GATE PI 2020 PYQ

An integrating factor for the differential equation is

General solution of is

For the complex numbers z 1 = 2 + 3i and z 2 = 4 - 5i, the value of (z 1 + z 2 ) 2 is

To solve x 2 - 2 = 0, the Newton-Raphson method has been employed. If the initial guess x 0 = 1.0, the next estimate of the root, x 1 , will be

For the matrix , the eigen-vectors are

For y = -x 2 + 9x - 2, the value of using Simpson's rule with two intervals (rounded off to two decimal places) is _____.

The divergence of the vector

If the probability density function of a random variable x is given by the value of k is ______.

If x is a random variable with the expected value of 5 and the variance of 1, then the expected value of x 2 is

There are five levels {P, Q, R, S, T} in a linear supply chain before a product reaches customers, as shown in the figure. At each of the five levels, the price of the product is increased by 25%. If

In one of the greatest innings ever seen in 142 years of Test history, Ben Stokes upped the tempo in a five-and-a-half hour-long stay of 219 balls including 11 fours and 8 sixes that saw him finish on

While l agree _____ his proposal this time, I do not often agree ______ him.

Select the word that fits the analogy: White : Whitening ∷ Light : _____

Find the missing element in the following figure.

Climate change and resilience deal with two aspects – reduction of sources of non-renewable energy resources and reducing vulnerability of climate change aspects. The terms ‘mitigation&rsq

An engineer measures THREE quantities X, Y and Z in an experiment. She finds that they follow a relationship that is represented in the figure below: (the product of X and Y linearly varies with Z) Th

The two pie charts given below show the data of total students and only girls registered in different streams in a university. If the total number of students registered in the university is 5000, and

It was estimated that 52 men can complete a strip in a newly constructed highway connecting cities P and Q in 10 days. Due to an emergency, 12 men were sent to another project. How many number of days

The recent measures to improve the output would ______ the level of production to our satisfaction.

A mass of 3 kg of Argon gas at 3 bar, 27°C is contained in a rigid, insulated vessel. Paddle wheel work is done on the gas for 30 minutes at the rate of 0.015 kW. Specific heat at constant volume,

A tank of large cross-sectional area contains water up to a height of 5 m as shown in the figure. The top water surface is under a pressure of p 1 = 0.2 MPa. A small, smooth and round tap at the botto

A Carnot heat engine receives 600 kJ of heat per cycle from a source at 627°C and rejects heat to a sink at 27°C. The amount of heat rejected to the sink per cycle (rounded off to the nearest

In a uniaxial tensile test on a specimen of a ductile material, the ultimate tensile strength is found to be 400 MPa and the elongation up to the maximum load is 25%. The true stress at the maximum lo

Group I lists phases of steel and Group II lists crystal structures in the table below. Group I Group II P. Ferrite 1. Hexagonal Close Packed (HCP) Q. Austenite 2. Body Centered Cubic (BCC) R. Martens

Consider flow of an oil with Reynolds number 1500 in a pipe of diameter 5 cm, The kinematic viscosity of the oil, v = 0.75 cm 2 /s. The value of average velocity in m/s is

A solid shaft has to transmit 50 kW of power at a speed of 1910 RPM. Ignore any possible bending of the shaft. The maximum allowable shear stress for the material of the shaft is 80 MPa. The minimum d

The figure shows a beam of length L (in m) with a uniformly distributed transverse load of W (in N/m) acting over it. The width and depth of the beam cross section are b (in m) and t (in m), respectiv

The figure shows two bodies connected through a riveted joint with one rivet. The diameter of the rivet is d (in m). The joint transmits a load of F (in N) whose line of action is perpendicular to and

The figure shows a mechanism with 3 revolute pairs (between the links 1 and 2, 2 and 3, and 3 and 4) and a prismatic pair (between the links 1 and 4). Which one of the four links should be fixed to ob

A steel ball of 12 mm diameter is heated to 1225 K. It is then slowly cooled in the air to a temperature of 475 K. During the cooling process, the ambient temperature is 325 K and the heat transfer co

A flywheel is to be used in an IC engine to limit the fluctuation of angular speed. The average of the maximum and the minimum angular speed is 500 RPM, and the maximum fluctuation of energy is 10,000

A truss with two bars PR and QR, making angles α and β, respectively, with the vertical, is shown in the figure below. The connections at P, Q and R are hinged connections. The truss suppor

