GATE PI 2026 PYQ

Consider the line integral [equation] where is a semi-circle in the plane with start point at and end point at . The value of the line integral is ______ (in integer).

The number of soldering defects that occur in a semiconductor device follows a discrete Poisson distribution with a probability mass function [equation] The average number of soldering defects per sem

Which ONE of the following options CORRECTLY matches the matrices to their properties? Matrix Property P 1 Singular Q 2 Triangular R 3 Symmetric S 4 Trace free

In statistical analysis of numerical data, which ONE or MORE among the options is/are possible value(s) of correlation coefficient?

A box in a machine shop consists of 5 coated and 10 uncoated cutting inserts which are of otherwise similar characteristics. The inserts got mixed up randomly in the box. An operator has taken 4 of th

Which ONE of the following options is the closest approximation to the value of the given definite integral? [equation] Note: Use numerical integration

If , and the value of at is , then the value of at is ______ (rounded off to two decimal places).

In the given weighted graph, the weights represent distance between the corresponding vertices. The shortest distance between vertex A and vertex E is . The number of paths with distance is . The valu

‘If Anish had scored hundred runs in today’s match, he would have been made the captain of his team. He would have then become the youngest captain in his team’s history. Unfortunately, he got out wit

In the given figure, is the diameter of a circle with center . Two points and are chosen on the circle such that . When and are extended, they meet at . The value of is _________________

Which ONE of the following is the value of ? where , and is an even positive integer.

Which one of the following figures P, Q, R, or S, correctly shows the clockwise-rotated version of figure (I)?

In the composite filament winding process as shown in the figure, the mandrel diameter is and is rotating at a speed, . If a helical winding angle is needed, the axial velocity, , of the slider should

Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are ch

Based on the relationship between each polygon and the number inside it, the value of ‘X’ is ______

At how many points will the curves and intersect in the real plane?

‘The shopkeeper sells lemons.’ In this sentence, the word ‘lemons’ is the ________.

Option and are two positive integers such that . The product of the numbers and is _________

The figure below is supposed to show three non-overlapping shapes – one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated by ‘?’ and completes

Match the words in Column I with their synonyms in Column II. Column I Column II (i) Lonely (p) Verbatim (ii) Literal (q) Solitary (iii) Lousy (r) Deadly (iv) Lethal (s) Terrible

A student is trying to determine the flatness and parallelism of the top surface of a part whose cross-section, assumed uniform in the Z direction, is shown in the figure. Which ONE of the following o

An Iron-Carbon alloy at room temperature has pro-eutectoid ferrite as a constituent in the microstructure, that formed above the eutectoid temperature. The alloy also has pearlite as another constitue

Which ONE or MORE among the following processes of the Carnot cycle is/are isentropic? Note: Figure is not to scale

Iron powder produced by gas atomization has a tap density and an apparent density of and , respectively. The density of solid iron is . Which ONE of the following options is the closest approximation

A glass tube of diameter is immersed vertically in a fluid. Assume contact angle is zero. The surface tension of the fluid is , density of the fluid is and acceleration due to gravity is . The approxi

An engineering student is fabricating a setup and needs a key for connecting a shaft to the hub of a rotating machine element. The student uses a sunk key which is tapered and prevents relative axial

A plain carbon steel sample of eutectoid composition is heat treated from austenizing temperature to achieve a microstructure consisting of ONLY bainite. Which ONE of the following is the correspondin

The ratio of hydrostatic stress to volumetric strain is known as ______.

Which ONE or MORE among the following tube cross-sections shown can be produced by true centrifugal casting method? Note: The cross-sections shown are perpendicular to the axis of rotation. Figures ar

Which ONE of the following CORRECTLY matches the metrology instruments and their respective most common applications? Metrology Instrument Application P Sine bar 1 Surface roughness of milled planar s

A cylindrical metal component of diameter is subjected to uniform uniaxial tension during operation. It was observed that a force of produces a uniform reduction of in diameter. Assume that material b

A custom pinion, with a width equal to 10 times the module, has 20 full depth teeth and a pressure angle of is being designed. It should transmit a torque of to a corresponding spur gear. Considering

A company has a fixed cost of INR and a variable cost of INR per unit for manufacturing of a product. The company sells units of that product making a profit equivalent to of the total sales revenue.

A customer has made a lumpsum investment of INR with a bank. The discount rate is per year. The investment enables the customer to receive a payout of INR yearly for next three consecutive years. The

The operation chart of a method of assembling nuts and bolts for a left-handed operator has been illustrated in the figure. Which ONE or MORE among the following options is/are CORRECT?

Which ONE of the following steps is NOT a part of product concept selection?

A time study was carried out for a job broken into two elements. For each element, three iterations of task were observed, and observed time was recorded. The observed times (in seconds) and the ratin

Consider an assembly line producing an item through a process involving three activities in the following order: cutting, welding, and polishing. There are three workers available: one is assigned onl

In the theory of orthogonal machining, assuming that the shear plane will take up an angle that minimizes energy, the shear angle can be shown to be [equation] where is the shear angle, the rake angle

A modified Taylor tool life equation is given as follows: [equation] where is the cutting speed (m/s), is the tool life in minutes and is the feed in mm/rev, and . Under two different cutting conditio

A steel cube of side is made by the sand-casting process. A cylindrical side-riser with diameter, , and height, , needs to be used. Assume: No surface sharing between the riser and casting. . The conn

An arc welding process is being carried out with a power source of to weld two similar metals. The total energy loss is , the area of cross-section of the weld is , and the specific energy needed to m

A linear slot is to be milled in a single pass from the point to on XY plane by a CNC machine. The actual velocity along the Y-axis is less than the intended value. The programmed feed rate along the

Which ONE or MORE among the following work materials is/are NOT commonly machined using diamond cutting tools?

A square of side length is to be blanked from a strip of thickness. The sheet metal has a shear strength of . To enable a single step blanking operation, the theoretical minimum blanking force require

In laser beam machining, the time ( ) required for the material to attain the melting temperature from a room temperature ( ) of is expressed by the following expression, [equation] where is thermal d

Which ONE or MORE among the following options CORRECTLY match(es) the type of defects with the corresponding metal working processes in which they are likely to occur? Defect Process P Centerburst 1 D

Which ONE or MORE among the following homogeneous representations in robotics involve(s) rotation about Y-axis by an angle ?

Which ONE of the following is FALSE with respect to filler material used in brazing?

In a polymer extrusion process, some cross-sectional shapes of the extruded polymers are shown. Cross-sections of available dies are also shown. Which ONE of the following CORRECTLY matches the extrud

Which ONE of the following options CORRECTLY matches the machining process and associated predominant material removal mechanism? Advanced machining process Predominant material removal mechanism P La

Which ONE or MORE among the options given is/are well established format(s) of data transfer used in geometrical modelling related to computer aided design (CAD)?

A sheet metal drawing is considered feasible if the following conditions are met: Reduction ratio 1% A sheet metal drawing process is being planned on a sheet metal with a thickness of 2 mm with a pun

In a rolling operation, a wide strip of thickness needs to be reduced to in a single pass. The roll diameter is . Four lubricants P, Q, R, and S with coefficient of friction , , , and , respectively,

Which ONE of the following is NOT an assumption of the economic order quantity (EOQ) model?

The computer centre (CC) in an institute manages the central server for which researchers queue to run their computer programs. CC processes programs only one at a time. Four computer programs are ava

In an M/M/1 queuing system, the customers arrive at a rate of 3 per minute, and the average number of customers in the system is at steady state. Assume that the server utilization is less than 1. Whi

Consider the aggregate planning problem for a toy car manufacturing organization whose demand at a plant is as follows: Month September October November December Demand (in units) The organization has

Which ONE of the following options represents correctly ALL the constraints resulting in the feasible region for the given linear programming problem as shown in the figure? Note: Figure not to scale

A company must allocate oil produced from their two plants to meet all the demands of two markets. The cost per litre of allocation from plant to market is denoted by . The market demand , plant produ

Painting is one of the activities in a construction project. For the painting activity that takes 6 days, both the total float and the free float are zero. Which ONE of the following is TRUE for the p

Which ONE or MORE among the following options is/are TRUE for the ideal operating characteristics (OC) curve given in the figure? Note: represents the acceptable quality level (AQL) and represents the

In the measurement of surface roughness using a 2D stylus profilometer, a surface profile measured over a length of was recorded on a graph paper. During recording, vertical magnification of and horiz

The function, , signifies the likelihood that a component has survived up to time and fails in the next instant of time. [equation] where denotes the probability density function for time to failure w

In a hole-shaft assembly, the following are the dimensions and tolerances (all in mm) provided for the hole and shaft: Hole: Shaft: The magnitude of the clearance when the shaft is at the minimum mate