the temperature at any location (x, y, z), then the magnitude of the temperature gradient at point P (1,1,1) is

Choose the word from the options given below that is most nearly opposite in meaning to the given word: Amalgamate

Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting. Based on the above passag

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the order

A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre o

P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving

A system that acquires knowledge, creates a knowledge base and applies a large but standard set of probability based rules to make a decision in a specific problem setting, is termed as

The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to

If Log (P) = (1/2)Log (Q) = (1/3) Log (R), then which of the following options is TRUE?

Which of the following options is the closest in the meaning to the word below: Inexplicable

Choose the most appropriate word(s) from the options given below to complete the following sentence. I contemplated ________ Singapore for my vacation but decided against it.

Choose the most appropriate word from the options given below to complete the following sentence. If you are trying to make a strong impression on your audience, you cannot do so by being understated,

A cantilever beam AB of length L, rigidly fixed at end A, is uniformly loaded with intensity q (downwards) over two-thirds of its length from the free end B as shown in the figure. The modulus of elas

Match the following materials with their most appropriate application: Material Application 1. Low carbon steel P. Machine tool base 2. Stainless steel Q. Aircraft parts 3. Gray cast iron R. Kitchen u

In sand casting, fluidity of the molten metal increases with

Cold water flowing at 0.1 kg/s is heated from to in a counter-flow type heat exchanger by a hot water stream flowing at 0.1 kg/s and entering at . The specific heat of water is and density is . If the

Which of the following welding processes results in the smallest heat affected zone?

Water is flowing through a horizontal pipe of constant diameter and the flow is laminar. If the diameter of the pipe is increased by 50% keeping the volume flow rate constant, then the pressure drop i

An ideal air standard Diesel cycle does NOT contain the following process:

Which of the following is a surface (two-dimensional) imperfection in the crystal structure of common metals?

A circular steel shaft is under elastic deformation due to torsion. The relationship between modulus of elasticity ( ) and shear modulus of elasticity ( ), taking as Poisson's ratio, is

The best wire size (in mm) for measuring effective diameter of a metric thread (included angle is ) of 20 mm diameter and 2.5 mm pitch using two wire method is

In a steady state and adiabatic flow of air through a horizontal nozzle, the pressure and temperature drop from 105 kPa and 300 K to 100 kPa and 296 K respectively. Air is considered to be a perfect g

Which of the following powder production methods produces spongy and porous particles?

A short column of length L having cross-sectional area of 50 mm by 100 mm is pinned at the ends. The proportional limit of the column is 250 MPa and modulus of elasticity is 200 GPa. The minimum lengt

Which of the following casting processes uses expendable pattern and expendable mould?

To measure the effective diameter of an external metric thread (included angle is ) of 3.5 mm pitch, a cylindrical standard of 30.5 mm diameter and two wires of 2 mm diameter each are used. The microm

Match the following : Type of material Name of material 1. Thermoplastics P. SIAION 2. Thermosets Q. Polyvinylchloride 3. Elastomers R. Epoxy 4. Ceramics S. Latex

Two circular steel bars having same length are subjected to equal load . The first bar has diameter over its entire length, while the second bar has diameter over two-thirds of its length as shown in

In a value analysis exercise, the cost of a product has come down by 20% without any change in its quality. The product value has improved by

The number of defectives produced by a six sigma process (in parts per million) is

A shop-floor engineer is looking at an control chart for outer diameter of a cylindrical component with design specifications as . The control chart uses a sample size of 25, and has a standard deviat

A manufacturing cell has 5 machines A, B, C, D and E. The average cycle time (in minutes) for a job on each of the machines is given in the following table: Machine A B C D E Average cycle time 5 6 5.

Which one of the following is NOT a method of calculating depreciation?

An operation consists of four work elements with the following data obtained during a work measurement exercise: Element No. Average element time (in centi-minutes) Rating factor 1 40 1.00 2 50 1.05 3

It is proposed to conduct a work sampling study of workers in a machine shop. Which of the following information would be necessary to determine the number of observations?

A company proposes to spend Rs 2,00,000 for a new machine. The service life of the machine is three years and the minimum acceptable rate of return per year is 25%. The annual savings (in rupees) due

The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600 mm. Assume that there is no change in width. If the coefficient of frict

While removing material from iron (atomic weight = 56, valency = 2 and density = by electrochemical machining, a metal removal rate of is desired. The current (in A) required for achieving this materi

The ultimate shear stress (in N/mm²) of the work material is

The total true strain applied and the final length (in mm), respectively, are

The shear angle and shear force, respectively, are

The binding material used in cemented carbide cutting tools is

Neglecting friction and redundant work, the force (in kN) required for drawing the bar through the first die, is

In resistance seam welding, the electrode is in the form of a

Grinding ratio is defined as

In a sand casting process, a sphere and a cylinder of equal volumes are separately cast from the same molten metal under identical conditions. The height and diameter of the cylinder are equal. The ra

A dedicated machine receives jobs at a rate of 20 per hour and the processing rate of the machine is 30 jobs per hour. Assume the following: (i) inter-arrival time and processing time for jobs follow

A small project is composed of seven activities whose time estimates are given below. The activities are identified by their beginning nodes (i) and ending nodes (j). Activity Optimistic time (days) P

The average demand for a component is 10 units per day. A store follows a periodic review system for this component. The stock level for this component is checked after every 30 days. The lead time to

For a simple moving average forecasting method, as the length of averaging period increases, the forecast sensitivity

If the lot size is 50 and it has 10% defective items, then the average total number of items inspected (ATI) per lot would be

The slope of the operating characteristic curve (OC Curve) of this plan would be

If the four components in the previous question are connected in a series-parallel structure as shown in the figure, the system reliability at the end of 1000 hours of operation will be

The reliabilities , , and for these four components after 1000 hours of operation will be

Observation of a slip gauge on a flatness interferometer produced fringe counts numbering 10 and 14 for two readings. The second reading is taken by rotating the set-up by . Assume that both faces of