GATE PI 2022 PYQ

Matrix A as a product of two other matrices is given by The value of det(A) is ___________. [round off to nearest integer]

If a matrix is squared, then

If a, b and c are three vectors, the vector triple product is given by

The value of is ______ . [round off to one decimal place]

The numerical integration of the function is carried out between and , by using ordinates at and . Which one of the following statements is TRUE?

Consider the following ordinary differential equation: . Given that and are constants, the general solution of the differential equation is

A market survey with a sample size of 1000 was conducted for a parameter that follows normal distribution. The confidence interval was estimated as [500, 700] with a mean of 600. It is now desired to

An operator manufactures 10 identical spur gears in a lot. One spur gear is defective in the lot. Three spur gears are drawn at random without replacement. The probability of getting all three gears a

Inhaling the smoke from a burning _________ could _________ you quickly.

Given below are three statements and four conclusions drawn based on the statements. Statement 1: Some engineers are writers. Statement 2: No writer is an actor. Statement 3: All actors are engineers.

Rice, a versatile and inexpensive source of carbohydrate, is a critical component of diet worldwide. Climate change, causing extreme weather, poses a threat to sustained availability of rice. Scientis

In injection blow molding of plastic beverage bottles, the blowing is accomplished by

A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors num

A sphere of radius cm is packed in a box of cubical shape. What should be the minimum volume (in ) of the box that can enclose the sphere?

Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute. P, Q and R operate at a

Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

Consider the following inequalities. (i) (ii) Which one of the following expressions below satisfies the above two inequalities?

A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially. What is the minimum number of doors that need to be opened in order to go f

The order of the following differential equation is ___________. [in integer]

Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements: • P sits next to S and T. • Q sits diametric

A shaft is used to transmit a power of 10 kW. The shear yield stress of the material is 150 MPa and factor of safety is 2. The shaft rotates at 1440 revolutions per minute. The diameter of the shaft (

A thick-cylinder has inner diameter of 20 mm and outer diameter of 40 mm. It is subjected to an internal pressure of 100 MPa. Follow the convention of taking tensile stress as positive and compressive

In the three-member truss shown in the figure, AC = BC. An external force of 10 kN is applied at B, parallel to AC. The force in the member BC is

In a slider crank mechanism (schematic shown in the figure), the crank rotates at 60 revolutions per minute. The radius of the crank is 30 mm and the length of the connecting rod is 120 mm. The averag

A eutectoid steel with 100% austenite is cooled from a temperature of 750 °C to a room temperature of 35 °C. Match the cooling methods with transformed structures. Cooling method Transformed structure

Which one of the following metals has a face-centered cubic (FCC) structure?

Air at an initial temperature and pressure of 15 °C and 1 bar, respectively is heated in an irreversible process. The final temperature and pressure are 303 °C and 2 bar, respectively. Take gas consta

Water (kinematic viscosity m /s) is flowing through a circular horizontal pipe of diameter 8 mm. If the flow is laminar and fully developed with a maximum axial velocity of 0.5 m/s, the Reynolds numbe

Match the processing steps related to production of powder metallurgy parts with their descriptions. Processing step Description P Atomization 1 Blended powders are pressed into shapes using dies and

Match the casting methods with products. Casting method Products P Continuous casting 1 Thin and intricate shaped components Q Investment casting 2 Hollow axisymmetric parts (such as pipes) R Centrifu

If denotes the shear modulus of an isotropic material, then the maximum possible value of Young's modulus of the material is

A time study engineer recorded the cycle time (in minute) for machining of a component. The recorded time study data is provided in the table. The performance rating of the worker is 110%. The standar

Which one of the following statements is TRUE?

A company is planning to produce 24 electric cars per day. The setup cost of the plant is estimated as ₹ 19476 million and the variable cost is ₹ 0.6 million per car. The car will be sold at a price o

Match the therblig symbols with their meanings. Therblig symbol Meaning P 1 Rest for overcoming fatigue Q 2 Avoidable delay R 3 Inspect S 4 Search

Match the types of layout with the types of production. Type of layout Type of production P Process layout 1 Job production Q Product layout 2 Batch production R Fixed position layout 3 Mass productio

Match the processes of product development with their characteristics. Process Characteristic P Product synthesis 1 Process of conversion of conceptual design into engineering science based model Q Pr

A company buys a machine worth ₹65000, which has a salvage value of ₹5000. The annual depreciation cost is ₹10000 based on the straight line depreciation method. The useful life (in year) of the machi

