List of top Questions asked in GATE Production and Industrial Engineering- 2025

The left-hand side of a 20 cm thick wall is maintained at 25°C. The right-hand side of the wall is exposed to hot air at 50°C. There is no heat generation inside the wall and its thermal conductivity is 100 W/m·K. The convective heat transfer coefficient is 50 W/m²·K. Under steady state condition, the temperature (in °C) of the right-hand side surface of the wall is ........ (Rounded off to one decimal place).
Water flows through a smooth circular pipe of diameter 10 cm and length 10 m. The pressure drop across the length of the pipe is 0.2 Pa. Kinematic viscosity and density of water are \(1 \times 10^{-6} \, {m}^2/{s}\) and 1000 \({kg/m}^3\), respectively. Assuming laminar and fully developed flow throughout the pipe, the velocity of water (in mm/s) at the center of the pipe is ........ (Rounded off to one decimal place)

The table shows the data of running a machine for five years. The original machine cost is Rupees 70,000. In order to minimize the average total cost per year for running the machine, the machine should be replaced after ............. years. (Answer in integer) 

The zero line of the Vernier scale lies between divisions 20 and 21 of the main scale. The 4th Vernier scale division exactly coincides with a main scale division. The 5 divisions of the Vernier scale are equal to 4 divisions of the main scale. If one main scale division is 1 mm, the measured value (in mm) is ........... (Rounded off to one decimal place)

A company purchases items in bulk for getting quantity discounts in the item’s price. The price break-up is given in the table. The annual demand for the item is 5000 units. The ordering cost is Rupees 400 per order. The annual inventory carrying cost is 30 percent of the purchase price per unit. The optimal order size (in units) is .......... (Answer in integer) 

Three plants P1, P2, and P3 produce 6, 1, and 9 thousand liters of fruit juice, respectively. The produced fruit juice is transported to three distribution centers D1, D2, and D3 with a requirement of 7, 5, and 4 thousand liters of juice, respectively. The transportation cost (in hundreds of Rupees) from each plant to each distribution center is given in the table. The total transportation cost (in hundreds of Rupees) in the initial basic feasible solution using Vogel’s approximation method is ............. (Answer in integer) 

The annual profit of a company depends on its annual marketing expenditure. The information of the preceding 3 years' annual profit and marketing expenditure is given in the table. Based on linear regression, the estimated profit (in units) of the 4th year at a marketing expenditure of 5 units is ............ (Rounded off to two decimal places)

A steel plate is fastened to a channel using three identical bolts as shown in the figure. The bolts are made of carbon steel of permissible yield strength in shear as 400 N/mm². The plate is subjected to a force of 12 kN. Neglect the weight of the plate. The magnitude of the resultant shear force (in N) on bolt 2 is ............. (Answer in integer) 

A force of 1000 N is acting at point \( A \) on a bracket fixed at point \( B \) as shown in the figure. The magnitude of the moment of the force about \( B \) (in N·m) is .............. 

A link \( OA \) of length 200 mm is rotating counterclockwise about \( O \) in the \( x \)-\( y \) plane with a constant angular velocity of 100 rad/s, as shown in the figure. The absolute value of the \( x \)-component of the linear velocity (in m/s) of point \( A \) at the instant shown in the figure is ..............

In casting a cube of 80 mm side, the volumetric shrinkages due to solidification and solid contraction are 4.5% and 2%, respectively. Assume uniform cooling in all directions. The side (in mm) of the cubical pattern for getting the required size casting is .............
During orthogonal cutting with a tool of 10° rake angle, the cutting and thrust forces are 900 N and 275 N, respectively. The coefficient of friction on the rake surface of the tool is .............
In the iron-carbon equilibrium phase diagram, the eutectoid reaction occurs at 723°C with the eutectoid composition of 0.83 weight % carbon. Ferrite and cementite phases are considered to contain 0.022 weight % carbon and 6.67 weight % carbon, respectively. If a steel specimen with 0.7 weight % carbon is cooled from 950°C to below 723°C, the fraction of eutectoid ferrite is .............
The value of the integral \[ \int_1^3 \left( x^2 - 2x \right) \, dx \] obtained by using Simpson’s 1/3 rule with 4 subintervals is equal to \( \frac{n}{3} \). The value of \( n \) is .............
The benefit(s) of product standardization is/are:

The network diagram of eight activities (A to H) along with their time durations (in days, given in bracket) of a project is shown in the figure. The critical path of the project is: 

A CNC vertical milling is used for cutting a straight line slot in the x-y plane. The cutter is located at point P. The slope \( \frac{dy}{dx} \) of the straight line created by the cutter is 1.25. The feed rate of x-axis is 120 mm/min. The new position of the cutter after 20 seconds is: 

Match the operation/phenomenon in a grinding process with the corresponding definition listed in the table. 

Match the following with reference to the machining process and its feature. 

The hole and the shaft dimensions (in mm) are given as
Hole dimension = \(30 \pm 0.04\)  and  Shaft dimension = \(30 \pm 0.06\). 
The maximum possible clearance (in mm) is .......... (Rounded off to two decimal places)
 

While inspecting final assembly of automobile-gear-boxes, 15 features were considered critical-to-quality (CTQ). During last quarter, 40000 gear boxes were produced among which 1500 defects were found of the CTQ features. The defects per million opportunities (DPMO) is .......... (Answer in integer)
Two options are available to meet the annual demand of batteries in a toy company. In option 1, batteries are manufactured in the plant having fixed cost of Rupees 2,00,000 and a variable cost of Rupees 70 per unit. Option 2 consists of buying batteries from the market at a price of Rupees 90 per unit. The annual demand (in number of batteries) at which the company should switch from buying to making the batteries in the plant is .......... (Answer in integer)
The pitch of the single-start lead screw of a lathe is 6 mm. It is used to cut double start thread of 3 mm pitch on a cylindrical work piece. During the thread cutting, the spindle rotates at 400 revolutions per minute (RPM). The speed (in RPM) of the lead screw is ............ (Answer in integer)

Three principal stresses at a point in a material are 300 MPa, 250 MPa, and 100 MPa. If the yielding just starts at that point, the yield strength (in MPa) of the material as per Tresca criterion is ............ 

For an ideal Diesel cycle, the heat addition is an: