GATE 2026 Production & Industrial

'The shopkeeper sells lemons.' In this sentence, the word 'lemons' is the _________.

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...

At how many points will the curves y = x² and y = -x² – 2x - 1 intersect in the real (x, y) plane?

'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. Unfortuna...

Which one of the following figures P, Q, R, or S, correctly shows the 45° clockwise-rotated version of figure (I)?

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

In the given figure, $\overline{PQ}$ is the diameter of a circle with center $O$. Two points $R$ and $S$ are chosen on the circle such that $\angle ROS = 80^{\circ}$. When $\overli...

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

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...

P and Q are two positive integers such that P² = Q² + 13. The product of the numbers P and Q is _________

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

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

An arc welding process is being carried out with a power source of 6 kW to weld two similar metals. The total energy loss is 50%, the area of cross-section of the weld is 10 mm², a...

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:...

Which ONE of the following options is the closest approximation to the value of the given definite integral? $\int_{0}^{1} e^{-x^2} dx$ Note: Use numerical integration

Which ONE of the following is the value of $\frac{1}{i^n}$? where $i = \sqrt{-1}$, and $n$ is an even positive integer.

Which ONE of the following CORRECTLY matches the metrology instruments and their respective most common applications? Metrology Instrument P Sine bar Q Profilometer R Vernier calli...

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...

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...

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 prev...

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

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

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

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 followi...

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...

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 P Cen...

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)?

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

Which ONE or MORE among the following processes of the Carnot cycle is/are isentropic?

A square of side length 50 mm is to be blanked from a strip of 2 mm thickness. The sheet metal has a shear strength of 200 MPa. To enable a single step blanking operation, the theo...

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 operat...

A customer has made a lumpsum investment of INR 2,00,000 with a bank. The discount rate is 15% per year. The investment enables the customer to receive a payout of INR 1,00,000 yea...

A modified Taylor tool life equation is given as follows: $VT^n f^m = constant$ where V is the cutting speed (m/s), T is the tool life in minutes and f is the feed in mm/rev, n = 0...

Consider the line integral $\int_C (2x dx + 2y dy + 2z dz)$ where C is a semi-circle in the z = 0 plane with start point at (0, 0, 0) and end point at (1, 0, 0). The value of the l...

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)...

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 CORRECTL...

Iron powder produced by gas atomization has a tap density and an apparent density of 3.26 g/cm³ and 2.66 g/cm³, respectively. The density of solid iron is 7.85 g/cm³. Which ONE of...

Which ONE of the following options CORRECTLY matches the matrices to their properties? Matrix P [-30 17 5 17 0 -12 5 -12 4] Q [0 1 9 7 0 2 12 3 0] R [2/3 1/3 2/3 0 2/3 -1/3 0 4/3 -...

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 thickn...

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 ON...

The function, r(t), signifies the likelihood that a component has survived up to time t and fails in the next instant of time. r(t) = f(t)/(1 – F(t)) where f(t) denotes the probabi...

Which ONE of the following options CORRECTLY matches the machining process and associated predominant material removal mechanism? Advanced machining process P Laser beam machining...

A glass tube of 2.5 mm diameter is immersed vertically in a fluid. Assume contact angle is zero. The surface tension of the fluid is 0.1 N/m, density of the fluid is 1000 kg/m³ and...

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 n at steady state. Assume that the server utilizati...

A steel cube of side 10 cm is made by the sand-casting process. A cylindrical side-riser with diameter, d, and height, h, needs to be used. Assume: * No surface sharing between the...

In a rolling operation, a 200 mm wide strip of 23 mm thickness needs to be reduced to 20 mm in a single pass. The roll diameter is 200 mm. Four lubricants P, Q, R, and S with coeff...

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 $\phi = C - \frac{\alpha}{2} +...

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

Which ONE or MORE among the following options is/are TRUE for the ideal operating characteristics (OC) curve given in the figure? Note: $p_0$ represents the acceptable quality leve...

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 COR...

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

A linear slot is to be milled in a single pass from the point (0, 0) to (180, 180) on XY plane by a CNC machine. The actual velocity along the Y-axis is 5% less than the intended v...

In laser beam machining, the time ($t_m$) required for the material to attain the melting temperature from a room temperature ($\theta_0$) of 32 °C is expressed by the following ex...

In the measurement of surface roughness using a 2D stylus profilometer, a surface profile measured over a length of 0.8 mm was recorded on a graph paper. During recording, vertical...

A cylindrical metal component of 10 mm diameter is subjected to uniform uniaxial tension during operation. It was observed that a force of 14 kN produces a uniform reduction of 3×1...

A custom pinion, with a width equal to 10 times the module, has 20 full depth teeth and a pressure angle of 20º is being designed. It should transmit a torque of 95 N-m to a corres...

A company has a fixed cost of INR 3,00,000 and a variable cost of INR 150 per unit for manufacturing of a product. The company sells 5,000 units of that product making a profit equ...

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 $i \in \{1,2\}$ to market $j \in \{1,...

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 compu...

If $\frac{dy}{dt} = 2y$, and the value of y at t = 0 is 2, then the value of y at t = 1 is ______ (rounded off to two decimal places).

The number of soldering defects that occur in a semiconductor device follows a discrete Poisson distribution with a probability mass function $p(x) = \frac{e^{-\lambda}\lambda^x}{x...

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 se...

In a hole-shaft assembly, the following are the dimensions and tolerances (all in mm) provided for the hole and shaft: Hole: $22^{+0.018}_{+0.010}$ Shaft: $22^{+0.075}_{+0.004}$ Th...

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:...

In the composite filament winding process as shown in the figure, the mandrel diameter is 700 mm and is rotating at a speed, N = 6 rev/min. If a 45° helical winding angle is needed...