A machine component is to be processed at 5 workstations sequentially. The table provides the cycle time (in second) of each workstation. In mass production, the number of components produced per hour

In a manufacturing system, four different types of products (P, Q, R and S) are produced. The batch size of each product is . The numbers of defective units are 60, 71, 80 and 55, for P, Q, R and S, r

For an electrochemical machining process where is the inter-electrode gap in mm at time in minute, and is the feed of the tool in mm/minute. The value of is cm /minute. For maintaining a constant inte

In an electro-discharge machining process, the discharge voltage is . The energy dissipated per spark across the inter-electrode gap is proportional to

Yielding starts in a material when the principal stresses are 100 MPa, 100 MPa and 200 MPa. As per the von Mises criterion, yield stress (in MPa) of the material is ___________. [round off to nearest

A workpiece of 30 mm diameter and 40 mm height is compressed between two platens in an open die forging process. Assume a perfectly plastic material with a flow stress of 300 MPa. The ideal forging lo

A single-point cutting tool with zero rake angle is used for orthogonal machining. If the chip-compression ratio is 1.25, then the shear angle (in degree) during machining is ___________. [round off t

During straight turning of a 20 mm diameter steel bar at a spindle speed of 400 revolutions per minute (RPM) with an HSS tool, a tool life of 10 minute was observed. When the same bar was turned at 20

In a gas tungsten arc welding process under steady state condition, the input voltage and current are measured as 18 V and 160 A, respectively. Heat loss during creation of arc is 40% of the input pow

Match the codes used in CNC part programming with their functions. Code Function P G91 1 End of program Q M02 2 Programming in incremental coordinates R G32 3 Spindle stop S M05 4 Thread cutting in tu

The worktable of an open loop positioning system is driven by a lead screw with a pitch of 4 mm. The lead screw is connected to the shaft of a stepper motor. A gear of 80 teeth mounted on the stepper

During a hot-working process, the homologous temperature is 0.8. The melting point of the work metal is C. The temperature (in C) during hot-working is _______________. [round off to nearest integer]

It is required to cut a single-start thread of 2 mm pitch in a lathe machine with a single-start lead screw of 4 mm pitch. For one revolution of the workpiece, the number of revolution of the lead scr

A project comprises of seven activities. The expected durations of activities and their variances are as follows: Activity Expected duration (minute) Variance (minute) A 4 1 B 5 1 C 4 1 D 1 0 E 7 4 F

Consider the linear programming problem: Maximize , subject to , (C1) , (C2) , (C3) . The optimal solution is given as , and . The dual variables of constraints C1, C2 and C3 are , and , respectively.

A company forecasts the weekly demand of oxygen cylinders using exponential smoothing method with smoothing constant . The actual demands in Week 1, Week 2, Week 3 and Week 4 were 375, 412, 592 and 43

If the interarrival time is exponential and 8 customers per hour arrive in a bank, then the probability of no arrival of customer during a period of 15 minutes is ______ [round off to two decimal plac

A vaccine has to be distributed from two warehouses to three hospitals. The supplies at warehouses W1 and W2 are 200 and 150, respectively. The demands at hospitals H1, H2, and H3 are 100, 150 and 125

A company procures 384 parts annually. The annual holding cost per part is ₹ 30. If the ordering cost is ₹ 1000, then the economic order quantity is ______________. [in integer]

In a machine there are two motors, but only one motor is needed for the functioning of the machine. The reliabilities of the motors are 0.90 and 0.70. The overall reliability of the machine is ______

The absolute deviations of 8 points from the datum line of a surface are 10, 15, 12, 10, 13, 12, 20 and 25 m. The root mean square value of the surface roughness (in m) is ___________. [round off to o

In a factory, 100 bulbs are in use. The table lists the cumulative probability of the failure of a bulb for various durations. Duration (month) Cumulative probability 1 0.10 2 0.25 3 0.47 4 0.68 5 1.0

The diameter of a cylindrical cavity is measured by using two spherical steel balls of diameters 3 cm and 4 cm. The balls are placed inside the cavity such that the bigger ball is above the smaller on

The control chart for a number of defects in a welded joint is

In an assembly comprising shaft and hole, the nominal sizes with tolerances are specified as Hole: mm, Shaft: mm. The type of fit is

In a mobile screen manufacturing process on a mass scale basis, 5 samples of size 80 are inspected. Consider a p-chart with limits ( is the standard deviation). The numbers of defective items are give

A cylindrical workpiece is turned using two different tools. Tool 1 has zero nose radius; side and end cutting edge angles are and , respectively. Tool 2 has 0.5 mm nose radius. Both the tools machine