The figure shows two bodies P and Q. The body Q is placed on the ground and the body P is placed on top of it. The weights of P and Q are W P and W Q , respectively. The bodies are at rest and all the

The state of stress at a point in a body under plane stress condition is shown in the figure. The positive directions of x and y axes are also shown. The material of the body is homogeneous and isotro

The process capability ratio C p is given by

A company manufactures products P and Q in quantities x 1 and x 2 , respectively, using two resources. The following Linear Programming Problem (LPP) is formulated to maximize the profit Z. Maximize Z

A project consists of seven activities as listed in the table. The time required for each activity and its immediate predecessor(s) are also given. Activity Time required (in weeks) Immediate Predeces

The Bellman’s principle of optimality is related to

Ina work study experiment, it is observed that a worker completes a job in an average time of 15 minutes with a performance rating of 120%. The time required for another worker having a performance ra

The product structure tree in the figure below shows the components needed to assemble one unit of product P. The number of units of component D needed to assemble 10 units of product P is ______.

An approach used in the product development which combines the efforts of design, manufacturing, and other functions to reduce the total time in introducing a new product in the market is

A company is planning to procure a machine to produce a component. There are two alternatives available - machine A and machine B. The cost of producing x units of the component (in Rs.) using machine

Which of the following is a casual forecasting method?

A car company manufactures 200 units of a component per day. The component is installed in different car models at a rate of 15000 units per year. The company operates its production facility 300 days

Company has to perform five tasks (P, Q, R, S and T) to make an assembly. Task times and immediate predecessors of the tasks are listed below. If an assembly line is designed to obtain the maximum out

The figure shows the revenue generated over different product life cycle stages marked as P, Q, R and S. Group I lists these product life cycle stages. Group II lists typical efforts leading to revenu

A rectifying inspection is performed on a lot of size N = 1000 using a Single-Sampling Plan with the sample size n = 60 and the acceptance number c = 1. If the Acceptable Quality Level is 1.0%, the pr

Suppose the control system of a fighter jet consists of three unrelated components in series, and it is desired to have 98% reliability of the system. If the reliability level of all the components is

The availability of an old photocopier was 90% and the Mean Time Between Failure (MTBF) was 200 days. It has been replaced with a new photocopier having an availability of 95%. Now, the Mean Time to R

To manufacture a product by casting, molten metal is poured in a cavity of rectangular cross section in a sand mold with a side blind riser as shown in the figure. The dimensions of the mold cavity ar

The statement that best describes the function of a GO gauge in the context of Taylor's principle of gauging is

Self-sharpening tendency of a conventional grinding wheel depends upon

A non-traditional machining process which utilizes mechanical energy as the principal energy source for removing the material is

In manufacturing of self-lubricating bearings by powder metallurgy, an important secondary operation that is carried out after sintering is

For a particular tool-workpiece combination, the value of exponent n in Taylor’s tool life equation is 0.5. If the cutting speed is reduced by 50% keeping all the other machining conditions same

End mill cutters are mounted on the spindle of a vertical milling machine using

The purpose of the ratchet in a micrometer is to

The figure shows drawing of a part with dimensions and tolerances, both in mm. The permissible tolerance for slot A (rounded off to one decimal place) in mm is ± _____

The movement along the z-axis of a CNC drilling machine is controlled by using a servo motor, a lead screw and an incremental encoder. The lead screw has 2 threads/cm and it is directly coupled to the

In a waterjet machining process, the water pressure used is 500 MPa. The diameter of orifice of the nozzle through which the waterjet comes out is 0.25 mm. Neglecting frictional and other losses, and

The vertices of rectangle PQRS are as follows in a 2 - D CAD system. P(-4, -2); Q(-2, -3): R(-3, -5); S(-5, -4) The coordinates of the corresponding new vertices, P', Q', R', S' after translation of t

A vertical boring operation is performed in a cast iron plate to enlarge a blind hole to a diameter of 25 mm up to a depth of 100 mm in a single pass. The cutting speed and the feed used in the proces

The heat generated in a resistance spot welding operation for joining two metal sheets with a certain set of process parameters is 2000 J. For a second spot welding operation on the same sheets withou

A cylindrical billet of 90 mm diameter is extruded to produce an I-section as shown in the figure (all dimensions in mm). The total extrusion pressure (p e ) in MPa required for the above process is g

The process used for producing long bars of fiber reinforced plastics (FRP) with uniform cross section is