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

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) 

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 ..............

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 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: 

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

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)

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 ............ 

The starting simplex table of a linear programming problem is given below, where \( S_1, S_2, S_3, S_4 \) are the slack variables. The objective of the problem is
Maximize \( z = 6x_1 + 4x_2 \)
The leaving variable among the basic variables is:

Match the following with reference to the CNC machine and its minimum number of axes available in the machine.

Atomic packing factor of a body centered cubic structure is closest to:
A broaching machine makes key slots with a mean dimension of 10.56 mm and a standard deviation of 0.05 mm. The upper control limit for mean of sample size 5 calculated using X-bar (\( \bar{X} \)) chart is .............. (Rounded off to two decimal places)
A product has to be manufactured in a single-line layout by carrying out the six tasks in a sequence. The time (in minutes) of the six sequential tasks are 37, 8, 19, 34, 36, and 17. These tasks cannot be further sub-divided. For minimizing the cycle time, the number of stations to be used is .............
A through hole of 10 mm diameter is to be drilled in a mild steel plate of 30 mm thickness. The selected spindle speed and feed for drilling hole are 600 revolutions per minute (RPM) and 0.3 mm/rev, respectively. Take initial approach and breakthrough distances as 3 mm each. The total time (in minute) for drilling one hole is ............. (Rounded off to two decimal places)
If \( i \), \( j \), and \( k \) are the orthogonal unit vectors in Cartesian x-y-z coordinate system, the rate of change of the function \( f(x, y, z) = x^2 + 2y^2 + z \) at point \( (1, 1, 1) \) in the direction of \( 3i + 4k \) is .............
In a cold rolling process without front and back tensions, the required minimum coefficient of friction is 0.04. Assume large rolls. If the draft is doubled and roll diameters are halved, then the required minimum coefficient of friction is .............
Which one of the following functions is analytic, given \( i = \sqrt{-1} \)?
Which one of the following statements is FALSE with respect to the injection molding of polymer composite?
A through hole of 8 mm diameter is to be drilled in a 30 mm thick mild steel plate. Which one of the following processes is the most appropriate to achieve high dimensional accuracy with less processing time?
The relationship between the hoop stress \( \sigma_1 \) and the longitudinal stress \( \sigma_2 \) of a closed cylindrical thin-walled pressure vessel is: