GATE PI 2018 PYQ

In order to evaluate the integral with Simpson’s 1/3rd rule, values of the function e x are used at x = 0.0, 0.5 and 1.0. The absolute value of the error of numerical integration is

Consider the analytic function of the complex variable z = x + iy, where . The derivative f’(z) is

Consider the differential equation: With initial conditions: At t = 0, y = 0 and . The value of y (up to two decimal places) at t = 1 is _______.

The value of the surface integral over the surface S of the sphere x 2 + y 2 + z 2 = 9, where n is the unit outward normal to the surface element dS, is _______.

The probabilities of occurrence of events F and G are P(F) = 0.3 and P(G) = 0.4, respectively. The probability that both events occur simultaneously is P(F ⋂ G) = 0.2. The probability of occurren

Vector triple product a × (b × c) of three vectors a, b and c is given by

A real-valued function y of real variable x is such that . At x = 0, the function is

The diagonal elements of a 3×3 matrix are -10, 5 and 0, respectively. If two of its eigenvalues are -15 each, the third eigenvalue is _______.

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students wat

The perimeters of a circle, a square, and an equilateral triangle are equal. Which one of the following statements is true?

Find the missing group of letters in the following series: BC, FGH, LMNO, _____

A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number. If the house number is a multiple of 3, then it is a number f

A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots w

“The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.” The word that best fills the blank in the above sentence is

An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the

The value of the expression is ________.

“The dress _________ her so well that they all immediately _________ her on her appearance.” The words that best fill the blanks in the above sentence are

Weights (in kg) of the six products are 3, 7, 6, 2, 3, and 4. The median weight (in kg, up to one decimal place) is ______.

A wire would enclose an area of 1936 m 2 , if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent

In a V-thread, a wire is fitted such that it makes contact with the flank of the thread on the pitch line as shown in the figure. If the pitch p of the thread is 3 mm and the included angle is 60°

A spherical pressure vessel (made of mild steel) of internal diameter 500 mm and thickness 10 mm is subjected to an internal gauge pressure of 4000 kPa. If the yield stress of mild steel is 200 MPa, t

A square cross-section wooden column of length 3140 mm is pinned at both ends. For the wood, Young’s modulus of elasticity is 12 GPa and allowable compressive stress is 12 MPa. The column needs

If u = 2 (x 2 - y 2 ) and v = -axy represents the x and y components of the two-dimensional velocity field of an incompressible flow, the value of the constant a is ______.

A flywheel in the form of a solid circular disc of radius 100 mm and uniform thickness has a mass of 10 kg. If it is rotating at a uniform angular velocity of 20 rad/s, the kinetic energy (in J) of th

One kg of air (that can be considered a calorically perfect gas with characteristic gas constant R = 287 J/kg K and specific heat ratio γ = 1.4) undergoes a constant volume process from an initi

Length, width and thickness of a plate are 400 mm, 400 mm, and 30 mm, respectively. For the material of the plate, Young’s modulus of elasticity is 70 GPa, the Yield stress is 80 MPa and Poisson

When austenite decomposes upon cooling into two phases-ferrite and cementite, the reaction is called

A cylindrical wooden block of length 50 cm is floating in water in such a way that its axis is vertical. The densities of wood and water are 800 kg/m 3 and 1000 kg/m 3 , respectively. The submerged de

A rigid link PQ of length 1.0 m is pinned at P. It rotates about P in a vertical plane with a uniform angular acceleration of 1.0 rad/s 2 . At an instant when the angular velocity of the link is 1.0 r

Considering the coordinate system shown in the figure, a force of magnitude 10 kN has x-component of -6 kN. Possible y-component (s) of the force is/are

Processing times on a single machine for 3 jobs are given below. All the jobs are available at time t = 0. Job 1 2 3 Processing time (minute) 15 3 6 The mean flow time (in minute) as per the shortest

The control chart used for the fraction of defective items in a sample is

A machine is procured at a price of Rs. 47000 with a 2-year warranty. After two years, the annual maintenance cost (AMC) in Rs. Is given by the following formula: AMC = (i -2) × 2000, for i >2 w

A machine consists of three components P, Q and R connected serially. The reliabilities of P, Q and R are 0.97, 0.86 and 0.93, respectively. To increase the reliability of the machine, two additional

The mean time between failures of a machine is 400 hour. If the availability of the machine is 80%, the mean time to repair (in hour) is ________.

In ASME process chart, the symbol represents

A company has two manufacturing plants (C 1 and C 2 ) and two distribution centres (D 1 and D 2 ). The capacities of C 1 and C 2 are 100 and 200 units, respectively. The demand for D 1 and D 2 are 190

The breakeven point of a manufacturing company is 50000 units. The fixed cost is Rs. 200000 and the variable cost per unit is Rs. 20. The selling price per unit (in Rs.) of the product at this breakev

A project consists of three activities P, Q and R. The durations of activities follow the beta distribution. The predecessors and durations of activities are as per the following table: Activity Prede

A production line operates 7 hours a day in a 5-day week. The processing times for various job elements are as follows: Job element p q r s t Processing time (s) 5 10 12 3 15 If the line is designed f

Each of three firms P, Q and R manufactures 100 lakhs components. The number of defective components produced by P, Q and R are 30, 42 and 47, respectively. The firm(s) in conformance with Six Sigma s

The machines and auxiliary facilities are located according to the processing sequence of the product (produced in very large quantities) in

In a work sampling study of a worker, the information available are as follows: total time of study: 30 hour, number of items produced: 320, total number of observations: 1000, number of observations

The actual and forecasted demands of a product are as follows: Period 1 2 3 4 5 Actual demand 180 170 165 170 200 Forecasted demand 190 190 190 190 190 The forecast error measured in terms of mean abs

The annual demand of an item is 19845 units and the production rate is 100 units per day. The per-unit production cost (excluding setup cost) is Rs. 50, the per-unit holding cost is Rs. 10 per year an

In a service centre, cars arrive according to Poisson distribution with a mean of 2 cars per hour. The time for servicing a car is exponential with a mean of 15 minutes. The expected waiting time (in

Match the geometric tolerances with the correct symbols.

In a planar 2-degree-of-freedom robot, Link 1 of 30 cm length is connected to base by a revolute joint and Link 2 of length 20 cm is connected to Link 1 with a revolute joint as shown in the figure. T

A cylindrical workpiece is turned at a feed of 0.1 mm/rev with a perfectly sharp tool. In the ASA system, the side and end cutting edge angles are 15° and 5°, respectively, as shown in the fig

In a two-pass wire drawing process, there is a 40% reduction in wire cross-sectional area in 1st pass and further 30% reduction in 2nd pass. The overall reduction (in percentage) is ______

A pressure die casting setup was tested by injecting water (density 1000 kg/m 3 ) at a pressure of 200 bar. Mould-filling time was found to be 0.05 s. Afterwards, the actual casting is made by injecti

To make holes of 0.5 mm diameter and 30 mm depth in a mild steel component, the most suitable process is

Which one of the following defects is NOT associated with the casting process?

In electrochemical machining of aluminium with plane parallel electrodes, the current density is 70 A/cm 2 . The cross-section area of each electrode is 3 cm 2 . The current efficiency (i.e. the fract

The worktable in a CNC machine is driven by a leadscrew with a pitch of 2 mm. The leadscrew is directly coupled to a stepper motor of step angle 1.8°. The number of pulses required to move the wor

During orthogonal machining of a job at a cutting speed of 90 m/min with a tool of 10° rake angle, the cutting force and thrust force are 750 N and 390 N, respectively. Assume a shear angle of 35&

Two metallic sheets are spot welded by passing a current of 8000 A for 0.2 s. Assume that a cylindrical nugget of 8 mm diameter and 3 mm depth is formed. The density of the nugget is 7500 kg/m 3 , the

A 10 mm thick plate is rolled to 7 mm thickness in a rolling mill using 1000 mm diameter rigid rolls. The neutral point is located at an angle of 0.3 times the bite angle from the exit. The thickness

In a mass production firm, measurements are carried out on 10000 pairs of shaft and hole. The mean diameters of the shaft and the hole are 37.53 mm and 37.59 mm, respectively. The corresponding standa

The process in which molten thermoplastic is forced between rolls to produce thin sheets is called

Which one of the following instruments makes use of the principle of interference of light?

In an oxy-acetylene gas welding process, oxygen and acetylene are mixed in a ratio of 1.5 ∶ 1 (by volume). The flame is

A double-start thread with a pitch of 2 mm is to be cut using a lathe machine. The pitch of the leadscrew of the lathe is 6 mm. The job rotates at 60 rpm. The rpm of the leadscrew is _______?

In a shaft-hole system, the dimensions with tolerances (in mm) are as follows: where both x and y are positive real numbers. Which one of the following will provide an interference fit?

Which one of the following processes is NOT used for producing powders?